⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⡀⢰⣆⣤⡴⢤⡀⠀⠀⣠⣤⢤⣠⣆⠠⡤⡶⠶⠀⠠⣴⠦⣤⣴⠶⠄⣠⡄⣠⡄⢠⡀⢦⣠⡴⠀⢠⡄⠀⣠⣤⣀⡤⣴⠂⣠⡖⠆⠀⠀⠀
⠀⠀⢸⣿⠻⣦⡿⣿⠀⢘⣧⠀⠰⣿⠁⢨⣟⡟⣧⣷⣷⠲⠀⢘⣿⡴⠟⣼⡶⢶⣿⣻⢼⡇⣹⡇⠘⣿⠁⠀⢻⡇⠀⢿⣿⣿⢁⣿⠲⣈⡓⢆⠀⠀⠀
⠀⠀⢰⣿⠀⠛⠏⠹⣶⠾⠃⠀⠐⠹⢶⠿⢋⡇⠘⠧⠿⠴⠀⠨⣿⠙⠶⣸⣴⡾⠋⢹⡾⣧⡾⠥⠜⠿⠀⠀⠛⠧⠴⠿⠙⠏⠳⠻⠴⠛⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⣰⣆⡤⣠⢀⣤⣦⢴⡶⡄⣤⣤⡀⣤⢠⣤⣤⠀⠠⣤⣴⣤⣄⢠⣠⡄⠀⠀⠀⢠⣤⣄⢠⡶⠲⡄⠀⠠⣶⡴⢤⣀⡦⡶⠒⢦⡖⠈⣩⡿⠀⠀⠀
⠀⠀⢾⣿⡀⣽⡏⡛⣤⠊⢷⡔⣿⣹⢿⣿⣻⣁⣠⠀⢘⣿⠜⣟⣸⣾⣹⡇⠀⠀⠀⠹⡇⣸⡏⡇⢨⡇⠀⠀⣹⡇⢾⢻⡗⡟⠂⣸⠇⠰⠏⠀⠀⠀⠀
⠀⠀⠚⠁⠙⠾⠋⠛⠋⠙⠛⠁⠙⠘⢘⠛⠘⠓⠛⠀⠀⠛⠈⠙⠋⠈⠉⠰⠋⠀⠀⠐⠛⠉⠀⠛⠋⠀⠀⢠⠀⠁⠈⠀⠉⠉⠁⠈⠁⠠⠶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⣰⠧⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢲⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⢏⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣣⠖⠀⠻⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡰⢏⡼⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢥⣋⢇⠀⠡⡀⠀⠀⠀⠀⢂⠀⢠⠀⠀⠀⣰⢏⡳⡜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣍⠞⣄⠀⡑⢤⢀⡀⠀⠈⠀⠀⠀⠀⣰⢏⢮⡱⠆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⡙⢶⡀⠀⠈⠢⡈⠀⠐⠀⠃⢀⡴⣋⠞⣦⠹⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣦⠹⠀⠀⠀⠘⠀⠀⠀⣠⠞⡴⣩⠞⡴⠋⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠻⣔⣯⣽⣯⣷⣶⡄⣠⢞⡱⣾⡵⣷⣿⣾⣵⣄⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡚⢯⡜⢯⡽⣸⣿⣿⣇⡴⣫⠵⢎⠿⡳⣌⣹⣿⡏⢐⡿⠂⠀⠀⠀⠈⠐⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠼⢶⣹⡒⠀⠀⠙⠻⢟⡿⢽⣸⣅⣬⠩⠤⢤⣙⠻⠛⠋⠉⠀⠀⠀⠀⠀⣀⡤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠅⠀⠀⠀⣀⠶⠉⣀⠷⠙⣮⣄⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠁⠀⠀⢀⡔⠚⠈⢀⡴⣏⠇⠀⠀⠙⣿⡏⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⢭⠲⣥⢀⣀⣈⣁⣀⣀⣴⣫⣼⣭⢟⡖⠚⠋⠓⠙⠲⢦⠶⠚⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣠⠼⡶⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠈⠉⠈⠁⠉⠉⠉⠈⠁⠁⢸⠏⠜⢳⠶⣤⠶⠛⠉⢸⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡆⠀⢜⡆⠀⠀⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⡟⡤⠀⠈⠇⠀⠀⠇⠀⠀⠈⠓⠠⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡤⠤⠶⠛⠉⠁⠀⠀⠁⠁⠒⠒⠀⣰⠂⠛⠉⠁⠀⠀⠀⠀⠈⠑⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠧⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡴⣃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⠂⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠚⢻⡥⠀⣆⠀⠀⢢⣴⠼⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢮⠁⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⢶⣽⢾⣣⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢫⠀⠀⠀⣺⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠸⠭⡟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀