⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠿⠿⠶⣶⣶⣮⣭⣭⣝⣛⣻⣤⣤⣄,,,,
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⢀⣼⠟⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣣⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢤⣀⠸⣿⠀⠀⠀ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠃⠛⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⣴⡾⠟⠛⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡾⠟⠛⠉⠁⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⠶⠛⠁⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⣄⡀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡴⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣄⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⡿⠀⠀⢸⡇⠀⠀⠀⣰⢿⣿⣦⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠙⠷⣄⡈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡇⡀⠀⠈⣧⡀⠀⣸⠃⠀⠻⣿⣿⣾⣇⣼⡄⠀⠀⠀⠀⠀⠀⢀⣾⣁⣤⣴⣶⣿⣿⣿⣿⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣷⡇⠀⠀⠈⠻⡶⠃⠀⠀⠀⠘⣿⣿⠟⢿⣿⣄⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⠛⠛⠉⠉⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠛⠶⠦⠞⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⣀⣴⣶⣤⡀⠀⠀⠀⠀⠀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡇⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣆⠀⠀⠀⢻⡳⣦⣄⡀⠀⠀⠙⠷⠿⣿⠉⠛⠷⠶⠾⠛⠁⠀⠈⢻⣆⠀⠀⠀⠘⣧⣀⠀⢀⠀⠀⠀⠀⠀⣦⠀⣸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠷⣄⠀⠈⢷⣦⣹⣿⣷⣦⣄⣀⠀⢿⡄⠀⠀⠀⠀⣀⡤⠶⠀⠀⣿⠀⠀⠀⠀⢀⡿⠉⠉⠀⠀⠀⠀⠀⡟⠀⢹⡗⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠊⠉⠈⢷⠉⠙⠛⠻⢿⣄⡀⣠⠞⠉⠀⠀⠀⢀⣿⣤⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⢀⣼⣡⡶⠦⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⢳⡄⠀⢠⡉⣻⠃⠀⠀⠀⣰⣷⠟⣻⣿⣏⣁⡀⠀⠀⠀⠀⠀⢀⣠⣞⣋⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣿⡿⣦⣤⡴⠞⣽⠁⠀⠒⢚⡻⢿⢲⠶⢤⣴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠈⠙⠓⣿⢤⡀⠀⠀⠀⠘⣎⠓⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠀⠀⢹⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡾⠀⠈⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠒⠶⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡠⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡍⢙⠀⠀⠀⠀⠀ ⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠑⡶⠎⠀⠀⠀⠀⠀ ⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⠳⠇⠗⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠶⣤⣤⣤⡴⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠇⠀⠀⢀⡴⠊⠻⣦⣀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠲⠶⠚⠁⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠾⢿⣃⠀⠀⠀⠉⠛⠷⠶⠶⣤⣤⡿⢻⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣆⣀⣀⣀⣀⣴⠟⠁⠙⠳⠿⠷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀