⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠶⠖⠒⠚⠉⠺⠳⠲⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⢳⣆⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⣀⣤⠀⠹⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣵⠟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠰⣼⠟⠃⠀⠀⣿⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⢾⡗⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢻⣯⠀⠀⣄⣰⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⡇⠀⣹⣷⡄⡀⠀⠀⠀⠀⠀⣂⣤⣦⣴⣤⡟⠀⠀⠀⠳⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡿⢴⡃⠀⠈⠛⣿⡃⢷⣴⣤⣶⠟⠉⠀⢀⣽⠏⡆⠀⠀⠀⠀⢙⢿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡄⠈⡙⠓⢶⡾⣋⡀⠘⢻⣯⣁⣤⡶⠞⠋⠁⡸⣤⣶⣟⣒⡦⣞⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⣿⣷⡄⢀⡟⢿⡆⠀⠀⣀⣠⣠⣤⣤⣾⡿⣫⣄⣿⠇⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠿⣦⣀⠀⢀⣹⠿⠀⣾⢷⣼⠇⣠⣶⠯⣿⢫⡭⠝⣼⢸⡟⠔⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡟⠀⠀⡀⡴⢤⡙⠻⣿⠋⠀⠀⠀⠀⢉⣸⠛⣁⣴⡿⠋⠀⣰⡟⣼⠳⢰⣗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⣀⡤⠖⠚⠛⢻⣼⠁⠀⠀⠀⡷⣾⣿⣷⡿⡗⣧⣦⣴⣠⣾⢶⠾⣿⠼⢊⣀⣠⡾⣡⡗⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣨⣞⠋⠀⠀⠀⢀⣻⢻⡀⠀⠀⠀⠹⣿⣿⣿⣿⡶⣯⢽⣼⣯⢼⡼⡟⡗⣮⠿⠻⠫⠚⠋⢠⣾⠃⢙⡽⡄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠫⠂⠀⠀⢠⣴⡟⠁⠸⡅⠀⠀⠀⠀⠹⣿⣻⡟⡓⠛⠾⠿⠟⠞⢻⠻⠉⠁⣠⡤⠴⢖⣲⣷⣷⣶⢪⢘⠳⠶⠲⢶⣦⢤
⠀⠀⢀⣾⡿⠁⠀⠀⣔⣿⢯⠀⠘⡍⢷⠀⠀⠀⠀⠀⢳⣽⠟⠩⠻⠐⠲⠆⠒⠀⠠⣠⢾⣿⣶⣿⣾⣿⣿⣿⣿⣿⣛⣯⠭⠟⠶⠊⠙
⠀⠀⣳⣽⠡⠀⠀⠠⣿⡿⠀⠀⠀⢻⣙⡂⠀⠀⠀⠀⠘⣟⡳⣄⣀⠀⢀⢀⣠⡵⠺⣽⣿⡿⣿⣟⡻⠿⠛⠉⠉⢁⣤⣶⣦⡴⠤⣤⣄
⠀⠀⣿⡇⠀⠀⠀⣸⡏⠁⠀⠀⠀⠈⢯⣇⠀⠀⠀⠀⠀⠀⠙⢿⣯⣿⣿⣿⣿⣗⡉⠽⠟⠁⠉⠀⠀⢀⣠⣴⣿⡿⠛⠉⠉⠀⠀⠀⠹
⠀⠀⢹⣷⠀⠀⠘⣿⡭⠀⠀⠀⠀⠀⠘⣞⢄⠀⠀⠀⣀⡀⠀⠀⠉⠛⠛⠟⠉⠁⠀⠀⠀⠀⠀⢀⣔⣿⣵⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡞⢿⣧⡀⠨⣿⠅⠀⠀⠀⠀⠀⠀⠘⣶⠧⡀⢰⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⡽⢡⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢡⠈⠀⢻⠿⠶⠯⠆⠀⠀⠀⠀⠀⠀⠀⠈⢳⠵⠼⠖⢊⡝⠦⠀⠀⠀⡤⠤⠤⠄⠒⠛⡧⠊⠀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀