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Сообщение оставил(а) GHHG в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) GHHG в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) manoj в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf в 04 November 2025, 15:00 по Московскому времени.

https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/updated-guide-to-coinbase-customer-service-helpline-numbers-24-7-assistance-Guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/complete-list-of-coinbase-customer-service-contact-numbers-247-live-person-assistance-guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/complete-list-of-coinbase-customer-service-contact-numbers-247-live-person-assistance-guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/complete-list-of-coinbase-customer-service-contact-numbers-247-live-person-assistance-guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/complete-list-of-coinbase-customer-service-contact-numbers-247-live-person-assistance-guide.pdf https://surgicalresearch.org/wp-content/uploads/formidable/11/complete-list-of-coinbase-customer-service-contact-numbers-247-live-person-assistance-guide.pdf
Сообщение оставил(а) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ в 04 November 2025, 15:00 по Московскому времени.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀
Сообщение оставил(а) https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) https://surgicalresearch.org/wp-content/uploads/formidable/11/12-FAQs-Of-Coinbase-Customer-Service-24-7-Numbers-A-Complete-Guide.pdf в 04 November 2025, 15:00 по Московскому времени.

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Сообщение оставил(а) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ в 04 November 2025, 15:00 по Московскому времени.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣶⣄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠐⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣾⡯⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡄⠀⣿⣿⣿⣿⣿⣗⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣷⡐⣿⣿⣿⣿⣿⡯⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣗⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀ ⠈⠙⣶⣤⣤⣄⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣄⣠⣀⣀⣀⡀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠏⠁⠀ ⠀⠀⠀⠀⠀⠐⠁⠝⠛⢻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠿⠿⠋⣹⠻⠿⣿⣶⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣸⣸⡐⡀⠑⠂⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⡟⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣭⡙⢻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣧⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⡿⢿⣿⣦⠀⠀ ⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣶⡍⠀⠱⢴ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠘⣿⠾⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⡿⢡⣶⣾⣿⣷⣶⣄⠸⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⢡⣾⣿⣿⣿⣿⣿⣿⡇⠘⠏⠻⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⣿⡿⣿⣿⣿⣿⣿⡿⡓⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⣒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⣷⣻⠿⣛⢟⣻⣟⣿⣷⣭⣀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⠏⠠⢀⡎⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢌⡀⠀⠸⡿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⢻⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢗⣤⣜⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠆⠙⢧⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡯⣽⣾⡿⣟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⣈⣹⢿⣻⣿⣟⣿⣿⣿⣿⣷⠮⠁⠀⠛⣿⣷⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡟⢀⠀⡀⠀⠹⠟⡵⣿⣻⣾⣿⣿⡿⡏⠀⠁⠀⠉⠚⢻⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⠀⢐⡄⠅⠀⠀⠈⣿⣿⣿⣿⣿⡟⠋⢀⠀⠀⠀⠀⢠⡎⢐⠂⠀⠀⠀⠀⠀⡀⠀

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