⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡠⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⢟⢥⣶⠀⠀⠀⠀⠉⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⣡⢋⠏⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⡴⣱⣋⣁⠀⠀⠀⠀⠀⠀⠠⣀⣠⣶⣄⠄⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢀⢎⡼⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⢟⠁⠘⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡰⢫⠟⠁⡸⡆⠉⠙⠛⢛⣿⡿⠛⠛⠋⠁⠀⢸⠀⠀⢻⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⡼⣰⣷⣄⡀⠀⡹⣄⠀⣾⣿⣿⣿⣷⡤⠀⠀⢠⠇⠀⠀⠸⣽⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡟⠀⠀⢀⣜⣸⣼⣻⣿⣄⡀⠀⠿⢿⣿⣿⣿⣿⣿⣇⣀⠼⠃⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡿⠋⠀⠀⠠⣞⢿⣟⣺⣿⡿⣿⣿⣄⡀⠀⢉⠽⡿⠽⣿⠿⠧⡴⢤⡀⠀⣀⡘⡿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡿⠋⠀⠀⢀⣮⣟⣟⣿⣟⣯⣿⣯⣻⣿⣽⣿⢾⠁⠀⡇⠀⢼⠀⠀⡇⠀⡳⠊⠁⠀⠹⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠾⡽⣗⣷⣿⣷⣿⣞⣻⣗⠾⣻⡻⠳⢤⣇⣀⣸⣀⣠⠧⠞⠁⠀⠀⠀⠀⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣗⢓⣺⣹⣹⣕⣻⡷⣯⣿⡻⠁⠀⡀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⣰⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡼⣿⣽⣗⣻⣷⣖⡿⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣿⣾⢿⢾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣔⠒⢛⡳⡦⣸⢴⡆⠈⠻⢿⠟⠀⡀⠀⢒⣠⣀⣀⣤⡲⠤⠴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣏⣳⣌⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⣥⣤⣴⣶⡶⣖⣶⢦⣄⠀⠀⠉⠛⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡝⡍⠀⡀⢿⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣀⠀⠀⠀ ⠀⠀⠀⠉⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⢻⠀⠈⢛⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢅⣄⠉⠉⢲⠀ ⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⣠⡾⣺⠞⣿⣿⡏⠁⡌⡀⠂⠘⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⣰⡾⡛⣋⡧⠐⠻⠀ ⠀⠀⠀⠀⠸⣞⣧⣇⠀⠀⢀⣴⡼⡿⠟⠁⠀⢻⣿⣿⠀⠀⡧⠀⠀⠙⡼⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⢵⣿⠫⠦⢶⣶⡀ ⠀⠀⠀⠀⠀⢫⡷⢿⣀⣴⣾⣯⠟⠁⠀⠀⠀⠀⢿⠇⢀⡠⠿⣤⣀⠈⠃⠱⣝⣷⠀⠀⠀⠀⠀⠀⠸⣎⣿⡀⣀⣸⣿⠟ ⠀⠀⠀⠀⠀⠈⢿⣏⣟⡹⠟⠁⠀⠀⠀⠀⠀⠀⠘⠚⠉⠘⣿⣝⣿⣿⡊⡀⠸⣿⣷⠀⠀⠀⢀⣰⣲⣷⣾⠿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⡛⣿⣿⣷⣧⡀⠹⣿⣴⣤⣠⣮⣿⡯⠋⠉⠀⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⣾⣿⣿⣿⣿⣷⡄⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⣿⠛⠻⣿⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡯⠀⠀⠀⠸⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡧⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣻⡃⠀⠀⠀⢰⣟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡯⡻⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⢈⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⠃⠀⠀⠀⠀⢸⠨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⠀⠀⠀⠀⠀⢸⠴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡏⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⠇⠀⠀⠀⠀⠀⢸⣶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣾⠀⠀⠀⠀⠀⠀⢸⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⡏⠀⠀⠀⠀⠀⠀⢸⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠃⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣷⠁⠀⠀⠀⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢯⡟⠀⠀⠀⠀⠀⠀⠀⣨⣷⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣽⣧⡟⣦⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⡿⣽⣽⣬⢯⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠬⠶⠥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀