⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡤⡂⠈⠁⠐⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣛⠀⣀⡀⡧⠴⡎⣝⣿⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢿⣿⣇⣣⠢⠹⣊⢓⣽⢠⢻⡗⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣦⢽⡟⡴⡿⠙⠃⠈⠙⢻⣾⠑⣳⡨⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡕⣫⢏⡍⠀⠀⠈⠳⡄⣀⢠⠖⠀⠀⢻⡄⠚⣌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠰⢃⠞⠀⠀⠀⠀⠐⢭⣗⠧⠄⠀⠀⢸⡟⠀⢡⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠡⢡⠊⠀⠀⠀⡆⢠⠀⠀⠈⡀⣀⡁⢸⣺⢃⡀⡄⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡰⢁⢢⠎⠀⠀⠀⠀⠇⢘⠄⠀⠀⠃⠉⠁⢘⡏⠾⠇⡇⠁⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⣰⢍⡿⠃⠀⠀⠀⠀⢸⣷⣶⠀⠀⠀⠡⢰⢸⣿⡧⡇⢀⠇⠸⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡴⢋⡢⡜⢡⠞⠀⠀⠀⠀⠀⠀⣼⣿⣿⣁⠀⣷⠆⢈⢺⣿⣿⡄⣾⡆⡄⡆⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⠖⠉⢀⠢⠂⣰⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠄⠰⡠⡠⠀⠘⣿⣿⣟⣽⡁⠁⢐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣠⠳⠊⠁⢀⣠⠤⠒⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋⠐⠀⢀⣾⣇⠀⠀⠸⣿⣿⣽⡆⠀⠈⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠜⠃⠁⠀⡠⠚⠈⠀⢀⣠⣾⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡈⠀⢀⣾⣿⣿⡄⠀⠡⠘⣿⣿⣧⡇⠀⡇⢎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠚⠁⠀⠀⡠⠂⠀⢀⡨⢶⣛⡿⡜⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣷⣤⣾⣿⣿⣿⣧⢀⣴⣿⣿⣿⣿⣦⠀⣏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡍⠀⠀⠀⢼⠁⢡⠞⠉⠀⣏⡋⢱⡇⠀⠀⠀⠀⠀⠀⠀⠹⠋⢹⠯⢛⠿⢿⣿⣿⣿⣿⡿⢿⣟⡻⣿⢫⡙⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⢰⢃⡴⠃⠀⠀⠀⣏⡇⢎⣇⠀⠀⠀⠀⠀⠀⢠⣻⡚⢻⠀⠀⠈⠀⠇⠐⠂⠀⠈⠁⢸⠃⠘⢮⠺⣪⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠣⢀⠀⠂⡚⠀⠀⠀⠀⠀⢘⡃⠘⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⡠⠀⠀⢁⣀⣀⣠⣿⠀⠀⠐⠭⣆⠧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠈⣅⠀⢛⢒⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣽⡇⠀⠀⢹⣿⣻⣿⣍⠀⠀⠀⠈⠸⢟⡁⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠀⠉⠔⡄⡀⠀⠀⠀⠀⣿⣿⣻⡾⠀⠀⠀⠘⣿⣿⣿⢾⠀⠀⠀⠀⠀⠹⣫⢑⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠈⠈⠁⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠈⡂⠀⠀⠀⠀⠀⠱⡃⠈⠑⠱⣄⡀⠠⡀⠀⠀⠀
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⠀⠹⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠑⢃⠀⢔⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠙⢀⡀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢸⠆⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀