⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⠞⢳⠊⠓⠣⢸⡸⣲⠇⣘⣦⠚⢗⣻⠉⠻⡴⠂⢀⣀⠀⠀⣠⠂⠀⡇⠀⠀⠀⠀⡚⡲⢃⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠤⢼⡀⡞⢶⠦⣤⡖⠯⠭⡽⠟⡲⠀⠀⣆⠴⠊⢀⠀⠈⠅⡜⠒⠁⠀⠀⠉⢱⠀⠀⠀⠈⣑⡼⠁⢀⢠⢠⠄⢠⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠢⢄⢳⣁⣀⠆⠃⣇⡇⠜⠍⢳⡄⢰⢃⡈⡩⣲⠾⡃⢀⠀⠘⠤⢁⣠⠃⢠⢼⣇⣰⢃⣼⠀⠀⠀⣩⡾⠦⣆⠷⣅⠜⠉⠁⠀⠀⠀⠀
⠀⠀⠀⢦⠀⠈⠒⡥⣽⢁⠌⢹⢶⡤⡧⣾⠀⠀⠙⣾⣤⠖⠿⡿⣄⡗⢴⢣⡌⢲⣩⠚⠸⣌⣍⠹⣸⣚⡙⢷⣤⠞⠡⢄⣀⡳⣎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢄⣣⡈⠦⡜⣸⡹⣰⠃⡀⢱⣛⣰⣑⢽⣧⠀⢰⣿⡇⠰⠋⠑⡜⡗⡞⠋⠂⠘⢦⠳⣠⠿⠦⣼⢩⣤⢊⡾⠋⠀⠀⠀⠋⠀⢨⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢁⠇⠀⡏⠀⠈⢾⡄⠙⣤⠃⣟⠀⠋⣿⣅⡾⢻⢀⡀⡆⣰⣥⣟⢱⣞⣀⠀⣨⠧⣯⡀⠀⢸⣈⣷⡟⠀⢀⢦⠀⠀⠀⢠⠏⠀⠀⡀⣷⠀⠀⠀⠀
⠤⢲⠚⢒⢻⠙⢶⣴⢺⠉⠒⡧⠔⠛⠲⢤⣸⣿⠁⣼⡶⠿⠿⣽⣓⣸⢿⣓⡶⣚⢧⡷⣿⢫⣦⣸⣿⠏⢹⡴⠋⠸⡄⠀⠀⡞⠀⢰⣰⢣⠊⠀⣰⡠⠀
⠀⠈⡄⠀⢭⡇⡀⠉⠻⣇⠀⡇⠀⠀⠀⣀⡝⢿⡆⣿⢁⢀⡴⠋⣏⣏⡼⠋⡷⣇⡝⣇⣿⡜⠋⣿⣿⡆⣼⡝⡄⣠⢹⠀⣸⠁⠀⠀⠀⠛⣄⣸⡖⠊⠀
⠐⠴⣅⡆⠘⡎⢢⠀⠀⢹⣎⣷⠀⠀⣀⡕⠻⢚⣿⣿⡉⠉⠳⣄⣰⠟⠑⢶⠁⠹⢴⠁⡇⣠⣴⠿⣏⣾⡇⢹⡃⡗⢸⣷⢃⣠⠔⠋⠀⢠⠃⠀⠑⠹⠀
⠀⢤⢎⣈⡲⠵⣈⠉⠓⣾⠙⣾⣇⠀⠀⠛⣆⡇⢻⣿⡇⠀⣠⡾⠛⢶⡆⠈⣇⣰⠏⢰⣿⢏⡏⢠⣏⣼⠞⠉⠉⠱⣿⢿⡭⣄⠀⠀⢠⠏⠀⠀⠀⠀⠀
⠐⠚⠒⠂⠼⣄⠀⠉⠢⣼⡀⠈⢻⣆⠠⡄⠳⡇⢸⣿⣧⣾⡟⠀⠀⢸⡇⠀⣸⠋⠀⣼⡏⢾⠛⣿⢹⡏⠀⠀⢀⡼⠃⢘⠂⢨⠀⢀⡞⠀⢀⠄⢀⠆⡀
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄⠀⣿⣆⠸⡠⠜⣆⣿⣿⠏⠀⠀⠀⢸⡇⢰⠇⠀⢀⣿⠁⣿⢰⡇⣼⠁⠀⢠⡞⠁⠀⠸⣚⣮⠵⠟⠓⠦⣸⠀⡤⠼⠓
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣈⠳⣜⢿⣯⠀⠀⢈⣿⡿⠦⣤⣀⠀⢸⣷⡏⠀⠀⣸⣿⡾⠋⣿⢁⡟⠀⣰⣯⣤⠶⠞⣋⠽⢓⣒⡡⠤⠒⠛⠳⢧⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⣿⣷⡀⢸⣿⡇⠀⠀⠉⠛⢾⣿⠀⠀⠀⣿⡟⠁⣸⣿⣾⣿⣿⠟⢉⣠⣴⠞⠋⠉⠉⠉⠂⠀⠀⠀⠀⠈⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸⡟⢀⣼⡿⠋⣼⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⣿⡀⠀⣿⣷⡿⠋⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⢿⡇⣸⣿⠟⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⣸⣷⣿⡇⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⢿⣿⣦⣀⣾⣿⢯⣿⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣮⣿⣿⣿⡿⠁⣸⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠀⢠⣿⠃⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣠⣾⣿⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠛⠻⣿⣿⠿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀