Wishing well Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠶⠶⠶⠶⣶⣼⣇⢀⣿⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢿⡀
⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠘⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠘⣆
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡆
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿
⠀⠈⠳⣦⠀⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣤⣤⣤⣄⡀⢀⣾⠁
⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⣿⠀⣴⠳⠟⠻⠛⠛⠛⠻⠛⠿⠛⠿⠛⠟⢻⠛⢶⠻⡞⠳⠶⣶⠷⣶⢦⣤⡀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⣠⡿⠀⠿⠶⠿⠂⢠⠀⠀⠀⠀⠀⢀⠀⣆⠀⠀⠐⠀⠀⠀⡆⠀⠀⢀⠀⠂⠱⠀⠁⠹⠟⠛⠻⢿⡇⠀⠿⢤⣄
⠀⠘⠳⣶⠀⢸⡗⠛⢿⡄⢀⣀⣇⢠⣇⣰⣄⣿⠀⣤⣠⣧⣴⣤⣧⣀⣇⣸⣄⣰⣀⣤⣀⡄⣶⠶⠦⣴⡇⢀⣦⣤⢹⡆
⠀⠀⠀⣾⠀⢸⡇⠀⠀⠙⠛⠉⠙⠋⠉⠉⠙⣿⠀⣿⠉⠈⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠛⠛⠛⠀⠀⢾⠇⢸⣿⣿⢸⡇
⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡇⣿⠘⣷⣄⣀⣀
⠀⠀⠀⢼⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠹⢤⣤⣀⣈⣉
⠀⠀⠀⣾⠀⢸⣧⣠⣤⡴⠶⠶⠶⠶⠶⠶⠾⢿⠀⣿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠶⣶⣦⣾⡇⢸⡇⠀⠀⠀⠈⠉⠉
⠀⢀⡤⠿⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠰⠿⣤⡀
⡰⠋⠀⠼⠀⠘⠦⠀⠠⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠚⠃⠘⠦⠄⠙⣦
⣇⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠋⠀⠒⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠉⣿
⢹⡄⠀⠀⠉⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⠤⠤⠤⠤⠤⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠃⠀⠀⠀⠀⠀⢰⡇
⢸⡇⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾
⠀⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣼⠁
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡿
⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠿⣦⣄⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠲⠶⠦⢤⣤⣀⣀⣬⣄⣀⣀⣀⡀⠀⠀⢠⣄⠀⠀⠀⣀⣀⣀⣀⣄⣴⠤⠴⠶⠟⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠍⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣾⣿⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠁⠈⠻⣿⣦⣤⣾⣿⡇⠻⣿⡿⠉⠈⠙⠟⠻⣿⠿⠋⠹⠛⠻⣷⣾⣿⣿⣿⣁⣴⣿⡿⠋⠙⢿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠛⠻⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⢀⣤⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⠛⠋⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⠛⠛⢋⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣀⡀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⢻⣿⣿⣿⣴⣿⣿⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣤⣿⣭⣿⠽⠿⠿⠻⠿⡿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⠿⢿⠺⢿⣿⡿⣿⣿⣿⣟⣻⣭⣿⣿⣷⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡿⠏⣾⣿⢼⣿⣿⣿⣿⣿⠃⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣭⣿⡅⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⢿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡜⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣿⣿⣎⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣾⡛⡇⠀⡟⢋⣽⣧⡹⣦
⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣉⣉⣁⢨⣉⣉⣉⣉⣱⡌⢷⡀
⠀⠀⠀⠀⠀⠺⠶⠶⠶⠾⠶⠾⠶⣶⣶⣦⣴⢦⣤⣼⣿⣿⣯⣻⣿⠧⢸⣿⣯⣻⣝⣿⣿⣆⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠛⣿⡟⢻⣦⠀⠀⠉⠉⢉⢁⢴⣾⣓⠲⣍⠫⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⡄⣿⣿⢶⠿⡧⠀⣤⠀⢐⣯⡸⣿⢻⢠⡶⢷⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⣤⣹⣿⡇⡇⢠⣴⣡⣶⠂⣧⣮⠷⣮⢿⣾⣤⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡍⠀⣼⣿⣿⣾⣾⣿⡿⢿⡆⠿⠿⡿⣻⣾⣿⡀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⢾⠋⣿⡁⢠⣽⠇⡇⠀⢷⡠⣠⢿⣿⣽⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠚⢛⠀⣘⠀⠀⡇⠀⠘⢷⣅⠼⣿⣻⠤⢂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣿⡁⠛⠭⣿⣖⣂⣷⣶⣲⣶⢽⣷⣶⣶⣋⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠹⢾⡏⠀⠀⠀⣸⠊⠩⢯⣝⢛⡟⠋⢻⠃⠀⡉⠀⣰⠆⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣖⣬⠻⠶⣄⣔⠉⠙⢷⣩⡟⠉⠳⠶⢿⢀⠀⡏⠉⢹⡯⢴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡿⠿⣿⣶⣾⣿⣭⡧⢦⣼⠂⢡⢀⣼⢸⠀⡗⠒⠻⣄⣐⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣦⣮⣭⣙⣛⡿⣽⣹⡄⣤⣠⣼⣸⣗⣿⣧⣾⠿⢿⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠻⠻⠷⠿⠟⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠤⠤⣤⠤⠤⠴⠖⠒⠒⠒⠒⠒⡟⠛⠉⠉⠉⢳⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠛⠛⡏⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠘⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢷
⣠⠤⠤⠤⠶⠆⢤⡀⠀⠀⠀⠀⣴⠶⠿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⣇
⠙⠒⠶⠶⠒⢶⡌⢧⠀⠀⠀⢰⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠈⣷⣈⠛⠛⣋⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢷⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣀⣀⠀⠀⠀⡇⠀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣤⡴⢦⣤⣤⡤⠤⠤⠤⠴⠶⠶⠶⠦⠤⢤⡴⠙⡟⠓⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢻⠁⠙⢳⡶⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣾⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⡿⠉⠀⠀⢻⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠚⠛⠒⠒⠚⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠤⠤⠤⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠀⣿⠀⣀⣀⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⡤⢤⣤⣄⡤⠶⠶⠶⠶⠖⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠓⠀⠀⠙⠉⠉⠉⢿⠋⠉⠀⠀⠀⠀⠀⠀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠤⣤⠀⠀⠐⠚⠓⠒⠒⠲⡖⠒⠂⠈⠉⠉⠉⠉⠻⠂⠀⠀⠀⠉⠉⠀⠀⠀⠋⠈⠈⠀⠈⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⣀⠆⣀⣀⣀⢀⣀⠀⠀⠴⣀⡀⠀⠀⠀⣀⣀⠀⠀⠦⠀⠀⠀⡀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠉⠁⠈⡏⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣀⣀⠀⠀⠀⠠⠄⠚⠠⠄⡤⠠⠀⠀⠐⠓⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠐⡒⠐⠒⠈⠁⠀⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠐⠧⠀⠀⠀⢀⡄⠀⠤⠚⠒⠂⠒⠀⠐⡆⠒⠒⠛⠒⠒⠀⠐⠆⠀⠀⠈⠉⠀⠀⢘⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠀⢀⡠⠀⠄⠘⠂⠀⠀⣀⠀⠀⠀⠐⠂⠀⠀⠠⠄⠀⠀⠘⠁⠀⣿⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡏⠀⠀⠀⢉⠀⠀⢠⡄⢀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⡀⠀⠤⠟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠀⠈⠉⠁⠀⠚⠒⠒⠊⠑⠃⠈⠒⠚⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⡠⢤⣄⣢⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡭⢷⣁⣀⠧⠤⠤⢤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠒⠒⠚⠛⠛⠛⠉⠙⠉⠉⠁
⣿⣿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠖⢲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⣤⠤⢤⡤⢤⡤⢤⡤⠤⠤⠤⠤⢤⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠒⠺⣇⠀⢀⣇⢸⣇⢸⡇⠀⠀⠀⠀⣸⠗⠒⢻⠀⢸⠗⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠈⠉⠉⠉⠉⠉⣹⣏⠉⠉⠉⠉⠁⠀⠀⢸⠀⢸⠀⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣼⠁⣤⣤⣤⣤⣤⣤⡀⣷⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠘⠛⣧⠀⠀⠀⠀⣸⠛⠋⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠛⠛⡟⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⢻⡟⠛⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⣤⣤⣧⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣼⣧⣤⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠉⠙⡏⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⢹⡏⠉⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠧⠤⠴⠧⠤⠤⠤⠤⠤⠿⠤⠤⠤⠤⠤⠼⠧⠤⠼⠦⠼


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠡⡆⣆⠀⣆⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠖⠒⠲⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⡃⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡤⠤⠔⠒⢤⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡎⠧⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⠴⢄⣀⡤⠤⠴⠒⠲⠶⠒⠲⡆⢳⠒⠒⠒⠒⠋⠉⠛⠓⢶⠈⡏⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟⠺⡝⡄⠀⠀⠀⠀⠀⠀⠸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⢠⡷⠧⠤⠤⠟⢷⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢷⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣉⢉⣉⣉⣁⣀⣤⣀⣠⠠⠤⠤⠾⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠈⠉⠉⠙⠋⠉⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⡀⠀⡠⠧⠄⢀⡀⠀⠤⠓⠀⠤⡄⠀⠠⠐⠓⠂⠲⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠠⠇⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠠⠄⠀⠀⢠⠀⠀⠤⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢀⣀⡀⠀⠀⠄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣠⠀⠀⡀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠂⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⠀⠀⠄⠀⠀⣀⠀⠄⠀⠠⠄⠀⠠⠴⠄⠀⠀⠀⠀⠓⠘⣇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⠅⠀⢨⡅⢀⢆⠐⢀⣠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠘⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠤⠤⠤⠤⠄⠲⠒⠒⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠜⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠘⣆
⠀⠀⠀⠤⣤⣶⠶⠿⠟⠓⠖⠌⢇⠀⠀⠀⠠⢤⣴⡶⠾⠿⠛⠲⠂⢻⡀⠀⠀⠀⢤⣴⣶⠾⠿⠛⠓⠂⠘⡆
⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠃⠛⠛⢻⠛⠃⠛⠃⠄⠀⠀⠀⠀⠚⠘⠛⠛⡟⠛⠘⠋⠀⠀⠀⠀⠀⢚⠒⠛⠛⠻⠛⠂⠛
⠀⠀⠀⠤⣄⣀⣀⠀⠀⠠⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⢰
⠀⠀⠀⠰⠆⠀⠀⠈⡤⠠⠠⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠤⠄⠂⠀⠐⠀⠀⠀⠦⠀⠀⠀⠠⠠⡤⠘
⠀⠀⠀⠀⠀⠒⠖⢐⡠⠀⢠⠄⠀⠀⠀⠀⠐⠀⠐⠲⠀⡂⠄⠀⡤⠀⠀⠀⠐⠀⠂⠀⠀⠀⢤⠀⠀⠠⠄⠐
⠀⠀⣁⠂⠀⠀⠀⠠⠀⠀⠀⠀⠖⠀⠀⢈⡀⠀⠀⠀⠀⠄⠠⠀⠀⠐⠂⠀⠀⡑⠀⠀⠀⠀⠠⠀⠄⠀⠠⠒
⠀⠀⠈⠁⠐⠀⠐⠒⠒⠂⠀⠀⠁⠀⠀⠀⠉⠀⠂⠐⠒⠒⠒⠀⠀⠈⠀⠀⠀⠈⠀⠒⠀⠒⠒⠒⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠉⢉⠉⠉⠉⠉⣿⣿⣿⠀⠿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⠃⠀⢠⠒⠊⠀⢲⡄⢠⠛⠻⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣼⡏⠉⡀⠤⡌⠉⠑⠒⢺⡇⢨⠦⡼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣯⣍⣀⡑⠀⠉⠀⠀⣹⣁⡰⠍⣀⠙⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣤⣿⠀⢸⠤⡔⠭⠍⢹⡁⡇⠐⠄⠁⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣞⣽⣶⣾⣯⣥⣷⡁⠰⠀⣸⣇⣷⠤⢴⡀⢉⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣴⣾⣷⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠠⠄⠂⠀⠄⠀⠀⡼⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡰⠋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⣠⠋⢣⡀
⠀⠀⠀⠀⠐⠀⠁⣂⣀⣠⣤⣜⣀⠀⠘⣦⠀⠀⠀⠀⠀⢐⠂⠀⣐⣀⣠⣤⣼⣁⡀⠈⢷⡀⠀⠀⠀⠀⠀⠂⠄⢀⣀⣀⣤⣴⣁⡀⠀⢳⡄
⠀⠀⠀⠀⠒⢾⡿⠿⠟⠛⠛⠉⠉⠋⠋⠉⡇⠀⠀⠀⠀⠒⢾⡿⠿⠿⠛⠛⠉⠉⠉⠉⠉⡧⠀⠀⠀⠀⠒⢺⣿⠿⠿⠛⠛⠉⠉⠉⡉⠉⡭
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠁⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⢠⣦⣰⣤⣶⣤⣴⣦⠄⣧⠆⠐⠀⠀⠀⠀⠀⠀⣴⣠⣤⣶⣦⣤⣶⡄⢰⡤⠀⠂⠀⠀⠀⠀⠀⣤⣀⣦⣶⣦⣤⣶⡄⢰⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠐⠖⠢⢠⢠⣀⠀⠀⠀⠒⠀⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠀⢈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠁⠀⠒⠀⠉⠀⠈⡄
⠀⠀⠀⠀⠰⠦⡀⠀⠀⠈⢠⣀⣠⠀⣤⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠄⣠⡤⠘⡄⠀⠐⠂⠠⠀⠀⠸⠄⠀⠀⠀⠀⠄⣠⡤⠐⠃
⠀⠀⠠⠀⠠⠀⠠⢤⠤⠠⠌⡀⠀⠀⣀⡀⠰⠀⠀⠠⢄⠠⠀⠀⠤⡤⠀⠄⣁⠀⠀⢀⡀⠠⠂⠀⠀⠄⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠠⢄⡀⢸⠀⠀⠁⠀⠋⠉⠁⠈⠀⢀⣀⠀⠀⠀⠄⡀⠀⠇⠀⠀⠀⠊⠉⠁⠈⠁⠀⣀⠀⠀⠀⠤⣀⠀⡉⠉⠁⠀⠉⠉⠀⠈⠃⠀⣀
⠀⠀⠠⢤⡀⠀⠐⠂⠀⠀⠁⠀⡆⠀⠀⢙⡠⠀⠀⠀⢤⣆⠀⠀⠂⠀⠀⠁⠀⢂⠀⠀⢨⢀⠀⠀⠀⠤⡄⠀⠀⠂⠀⠀⠉⠀⢐⠀⠀⢈⣁⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠘⠓⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠓⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠓⠒⠀⠉

⢸⠇⠀⠤⠤⠤⠤⠄⠀⣀⣀⣀⣀⡀
⢸⡆⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠒
⢸⡇⠀⠀⠒⠒⠂⠀⠠⠤⠤⠤⠀⠀⢀⡀⠀⠉⢀⠀⠀⠀⠀⠀⠒⠀⠀⠂
⢸⡇⠉⠁⠀⠁⠐⠂⠒⠒⠒⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⢁⠀⠈
⢸⣯⠀⡀⢉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣸⣿⠀⠉⠈⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀
⣿⣿⡀⠁⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣿⣿⣷⠀⠀⠂⠀⠐⠐⠂⠒⠒⠒⠒⠀⠂⠀⠀⠀⠀⠘⠀⠄⠀⠀⠀⠤⠤⠄⠤⠠⠀⠤⠄⠠⠤
⣿⣿⣿⠂⠒⠒⠂⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠠⠄⠠⠄⠤⠤⠤⠤⠴⠤⠤⠄⠤⠄⠰⠶⠄
⣿⣿⣿⡦⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀
⠛⠻⠿⠿⣿⢿⣿⣿⣿⣿⠿⢿⡿⠿⠿⠿⠿⠿⣿⠿⣿⣿⣿⢏⣿⣿⡏⠉⠉⠉⠉⠉⢻⣿⠁
⠀⠀⠀⠀⠓⠸⣿⢹⡏⠛⠀⠘⠁⠀⠀⠀⠀⠀⠋⠀⢸⣿⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣴⡶⣶⡦⣶⣤⣤⣴⣴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⡇⣹⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⠙⠛⠛⠓⠈⠉⠋⠙⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⡷⠀⢶⢄⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣠⣿⣛⣟⢚⢋⣀⣀⣀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⡿
⠀⢦⡀⠀⠀⠀⠀⠶⠒⠉⠉⠛⠛⣿⡟⠛⠟⠛⠛⠛⢧⣤⡀⠀⠀⠀⠀⢀⡄
⠀⢸⣷⣦⣖⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣈⣉⢀⣐⣤⡶⢿⠇
⠀⠘⣽⣿⣹⡟⠿⣿⣿⣶⣦⣾⣿⣴⢷⣶⡄⢶⣶⡾⠟⠋⢻⡟⠹⣿⣤⣴
⠀⢠⣿⢿⣿⣿⠻⠛⣿⢿⣷⣾⠿⣿⣦⣀⣠⣾⣿⢇⣀⠀⠟⠛⣞⠋⠙⣟
⠀⠘⣹⣤⣹⡁⠀⢸⡁⠈⡙⠃⠀⠀⢸⡇⠀⠀⣀⠈⡃⠀⠀⣈⡿⠤⡻⣧
⠀⠈⣽⠅⠀⢹⡇⠸⠓⣴⡞⠒⠶⢲⠾⠛⢲⣦⠜⠛⠓⠀⣾⠋⠀⢸⣧⣮⡀
⠀⠀⣿⣦⣄⣸⣷⣦⢀⣴⣷⠀⠠⢸⣧⠙⣀⣻⣆⢀⣠⡄⢹⡷⣦⣤⠙⣿⡇
⠀⠀⠛⢻⣿⣿⣏⣩⠯⢨⣟⡲⢦⡄⠯⠚⠉⠉⠛⢛⣿⠟⢻⡁⠀⣀⣠⣿⡇
⠀⠀⣀⣠⣼⡏⠙⣻⣶⣼⣿⠁⣥⣿⡄⠄⠀⠀⣵⢀⣿⣤⣾⣧⠞⣩⣿⡿⠃
⠀⠀⠈⠉⢿⣿⢭⣥⣤⢖⣹⣿⣿⣧⠿⠦⣶⣶⣇⣿⡿⠜⡿⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠐⠚⠒⠋⠈⠙⠳⠏⠀⠀⠹⡧⠸⠁⠄⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⢀⣀⡀⡀⡀⡀⡀⡀⡀
⠀⠀⠀⠀⠀⣰⣾⣾⣾⣾⣶⣾⣶⣶⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⠛⠛⠛⠛⠛⠛⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⢼⣿⣿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣤⣤⣤⣼⣿⣿⣧⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡐⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠎⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠁⠐⡄
⠀⠀⠀⠰⡶⠿⠟⠛⠛⠛⠂⠻⠀⠀⠀⠀⢶⡾⠿⠛⠛⠛⠓⠒⠃⠀⠀⠀⠰⣶⠿⠿⠛⠛⠛⠒⠚
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⢠⣀⣤⣤⣤⣤⢠⡄⠀⠀⠀⠀⠀⣤⣠⣤⣤⣤⡄⣤⠄⠀⠀⠀⠀⢠⡄⣤⣤⣤⣤⢠⡤
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠈⢁⡁⠒⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠄⠀⢤⠄⠌⡁⠁⣈⠀⠀⠀⠀⠀⠀⠠⡤⠠⢈⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠂⠀⠁⡀⠀⡀⠀⠀⠀⠠⠀⠀⠐⠀⠀⢀⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠠⠄
⠀⠀⠙⠂⠐⠀⠤⠤⠀⠀⠀⠂⠀⠀⠈⠑⠀⠀⠠⠤⠤⠐⠀⠀⠂⠀⠀⠉⠀⠐⠀⠤⠤⠀⠂⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠒⠒⠒⠐⠀⠀⠒⣒⡶⢖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⠄⢀⠀⠀⡀⢀⣀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢲⢿⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣙⣡⣀⢀⣀⣈⣀⣉⣉⣁⠀⠀⣀⣉⣯⣤⣤⣤⣤⣀⣀⣀⠒⢛⣿⣟⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣄⣚⣓⣀⣠⣿⣿⣷⣶⣂⣐⣷⣖⣒⣂⣀⣙⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⣼⣀⣹⡉⠢⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⣀⣨⠟⠀⠀⠈⠲⣄⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠁⣠⣤⣀⣄⣿⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⠀⠀⠀⠀⠀⠸⠾⣿⠦⢬⣷⡤⡗⠇⠀⠀⠀⠀⠘⣶⡜⣡⠀⢸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⡀⢱⣴⠸⣿⠀⣀⡀⠀⠀⢀⡴⣄⣿⡵⣥⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣇⣰⣀⣰⣶⣶⣶⣇⣸⣿⣾⣿⣿⣿⣶⣤⣬⣿⣿⣯⣿⣿⣾⢟⡿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠻⠭⠉⠩⠭⡽⢿⣭⠽⠿⠿⠯⠭⢿⣧⣴⡿⠿⠉⠿⠿⠾⢿⣷⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣤⣠⣒⣶⣿⡻⠷⣹⣉⣀⢀⣀⡀⠀⠉⠉⢿⣇⠷⣦⣤⣤⣰⣼⣾⣿⠁⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣛⣙⡏⡉⠀⢈⣉⣍⣿⣿⠿⡟⢙⣿⠖⣋⡟⠉⠉⠻⡟⠉⣩⣿⣿⣽⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⡀⣜⣭⡙⠻⠼⢿⣁⣿⣷⣄⠀⠀⢀⡠⢾⣬⣦⣿⣧⣤⣤⣢⣥⣤⣽⣿⠿⢿⠃⣦⡇⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣽⣾⣿⣖⡀⠀⢀⣬⣻⠉⢩⣿⣿⣵⣮⣭⣭⣭⣼⣩⣿⡧⠤⠤⢴⣿⣧⣿⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣬⣿⣷⢤⣭⣽⣿⣿⡛⠿⣤⣾⡟⠿⠶⠦⠤⠤⠤⢿⠷⣾⣞⣽⣿⡿⣿⣴⣿⣼⠿⠋⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣥⣿⣥⡀⢉⣩⣽⡿⠟⠛⠛⠓⠒⣲⣶⡶⣿⡛⢻⣿⣛⣟⣿⣾⣿⣿⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣓⣛⢻⡾⠿⠶⠶⠶⠤⠴⣿⡿⣷⡟⠷⠋⠛⠛⣿⠽⠿⠿⠟⠐⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠠⠴⠚⠛⠁⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⢤⠤⠄⠒⠒⠒⠒⢲⠒⠒⠛⢳⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠭⠭⠥⣤⢻⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣉⣀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⢴⣤⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⠛⠳⡤⠴⠒⠛⠋⠉⠙⠛⠉⢹⡇⢺⠋⠉⠉⠉⠉⠀⠀⠉⠉⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠻⣎⢆⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠿⠷⠶⠖⠛⠺⡆⠀⠀⠀⠀⠀⠀⠸⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣧⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡈⠉⢉⣉⣉⣉⣀⣀⣀⢀⣀⣀⣠⠤⠷⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⠀⠛⠛⠛⠳⠉⠉⠉⠉⠉⠉⡏⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣀⠀⢀⠀⠀⣀⠧⢀⣀⡀⠀⠀⢀⠶⠀⠀⡄⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢉⠀⠈⠀⠀⠀⢈⡁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠀⠀⠐⠂⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠁⠀⠒⠀⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠄⠀⠀⢀⡀⠀⠶⠤⠀⠀⠀⠀⠄⠠⠀⠀⡄⠀⠀⠒⠀⠰⠂⠰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡷⠀⠀⠤⠀⠐⠃⠀⠀⠆⠀⠀⠁⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠑⠀⠠⠶⠠⠜⠅⠉⠤⠦⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠒⠂⢀⣈⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠧⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁


⣿⠿⠿⡿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣛⣻⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢽⢷⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣋⠀⢈⡳⣝⣷⣌⣛⣟⠶⣦⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣭⣾⣿⠀⢸⣿⣮⠪⡹⣭⣝⠦⠔⢷⣿⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣁⠺⣿⣿⣿⠀⢸⣿⣿⠇⣘⢎⢿⡓⣫⣉⠋⣴⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡌⠻⡿⠀⢸⠟⣡⣾⣿⣿⡿⣿⣞⣿⣥⣤⣽⣃⣜⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠂⢀⡾⠋⠀⠀⠁⠀⠈⢻⣿⣿⣷⠟⢋⣍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⣤⣤⣀⣀⡀⠀⠀⠸⣿⣿⣫⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⣿⡏⡎⡟⡟⡏⠛⠛⠚⠛⣿⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣼⠧⡳⢣⠁⢛⢠⠀⠀⠀⣉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡟⠛⠛⠛⠛⢸⡿⢳⣾⣷⢍⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⢠⣾⢟⠁⢸⡟⢹⢤⠉⠲⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠙⠁⣿⠀⢸⡇⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⡾⡆⢸⡇⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⣀⣀⣀⣀⣠⣣⣸⠇⠸⢸⣀⡀
⠀⠀⠀⠀⠀⢀⣤⠤⠖⠒⠊⠉⣉⣹⡇⠀⣿⡧⠤⢤⡤⠬⢭⢵⣩⣑⣋⣉⣉⡉⠉⠛⠒⠦⢄⡀
⠀⠀⠀⠀⢰⣏⠀⠒⠀⠀⠾⣉⡉⢸⡇⠀⣿⡇⠀⢸⠀⠀⢸⠀⢹⣆⣿⣿⣿⣿⠇⢀⡀⠀⠀⢹
⠀⠀⠀⠀⢸⠈⠙⣶⠾⠿⢿⣛⣛⡛⠧⠤⠟⠓⠒⠒⠒⠚⠓⠚⠛⠋⣛⣧⡀⠠⠤⠴⣖⠊⢻⢸⠃
⠀⠀⠀⠀⠀⢧⣀⡏⠀⠀⠀⢸⡇⠈⢹⡏⢩⠍⠉⠉⢹⠍⠉⠁⠀⠀⢸⠈⢷⡄⠀⠀⡟⢀⣴⠏
⠀⠀⠀⠀⠀⠀⣹⠙⠻⠶⣶⣬⣥⣤⣬⣤⣤⣄⣀⣀⣼⣀⣀⣀⣀⣀⣼⣤⣼⣧⡴⣶⠿⡟⢹⡆
⠀⠀⠀⠀⠀⠀⣿⢤⣀⠀⢸⣅⣀⣀⠤⠿⠶⢭⣭⣉⣹⠋⠉⠙⡙⠉⠉⣀⡘⣿⠴⣿⠀⢰⣾
⠀⠀⠀⡀⠀⠀⡿⠸⡋⠙⢛⣦⣄⣀⣀⣀⣀⣀⣀⣨⡏⠀⠀⢸⠜⢻⠋⠉⠁⣿⣤⠿⢶⡏⠰⠀⣠⡤⣤⡤⢀⣀⣀⡀
⠀⢀⢲⢱⣝⢶⣦⣠⠳⢶⡟⠀⠈⠉⠉⢻⣏⡉⠁⠉⠛⠓⣖⠻⠶⠿⠓⢦⠙⣿⠀⣀⣸⣇⣠⠎⣾⣿⣶⡸⠂⢻⣷⠙⣧
⠀⠪⠻⠛⠿⠟⠛⡿⢣⣴⣱⣶⠄⢠⢰⠋⠉⠉⠛⣧⠶⠖⠿⠤⠤⣴⠶⠛⠓⢻⡁⠉⣀⣸⣩⡆⠘⠛⠛⢁⡶⠘⣿⠂⣿
⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠈⠻⠇⠾⣿⡦⠀⣤⠀⢡⣄⣀⣀⡀⠠⠅⠀⠶⠖⠈⢧⣈⣹⡿⣿⣇⣀⠤⣶⣿⣁⣻⣏⣠⣟⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠚⠓⠠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⠞⠛⠛⠛⠋⠉⠁⠀⠁
⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⣤⣠⡀⢤⠤⠴⠶⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜

⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⡿⠿⠿⠿⣿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⡄⢲⣾⠏
⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠦⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢿⣬⠙⢇⡋⠀⣔⠀⣄
⠀⠀⠀⢹⡟⠛⡛⢛⢻⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡀⢤⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣼⡏⠀⠸⠧⠀⡠⠳⠏
⠀⠀⠀⢸⣇⣰⣿⣿⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⣾⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⢃⡼⢾⡿⢦⣐⣳⣴
⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⣽⣯⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡇⠂⡔⡃⢡⡆⢸⡄
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⡷⠃⡀⠒⠟⠉⠇⠁
⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠋⠉
⠀⠀⢂⢀⠄⣀⡀⠀⡀⡀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠤⠀⠀⠀⠀⠀⠀⡄
⠠⠄⡀⡈⢓⠒⠩⠏⠥⢢⢒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠉⠁⠀⠀⠵
⠑⠒⢶⣦⡥⢥⣬⣨⣃⣊⣥⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡖⠒⠒⠒⠒⣦⣶⡖
⠀⠀⢸⣿⡇⠀⣀⡀⢠⣿⡏⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡈⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣯⡀
⠀⠤⢿⣿⡇⠀⢸⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠋⠉⠉⠉⠉⢹⡟⠃
⠀⠀⢸⣿⡇⢦⣿⣷⢾⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⣤⣴⣶⣶⣶⣾⡇
⠀⠀⢀⣿⣷⣦⢒⡖⢘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠤⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁
⠀⠀⢉⢛⠯⡼⢶⡟⡽⠻⡟⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⡀

⠀⣀
⠀⣿⠀⠉⠉⠉⠁⠐⠒⠒⠒⠒⠀⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣀
⠀⣿⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⣿⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣿⡄⣠⣀⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢀
⠀⣿⡇⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠐⠒⠂⠀⠀⠀⠀⠀⠤⠀⠠⠀⠠
⠀⣿⣧⢀⡀⢀⣀⣀⢀⣀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠠
⠀⣿⣿⡀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠒⠒⠀⠀⠀⠐
⠀⣿⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⠀⠁
⠀⣿⣿⣿⠈⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠆⠀⠀⠀⠀⠐⠛⠂
⢰⣿⣿⣿⠦⠤⠤⠀⠤⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠
⢸⣿⣿⣿⣇⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⢀⣀⣀⡀⣀⡀
⠈⠛⠛⠛⢻⡟⢿⣿⣿⣿⣿⠛⢿⠟⠿⠿⠿⠿⠿⣿⠟⣿⣿⣿⡇⣿⣿⡏⠀⠀⠀⠀⠀⠹⣿⠁
⠀⠀⠀⠀⠘⠃⢸⡟⣻⡏⠋⠀⠘⠀⠀⠀⠀⠀⠀⠋⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⣤⡶⠀⢦⡄⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⡿⠶⠶⠒⢇⣀⡀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⢿
⠀⠰⣄⠀⠀⠀⠀⠀⠥⠌⠛⠛⠿⠿⢿⡿⠿⠿⠿⠛⠟⢋⣉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢹⣷⣤⣆⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⣀⣤⡤⣾⡇
⠀⠀⠟⣿⣿⢹⡿⣿⣷⣶⣤⣤⣴⣤⣤⣤⣤⣀⣰⣴⡾⠿⠟⢻⡿⠻⣿⣀⣠
⠀⠀⢰⣿⣍⣿⣿⠸⠿⣿⣿⣥⣼⣿⣿⣀⠀⣀⣾⣿⡅⠀⠀⠿⠿⢤⠉⠿⣛
⠀⠀⠘⢻⣘⢿⠃⠀⠸⠁⠂⠹⠇⠈⠁⢹⡏⠉⠉⠉⠘⠋⠀⠀⠐⢛⣀⡶⣎
⠀⠀⠘⣿⠁⠈⣷⡄⠴⣄⢄⠠⠤⣤⢤⣿⠦⣀⣄⡲⠔⠢⠀⣤⠖⠉⠀⣄⢹⡀
⠀⠀⢰⣿⣀⠀⢸⣄⣀⠀⣨⡆⠀⠀⢰⡄⢆⡈⢿⠄⠀⢀⡀⢻⣤⣀⣀⠻⢾⡇
⠀⠀⠘⠏⣿⢻⣿⠟⠙⣛⢛⡇⡀⠈⠠⡹⠄⠳⠛⠷⠲⠾⠶⣾⠋⠉⠉⠀⣼⣛
⠀⠀⠀⠀⢈⣻⡟⠷⣮⣅⣘⣿⠁⠸⣧⠀⠀⠀⠀⠄⠀⣿⡀⣸⣆⣠⠞⣾⣭⡏
⠀⠀⠀⠲⢾⣿⡇⢦⠦⠉⢉⢻⣴⣿⠛⢧⣀⣀⣀⡐⢢⣿⢛⣿⠉⣀⡼⠗⠉
⠀⠀⠀⠀⠀⠉⠃⠈⠳⣙⢀⠼⠻⢿⠿⠀⠨⢻⡍⠻⠛⠁⠠⠈⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⡞⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⡄
⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠤⢤⡤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⡇⠀⣿⠤⠤⠤⠤⠤⠤⠤⡏⠀⠛⠦⣤⡀⠛⠦⢤⡀⠀⢸⡦⠤⠤⠤⠤⠤⠤⢾⠀⢸⡧⠤⠤⢤⡀
⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⢽⡦⠤⠤⠽⠦⠞⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⢸⡇
⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠸⠦⠤⠤⣟⠉⠉⠉
⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⡇⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⡇⠀⣿⣠⡤⠶⠒⠛⠋⢉⣉⣉⣀⣀⣀⣸⣧⣀⣀⣀⣉⣉⣉⠉⠛⠓⠶⢤⣄⣸⠀⢸⡇
⣧⠖⠋⢁⣠⠴⠖⠛⠉⠉⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⢤⡀⠉⠳⣼⡇
⣯⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⢸⡇
⡟⠳⢤⣀⠉⠓⠶⠤⣤⣤⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⢁⣠⠶⢻⡇
⣧⠀⠀⠉⡟⠓⠶⠦⢤⣤⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣤⣤⠤⠶⠒⢻⡏⠀⠀⣸⡇
⡏⠳⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠞⢻⡇
⣇⠀⠀⠈⠉⠛⢲⠶⠦⢤⣤⣄⣀⣀⣀⣠⣇⣀⣀⣀⣠⣤⣤⠤⠶⠖⠚⠋⠁⢸⠀⢸⡇
⡟⢦⣄⡀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢻⡇
⡇⠀⡏⠙⠓⠶⠼⣧⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣇⢀⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⢸⡇
⡿⣤⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⠀⠀⠀⠀⣠⢾⡇
⡇⠀⠙⠓⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣯⣤⢴⡖⠋⠁⢸⡇
⣷⣀⠀⠀⣿⠀⠀⠉⠉⠉⠛⠛⠓⠒⠛⠒⢲⡖⠒⠒⠛⠛⠋⠉⠉⠀⠀⢸⡇⠀⢀⣼⡇
⡇⢹⡗⠦⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡧⠖⠋⢸⡇
⢧⣸⡇⠀⠀⠈⠉⠙⠛⠒⠲⠶⠶⠦⡤⠤⠼⠧⠤⠶⠶⠶⠒⠚⠛⣿⠉⠀⠀⠀⠀⣸⠇
⠈⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⢤⣤⣤⣤⣧⣀⣀⣀⣤⣤⣤⡤⠤⠶⠖⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠂⠤⠴⠡⠉⠇⠠⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⠌⠍⠭⠡⠍⠄⠐⡀⢒⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠴⠷⠢⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠁⣹⢀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⢀⠟⠲⠂⠀⠀⢀⠠⣔⡆⠀⠀⢰⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠐⠚⠋⠀⠴⠶⣶⡞⠀⠀⢀⣴⣴⡆
⠀⠀⠀⠀⠀⢀⣼⡷⠆⠲⠿⠿⠀⠀⠀⠀⠀⠀⠠⠀⡀⠁⠀⡽⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⠀⠐⠀⠀⠒⡉⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡙⢿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣦⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣊⣉⣮⠻⣟⢻⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠮⠤⠤⠤⠤⠵⢌⠳⡙⢿⢿⣿⢿⡿⣿⣿⣿⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠀⠀⠄⠳⢝⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠓⠒⠒⠒⢲⠒⠒⣶⢶⠖⠒⠚⠣⢽⠶⠛⠛⠛⣿⠛⢻⣾⡟⠛⠛⠛⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣀⣀⡀⣀⡀⠀⢀⣀⣀⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣤⠀⣿⣿⣍⣉⣉⣉⣿⣿⣿⣿⣉⣉⣹⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠟⢸⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠟⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣾⠀⠀⣿⣿⣷⣶⣾⣿⣯⣭⣭⠄⣧⣿⡖⣚⣓⢓⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⠀⠀⣿⣿⣿⡿⣭⡿⢿⡟⠿⣿⢿⣿⣿⣿⣏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣿⠀⠀⣿⣿⡾⢦⡼⢷⡾⢧⣴⢳⣿⢻⣿⣿⢻⣿⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣻⢸⠀⠀⣿⣿⡧⢾⣧⣴⡷⢶⠾⣾⡿⣾⣿⣿⣿⣿⣿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⣿⠀⠀⣿⣿⣧⠟⠁⢸⡟⢿⣸⣿⣆⣻⡿⣿⣧⣻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⢹⠀⠀⣿⣿⠋⣷⣤⣾⠦⠾⣍⢛⡟⢿⣵⣿⢩⡷⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⢻⠀⠀⣿⣿⡿⣇⣠⢧⡀⠀⢹⡁⣿⣿⢸⣿⣷⣞⣽⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⡀⢸⠀⠀⣿⣿⣶⡏⠀⢀⡟⠛⣏⣹⣫⣾⣿⣿⣝⣿⣿⣿⣿⡶⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠿⠿⠿⠿⣿⣿⣿⣶⣶⣷⣿⣿⣦⣤⣾⣷⣤⣴⣿⣿⣿⡿⠿⠿⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢷⡄⠤⡄⠠⣤⡤⢰⣤⠤⣀⡀⠀⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠘⢆⠒⠒⠦⠲⡆⠐⠒⠤⠠⠦⣉⢭⠬⠁⢬⣭⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⠌⠀⠐⣆⠈⠳⠔⠐⠓⠼⠳⠀⠲⠴⠦⠴⠶⠶⠴⠶⠤⠴⠦⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⣰⣟⣷⠀⢀⣿⣦⡀⠀⠲⠤⠶⠤⠬⠶⠤⠶⠄⢤⡄⠀⠰⠦⢤⠶⠄⡄⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢁⡞⠃⠀⠤⠀⠸⣿⡟⠉⠀⠀⠀⢄⡀⣀⣀⣀⡈⣠⢄⣉⣤⡀⣀⠠⡀⢀⣤⢐⠤⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢰⡌⠱⣶⠦⣤⠀⠀⣿⠇⠐⠃⣠⡀⠀⠠⡀⠀⣤⣀⣀⣦⣀⣀⣀⣠⣐⣤⣈⣁⣠⣁⣠⣤⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠘⢤⣤⠀⢠⣿⠄⠀⡰⣿⠋⠀⠀⢙⡿⢿⡟⠉⠉⠉⣽⠏⠉⣿⣅⣩⣟⡹⠉⠀⠀⢨⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠐⣼⠟⢀⣾⠁⢀⣤⣤⣤⣭⣤⣤⣤⣤⣄⣸⣝⠃⠀⢸⡟⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢴⣦⠙⣤⣾⡇⠀⠀⠀⠀⠘⠁⠃⠛⣿⠟⣿⣯⠀⠀⣉⣿⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢸⣿⠿⠶⠦⠴⠶⠶⠾⠿⠶⠷⠿⠶⠾⠿⠳⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣘⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠘⠓⠛⠻⠀⠀⠀⢹⣿⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⠐⣾⡕⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣿⡇⢀⠀⠀⠀⡀⣁⡀⡀⠘⠀⠀⠀⠁⠰⣧⡄⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣟⠐⠀⠤⠐⢺⣦⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡏⠘⠋⠛⠛⠻⠿⠿⢿⢿⣿⠄⠀⠀⠀⠸⠟⠋⠀⠀⡀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡿⠀⠠⣧⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⣿⡗⠤⣄⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣈⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠠⣿⢇⡀⠀⠀⠻⠁⢹⣀⠀⣼⠁⠉⠀⠀⢹⠦⠲⠚⠉⡤⠔⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠠⠀⣰⣬⠄⠰⣿⡟⠁⠀⠀⢻⠀⢸⠀⠀⢘⡦⠄⠀⠀⠀⠀⢨⠀⢰⠀⢀⠀⠉⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⢀⠀⠴⠞⢡⡈⠆⢸⣿⡿⠦⣄⣠⣴⠒⠚⠒⠠⢼⠀⠀⠀⠀⠸⠤⠚⠲⠋⣤⠈⠀⠁⠈⠃⣠⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠠⠑⠄⠰⣿⡇⠀⢈⠀⢸⠶⠦⢤⣤⠼⠦⠀⣠⠤⠐⠂⠀⢩⠀⢁⠏⠂⠀⠐⢀⡀⠀⠀⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡤⠒⠀⠀⠀⠀⠀⠢⣴⡏⢷⠀⢤⠀⢰⡀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⡀⠸⠆⠁⠀⠀⠀⠐⠊⠀⠀⠀⠈⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠠⠄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⡀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠀⠠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠉⠀⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⠤⠤⠶⠾⠿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡟⣹⡳⣄⣄⠀⠊⠉⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⠟⠽⡇⣷⡜⣦⡒⠂⢐⣀⣉⣀⡀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣰⢲⣶⣆⣤⡨⡍⣻⢏⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠙⡟⠙⠙⠈⣨⡟⠀⠹⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠶⣶⡄⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⣀⡀⣧⠤⠄⣠⣏⠀⣿⣇⠸⣇⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢩⡌⠙⠻⣿⣿⡿⠈⠿⠿⣿⣟⣛⣫⣽⣷⣔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣿⣍⣿⠾⠛⢹⠻⠿⠿⠾⣿⠷⣾⣿⣿⣿⣷⣤⡬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠘⠿⣧⠀⢸⠀⠀⣠⣠⣾⡦⣾⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⡤⠦⠲⢧⠮⠷⠿⣿⠿⠷⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⣿⣷⣿⠧⠤⠤⠤⠤⠤⠤⠤⠤⢿⠯⠥⠬⠭⠭⠭⠥⠤⠤⠬⣿⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⡏⠀⠑⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠛⠃⠀⠀⠀⠐⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣄⣄⣀⣀⠀⣤⡄⠀⠀⠀⠀⠀⣾⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣶⠦⠀⠀⠀⠀⡀⠀⣤⣤⣴⣾⡇⠀⠀⠇⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⡇⡀⠀⠀⢸⣿⠄⠀⠀⠀⣦⣅⣾⣿⣿⣿⣿⡇⠀⠀⢠⠀⠁⢀⡆⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠢⣧⣀⠀⣿⢄⣠⣄⢸⣟⠀⠀⠀⠀⠐⢿⢆⣹⢿⣿⣿⣧⣄⣰⣴⣇⠀⢸⡵⠋
⠀⠀⠀⠀⠀⢀⣀⣀⠩⢽⣿⡽⠟⠋⠁⠀⠸⢿⡆⠀⠀⠀⢿⣟⣿⣿⣾⣿⣿⣿⠿⠟⠛⢻⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⢩⡶⣾⡟⠋⠛⠀⠀⠀⠀⠀⢐⣈⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠉⢻⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠋⠉⠉⠙⠙⠛⠋⠉⠋⠙⠋⠙⠛⠉⠉⠉⠙⠛⠙⠉⠉⠛⠋⠉⠉⠉⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠠⡶⠷⡶⠀⠀⠀⠂⠀⠀⠀⠀⣸⠿⠛⠂⢀⠦⠤⡦⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⠀⠀⢠⠂⡀⠀⠃⠂⠀⠀⠀⠀⠀⠀⣀⠨⠀⠀⠀⠈⠖⠀⠃⠀⠀⢂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣳⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢠⣀⣀⣀⣀⡤⠤⠤⠶⠒⠛⢻⡿⠟⠂⠒⠒⠲⠶⠶⠶⠶⠆⢻⠀⠀⡄⠀⠀⠀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣧⣄⣀⠤⠄⠀⠤⠤⠐⠒⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣷⠀⠀⠀⣀⡀⠀⠀⠀⠀⠨⠷⠶⠔⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠶⠖⠀⣠⡶⠂⠀⠾⠷⠀⠀⠀⠀⠂⢶⠂⠀⠀⠐⠀⠐⠛⠛⠛⠛⠚⢻⡏⠉⠀⠀⠀⢸⣀⠀⣠⢐⠢⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣀⣀⣤⣤⠊⣉⠁⣭⣬⣤⣅⠀⠄⢤
⠀⠀⠀⠀⠀⠀⢈⠢⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠤⢤⡬⠩⣇⠼⢷⣯⡤⠄⠘⠂⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠑⣁⣄⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⡀⣀⣀⣀⠤⠄⠀⣿⠄⠀⢀⡀⠀⠀⠀⠀⠈⠻⣧⣄⡄⠀⠀⠛⡄
⠀⠀⠀⠀⠀⢀⡀⠰⡘⣿⠈⠉⠉⠉⠉⠉⠉⠀⠘⡟⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡁⠁⠀⠃⠀⠀⠀⠈⠃⠀⠀⠉⠛⠶⢤⡤⠆
⠀⠀⠠⠤⢄⠀⠉⣲⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⡇⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠦⡁⠘⠧⠄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢄⢀⣠⣶⠷⠟⢛⣿⣷⠀⠀⢴⠀⠀⠀⠀⡂⠀⠀⠀⠄⠀⣠⠀⠐⠂
⠀⠀⠁⠀⠀⠒⠒⠂⠐⢄⠀⠀⠀⠳⡎⠀⠀⢳⡴⣦⠄⠁⠀⠀⠀⡡⠀⠀⠠⠞⠋⠁⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠏
⠈⠁⠀⠀⠐⠂⢤⠀⠀⠀⠁⠂⠀⠀⢿⡄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣄⣀⠀⠀⢠⠀⠤⠔⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠋⠉⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢡⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣧⠜⠳⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⣹⠇⠆⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡄⢛⡗⠐⠒⣶⢶⡄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢶⠟⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠾⠟⠛⣧⠀⠀⡿⠀⢳⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⢹⣟⠀⠀⠘⠋⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⢳⡈⢄⠀⠀⠀⢀⣠⣤⣖⣪⣍⣀⣤⠴⠖⠛⠉⣱⠄⣼⢻⡇⠸⡷⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠈⠷⢬⣶⣶⢛⠋⡙⢍⢣⡱⡈⣅⣠⣤⠶⢾⡏⠀⠀⣿⠀⠧⣤⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣠⡤⠶⠒⠛⠉⢁⣀⡇⣇⣼⣸⣵⡇⣯⣥⣤⣀⣸⡇⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⢸⣍⣠⡤⢰⠒⠛⢿⠉⠁⠈⠁⠀⠈⢳⡥⡅⢀⣠⡎⠉⠃⢀⣠⡼⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡇⠀⢸⣿⡡⠀⢰⠀⢠⣾⣆⠀⠀⠐⢐⣠⣼⣗⡆⢄⣸⠈⠁⠀⣨⠽⠛⠛⠋⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣁⠴⠇⠀⠀⣿⢿⠛⣿⠛⡻⠟⠛⠛⣿⠟⡛⠛⢛⡭⡿⠛⠛⠿⡶⢦⣧⢀⡀⠀⠀⠠⢫⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⠃⠀⢆⣀⣀⡿⢦⣬⢾⡰⣋⢀⠀⠀⣯⡐⡘⠀⢨⣇⣅⣠⣏⣴⠞⠋⠀⠀⠙⣄⠐⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠁⠀⠀⢸⠟⠛⠛⠛⠛⠛⠻⢿⠛⠋⠉⠉⠉⠀⠀⠑⡄⠀⠀⠀⠀⣻⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣇⡴⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠗⠦⠤⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣿⣤⡶⢿⡟⠉⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠀⠀⠀⠀⠈⠉⠙⢷⡶⠦⠤⠤⠤⣴⣷⣾⠶⠶⠶⢿⠋⠉⠀⠀⠀⠸⡇⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣌⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣷⣤⢾⡋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠈⠛⠶⠤⣤⣀⣀⣀⣀⣼⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣇⣀⣠⣤⠶⠚⠉⠀⢨⡇⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠛⠛⠛⠛⠺⡶⠒⠒⡛⠛⠋⠉⠉⠀⣹⠀⡑⠀⠀⣰⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣯⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠶⠶⣤⣤⣾⣧⡶⠶⠶⠶⠶⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡰⢡⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠔⠀⠀⠘⣠⢀⠀⣰⠃⢀⡞⣠⠆⠀⡰⣡⣿⠀⣿⣇⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡜⠀⠀⠜⠀⢀⡜⡰⢃⡎⢰⠃⢠⡞⣴⢏⡎⡴⣱⣿⣿⠄⣿⣿⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢾⡶⠶⢾⣴⠦⠾⠶⡧⣾⣴⣧⣶⣿⣴⣷⣶⣾⡵⣛⣉⣛⠀⣛⣉⣙⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠺⣿⠀⢀⠞⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⡝⢛⣿⠀⠛⢹⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡿⠄⢞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠛⠛⠟⠟⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠻⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠧⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠓⠄⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣔⠀⠇⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡖⡂⢠⡤⡤⡤⠤⡤⢠⡖⣰⠀⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠙⠉⠙⢧⠿⠛⢶⠒⠒⠒⠛⠙⠧⠍⠉⣿⣿⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢠⠤⠀⠠⡀⢀⣘⣀⣐⣀⣀⣐⣀⠀⡀⣿⣿⠠⢄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠟⠐⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⠿⠿⢀⣠⠆⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⣷⣷⡦⠦⠤⣄⣤⣍⣉⣩⡉⠉⠩⡅⠤⠀⠒⢀⡉⢵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡶⡄⢸⣿⣿⣿⣿⣶⡟⣿⣶⠒⠚⡒⢒⠒⠓⠒⣾⡉⢉⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣰⡆⠀⠀⢸⣿⣿⣿⢟⡿⣶⣶⢇⡈⢤⠌⢈⠑⠀⠂⣇⢘⡿⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢧⡼⣤⣻⣿⣟⣿⢿⣟⣻⡷⢼⡅⢤⣁⠾⣀⣠⣤⡟⠀⡬⢩⣿⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⣴⣺⠿⠿⠿⠿⠯⡟⢯⣭⣾⣿⣟⣋⢡⡄⠄⠀⢸⡕⢊⡢⠿⠛⠉⠁⠙⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢠⡿⠚⣿⠉⠀⢸⡆⠀⠀⣸⠀⠀⠨⣷⠐⣇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣾⠁⠀⣯⠀⠀⠰⡇⠀⠀⢹⠀⠀⡀⣿⡆⢻⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢂⡟⠀⠀⡇⠀⠀⢸⡇⠀⠀⢺⠂⠀⠀⢸⡇⠘⢇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡇⠀⠀⠀⡷⠀⠀⢸⡇⠀⠀⢸⠀⠀⢺⡀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡼⠀⠀⠸⡗⠀⠀⠈⡯⠀⠀⢸⡇⠀⠀⠘⡆⠀⠈⣇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠊⢳⡒⠒⠚⠙⠂⠀⠈⠉⠀⠀⠈⠁⠀⠉⠉⠉⡟⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⠀⠄⠠⢤⢤⠤⠤⠀⠀⠀⠐⢢⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣾⠀⠀⠀⢀⣀⢀⣄⣀⣬⣇⣀⣆⠀⢀⣀⣈⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⢿⣽⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠭⠿⠟⠗⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠾⣅⣀⣄⣤⣤⣬⣤⣴⣴⢶⣦⣴⣤⣤⣥⡽⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠸⠄⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠁⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⡒⣴⣤⠬⠀⠈⠉⣭⠩⡭⡭⢭⠻⣍⠌⡓⠶⣾⣽⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⠂⠛⢩⣆⠀⠀⠀⠘⠦⣤⣄⠈⠼⢿⣀⣧⣆⣀⡖⢥⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡻⢿⣶⠦⠎⠋⣍⠀⠀⠀⠄⠀⠀⠀⠀⠀⠛⠁⠉⣡⣇⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣽⡇⠀⢈⡎⠛⠒⠀⠀⠢⠤⠠⠄⠰⣦⣀⣀⢋⡙⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⡟⡿⠿⠁⠐⠖⠀⠀⠀⡄⠀⠀⢠⢉⡍⠉⡀⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠷⢶⣖⡀⠀⠀⣀⠈⠛⠻⠺⠋⠾⣷⣦⣴⡽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⠿⠟⠋⠾⢿⣷⣾⣿⠿⠿⠃⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡟
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠐⠉⠠⠞⣀⣐⡄⡦⠀⣰⢂⠀⠨⠀⠀⡀⠀⠀⠀⠀⠀⠆⡇⠀⠀⠘⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠰⣦⡴⠟⠛⠂⠠⠄⡈⠀⠈⠉⠙⣀⠚⠀⠠⠀⠀⠀⠀⢰⠇⠀⠀⢀⠏
⠀⠀⠀⢀⠀⡀⠀⢀⣀⣰⠛⢁⡤⠖⠀⠀⠁⠋⠉⠀⠘⠓⠦⣀⡐⠀⠑⢛⠂⠂⠀⢸⠀⠀⢰⡟
⠀⠀⠀⡈⠀⠀⠀⠈⢉⣿⣯⡥⠐⠚⡀⣉⣉⠉⢄⣠⣀⡠⠄⠀⠐⢦⡦⣿⣶⡆⠀⠫⠖⢀⡞⠁
⠀⠀⠀⠀⠀⠠⠀⢡⠀⠈⢻⣦⣈⣋⣿⣿⣧⣧⣽⣿⣿⡂⢀⣼⣤⣴⡿⠋⢠⠀⠰⠃⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⠖⠋⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠑⡴⠋⢀⡗⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠐⠶⣄⠉⠓⠶⣾⣶⣤⣶⣾⣦⡶⢤⣤⡴⡦⠶⣶⡄⠞⠁⠀⠘⠁⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠉⠁⠉⠁⠈⠈⠁⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡓⠒⠲⢦⡤⢤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⣢⣌⢳⣦⡠⠤⣿⣈⡉⣹⣟⢒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣍⠉⠉⠛⠻⡗⠛⠷⠷⣾⠿⠧⣬⢮⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣖⣿⣿⣶⣶⢻⣤⣤⢼⡆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣈⢻⣉⢉⢉⣙⣏⡙⠛⢻⡛⠒⠚⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⡿⢻⣿⣿⣿⡿⢿⠿⠿⠿⠿⣯⠿⠿⠿⣾⣬⣿⣿⢦⡥⠽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢣⡀⢻⣿⣹⠀⢸⣿⠉⠙⠁⣸⣷⣲⣰⣶⣾⡦⠤⣄⠸⣦⣠⠠⡤⣷⡄⡌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⣿⠀⢸⣿⠆⠀⣴⡟⠉⠉⠛⠛⠛⣿⣿⡟⠛⣿⣷⣶⡶⠾⠿⠷⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢹⠀⢸⠃⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⣇⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠀⢸⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠁⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⣧⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⣦⡼⣧⣸⣿⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢸⡿⢲⡟⢹⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⠿⠟⡿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠲⢳⣼⡇⢸⡀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠛⠿⠃⢸⠂⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⠀⠀⠀⢀⣤⣼⣇⣀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⠀⠀⣠⣾⣟⣿⣿⣿⡄⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠀⢸⣿⣖⣒⣻⣭⣉⣋⣉⣡⣗⣒⠶⢧⣀⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢉⣠⣾⠀⢸⣿⣿⡿⠿⡤⡄⣥⢠⢴⠿⠿⣿⣿⣿⣿⣄⣈⠙⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶⣤⣝⣦⣼⣿⠿⠿⢾⡿⡷⠶⠶⠿⠶⠶⠾⢟⣛⣋⣥⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⣀⡀⠉⠉⠉⠉⠛⡛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⡅⣀⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣽⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠠⢠⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠓⠲⠶⠤⣤⣦⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⢻⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⡃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠳⠶⠦⢤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠒⠛⠹⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣶⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠤⢼⣤⣤⣤⣤⣤⣤⡤⠤⠶⠖⠛⠉⠁

⠀⠀⢀⠌⣉⠒⠂⠤⠤⠀⠀⣀⣀⣀
⠀⠀⡜⠤⣴⣄⣀⣀⣀⠀⠐⠢⠀⠀⠀⠈⠉⢸⣿⣦⡀
⠀⢰⣄⣀⣀⠀⢀⠀⠚⠋⠛⠉⠐⠲⠖⠳⠶⢿⣿⣿⣿⣷⣤⡀
⣰⡀⠀⠉⠉⠉⠉⠓⠲⠒⠲⠦⢤⣀⣤⣀⣸⣾⡟⠁⠉⠉⠉⠉
⠉⠙⢻⣯⣷⣤⢤⣴⣄⣀⣀⣀⣠⣁⡤⢤⡟⣿⢀⣾⠶
⠀⠀⣸⣿⣾⣧⣤⣀⣀⣈⡉⠉⠉⠉⠙⠋⠀⣿⢘⡽⠇
⠀⠀⢿⣷⣤⣿⡝⡟⣿⣿⡟⣿⠟⣷⠞⠂⠠⡏⢀⣤⣦
⠀⠀⢸⣿⣿⡏⠉⠉⠛⠛⢻⡿⠿⢿⠾⠷⢶⡇⢏⣷⣯⢶⣲⡎⣷⡀
⠀⠀⢸⠛⣿⢇⣀⣠⡤⠤⢼⡧⠤⢄⣀⣀⣀⡂⡦⣿⡇⠀⠈⢻⠏
⢀⠔⢻⣆⣥⣶⣦⣾⣿⣷⣿⣿⣖⠘⢻⠒⠂⠇⣿⣿⣧⡀⠘⡼
⣾⡤⠤⠈⢿⣽⣾⣿⢾⣟⣽⣿⣟⣓⠚⢤⣀⡄⠘⣿⣶⣴⣄⡇
⢻⠑⢄⣀⠠⠚⠉⠛⠛⢿⡿⠿⠿⢿⠿⠚⠛⠝⡛⠛⢹⣟⢸
⠘⣆⠀⡿⠑⠒⠢⠤⣴⣟⠀⠀⠀⢘⣀⣀⣀⣠⢜⡿⠹⢛⢉⡐⠀⢀
⠀⠸⣷⣧⡀⠀⠀⠀⣿⠀⠉⣬⣭⢽⢠⣥⣴⣦⣾⣗⡖⠉⠀⠁⠛⠃⠃
⠀⠀⣇⡉⠙⣷⠶⠶⣷⣤⣤⣽⣿⣶⣼⠽⢻⣟⢹⣿
⠀⡀⣇⠉⠓⢿⠦⣤⣀⣅⣀⣣⣸⣛⣕⣥⣾⢿⢿⣿⡄⢰⣼⡄⣤⢆⣶⡆⢠
⠺⠪⢿⢳⣦⣼⣀⠀⠈⡅⠉⣿⢻⣝⡿⡋⣿⣯⣾⣍⣄⢹⣸⢞⢽⢀⣃⢶⡮⡍⠰⡾⣶⢤⢀⣄
⠀⠈⠘⠿⢇⡋⠛⡿⡋⢛⠲⡾⣾⣻⢿⣯⣿⢿⡏⡑⠇⡨⡞⣾⢈⢉⡿⣘⢆⣉⡈⠹⣓⠈⢄⢏⠣⠘⠷⣢⢶⡦⡀
⠀⠀⠀⠀⠈⠉⠙⠙⠷⠺⠖⣯⣵⢿⣿⡿⢿⡟⢦⡽⣃⡧⠸⡉⡍⠧⠄⡝⢤⣊⢆⠼⠸⠣⠂⠦⠻⠈⠈⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⠀⡀⢀⠀⢀⣄⣠⣠⣤⣠⢀⣀⣀⣠⡄⠀⣀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⢴⡄⠤⠂⡜⢠⢰⠀⠀⠀⠀⢠⠀⠀⠄⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠠⢡⠹⠁⢫⠈⠇⡐⠈⢈⠄⡂⠀⠈⠉⠈⠃⠃⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠒⠃⠘⠐⠘⠰⢠⠧⠀⠐⠦⠂⠐⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠤⠀⠒⠀⠀⢈⣀⣀⣀⣹⢈⣘⣉⣀⠀⠀⠀⠔⠀⠠⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠣⠅⠂⣶⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⡦⠀⠤⠃⢂
⠀⠀⠀⠀⠀⠀⠐⢆⣠⠀⠀⠀⠀⠉⡩⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠠⣄⠉⠑⠂⠠⠤⠌⠠⠀⢄⡄⠀⠀⡀⢠⣄⠀⠀⠠⠤⠦⠒⠈⣙⡀⠔
⠀⠀⠀⠀⠀⠀⠀⡁⠉⠒⠐⠀⠀⠀⣀⣀⣀⣆⣀⣀⣀⣠⡄⠀⢀⡤⠠⠆⠀⢚⢁⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠠⣤⠀⠀⣀⡀⣀⠀⢀⣁⣀⣀⣀⣀⠤⠤⠴⠶⠊⠉⢀⠠
⠀⠀⠀⠀⠀⠀⠀⡃⠒⠠⠄⠠⢀⣀⣀⠀⡉⠀⠀⠀⠀⢈⣀⣀⣠⡀⠄⠐⠀⠈⠃⢀⣀
⠀⠀⠀⢀⠀⠀⠀⠲⠄⠴⠀⠀⠀⠀⠁⠀⠀⠀⠉⠏⠁⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠉⠁⠀⢰⠂
⠀⠀⠀⠈⠳⢀⢀⣤⣀⠀⠀⠉⠁⠀⠁⠀⠰⠂⠐⠃⠀⠐⠖⠊⠈⠉⠀⠀⡀⢀⣀⠤⠒⠃
⠀⠀⠀⠀⠀⠀⠢⠁⣀⠹⠁⠚⠀⠀⢤⠤⠤⠀⢀⣀⠀⢠⡦⠤⠄⠶⠂⠈⠉⠁⢁⡰⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠰⠀⠀⠀⢀⣄⠀⡐⢆⢄⡀⢸⠤⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢀⠀⠶⠤⠡⠍⡏⠠⠩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡀⠌⠍⠭⠩⠭⠍⠘⡀⢒⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠉⠉⠉⠉⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠴⠷⠤⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠂⢻⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣀⠿⠶⠆⠀⠀⢀⠠⣴⡆⠀⠀⢰⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣋⠠⠠⠚⠃⠀⠀⠄⡤⠜⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⣸⣷⠄⠲⠿⠿⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢈⡡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠀⠀⠤⡉⠥⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⣀⢀⣀⠤⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣰⣎⣡⣶⣉⣠⣿⣈⣠⣬⣤⣤⣴⣧⣤⣴⢿⣶⠾⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣋⢉⣽⣋⣁⣿⣉⣡⡏⢁⣠⣏⢁⣴⠭⣤⡾⢤⣾⠃⣿⡟⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣰⣋⣁⣜⣁⣠⣞⡁⢀⣞⡁⣠⡋⣁⣤⠁⢠⣾⢻⠀⢸⣿⠜⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠟⠉⡠⠋⠀⡸⠋⠁⠸⠋⠉⡘⠉⠀⠜⠁⣠⠿⠿⢼⠀⠸⠿⠷⢌⢻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠛⣹⠟⠃⡾⠛⢳⡾⠓⠒⡾⠖⢲⠞⠒⣶⠗⠒⣾⡻⣶⣶⠎⠀⢸⡾⡿⢋⣆⠹⣯⡀
⠀⠀⠀⠀⠀⣔⣩⣀⣀⣅⡀⣊⡀⣀⣋⡀⠀⢊⣁⣀⡉⢀⣐⡀⢀⣾⣛⣃⣙⣙⣉⡁⢸⣉⢉⣈⣉⣱⣨⣷⣄
⠀⠀⠀⠀⠀⠉⠁⠙⠁⠘⢿⡧⢹⣿⢹⣿⣾⠏⠙⠚⠿⠓⠿⠟⠿⠛⠻⠛⢷⡘⢯⠀⢸⡏⠜⠛⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⣿⠀⣏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⢨⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢈⠉⠉⠀⠀⠐⠊⠉⠉⠉⡉⠈⠀⠀⠉⢘⣿⠀⣘⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⣿⡀⠀⠀⢈⢧⡀⠈⠘⠆⡏⠀⠀⡐⣄⢸⣿⡘⣩⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣾⠛⠶⠒⠛⠛⠛⠓⠓⠛⢣⠛⠛⠛⠛⠺⠇⡆⢸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⡀⡇⢸⠀⠀⠹⠤⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣠⣶⡾⢁⠐⠛⠳⠲⠒⠒⠲⡠⠀⠀⠄⠀⡇⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠉⠀⣼⡿⡇⠀⠀⠀⢺⣯⣿⣷⣿⣧⣼⣧⣤⣶⡆⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⣉⠸⣇⡇⠀⠀⠀⢼⠿⣿⣿⡿⠿⠿⠿⠿⠿⡇⠃⠀⠦⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣿⣄⣿⡷⠶⠖⠒⣿⢥⣶⠠⠄⠀⠠⠀⠒⢓⡇⡇⢀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢸⢛⠻⣦⣽⡉⠙⠟⢻⡿⠛⣿⠾⠒⠒⠾⠛⠛⢻⡿⡏⠉⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡾⢧⣴⡈⠙⠛⠳⢺⡷⠸⡷⠀⢦⠤⠒⠐⠖⢻⣷⣇⠀⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⢿⠈⠹⢿⢤⡄⢨⣧⣼⠃⡀⣺⡀⠀⢀⣅⣼⣿⣿⠴⣿⡆⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠼⣾⣶⣀⣇⠀⠀⠈⢩⠁⡉⠈⣩⡈⢀⣸⣯⣿⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠛⠛⠛⠉⠉⠉⠀⠀⠋


⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠚⠋⠉⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⣐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⢀⡾⢀⣈⣿⠀⢲⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⣾⣫⣍
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⢸⠀⢸⡇⠘⣆⢀⠀⠀⠀⠀⣀⡠⠴⠒⣋⣩⠼⠇⡀⣭⡤⠈⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠘⢦⣤⣴⡶⡛⡙⢯⡝⣉⣡⡤⢶⡎⠁⣿⠸⣄⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠥⠴⠒⢋⣉⢡⡴⡠⠴⢶⠇⠯⠴⢤⣼⠇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠀⢸⡖⠒⠉⠀⣩⠀⠀⠀⠀⢘⣇⡂⠐⡃⠄⠀⢴⣯⠽⠷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣃⢼⠀⢸⡷⠶⣶⢒⡟⠲⢶⡶⠺⠛⣇⡶⠾⠷⣤⣤⣀⠀⠀⢀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠁⠘⠤⠴⠳⢮⣿⣼⣀⣀⣸⣄⣄⣀⣇⡧⠴⣼⠚⠁⠀⠱⡄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡜⠉⠀⠀⠉⠉⠙⡅⠀⠀⠀⠀⠀⢧⠀⠀⠀⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣗⢄⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⢸⠀⠀⣰⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠟⠒⠶⠷⣄⣀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣀⣴⠿⠶⠿⡏⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠄⠀⠀⠀⠀⠈⢻⠉⠙⠓⠛⠛⠛⠋⠉⣏⠀⠀⠀⠀⡇⣀⡼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠧⢤⣀⣀⡀⣀⣎⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⡤⠴⠛⠉⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⠈⡇⠉⠉⠉⠉⠛⠛⠛⡗⠚⠛⠉⠉⠉⢀⡇⠄⣀⣠⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠷⢤⣤⣤⣄⣀⣀⣠⣇⣀⣀⣤⣤⡤⠾⠗⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉