⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⡿⠿⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠉⠙⠻⠿⣶⣦⣀⣠⣤⣤⣤⣤⣤⣤⣶⠿⠟⠫⠉⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣠⣤⠤⣤⣤⣀⡒⠀⣀⣤⡤⠶⠶⠤⣄⡀⠤⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡼⠛⠉⠀⠀⠀⠀⠀⠈⠙⠟⠉⠀⠀⠀⠀⠀⠈⠙⠳⣏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣤⣿⣻⣿⣿⣷⣿⣧⠀⠀⠀⠀⠀⢸⣿⣸⠋⠀⠠⠴⠶⠒⠒⠲⠆⠀⠀⠀⠀⠘⠓⠒⠒⠲⠶⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢴⡿⣿⡿⠋⠉⠩⠙⣿⣿⣄⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⣠⣿⣄⣀⣀⣀⣀⣀⣴⣄⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⢰⣿⣿⠀⠀⠀⠀⠀⢀⣀⣨⣤⣤⠤⠤⠤⠤⠤⣬⣭⣄⣀⣀⠀⢀⡼⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣼⣿⣿⣠⠴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⢰⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡼⡀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣧⢅⠀⠀⢀⡾⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⡇⠹⣇⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⡌⡀⣰⡟⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡗⠀⠹⣆⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣧⣰⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣰⠿⠀⠀⢻⡄⠀⠀⠙⢿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⡟⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⢀⣴⠏⠂⠀⠀⠘⣧⡀⠀⠀⠀⠻⣷⡀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⢹⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠒⠒⠛⠛⠛⠛⠛⠛⢛⠛⠒⠒⠒⠒⠶⠶⠶⠶⠿⠥⠤⠤⠴⠶⡟⠁⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠹⣷⡀⠀
⠀⠀⠀⠀⠀⣼⡏⠀⢠⣄⠀⠀⠀⠀⠉⠙⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠾⢻⡇⢻⢀⠀⠀⠀⠀⠀⢻⣇⠀
⠀⠀⠀⠀⠀⣿⡇⠀⣾⠉⠷⣄⣂⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⡟⠁⠀⣼⣧⣼⡧⠄⢀⣠⣤⠀⣿⣿⣦
⠀⢀⣄⣀⣀⣿⣧⡶⢿⣀⣠⡼⠋⠉⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠈⠷⣤⠾⠛⠀⢨⡽⠟⠋⣩⣯⣾⣿⣙⣿
⠀⠸⣿⡉⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⣶⣿⢿⣿⣯⣿⡏
⠀⠀⢹⣷⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⣿⣿⣿⠛⠁
⠀⢠⣿⠁⠀⠀⠀⠀⠀⢀⡴⠚⠉⢉⣉⣉⠉⠉⠒⠲⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡠⣖⣦⣭⣤⣥⣐⠒⠦⢄⡀⠀⠀⠀⡤⠿⣿⣦⣤⠀
⣤⣾⣇⣀⡀⠀⠀⠀⣠⠎⣠⡴⠛⠉⠉⠉⠹⣆⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⢀⠎⣾⠋⠀⠀⠀⠀⠉⠳⣄⠀⠙⡄⠀⠀⣧⣀⣤⡾⠟⠀
⢿⣥⣀⣺⠇⠀⠀⢠⠇⣰⠏⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡜⠀⣇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁⠀⠀⢸⣿⠁⠀⠀⠀
⠀⠹⣿⡁⠀⠀⠀⢸⠀⣯⠀⠀⠀⠀⠀⢀⣴⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢦⡀⠀⠀⠀⣀⣴⠏⠀⢀⡇⠀⣰⡿⠁⠀⠀⠀⠀
⠀⠀⠈⢿⣦⡀⠀⠀⢣⡘⢦⣄⣀⣤⠶⠋⣡⣾⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⢿⣦⣀⠉⠉⠉⠉⠉⠀⢀⡤⢋⣠⡾⠋⠀
⠀⠀⠀⠀⠉⡛⣷⣶⣤⡭⠷⠤⣤⣴⣶⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣷⣶⣶⣶⣴⣷⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀