⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠡⠂⠙⠑⢠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⠈⠀⠀⠘⢦⠀⠀⠀⢀⣬⡥⠌⢑⢷⣄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣴⢿⢸⡈⡈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢁⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⢩⠃⠘⠘⣧⠀⠀⢇⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠘⢞⡆⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⢀⡖⠀⣠⠝⠋⠉⠃⣰⡆⠀⠀⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⠀⠤⠚⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠰⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠰⠒⠴⠤⢠⡾⠋⠀⠀⠀⠀⠀⠀⠁⠀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⢤⣤⡀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⡃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⡻⡎⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⡿⢁⡄⣹⠟⣠⢲⣦⣀⠤⠀⠀⠀⠀⡞⡇⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⡿⢋⣴⣿⢞⣯⣶⣿⣧⠹⡿⠁⠀⠀⠀⠈⠀⢣⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⢝⣿⢟⣴⣿⣿⡏⢆⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⡟⡎⢡⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣷⣦⣿⣮⣿⡿⢁⡌⠀⡀⠀⠀⠀⠀⢳⠀⡏⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⡿⠿⠿⣟⣤⡟⢠⠌⠀⠀⠀⠀⠊⢈⠰⢀⠂⣴⡶⠄⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⣠⡄⠁⡀⠀⠀⢀⠻⣿⣿⣿⣿⣭⣽⣓⣮⢝⣔⣡⠂⠀⠀⠀⠀⡜⡎⢆⠀⠈⠷⠟⣡⡇⢐⡑⠀
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡯⡇⠏⣿⣄⠀⠀⠀⢡⢆⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⠞⠹⠀⠀⠀⠀⢰⣾⡿⡇⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣼⢀⢨⢿⠀⣱⣈⣿⠟⡀⠀⠀⠈⡏⣧⡀⠙⠿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⡘⢸⣿⢃⠁⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠀⢸⣿⠦⠚⠘⠀⣿⠟⢁⣾⣴⠀⠀⠀⠌⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠄⣿⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠈⠳⡠⠵⠀⠀⣿⣾⣧⡞⠻⠟⠁⠀⠀⠀⢀⡄⠹⣿⣧⠀⣠⡴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⢲⠆⢻⣿⣿⠀⠵⠆⠀⠀⠀⣬⢸⡇⢷⣿⣿⣸⣋⣤⣶⣶⣿⠁⣠⣶⣧⠀⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠋⠁⠀⠀⠀⣴⡞⠀⢿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⡿⢁⢦⠀⠀⠀⠀⠀⢀⣴⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠄⠀⠀⠀⠀⢠⣧⣤⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⢀⠞⡊⠀⠀⠠⠤⢀⠋⡘⠈⡴⣤⢤⡀⠀
⠂⠀⠀⠀⠀⠀⢀⡠⠄⠨⠆⠀⠀⠀⠀⠀⠈⠿⣿⣿⣦⠙⡿⢟⣻⣿⣿⣿⣿⣑⡿⢛⣥⣾⣓⠿⠁⠀⠀⠀⠀⠀⡼⠀⠀⠶⢙⡥⣬⢇
⠀⠀⠀⠀⠀⣒⡽⠑⠀⣠⢶⠀⠀⠀⠀⠀⠀⢠⣌⡙⢛⠳⠶⣅⠙⠉⠻⢟⣃⣵⣾⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠘⠁⢀⡵⢻⠀⠙⠹⣿
⠀⠀⠀⠐⠋⣭⠔⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣶⢜⣧⣤⣾⢟⣫⡷⠶⣶⣶⠦⠚⠁⠀⠀⠀⠀⠀⠀⠠⢀⢆⠋⠀⠀⣶⡙
⠀⠀⢴⠎⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠉⠐⠈⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⡳⡼⠀⠀⠀⠐⠃⠀
⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣴⠀⡄⢀⡀⢀⡀⢀⠀⢀⢀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠰⠁⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⠉⣤⡉⠁⠈⢀⣤⠋⣀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛