⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠉⠀⠀⠈⠉⠛⠿⢷⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⣠⣴⢶⣦⣀⣈⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⢺⣿⡿⣦⣀⠀⢸⢟⣷⠛⠩⡉⡿⢏⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢹⣇⣮⣞⡙⢿⣝⢀⡠⡛⣀⣄⣢⠉⠻⢮⢫⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧⡜⠛⠻⢿⣿⣼⣿⡿⢣⣹⣿⠏⠀⢸⠇⠀⠹⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠳⣄⣀⣲⠿⠋⣡⡏⠳⠋⢥⣂⡴⠋⠀⠀⠠⣿⣿⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡒⢢⠴⣭⢝⠀⠀⢰⣿⡁⣠⡢⠕⠉⠀⠀⠀⠀⠀⢉⢹⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠆⠲⡁⢿⠧⣌⡓⠬⡿⠤⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⣳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡀⠀⠙⠧⡱⢮⠭⠯⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡵⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⣀⣀⣀⡀⠀⠀⠀⢀⡀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⡤⠖⠒⠂⡲⡲⣲⡒⣲⣤⢷⠯⠍⠑⠉⡉⣶⣖⣶⡶⣶⣶⣤⣤⣤⣤⡀⢀⣀⠤⡤⣤⡴⠶⠶⣢⣤⣤⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠔⣲⣋⡯⣶⣾⣵⣝⣽⡻⣬⣕⢮⣗⡻⣧⣄⠡⢀⡀⣿⣷⣿⡋⠉⠊⠉⠺⢞⣿⣿⣿⣯⣋⣻⣿⡿⢕⢄⡐⢀⣨⣽⣿⣿⣮⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣿⢛⣿⢏⡞⢗⡖⣸⣳⣯⣿⣭⣿⠟⢒⠾⣘⠡⡨⣎⠚⣿⡙⢟⣿⡯⡑⡅⣀⡸⣿⣿⢿⣿⣿⣿⣿⣿⣾⣒⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣯⠔⢎⡈⡉⠉⢜⣶⣦⣷⣿⣿⣆⠈⣏⠎⣼⣅⣀⠊⣻⣼⣿⣿⣿⣿⣿⣷⢮⡋⢻⣷⣄⠀⠀⠀⠀⠀ ⣿⢳⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⣮⣾⣿⣿⣿⣿⣟⢿⣿⢳⡢⢲⠑⠡⡀⣴⣊⣺⣽⢿⣿⣿⣞⣆⢀⢡⠘⢧⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⢦⣿⣿⣿⣿⡟⢁⢄⢜⡿⠁⢪⣡⣾⡼⣿⣟⣿⣿⣿⠉⣹⣿⠠⡜⢷⣣⠥⣴⢧⠷⡃⣟⣣⡿⣿⡺⡿⣞⡄⠀⠠⠀⡒⠝⢛⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣄⠀⠀ ⣾⣿⣿⣿⣟⡒⢛⣋⣃⣤⣷⣾⣿⣿⠁⡿⣻⢠⢟⢮⣸⡴⠻⣹⡷⣉⣅⣢⢩⢽⢿⡍⣽⢺⡌⢷⢶⣿⣹⣴⠀⠢⠀⢈⠢⡀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣗⡀ ⣿⡿⠛⣛⣿⣿⠿⣿⣿⣿⣿⣿⢻⠏⣒⡳⠑⣩⡞⡱⣦⣼⠿⣖⡼⣟⡒⣽⣽⢛⡍⣣⢶⢷⢾⣁⣏⣻⣽⢱⣗⠄⠁⠀⠀⠀⠀⠀⠈⠉⢛⠟⠛⠻⠻⠀⠸⣿⣿⣿⣿⣯⡩ ⣿⡁⠀⠉⠉⠉⢸⣿⣿⣿⠟⡃⠴⣭⢉⣱⠞⣢⡵⠷⣽⠹⢙⣟⡕⢺⡌⡧⢣⢽⠱⢻⢴⠣⣽⢻⡘⢕⠻⢾⣽⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣥⣦⣤⣽⣿⣿⣿⣿⣿ ⠟⠁⠀⠀⠀⠀⣼⣿⠿⢏⣠⡉⡀⠷⠐⣍⣷⣪⢧⡏⢎⡍⠎⣄⣫⡞⠁⠋⢙⣡⣤⣄⣧⣿⣿⣽⡣⡚⣼⣝⡼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿