Traveller Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠉⠉⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠤⠄⠒⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠉⠉⠁⠒⠒⠠⠤⢀⡀
⠀⠀⠀⠀⠀⣀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⠒⠀⠉⠉⠉⠉⢛⠉⠉⠉⠉⠁⠀⠀⣹⠁
⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠀⠉⢧⠀⠀⠀⠀⠀⠘⠇⠀⠀⢀⡀⠄⠚⠁
⢷⡤⠤⠀⢀⣀⣀⣀⣀⣠⠤⠴⠄⠚⠃⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⣀⠀⠀⣶⠀⠚⠁
⠀⠈⠁⠒⠒⠀⠀⣤⠋⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠎⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣀⢘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⠄⢀⠀⠀⠀⠀⣀⠴⠊⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⣶⣶⣾⠁⠒⠂⠉⣷⣶⣦⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⣿⡿⡀⠀⠀⢀⣿⣿⣿⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠎⠀⢸⣿⣿⠇⠉⠒⠒⠁⢸⣿⣿⡇⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⠖⢹⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⡇⠑⢄⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠶⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢸⠓⣄⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠉⡄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⣴⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣄⡎⠀⠀⠸⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢏⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡙⠀⠀⠀⠀⠡⡄⠸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢇⠀⠀⢸⡅⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢬⡄⠀⠀⠀⠀⢀⠜⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠑⢄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠔⠁⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠐⢄⣀⢠⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢢⣤⣔⣃⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣷⣤⣤⠄⠤⠤⠤⠾⠿⠯⠤⠤⠤⠤⠼⠿⠷⠤⠤⠤⠤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⣿⠟⠁⠀⠀⠀⢀⣤⢶⣄⠀⠀⠀⣿⠋⠀⠀⠈⣿⡆⠀⠀⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢾⡋⢁⣠⡿⠆⠀⠀⢿⣦⡀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⡃⠀⢀⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠁⠀⢻⠀⠀⡋⠀⠈⠉⠉⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀⠀⠀⢀⣠⣤⣴⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠧⣀
⠀⠠⣶⣄⣄⡙⡿⣦⣤⣠⣴⠶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠢⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠂⠀⠀⠀⠘⠑⠂⠈⠁⠉⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠠⠤⠠⠰⠄⠐⠂⠀⠠⣤⣴⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⢒⠀⠀⠄⠀⣤⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⢤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠈⢂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢫⣼⢢⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈
⠀⠂⠐⠂⠀⠠⠀⢀⠀⠀⠀⠀⠈⠁⠈⠃⠀⠁⠀⠠⠤⠐⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠤⠄⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠠⠠⠀⠀⢀⠤⣅⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠞⡂⡀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⡦⠄⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⢸⢀⢈⠁⠙⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣠⣤⣤⣠⡀⠠⡶⠦⠾⠿⠿⠿⠇⠀⠀⢸⢀⠉⠉⠙⠂⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡄⠀⠀⠀⠉⠉⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠁⠙⠈
⠀⠀⠀⡀⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠈⠙⠒⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⠀⠀⠀⣐⠀⠀⠀⠀⠀⠄⠀⠠⠬⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀⠀⠀⠀⢠⠃⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⠁⡂⠞⠐⠠⣀⣈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣸⠉⡹⠳⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠈⠑⣶⡁⠀⠀⡇⢰⣵⠚⠓⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⢸⣾⠁⠀⠀⡸⠁⣸⠧⢄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠶⠤⠊⠁⠀⠋⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⣀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠄⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢟⠁
⡤⠀⢂⡈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⡡⢶⠁
⠈⠣⡀⠀⠀⢼⢫⡅⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⢀⡀⠤⠐⠊⡡⠔⠉⠀⠠⡄
⠀⠀⠈⠦⠴⠖⠰⡓⠀⠀⠀⢠⣄⠠⠄⠋⠃⠀⣠⠔⠉⠀⣄⠔⠈⠀⢀⡀⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠐⡰⢿⢆⡰⠁⠶⡻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠋⡟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⠃⠀⠘⡌⢒⢂⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠄⢀⣀⣀⠀⠀⢀⣀⣀⠠⠤⠐⠂⠁⠀⢸⠀⠀⠀⠩⣫⣡⢼⣕⠄⠀⠀⡰⠶⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡⢶⣾⢾⠦⠤⠤⠀⠀⠀⢀⣀⡠⠄⠚⠁⠀⠀⠀⠀⠀⢽⠥⠀⠦⠤⢎⠀⠀⠐⢄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢄⠢⡴⠾⢉⣹⣭⠁⠀⠀⠈⡟⠻⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠉⠢⡀⠀⠙⢍⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠒⠀⠃⠓⣘⣒⡒⠘⠂⠀⢀⡼⢳⣀⠕⠸⢓⠶⠦⣀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠂⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠩⠕⣳⣀⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣤⠄⠤⢤⢔⡃

⠀⠀⢀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠁⠀⠛⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠉⠙⢕⠠⡀⠀⠀⢀⡀⠀⠀⠀⢀⠄⠒⢇⡀⢀⡨⠓⠢⡀
⠀⠀⢣⡀⠀⠈⠒⠠⠄⠐⡒⣈⡡⠒⠢⢖⣉⠇⠈⠂⠐⠂⠉⢲⠂⠀⠀⠀⢀⠊⠀⠀⠀⠘⠀⠀⠀⠑⠬⡄⠀⠈⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠑⡤⠀⠠⡄⠀⠘⠠⠘⣀⢈⢁⣀⠀⠀⠀⠀⠠⠀⠀⢈⡶⠀⠀⠀⣸⠀⡠⠂⠀⠄⠀⠀⢀⠀⡀⢨⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃
⠀⠀⠠⣉⣠⠔⠋⠀⠀⠀⡤⠊⠀⠀⠂⢉⡇⠠⠤⠤⠄⠒⠂⠉⠀⠀⠀⠀⠞⠀⠀⢔⠊⠐⢀⠰⠓⠌⠀⢸⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠙⠋⠀⡱⠋⡀⠀⣀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠸⡇⠀⡸⠀⠀⣀⢀⠂⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠑⠊⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣄⠀⠗⠁⢀⠤⠘⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⢀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⠤⠄⣠⢊⣉⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢃⠘⠤⠃⡟⠀⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⠇⠀⠀⢠
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠢⣀⠜⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⠋⠀⠀⣤⡐⠒⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠶⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⡄⠀⠈⣼⡄⠀⠀⠀⢈⠉⠉⣹
⠀⠀⠀⢀⠀⠄⠐⠷⠀⠀⠤⢼⣀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠀⠀⠀⡼⠀⠠⠛⣣⠆⠀⢸⣿⠁⠀⠀⠀⠘⠧⠴⠃
⠀⠀⢀⡎⠀⠀⠀⠀⠀⢀⡀⢀⠈⢱⠀⠀⢇⠤⠒⠒⠒⠢⢆⣀⠀⢀⣀⡠⠒⠁⠀⠀⠀⠀⠀⢰⠉⠀⢠⡏⠀⠀⠀⣿⠇
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠃⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢴⡆⠀⠀⣦⠁⠀⠀⠀⠀⠀⣜⡾⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠁
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠓⠳⠄⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠶⠆
⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⡀⢸⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⢀⡦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣂⡠⠉⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢴⠂⡀⠀⡀⠀⢀⢿⢲⡀⡆⢸⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠁⠀⢉⣦⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠾⠟⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⡬⡄⠀⠀⠀⠀⠁⠀⣧⠀⡇⢸⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢀⣴⣤⡿⠃⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⢀⣴⣮⣅⠄⠁⠁⢸⡗
⠀⠀⠀⢁⠀⠀⠀⠀⠀⢠⢈⠀⡇⢿⠀⠀⠀⠠⠃⠀⠀⠀⠀⠠⡏⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢴⡆⠀⠀⠀⠀⠸⠀⠀⠠⢺⣿⣿⡿⠀⠉⠀⢧⠆
⠀⠀⠈⠐⠶⠧⡤⠴⢲⡾⠥⣾⠔⠃⠀⠀⠀⠂⠀⠀⠀⣀⡀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠉⠉⠀⠁⠀⣲⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⢦⣤⣄⣐⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠁⠀⠈⠂⠀⠀⠄⠀⠀⠀⠉
⠀⠀⢀⠀⠐⠀⢌⡤⠤⠖⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠈⢁⡠⠤⣀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⣀
⠀⠀⢰⡀⠀⠁⢀⡀⡎⢁⠀⢀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠋⢛⠖⠒⠶⠤⠂⠀⠀⠀⠀⠀⠀⠀⡠⡪⠓⠉⠀⠀⠀⠈⠢
⠀⠀⠈⡇⠐⠀⢀⡀⣅⠎⠀⠀⢇⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⢈⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢡⠀⠀⠉⠈⣁⣠⡀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡆⠀⡟⠀⠀⠀⠁⠀⠀⠀⠃⡀⠀⠀⠀⠐⠈⠀⡐⠤⠀⠀⠀⠀⡸⠳⡀
⠀⠀⠀⠈⡆⠸⠶⠚⠋⠉⠀⢀⡴⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣳⣶⣓⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢇⡀⢀⣀⣀⣀⠁⠀⠉⠁⠀⠀⠈⠁⢂
⠀⠀⠀⠀⠹⠀⠤⠤⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠠⠔⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠀⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠸⠗⢀⠀⡳⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠠⠶⣿⣏⣩⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠲⠼⡛⡃⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣦⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣿⣿⠀⠀⠢⠙⠮⣼⢿⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⠀⠁⠆⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⢰⠀⠀⠀⡄⠀⡈⣛⠾⣦⡀⠀⠀⠀⠐⠄⡀⠻⡄⠘⠀⠀⡇⠀⠀⠐⠂
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⢠⡟⠀⠀⣀⠁⣤⢹⣿⠃⢀⠙⢦⡀⠀⠀⠀⠈⠀⣷⠘⡎⠃⡇⠀⠀⠒⠐⢎⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⡀⠄⣻⣤⣄⣽⣄⣙⣰⠿⠤⠄⠀⠀⠈⠳⣦⣀⠀⠀⢻⡄⠁⠀⡁⡈⠚⠀⠀⡁⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠁⠀⠀⠋⠂⠀⢀⠀⣾⠀⢠⡟⢀⣿⠛⢉⠹⡟⡏⢽⠀⠀⠀⠀⠀⢀⡀⠀⠉⠐⠈⡋⠇⠘⣆⠃⠀⠐⠰⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⠁⢸⡇⠀⠀⢱⡀⠇⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠁⠀⠀⢉⠀⠀⠘⠅⡉⠀⠐⠂
⠀⢌⠀⠀⠀⢀⠀⢀⠀⠀⠸⠋⠋⠀⢿⡇⠀⠀⠘⡃⠀⠀⠀⠀⠀⢀⣐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⡨
⠀⠈⠈⠀⠁⠀⣀⠈⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠄⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⢀⠰⠀⡠⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⡘⠃⠀⣀⣀⢀⣀⣠⠄⡄⠀⠀⠀⠺⠅⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠴⣪⡄⢴⡀⢦⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢹⣥⠀⠘⡿⠁⠾⣀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠶⣦⣿⣟⢭⠀⢀
⠀⢀⣄⠴⠦⠄⠀⠀⠀⠀⠀⢺⡄⠀⠀⢹⢸⣿⣆⢠⡇⠀⠨⠛⢠⣍⣁⠀⠀⠀⠀⡄⢠⠀⠢⠆⠀⣾⣾⠓⠀⠾⣿⣿⣿⠃⠐⠏⠀⣳⠆
⠀⢐⡃⠁⠁⠀⢀⠀⠀⠀⠀⠀⢣⠀⢀⡈⠉⣿⠉⠙⠧⠀⠀⠀⠀⠀⠰⣤⠄⠀⠠⠃⠀⠀⠀⠁⠚⠋⢁⠈⠳⡶⡿⠟⠷⠠⠐⠊⠒⠂⠄
⠀⠀⠘⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣸⣆⣠⠀⣠⠤⠴⠤⠀⠐⠀⠁⠀⠀⠀⠉⠀⠰⢤⣷⠀⣠⡁⠉⣜⠂⢈⠺⣇⣀⠠⡄⠃
⠀⠀⠀⠀⠀⠈⠀⠈⠀⢠⡀⠀⠀⠀⢀⣿⡇⢸⣿⠏⢀⠁⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⣤⣿⣿⡝⢛⠧⠀⠉⠃⠋⠁⡤⠙⢃⣰
⠀⠀⠀⠀⠀⠀⠤⠒⠒⠉⠀⠶⠦⢶⠾⣿⠿⣿⣿⣷⣿⣷⠆⠀⠐⠶⠟⠚⠇⠀⠀⠀⠙⠋⠛⠻⣿⣟⠿⠶⢶⣴⣾⡶⢿⡼⠧⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠶⠆⠲⠍⠛⠙⠃⡤⠤⠀⢀⡠⠄⠠⠶⠆⠦⠐⠒⠀⠀⠐⠂⠂⠂⠒⠀⠓⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠀⠉⠉⠉⠉⠙⠉⠉⠉⠀⠴⠦⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⠔⠛⢱⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠐⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⠀⠘⠃⠀⠀⢀⡃
⠀⠀⠀⠀⠀⣤⠋⢻⠀⠀⢴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼⠙⢦
⠀⠀⠀⠀⠀⣿⠀⢸⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⢸
⠀⠀⠀⠀⠀⠿⡀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡄⢀⡸
⠀⠀⠀⠀⠀⠀⠉⢻⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⠇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⣀⣀⣀⣀⣀⣀⣀⠤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠒⣾⡏⠉⠉⠉⠉⠉⣿⡖⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠃⠀⣰⠋⢀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠀⠀⣿⡀⠘⠦⣀⣀⣠⠞⠁⣸⡇⠀⢸⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⠀⠀⢹⣷⣄⡀⢈⣉⡁⣀⣴⣿⠁⠀⢸⡇⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢾⠀⢰⠋⣩⣭⠉⢉⣩⣭⣭⡉⠙⠆⠀⠘⡇⠀⠀⠀⠀⢙⣤
⠀⠀⠀⠀⠀⠀⢠⡞⠳⢦⡀⠀⢠⡍⠀⢸⠇⠈⠁⢠⣾⠃⠀⠈⢿⣄⠃⠀⠀⣠⠀⠀⣀⠶⠛⢣⡀
⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⡿⠖⢿⠃⠀⢸⡀⠀⠀⠈⢻⣄⣀⣠⡾⠁⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⢳⡄
⠀⠀⠀⠀⢰⠁⠀⠀⣴⠋⠀⠀⢸⠀⠀⠘⠣⠤⠤⠤⠤⠍⠽⠉⠠⡔⠂⠀⠀⢰⠀⠀⠀⣷⠀⠀⢸⡇
⠀⠀⠀⢀⡘⠀⠀⢰⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠸⠃⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⡆⠀⢸⡇
⠀⠀⠀⠇⠀⢀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⣼⠀⢀⠟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⢸⡇
⠀⣠⠇⠀⢼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⢸⡇
⡞⠁⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⢸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾⠀⠀⠀⣠⠾⠀⠸⣇
⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣴⠁⠀⠀⠀⠈⣂
⠣⡀⠀⠀⣠⠟⠲⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠃⡀⠀⠀⠀⠀⣿
⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠖⠛⣄⡀⢀⣰⣅⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⣸⣿⡿⠛⠛⠛⠻⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠒⠒⠒⠒⠒⠚⢳⡶⠛⠒⠒⠒⠒⠒⠚⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢲⠖⠀⠀⠲⠖⠈⠉⠀⢲⠆⠐⠂⢰⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⢿⣦⡀⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣠⠴⢿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⠀⠀⠀⢾⣏⠁⣀⣤⡿⠃⠀⠀⠀⢹⣧⡀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠛⠓⠒⠛⠦⠀⠀⢀⡜⠓⠒⠛⠛⠛⠒⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣤⣤⣤⣤⣤⣄⣠⡖⠀⠀⠀⣦⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⡿
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⣀⡈⢢⠀⠀⠀⠀⠀⠀⠀⡔⡡⠒⠉⡈⠀⠑⠌⠄⠀⠀⠀⠀⠀⢀⣠⡤⣬⠠⣵⠚⠙⢦⡀
⠀⠀⠐⠘⠩⠭⣽⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠀⠑⠂⢄⠀⠀⠀⠀⠀⢐⢰⠄⠀⣀⠁⠀⠀⢼⢰⠀⠀⠀⠀⠀⢯⣀⠼⢏⣲⡟⢞⢲⣤⣿
⠀⠀⢠⠀⠤⢤⡤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⢠⡄⠀⠤⠀⠀⠀⠀⠀⠀⠘⡌⢆⠀⠀⠀⠀⠀⠔⡘⠀⠀⠀⠀⠀⠀⠉⠻⣍⠷⡋⣩⡧⠤⠛
⠀⠀⢰⣘⣁⣆⡈⢁⡇⠀⠀⠀⠀⠀⠀⠀⠈⠱⠚⢬⣭⡽⢂⠰⠉⠀⠀⠀⠀⠀⠀⠈⠢⢑⡂⢓⣒⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠉⠉⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⡀
⢠⣤⡀⢀⠄⠀⠠⢀⠀⠴⡀⠀⠀⠀⠀⠀⢀⠶⠶⠿⠿⠿⠏⡅⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠉⠉⠰
⠸⡩⠒⠁⠈⠲⡢⣎⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡛⣯⢉⡴⠶⣈⣛⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⠀⢘
⠀⣇⢀⠲⣄⣸⣫⠆⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⣿⠀⠈⠀⠀⠀⠀⠀⠀⠨⠉⠀⡏⠂⠀⢸⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⢘
⠀⠺⠀⠓⠬⠥⠅⠒⠁⠘⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⣲⣒⣃⡹⠶⠜⠀⠀⠀⠀⠀⠀⠠⠉⢀⠈⠀⢁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠾⠿⠆⠰


⠀⠀⠀⠀⠀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⡠⢄
⠀⠔⠒⠐⠤⣤⡴⠦⣈⠢⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠖⢀⣄⠀⠀⠀⠀⠀⠀⡠⠀⠘⠐⠀⠀⢸⠱⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣐⣀⣨⣭⣬⡆
⢀⠀⠀⠀⠄⠀⡈⠿⠀⠀⡇⠀⠀⠀⠀⠘⣀⠥⠒⢈⠀⢀⡤⠛⠒⠁⠀⠀⠀⠀⠀⠈⠄⣰⣇⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⣨⣏⡗⢀⣀⠀⣹⢀⡇
⠸⢄⡀⠀⠀⠀⠀⠇⠨⠴⠀⠀⠀⠀⠀⢠⣥⠄⢠⠋⠉⠉⠐⠂⡄⠀⠀⠀⠀⠀⠀⠱⡄⠐⢇⡀⡀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠧⢽⣗⣀⣠⣶⡟⠉⠁
⠀⠀⠀⠁⠛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠂⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⢀⣐⣐⡂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠀⣈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡜⠚⠁⡱
⡄⠚⠉⠙⠂⠒⠚⠓⠒⠰⠃⠀⠀⠀⠀⠀⢀⢶⡤⠸⠠⡌⠉⠹⢇⠀⠀⠀⠀⠀⠀⢎⣀⣃⠀⣗⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣤⣄⠐⢆
⡇⠀⠀⠀⢠⠖⢋⡠⠀⢰⠀⠀⠀⠀⠀⠀⢈⣼⡇⠀⠀⠢⢤⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣘⣁⢈⠆⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⢸⢈⠆
⠡⣀⣀⣀⣁⣀⣉⣀⣄⠸⠀⠀⠀⠀⠀⠀⡄⢻⣧⣿⣏⠷⢶⣷⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠱⣀⣀⣀⣴⢉⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠿⠻⠟⠻⠟⠞⠫⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠓⠚⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⣀⣀⣸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⣥⣄⠀⠀⠀⠀⠀⢀⣤⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⠛⠛⠉⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡰⠀⠀⠀⠀⢀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠂⠺⢠⣌⠀⠀⠀⠄⠀⠀⣄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠂⠠⠄⠀⠀⡈⠉⠁⠒⠓⠒⠒⠋⠁⠈⠁⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠾⠿⠦⠻⢶⣈⡁⢀⠀⠀⠒⠂⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣽⢦⠀⢰⡆⢠⣍⠠⠀⠀⠀⠀⠀⠀⠙⣤⠠⠄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣟⡤⠀⢸⠿⡀⢈⠑⡃⠀⠀⠀⠀⠀⠀⢰⠀⠀⢄⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠀⠀⠈⠛⠉⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⡈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠲⡀⠀⠀⣀⣀⡐⢠⠄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⠀⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢈⠀⡀⠸⣎⠀⠁⠀⠀⡀⠛⡄⠀⠀⠀⠀⢀⠴⠋⠘⠀⠐⠓⠁
⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⡈⢲⡔⠂⠏⠀⠐⡇⠀⠀⠐⠈⠀⠤⠼⠤⢈⡲⠂⠁
⢠⠁⠀⠀⠢⣀⡐⠀⠀⠈⠋⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⢂⡀⢸⠀⠘⠀⠀⠀⢙⠟⡐⠣⣄⠀⠀⡀⠀⠨
⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠈⣠⡷⠊⠉⠁⠚⡄⠆⠀⠀⠘⠀⢸⠀⠀⢠⡀⠡
⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠄⠺⢇⣄⠆⠀⠀⡌⠠⠀⠀⠀⠀⠘⠀⠀⠀⠀⣷⠈⡖⢲⠂⠰⠞
⡇⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠺⠀⣄⠆⠀⢀⢠⡁⠀⢀⠄⠓⠎⢠⠴⠀⠸⠠⠠⠀⢠⠀⢠⠀⡇⠀⠈⠁
⡧⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣌⠀⠀⣤⠤⢀⣜⠁⠀⠀⠀⠈⡆⢀⡚⠳⠤⡀⢰⡀⠈⠀⡇⣄
⡇⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠆⠙⡇⢤⠐⠈⠁⠠⠀⠄⡠⠂⢰⡆⠀⠀⠀⠈⠛⡇⠀⠀⡇⠛⠀⠀⢀
⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⢁⠈⠀⠀⠀⢸⠀⣿⠃⠀⠀⠀⠀⠈⢸⠁⠀⠈⠖⠀⠀⢀⡠⠀⠀⠠⠀⠈⠳⠄⢰⠊
⠈⣄⠀⠀⠀⠸⣄⠀⠠⢀⡀⠀⠀⠀⠀⠀⠒⠀⠤⠤⠔⠀⠀⢁⢆⠀⠴⠀⠀⢌⡵⠉⠆⡀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠉⡙⣉⠱⣄⡠⠀⠀⠀⠀⠀⠸
⠀⠘⢦⠀⠀⢀⡼⢃⠀⠉⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠘⠒⠉⡀⠀⠚⢊⠤⠀⢈⣤⠃⠀⠀⠀⠀⠀⠘⣄⢳⣀⠀⠀⠀⠀⢀⣤⠂
⠀⠀⣀⠉⠠⠬⠐⠈⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⠤⠤⠬⣷⡽⠛⡃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢠⡤⠊⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⢀⣤⠘⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡤⡷⠀⠀⠀⠀⢧⠒⠖⢲⣆⡀⢀⣀⣀⣀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⡒⠒⠲⡞⢻⡄⣀⠤⠚⠁⠀⡇⠀⠀⠀⠀⡀⢀⠀⠰⡍⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠃⠀⢨⠀⠂⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠰⠀⠀⡅⠀⠁⠄⠀⢠⡀⠀⡇⠀⠀⠀⠀⠳⠲⠶⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠒⠀⠚⠃⠀⠀⠠⠀⠀⠃⠀⠸⠀⠀⠐⠘⡆⠀⠇⠠⠦⠠⠦⠠⠅⠀⣅⣀⣀⠀⣀⣀⣀⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡌⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠊⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣁⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⡀⢤⡀⠀⠀⠼⠒⠂⠤⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠠⠄⠤⡄⢀⡉⡅⢀⠡⠀⠃⠀⠂⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⠤⠄⢀⣠⣇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠀⠀⠀⠀⠀⠀⠔⠉⠙⠦⠀⣀⣀⣀⠠⠤⠄⢀⣀⣀⣀⠤⠆⠚⠃⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠲⠾⠿⣿⠟⠁⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢰⠀⠀⡀⠀⠀⠠⠀⠀⢀⠱⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⢧⣸⡆⢸⡇⡀⠐⣦⣤⠀⣷⠀⠀⠒⢿⣿⡂⢅⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡛⠦⠝⠚⠳⣈⣿⣷⠿⢷⡀⠀⠸⣆⢹⠀⢠⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⣉⡀⠀⠀⠀⠉⣀⣉⡀⠘⣿⡶⣦⣿⢶⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⠀⠀⠀⠈⣿⡟⠁⠀⢫⡌⣹⣿⣿⡄⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡟⣿⡄⢢⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣀⣔⠛⠛⠟⠻⣍⠁⢸⡿⡌⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣦⣤⣤⠶⡿⢿⡿⠟⢢⠀⢀⡙⢿⡞⢳⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢼⠟⣿⣀⢼⠗⠁⣀⣀⡼⠦⠢⣄⠉⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⣿⣼⢧⣤⣮⣤⣤⣾⣟⠉⠙⣶⣝⢂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠁⢉⠎⠁⠀⠉⢠⣯⣯⠀⠀⢸⣟⣼⠸⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⢸⠀⣀⣠⣀⣀⣰⣾⠇⠀⠀⢿⢿⠃⠀⠀⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⠀⠀⡏⢸⡏⠀⠁⣹⠈⣿⠃⠀⠀⢠⡞⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣻⣿⠀⢠⠁⠈⠀⠈⠁⢹⠀⢹⡆⠀⠠⠄⣱⡇⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⣸⠃⠀⡸⠀⠘⠒⠒⠒⠊⠀⠈⣷⡌⠀⡉⠹⡇⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠙⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠂⠀⠘⢳⠀⠀⢐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣐⣢⣭⣿⠁⠀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣟⠉⠉⡟⠀⠈⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠋⠈⠀⠀⠂⠄⠀⢠⠤⠀⠰⠶⠚⢻⢿⠀⠠⣧⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⣸⠀⡷⠤⢄⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠋⢹⠄⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠳⠜⣿⠀⡇⠀⠀⢈⠉⣉⠉⠉⠉⠉⠀⠀⠈⠀⢠⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⢰⣇⠀⠈⠁⠿⢶⣴⠀⠀⠀⠀⠀⠀⢰⢁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢸⡇⠘⠣⢤⣀⣀⠀⠠⢉⣇⠀⠄⢀⣀⠤⠜⡿⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠸⠁⠀⠀⠉⠈⠋⢹⡏⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣀⣤⣖⡋⡘⠟⠓⠺⠀⠀⠀⠀⣰⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⡇
⠀⠀⠀⠰⠃⠈⠉⠀⠈⠉⠕⠢⡶⠶⠶⠀⠀⠀⠈⡀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⡇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢒⣾⡄⠀⠀⠀⡃⠀⠀⠘⠀⠀⠀⢸⠀⠀⠀⣆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⣇⣀⣉⣿⠁⠀⠀⠀⣇⠀⢀⠿⡄⠀⠀⠸⣀⠀⡠⢻⡄
⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⠻⠆⠀⡄⣤⠀⠀⠀⢸⠋⠤⠚⣥⠀⠀⠀⠸⣗⠒⠥⠹⡄
⢀⡛⠝⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⡇⣿⠀⠀⠀⢸⠀⠂⠁⢸⠀⠀⠀⠀⠉⠁⠀⠀⢁
⢸⠷⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡄⣿⠀⠀⠀⠈⡀⠀⠀⢸⠀⠀⠀⠀⠈⡄⠀⠀⣸
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣇⣿⠀⠀⠀⠀⡧⠀⠀⢼⠀⠀⠀⠀⠐⢇⠒⢈⡹
⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢤⡄⣯⢸⡇⠀⠀⣴⠷⣤⢠⡆⠀⠀⠀⣀⣴⡿⢦⣼⠷⡄
⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⡶⠒⠓⠿⣽⡷⣶⣦⣭⡜⠀⠀⠘⢘⣿⢟⣲⡿⠉⠁
⠀⢰⣿⣷⢶⣦⣤⣤⣀⣀⣼⣤⣤⣶⠀⠀⢀⣴⣋⣵⠟⠁⠠⠀⠀⠀⢠⠞⠁⣹⠟⠀⠀⡇
⠀⠸⠿⠇⠀⠉⠁⠀⠉⠹⣿⣿⠛⠋⡴⠊⠉⠁⠋⠁⠀⠀⢀⠀⠀⠜⠉⠀⠉⠃⠀⢀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤⠀⠀⠀⠀⢀⣶⣀⡿⠀⠀⢲⣀⣠⠀⣤⣐⠞⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⢀⠀⡀⢀⣀⡀⡀⠀⡀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠸⠻⠥⠿⠇⠳⠇⠿⠇⠧⠄⢧⠸⠿⠸⠻⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣷⣾⠿⢿⣆⣛⣑⢿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣬⡶⣧⣤⣤⣬⠿⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⣿⣿⢟⣻⡿⠿⢿⢿⣿⠿⣿⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠁⠀⠀⣿⢧⣃⣱⣵⣵⣈⣣⣿⣶⢿⠀⠀⠈⢑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢭⣄⣀⠀⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣤⣤⣐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣉⣋⣉⡩⠍⣋⣙⣲⠄⠀⠀⠀⠀⡔⡩⢶⣒⣒⡶⢍⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣩⣟⣭⣶⠏⢻⢄⠀⠀⠀⠀⠀⠀⡇⡇⢸⠑⠂⡃⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡟⠤⣀⡏⠉⢚⡺⡆⡀⠀⠀⠀⠀⡇⡇⡜⠒⠚⢣⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢺⠦⢤⣎⠉⢰⡁⠈⠉⠸⡇⠀⢀⡞⡇⡇⡏⠉⠉⢹⠸⢸⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣎⣀⡕⣧⠵⢄⣠⠞⠑⠶⠁⢫⣇⡷⠧⠤⠤⠼⢴⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡀⠀⠀⣀⣠⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠒⣄⢘⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠒⢡⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠋⠙⠛⠋⠙⠛⡞⠁⠠⠀⠀⠀⠄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢲⡒⣝⣆⠀⢠⣤⠄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳⠘⣮⠶⡤⠤⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣶⢶⠀⠀⣨⡇⢹⠀⠑⠚⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠀⡴⠁⢹⢨⠟⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⡸⠃⠀⠀⢀⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⡄⠀⠀⠀⡇⠀⠘⠛⠉⠉⠉⠙⣧⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⡇⠀⠀⠀⠙⡖⠲⠖⠒⠒⠋⠉⠀⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡗⠒⠓⠶⠤⣤⣤⣤⣤⢼⣧⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⠃⠀⠀⣧⣤⠤⠤⠴⠓⠒⠒⠒⢶⠉⣆⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣼⠀⠀⠀⠀⢀⡀⠀⢸⠀⢸⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠚⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠍⠂⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠤⠒⠒⠂⠒⠒⠢⢄
⠀⢠⠄⢀⡂⠬⠐⠀⠉⠀⠀⡀⠈⠠⠀⠀⠀⠀⠠⠁⡠⠰⠎⠉⣉⢦⣠⠌⡄⠀⠀⠀⡀⠀⢀⡀⠠⠄⠐⠀⠉⠑⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠂⠁⠀⠀⠀⠀⢉⣿⣾⣥⡄⠄⠆⠀⠀⠀⠀⠀⡀⢀⠜⠀⠱⠃⠋⡁⢰⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠉⠟⢻⡀⠀⠰⠘⡀⠀⠀⠆⡀⠰⣁⠀⠀⠀⡱⡄⠇⠄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⣀⠀⢤⠚⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠇⠃⠀⠀⢀⡀⠤⠽⠳⠀⠀⢃⢁⠀⠀⢸⣡⢆⠀⠉⠀⠈⠀⢠⠘⠀⠀⠀⠀⠃⢀⡀⠀⠤⠉⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠸⠈⡄⠊⠁⢀⡀⠠⠀⠐⠂⣉⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡇⠑⠒⠉⠀⠀⠠⠔⠂⠉⠁⠀⢀⠤⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠞
⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⡔⠒⠈⠉⠁⠀⠀⠀⠀⠀⡨⠂⠀⠀⢠⠖⢉⠇⠀⠀⠀⠀⣰⠖⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣠⡤⠤⠄⠒⠊⠁⠀⠀⢰⠃⠀⠈⠲⡄⠀⠀⠘⣉⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠀⠛⠘⠓⠈⠉⢡⠀⠀⠀⠀⠟⡄⠀⠀⠀⣇⠀⠀⠐⢓⣙⢒⡷⠀⢺⠀⠀⡔⠤⠄⠀⠀⠒⠒⢐
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠈⠑⢄⠀⠰⡁⠀⠀⠀⢀⣀⣠⠤⠰⠀⠀⠀⠀⠂⣹⢾⣭⣭⡁⠀⠀⠘⣇⠀⠀⠀⡠⢿⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⡀⠀⠀⠁⠈⠉⡋⠀⠄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠀⠑⣆⡀⢰⢡⠂⠀⠀⣇⣀⡀⠀⠀⠀⢀⣸⡀
⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠘⡀⠀⢀⣀⠀⠀⣠⠗⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⡠⠖⠛⢉⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⢡⢀⡤⠶⠂⡡⣀⡴⡊⠁⠀⠐⡀⠀⠀⠀⡠⠶⠀⠐⠃⠄⢀⣰⠀⠀⠀⠀⠀⠀⡠⣀⠤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⢸⠻⣓⠴⢾⣿⣿⣿⣦⠀⠀⠀⢣⠀⠐⠊⠂⠈⠀⠰⠦⢀⣄⠀⠉⠀⠒⠂⠀⠠⠖⠁⡠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢏⠀⠀⠐⣝⣛⡿⠟⢀⡠⠐⠁⠀⠐⠢⠤⣀⠀⠔⠒⠒⠠⡀⠛⠀⠓⠀⠀⠀⣰⡉⡄⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠈⢢⡔⠔⠊⡁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⠀⢀⠧⠀⠐⠐⠒⠒⠉⠁⠈⠁⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠤⠤⠤⠤⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠬⢤⠄⡁
⠀⠀⠀⠀⠀⠀⠀⣇⠤⠔⣀⠔⠐⠀⢲⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠤⢀⡀⠀⠀⠑⢄⠀⠀⢀⠔⠋⠊
⠀⠀⢠⠀⠀⡠⠁⠉⠢⣀⠋⠀⠀⠀⠈⠀⠀⠀⣠⡄⠼⠏⠁⠀⠚⠁⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠑⠐⠁
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠴⠦⠵⠶
⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠀⡀⠔⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠠⠤⠄⠐⠒⠀⠁⠁⠀⠀⠀⠀⠙⠛⠳⠶⣶⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡿⠘⠀⠀⢻⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⣠⡠⠀⠠⢤⠴⠄⠀⠀⢀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄
⡀⠈⠛⠙⠚⣰⢊⡋⡛⠟⠧⠿⠎⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠤⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠁⠐⠒⠒⠚⠃⠀⠉⠈⠀⠰⠷⠿⢕⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⠀⠀⠀⠸⣉⡀⠂⠄⢠⣢⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠤⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠂⠀⠀⢸⡹⣆⡄⠄⢀⠀⠀⠀⠀⡀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠳⠈⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⡩⡺⢠⠀⠀⠀⠀⡀⠀⠐⢀⣁⠀⠀⠸
⠀⠄⠀⠠⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠒⠀⠂⠀⠁⣀⡀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠑⠁⠀⠀⠀⡀⠀⠠⠀⠀⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠤⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠁⠈⠀⡖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠇⠄⠀⠀⠀⠀⠀⢦⡰⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠂⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⡀⣀⣀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⣰⣀⣠⠤⠤⠠⠯⠿⠯⠿⠗⠀⠀⠀⡇⠀⠉⠉⠉⠛⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢁⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢤⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠒⠀⠄⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⡐⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣀⡀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⡟⠉⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⣀⠀⠀⣿⢿⡇⠀⠀⠠⠤⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⣯⣤⣿⡄⠀⠀⠀⠀⣾⣿⣿⣇⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢳⣶⣦⣀⠀⠀⣀⣤⡀⠀⣰⡿⠛⡙⠛⣷⡄⢀⣴⣾⣿⣿⣿⡋⣴⣿⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠘⣿⣿⣿⡶⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣅⣶⣿⣿⡇⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⣸⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⢀⡀⡄⣆⢳⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢺⡜⡎⣧⢳⢹⡜⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠧⠼⠘⠈⠁⠀⠀⣶⡄
⠀⠀⠀⠀⢀⣤⣤⣴⡖⠒⣶⣶⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣤⡀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠷⠤⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢽⣽⣧⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣾⣿⣿⠀⠀⢸⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡷⠿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠚⠋⠁⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⢱⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠴⠦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢳⣀⣀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠙⠯⣭⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠍⠅⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⠿⡀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⣴⣿⡿⡟⠻⠆⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣼⡿⠋⡀⠀⢠⣼⡿⠃⢸⣿⣿⣿⣿⡏⠉⢻⡟⠀⢹⣿⡄⠁⠉⠻⠿⡉⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠙⠀⣸⡿⠁⠀⢸⣿⣿⣼⣯⡇⠀⠘⡁⠀⢀⣽⣿⠖⠒⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⢸⣿⠏⢹⣿⠇⠀⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠈⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠀⠈⠉⠉⠉⣩⠸⣶⣶⡤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⡀⠠⠶⠀⠀⢤⣰⠞⠙⠫⢴⣷⣶⣿⣖⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣁⣀⣀⠀⣀⡀⢸⣿⣶⠆⠒⢀⣴⣟⣜⢢⡀⠀⠈⠙⠛⠿⣷⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⠛⠫⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣿⡤⠀⢈⣿⡁⢉⠢⡀⠀⠀⠀⠀⠉⠐⠬⢦⡀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠂⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠂⣀⠛⠿⠋⠀⠰⣎⠢⡀⠀⠀⠀⠀⠀⠀⠈⢑⡶⠈⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠡⠛⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⣘⣿⣧⣴⡀⠀⠀⠙⠓⠈⠢⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡿⠿⢷⡀⠀⠀⠀⠀⠐⢌⠢⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠤⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠀⠀⠀⢀⠔⠁⠰⡀
⠀⠀⠀⠀⡀⠤⠃⠉⠀⠀⠐⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠱
⣠⠤⠂⠁⠤⠤⠤⠤⠴⠶⠤⠰⠄⠹⢿⣿⣿⣿⠟⠉⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣠⣦⡡⡀⠀⠀⠀⠀⠀⢡
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⢿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠒⠠⠔⢁⡀⠀⠀⢀⣴⣾⣿⣿⣿⣬⠢⡀⠀⠀⠀⠀⢣
⡇⠀⠀⠀⢀⣤⡴⢶⢶⣤⣀⠀⠀⠀⡇⡇⠀⠀⠉⠙⢶⡀⠀⣀⣀⣀⠔⠁⠀⠀⢀⢎⣴⡿⠃⡠⠒⠉⠻⣿⠿⠿⢿⡇⠀⢈⠢⡀⠀⠀⠀⢃
⡇⠀⠀⡴⠯⣾⠥⣾⠤⢷⡬⢷⡀⠀⡇⡇⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣄⢒⠒⢿⡫⠒⠉⠇⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠑⠌⠢⡀⠀⠀⢂
⡇⠀⢸⣇⣀⣇⣀⣿⣀⣸⣇⣀⡇⠀⡇⡗⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠐⢌⡢⡀
⡇⠀⠘⣇⠀⣇⠀⣿⠀⢸⡇⢀⡇⠀⡇⣇⠘⡄⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⡀⡠⠊⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡠
⡇⠀⠀⠙⢯⣹⣍⣿⢉⣟⣩⠏⠀⠀⡇⣟⣠⠴⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠀⠉⠀⠀⠀⠀⠀⢀⠔⠁
⡇⠀⢀⣀⣀⣈⣉⣛⣋⣉⣀⣀⡀⠀⡇⡏⠔⠢⡘⡄⠀⠀⠀⠀⢸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁
⡇⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⡇⣿⡌⠄⠡⠘⡄⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡜⠤⣃⠬⢀⣀⢀⠘⣿⢀⣀⡀⠤⠄⠒⠉
⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠇⣏⠥⠒⠉
⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⣀⣀⣀⡀

⠀⠀⠀⠀⢀⡤⣾⣧⣀⣀⣈⣀⡂
⠀⠀⠀⠀⣼⠀⠉⠀⠈⠉⠉⠉⠁⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢿⡀⡶⠛⠛⠛⠛⢳⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⠄
⠀⣤⠄⣿⡏⠀⠐⠊⠉⠛⠓⠺⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣊⠵⠊⠁
⣼⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⢀⡤⠀⠀⣠⠟⣛⠿⠟⠛⠋⠁⠀⢀⣀⡄⡀
⣿⠀⠀⡿⡇⢀⣄⡀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠈⠙⢢⠤⠖⠋⡁⠤⠄⠀⠒⠒⡶⠤⣄⡀⠘⠢⢀
⣿⠀⠀⣟⠇⢸⣿⣷⣀⣀⣀⣠⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⠟⡁⠀⠀⠀⠀⠀⠀⠀⠿⡿⢶⣄
⣻⡄⣀⡝⠀⢸⣿⠉⠛⠛⠉⠀⠀⣿⡆⠀⠀⠀⠀⢀⡢⢊⣼⠿⠁⠀⠀⠀⠀⠄⠀⠀⠐⡄⠀⠀⠀⢻⣧⡀
⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠄⠀⠰⠁⡘⢷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣧⡁
⣿⡇⠀⠀⠆⢰⣷⣀⠀⠀⠀⣾⠃⣿⠀⠀⠀⡇⠀⠀⠀⢳⣿⣿⣶⣄⠀⠀⠄⠀⠀⠀⠀⠙⠻⠿⠶⢶⣿⣿⡆
⣿⡇⠀⠠⠀⠀⠙⠛⠇⠀⠀⠉⠀⣿⡄⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⣿⣧⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡤⡇⠀⠀⠀⣆⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⠐⢻⡄⣿⣿⠇
⢹⣟⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡃⠀⠀⠁⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⡟⠀⠀⢠
⣸⣿⡄⠸⢇⠀⠀⠀⠀⠀⠀⠀⢀⡏⢁⣶⣾⡇⠀⠀⠀⠀⠹⣿⣿⣿⡥⠀⢀⣀⠀⠀⠀⠀⠀⠀⣯⡿⠋⠀⠀⡀⠃
⢿⠻⠿⣶⣼⣿⣿⣿⣿⣿⣦⣿⣿⣇⠹⠟⢻⡇⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣼⣯⣥⠀⠀⠀⠹⠟⠋

⠀⠀⠀⢛⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣠⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢠⠀⠀⠀⠀⠀⠀⠀⠌⡔⠊⠁⡄⠈⠑⡁⠀⠀⠀⠀⠀⠀⣠⠤⣴⠠⣴⠊⠙⢦⡀
⠀⠀⠈⠙⠡⠤⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠁⠉⠒⢄⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠺⣄⡐⢃⣰⢟⣲⡳⠦⢿
⠀⠀⠀⠠⠤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⣠⣄⠀⠲⣀⠀⠀⠀⠀⠀⠐⡌⢆⡀⠀⠀⠀⡠⢂⠂⠀⠀⠀⠀⠀⠀⠙⢭⡑⢋⠥⠵⠒⠋
⠀⠀⢠⣈⣰⣆⣈⣠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠊⠰⠶⠼⠃⠐⠑⠀⠀⠀⠀⠀⠀⠈⠂⠌⠈⠁⠩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⢀⠄
⢰⣶⢀⠔⢂⡁⠐⢄⠠⢱⠀⠀⠀⠀⠀⠀⡞⠋⠛⠛⠛⠓⢤⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢘
⠈⡎⠁⡀⢀⢙⢜⠇⡆⡎⠀⠀⠀⠀⠀⠀⠆⠀⠴⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠇⣔⠊⠑⣢⠤⠝⠀⠀⠀⠀⠀⠀⠀⢠⠀⠨⢀⡁⢨
⠀⣣⠠⡙⠦⠾⠞⠠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠪⠭⠼⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⣏⡀⣀⢼⢁⠀⡇⠀⠀⠀⠀⠀⠀⠨⠀⠀⠉⠅⠠⠄
⠀⠉⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠙⠃⠀⠙⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⢠⣤⡄⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⣀⠀⠈⣈⣐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠨⢉⠒⠉⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠈⠉⠡⡖⠀⠉⠀⠀⠀⠀⠀⡄⠀⣀⠄⠀⠀⢁⡴⠥⠆⠀⠀⠀⠀⠀⠦⡀⢀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠐⡭⣥⠀⠚⠛⢻⠛⡇
⢐⠀⠀⠀⠀⠀⠀⠅⠀⡀⠀⠀⠀⠀⠀⣘⡈⠀⡄⠒⠒⠫⢄⠀⠀⠀⠀⠀⠀⠀⢆⠈⠘⠂⠀⡄⠈⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣀⡘⠐⠂
⠀⠁⠐⠂⠤⢄⠌⠀⠁⠀⠀⠀⠀⠀⠀⡏⡁⠈⠒⠄⠖⠒⠒⠁⠀⠀⠀⠀⠀⠀⠈⠣⠄⣀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⡐⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠀⡂
⡄⠐⡒⠒⠒⠛⠛⠁⠠⠬⠀⠀⠀⠀⠀⠀⡠⣤⠈⠆⣈⠀⢙⡾⠀⠀⠀⠀⠀⠀⠎⠙⡉⢹⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⠀⢄
⡇⠀⠀⠀⣠⠖⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣿⠀⠀⢠⢤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢛⡉⠱⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣀⠆
⢁⣀⣀⢀⣃⣐⡉⣀⣀⠄⠀⠀⠀⠀⠀⢀⠙⣯⣹⣿⠲⠤⣶⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠹⣀⣀⣀⣠⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⠩⠛⠿⠛⠟⠿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⡀⠎⠀⠀⠀⠘⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠞⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣤⡔⠀⠀⢮⠈⢠⡆⠙⠂⠀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠘⠷⠃⠀⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣄⠸⠏⢠⡆⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣠⠜⠉⠀⠀⠀⠀⠄⠐⠒⠲⠄⠂⠀⠀⠘⢿⣷⣾⡟⠁⠀⠀⠀⠂⠾⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠐⠂⠂⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠓⠄⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠀⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢠⠀⠀⠀⣀⠀⠀⠀⠈⠀⠄⣀⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⣙⡓⢶⡤
⠀⠀⠀⠀⠠⣄⢠⢠⡀⠀⠀⠀⠀⡆⣆⡛⢶⠀⠀⠀⠂⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⢸⡜⣞⠃⠀⠀⠀⠀⣧⣌⠳⣾⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣴⡄⡀⡄⠀⠀⠀⠀⠀⠠⠤⠀⠠⠶⠶⠄⢺⣒⠲⠼⠷⠃
⠀⠀⠀⠰⡌⣇⠃⠀⠀⠀⠀⠀⠀⣇⡙⢷⣬⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠙⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠰⠟⡁
⠀⠀⢀⢧⢳⡈⠀⠀⠀⠠⣤⠀⠀⢅⡙⢦⣉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠈⠀⠳⡁⠀⠘⠳⣷⡝⠀⠀⢀⠹⣦⡙⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠛⠀⠀⠘⢷⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢑⡈⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⢀⡀⠄⠈⠁⠀⢰⠄⡀
⠀⠀⠀⠀⠛⠙⠄⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠈⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡢⢒⠔⡢⡠⢄⠄⠄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠛⠒⠒⠒⠒⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⠔⠁⠊⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⢉⡉⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡟⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠖⢉⠤⣴⢂⡔⠁⡅⠀⠁⠑⡄⢠⡈⠉⠢⣀⠀⠀⠀⠀⠀⢀⣷⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠊⣠⡀⠙⠶⢃⠎⠀⠀⠇⢰⠀⠀⠰⡈⢯⠓⡄⠈⠳⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡔⢁⠞⠁⠈⢢⠀⠈⠒⠤⣠⠃⢸⠀⠀⠠⠗⠀⢉⡤⠒⢄⠈⢆⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡜⢠⠋⠀⠀⠀⡏⢠⠋⠒⠤⠄⠀⡤⠤⠤⠤⢰⠀⢸⠀⠀⠈⡆⠈⡄⠀⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠰⠤⠤⠄⠤⠇⠸⣀⣀⠀⡇⢰⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢰⠀⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⡏⠉⠉⠐⠒⡆⠠⠶⠄⢬⠀⢈⣉⣁⡒⠒⠚⠀⠘⠒⠦⠶⠞⠀⡇⠀⣿⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄⠰⠀⠀⠀⠀⣃⠀⡇⠀⢨⠀⠆⠀⠀⠀⠈⡕⠀⡞⠉⠉⠉⡇⢠⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⢱⠀⢣⡀⣀⠤⠞⠀⢓⡚⡋⠀⠓⠒⠤⢄⡰⠁⡜⠀⠀⠀⡐⢀⠆⠀⢸⣿⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠣⡀⠙⢶⠊⠙⡀⢻⠀⡛⢰⠉⠒⠒⡤⠀⠘⢤⡀⠀⡜⢀⠎⠀⠀⣸⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠑⠦⣥⢸⠀⡇⠸⠀⢀⠔⣡⠋⠢⡀⠙⠊⣠⠊⠀⡄⠀⣿⡾
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡀⠛⠁⠧⠤⠊⠴⠥⠔⠒⣁⠤⠚⠁⣀⠎⠂⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⠐⠑⠀⠸⢻⠃
⠀⠀⠀⠀⠀⠀⡄⡚⡊⠀⢧⡎⠂⣐⡩⡑⠀⡤⡠⡄⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⣾⡆
⠀⠀⠀⠀⡇⠀⡇⠍⠔⢰⢘⡃⠀⠨⡳⢌⠀⡯⡉⠆⢰⠐⢁⢸⡶⠶⠖⠸⠛⠺⠲⠏⠛⠶⠿⠿
⠀⠀⠀⠀⠁⠀⡣⠀⠀⡄⡇⠁⡇⣗⠈⢞⢠⠜⢪⡃⠘⣨⠡⠃⣿⠁⠟⡟⡛⣺⠇⡘⠃⢸⢻⠟
⠀⠀⠀⠸⠠⡀⠀⠀⠀⠉⠀⠘⠃⠙⠓⠋⠈⠻⠱⠃⣇⡂⠀⠀⡿⠤⡃⠛⢻⢸⠀⡇⠃⢸⢼⡇
⠀⠀⠀⢸⡠⢅⣁⣐⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠛⠈⠶⠀⠤⠀⣼⣿⠁
⠀⠀⠀⠀⠉⠙⠙⠛⠫⠽⢙⣿⡿⣿⡷⣶⣦⡤⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠛⠭⠷⣺⣿⣽⣬⣘⡛⠭⢭⢕⣒⣒⣋⡵⡲⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⠀⠀⡀⠀⣀⠀⣀⠄⢀⠀⢈⠉⠉⠙⠛⠓⠒⠶⠶⢴⠮⠗⠀⠀⡀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠈⠑⠉⠐⠉⠐⠈⠐⠂⠁⠂⠉⠂⠉⠐⠈⠔⠊⠥⢂⠥⢒⡩⠐⡈⠅⣂⠭⣒⠍⢂⠬⢒⡩⠐⡨⠐⠫⠕⠪⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⢄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠈⢆⠀⠀⠀⠀⠀⠀⠈⠀⡀⠄⠀⠀⠀⠀⠐⠊⠉⠁⡀⠀⠀⠠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠘⠢⠑⢄⠀⠀⢠⡄⠀⠀⠀⠀⠱⠀⠀⠸⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣕⠀⠀⠀⠀⢐⣲⡶⠖⠉⢐⠂⠀⠉⠉⠉⠀⠀⠁⠉⢠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠢⠀⣀⡤⠒⠋⠤⠙⠸⡂⣸⠀⠐⠀⠠⠤⠤⣤⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠈⠀⠳⡀⠀⠉⠁⠈⢁⣿⠀⢀⣀⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⡹⢏⡀⣨⠷⠶⠦⠴⠃⠌⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠐
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⣠⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠁⠀⠈⢆⠰⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠂⠀⠀⢆⡈⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠁⠄⢄⢂⠄⠘⠠⠬⣃⡑⣀⣀⠿⢉⣤⢤⠤⢤⠀⢸⡟⠝⠛⠛⡏⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠦⣞⡦⠔⣂⠴⠚⠩⡦⠀⠀⣀⣤⣀⠀⠀⡾⠉⠈⢄⣠⡄⠀⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⢠⠔⠂⠀⠐⠉⢄⠀⠀⠀⠀⠀⠃⣧⣀⣼⠀⣰⣿⡤⠖⢊⠁⠐⣰⡧⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠘⣿⠠⠓⣀⡥⠖⠋⣿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠲⣦⣅⣀⡀⢰⡇⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠁⠰⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⣰⡖⢥⣃⡂⠄⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⡁⢀⣴⠾⣧⣼⢟⠘⢍⠀⠉⢳⢌⠢⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠊⠀⠈⠀⠉⠑⣊⡟⡄⣡⢀⠀⢀⡼⠀⠑⠌⢂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠂⠡⠀⠀⠀⠀⠘⢄⡌⠙⢂⠀⠒⠁⠀⠀⠀⢈⡆⢃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⡀⠸⠙⠂⠀⠀⠀⠀⠘⡷⢛⡀⡀⢀
⠀⠀⠀⠀⠀⠠⠂⣀⣀⣐⠂⠄⠀⠐⣄⠀⢀⠤⢤⠘⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠚⠇⠁
⠀⠀⠀⢀⠤⠤⠤⠤⠤⠬⠧⠦⢤⡀⠈⠑⠴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠃⠆⢠
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠙⠉⠁⠁⠢⠄⡀⠀⠀⠀⠈⠀⡙⠠⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢁⢠⡄⠀⠀⠀⢠⠀⡄⠀⡀⠀⠀⠀⠈⠢⡀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠗⠛⠉⠉⢝⡭⢭⣍⢂⠀⠀⠀⠀⡰
⠀⠀⠸⠀⠀⠸⠇⠀⠀⠀⢹⠋⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⡠⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣤⠂⣿⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠄⡀⠀⠀⢃⡈⠀⢀⣘⠂⠄⠀⢀⡀⢸⠄⠄⠊⢂⠈⠉⠁⠰⠀⠀⠀⠀⠠⠂
⡔⠐⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠉⢳⠂⠀⠈⠉⠁⠀⠐⠊⠒⠀⠈⠁⠀⠒⡀⠀⠀⠀⠣⠀⠀⡄⠀⢀⡀⠤⠐⡞
⡯⢁⠀⢠⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠍⠁⠀⠒⠀⠀⠒⠀⠉⡀⠀⠀⠀⠀⠀⠛⠀⠀⢀⢔⣑⡀⠃⠀⠀⠀⠀⠀⠐
⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⢈⢀⠀⣄⠀⠀⣠⢀⠈⢠⠀⠀⠀⠀⠀⠘⠈⡠⠢⠈⢹⡟⢻⠀⠀⠀⠀⠀⠰
⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠠⠀⠀⠀⠀⠀⠀⠃⡀⣄⣀⣀⣠⠀⠐⣋⢀⣀⣀⣤⠤⠼⠤⠤⠤⠤⠤⠴
⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠐⠀⠩⠞⠋⠉⠀⠀⠘⠛⠋⠉⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠑⣀⠀⠠⠃⠉⠉⠉⠉⠉⠙⠀⠀⢠⠁⠐⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡀⠀⠀⠐⡀⠀⠖⢀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠉⢁⠔⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠦⠀⠀⠃⠀⠀⢄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⢶⡤⠺⡿⣧⣴⡆⠀⠀⠀⠡⠀⠀⠀⠀⠁⠀⠤⠄⠀⠀⡉⠀⠁⠀⠀⠂⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⡖⣷⡀⣏⡉⣿⠏⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⠤⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠠⣆⢁⠀⣿⣿⣿⣀⠉⠀⠀⠀⠀⠀⠃⡀⠀⡴⠄⠀⠀⠀⠀⡌⠀⠟⣧⠠⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢠⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠘⠢⠀⠈⠄⠀⠀⠐⡄⠠⢋⠞⣰⠃⣠⢆⡕
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠈⠀⠀⠀⢤⡀⠀⡜⣕⡡⠾⣁⠜⠀⠋
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⢼⠟⠺⢅⡲⢼⣯⠆
⠀⠀⠀⠀⠀⠀⠨⣀⣂⠰⣏⠀⣹⣏⠀⢙⣦⣤⡤⣤⡤⠾⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈⠲⠉⠂⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡆⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⢄⠖⠌⡀⠀⠀⢀⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠊⠂⠀⠠⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠂⠐⠀⠐⠀⠐⠀⠈⠀⠀⠀⡀⠉⠁⠀⠈⢀⠘⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠑⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠠⢀⠐⠄⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠒⠑⠄⠀⢀⠀⠀⠀⠀⠀⠂⠛⠋⠁
⠀⠀⠀⠀⠀⠄⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠒⡀⡁⠀⠐
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⡄⢀⠢⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⢀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁
⠀⠀⣠⠀⠀⠁⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⢠⠂⣮⠢⠀⠨⠀⢠⠁⠀⠀⠀⠀⠀⢂⠀⠺⠀⠀⠀⣀⠀⢠⠤⠤⠄⢀⢀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠈⠀⠀⠁⠘⢀⠀⠀⠀⠁⠀⠂⠃⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠆⠀⠀⠂⠐⠐⠀⠀⠄⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠐⠗⠀⠀⠉⠓⠃⠀⠀⠒⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⢋⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⣉⡥⠶⠚⢉⣷⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⢋⣡⡴⠞⠋⣁⡤⠶⢚⣩⡤⠶⠻⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢉⣠⡴⠞⣋⣥⠴⢚⣋⡥⠖⠚⠉⢀⣠⣴⠾⠋⠙⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢉⣠⣴⣚⡭⠶⣚⣫⡥⠶⠛⠉⣁⣠⣴⡶⠟⠛⠉⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢀⣠⣾⣋⣥⡶⢿⣛⣫⡭⠴⠒⣋⣉⣤⣤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣭⣥⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⢹⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡘⠻⡏⠀⠀⠀⠀⠸⣧
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⡛⢦⣰⠋⠙⣆⢷⣾⡁⠀⢻⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢿⡄⠀⠀⢀⣀⠀⠀⣄⢠⣖⠓⠘⠧⢤⣀⠈⣟⠋⠹⣤⣤⠟⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠸⣧⠀⠀⢼⣹⠇⢸⣻⡆⠉⠙⣷⢀⣀⡽⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢿⡄⠀⢸⡇⠀⠏⠉⠛⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣷⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣠⣿⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠙⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠛⠛⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⠶⠶⠿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⣿⣷⣄⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠘⢿⣿⣦⡀⠀⠘⠋⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⠀⠘⠻⣿⣿⣦⡀⠀⠙⠛⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠿⣆⢿⡀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⣰⢿⣿⡟⢻⡏⢠⣼⣿⠠⣶⣿⡌⢇⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣰⡟⢸⣿⣿⠸⡇⢈⣉⣭⠀⠛⢛⣿⢸⠇⣤⣤⣄⡀⠀⠈⣿⣧⠀⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⢿⣶⣄⠀⠀⠀⠀⢀⣿⠀⣾⣿⣿⠀⡇⢸⣿⣿⠀⣿⣿⣿⡎⣶⢹⡟⡍⢳⡄⠀⣿⡿⢰⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠙⠋⠀⠀⠀⠀⣸⡇⠐⠟⠛⠟⠀⣧⠸⣿⣿⡀⠛⣉⣉⣅⣿⢸⣷⣄⣼⡇⠀⠈⣰⣿⣿⠏
⠀⠀⠀⢰⣶⣦⣄⡀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠿⠟⣛⣹⣿⠀⡎⢿⠿⠋⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠉⠛⢿⣿⣦⡀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⢻⡟⣿⠉⢿⣯⣶⣶⣿⡿⣿⣿⡆⡇⠀⠀⠀⠀⠠⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⢿⡟⠛⠗⠘⢿⣧⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⣾⣿⡧
⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠻⣿⣿⡟⢡⣾⣿⣿⣶⣦⠈⢿⢸⡄⠀⠀⠀⠀⢀⣴⣶⠀⠀⢀⣼⣿⣿⡿⠃
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣸⣿⣿⣷⣄⡈⠻⢷⣄⠙⠿⢋⣸⣿⣷⣾⢸⡇⠀⠀⠀⠀⠈⠛⠁⢀⣴⣿⣿⣿⠟⠁
⣰⣿⣿⠟⠉⠁⠈⠉⠛⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠛⠿⣦⣈⠙⢿⣦⡈⠛⠿⢁⣿⢸⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠻⢿⣷⣄⠈⠙⠳⣤⠈⠻⣷⣤⣾⣿⣼⠇⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⣿⣿⡟⠀⣶⣦⣄⠉⢿⣶⣄⠀⣤⣀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠘⣿⣿⣷⣤⣤⣴⣿⡇⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣦⡈⠻⣿⣧⠀⣿⣿⣷⣄⠙⢿⣷⣶⣾⣿⡇⢀⠀⠀⠀⢠⣿⣿⠃
⠀⠈⠻⠿⣿⣿⠿⠟⠁⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⢸⣿⣿⣯⡙⠿⣦⡈⠉⠀⠙⠛⠛⠛⠷⣄⣿⣿⣿⣿⡇⢸⠀⠀⠀⠘⠟⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣦⡈⢻⣦⡀⠻⣿⣿⣶⣶⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣷⣌⠙⢿⣿⣷⣄⠙⠿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠿⢿⠟⠳⢤⡙⠻⣿⣆⠀⣤⣽⣿⣿⡿⠛⠋⠀⢻⣿⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⢸⣷⡀⠰⣶⣄⠙⢦⣈⠛⣀⣿⣿⣿⢧⣤⣴⡆⢀⣼⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠸⢁⡙⢦⣌⠙⠗⢈⣿⣿⣿⣿⣿⡿⠀⠀⠰⢇⣸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⣠⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⣴⣿⡿⠦⠘⣿⣶⣿⣿⣿⣿⣿⣿⣷⣦⣀⣶⣾⣿⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⣿⣿⠟⢻⣿⢸⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠸⣿⣷⣶⣤⣀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢠⣿⠟⣛⣻⡟⢻⡟⢻⣉⣉⠙⣿⣧⣤⡀⢻⣦⣈⠋⢀⣿⣿⢸⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠉⠙⠻⣿⣷⣦⠀⠘⣿⠀⠀⠀⠀⠀⢸⣿⠘⠿⣿⡇⠀⠂⢸⣿⣿⡀⣿⠀⣿⡇⢠⣿⣿⠀⣸⣿⣿⢸⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢻⡆⠀⠀⠀⠀⣸⡟⢰⣶⣿⠃⣠⠀⣸⡿⡿⠃⣿⣇⠈⢁⣼⣿⡇⢰⣿⣿⣿⢸⠀⠀⠀⠀⢀⣴⡟⠀⢠⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣧⣬⣭⣭⣴⣿⣤⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⢸⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⠿⠻⢿⣿⣿⣿⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣍⠁⢨⣿⣿⣆⣿⣀⣟⣀⣿⡿⢂⣠⣾⣿⣿⣿⣿⢧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣩⡙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⣾⡿⠛⠋⠉⠛⠻⣿⠋⢻⡏⠉⠻⣿⣿⣿⠟⢛⡛⠛⠛⣻⠋⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⢿⣷⢸⣿⡆
⠀⠀⠀⠀⢸⣧⡀⠀⠸⣿⣿⡄⠀⠀⠀⠀⣿⠀⣴⣿⣿⣷⠀⠹⠀⣿⠃⣶⡄⠘⣿⣿⠀⣿⣿⣿⣿⡿⢁⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⣭⣼⣿⠇
⠀⠀⠀⠀⠈⢿⣿⣄⠀⠹⣿⣿⡄⠀⠀⢀⣿⠀⣿⠿⠟⠁⣠⡆⢠⣿⠀⣿⣿⡀⠸⣿⠀⠻⠿⢿⣿⢣⠉⠀⠀⠀⢀⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠈⠛⠋⠀⠀⢸⡏⠀⠀⣤⣶⣾⣿⠇⢸⡇⢰⣿⣿⡇⠀⡿⢰⣶⣶⣾⠁⡎⣴⣿⣿⣿⠟⠋⠀⠙⠻⠿⢿⣿⠿⠟⠋⠀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣄⠀⠀⠀⠀⢸⡇⢠⡄⢻⣿⣿⣿⠀⣼⠇⢸⣿⣿⡇⠀⠁⠸⣿⡿⢣⠛⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠺⢶⣤⠈⠛⠀⠀⠀⠀⢺⡇⣸⣇⠈⣿⣿⣿⠀⣿⠀⣿⣿⡟⠀⣸⣷⣶⢎⡴⠋⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⣥⣿⣿⡄⠸⣿⡇⢠⡟⠘⠛⢉⣠⣾⡿⢟⣡⠞⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⡛⢿⣿⡀⢻⣇⣸⣷⣤⣶⠿⠛⣩⡶⢋⣵⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢶⣤⣭⣭⣭⣭⡴⠶⠞⣋⣥⣾⣿⣿⣿⡿⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠛⠋⠀⣠⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡴⣫⢋⣀⣏⢻⢢⡀⠀⠀⠀⠀⣼⡗⠒⠒⠒⠒⠒⠶⠦⠤⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⣀⣇⠀⢀⠁⠈⠋⢱⠀⠀⠀⢠⣿⢀⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠉⠉⠉⠛⣦
⠀⠀⠀⠀⠀⣼⠀⠀⠀⢣⠀⡄⠀⠸⠀⢉⠃⣸⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠓⠂⠲⠲⠂⠆⠀⣿⠉⠛⢲
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠻⢯⡉⡟⢐⣞⠶⠁⠀⠀⠀⣿⠁⠀⠒⠐⠒⠒⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⣀⠀⠀⠀⡟⠀⠀⣾
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⢰⠇⠀⠀⡏
⠀⠀⠀⠀⡏⠀⡬⢥⣶⠰⡁⢆⢀⣲⠠⢢⡠⠄⣄⠀⣾⠇⠀⠉⠉⠁⠒⠂⠀⠀⠀⠀⠀⠀⠒⠒⠀⠤⠀⠀⠀⡿⠀⠀⢸⠃
⠀⠀⠀⢰⠇⠀⠀⠈⠀⠀⠃⠐⠉⠀⠐⠜⠋⠁⠅⢰⡻⠀⠀⠐⢖⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⢀⡇⠀⠀⡟
⠀⠀⠀⢸⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣾⣇⣀⣀⣀⣀⣈⣁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣸⠁⠀⢰⠃
⠀⠀⠀⠈⠻⠷⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣛⣻⣿⡿⠒⠶⠤⠤⢤⣌⣉⣉⣉⡉⠛⠒⠒⠒⠲⠶⠶⠶⠶⠒⠃⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠒⠒⠲⠶⠦⠤⠤⠤⠤⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⢄
⠀⢀⣴⡆⣀⠐⣖⣆⣀⡀⣠⢤⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄
⠄⠀⠁⠉⠤⢃⠄⠘⠒⠙⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠄⠀⣀⣀⣀⡄⠁⠠⠠⠀⢀⣀⣀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⢸⣯⠑⠀⠀⠀⠁⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⠨⠟⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠄⠠⠀⠂⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠀⠀⢀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠦⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡎⠑⣆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠲⠐⢖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠀⡄⠠⠤⢀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠧⠤⢀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣀⠀⠉⠉⠀⠒⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⣀⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠹⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣠⡆⠀⢀⣰⣾⣰⢃⡄⢺⡔⠄⠙⠀⠀⠢⠔⢀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣤⣾⠿⣤⣿⣠⡛⠖⠛⠿⣿⣏⣱⣠⣄⡦⣤⣰⣶⣧⣦⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁⠠⣶⣶⣶⣿⣯⣹⣿⣙⣿⣿⣾⣿⣿⡟⠉⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠸⡷⠀⢀⣄⠀⠈⠁⢾⣿⣯⣿⣿⡿⢋⣄⡟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠃⠀⠈⠉⢉⣠⣄⣿⣿⣿⣵⣿⣤⣠⣄⠴⡄⢀⣀⠀⠀⣄⠀⠀⠀⠒
⠀⢀⡀⣭⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⠛⠻⠿⠿⣿⣾⣿⣶⣼⣖⢠⡤⣀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠶⣾⣾⡯⣿⣿⣿⣿⡿⣻⡧⠱⣦⣄⣀⡀⠀⠉⠉⡀
⠀⠀⠀⠙⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⠦⠌⣉⣠⣽⣻⣿⣿⣿⡿⣿⣞⡉⠀⢾⣧⡀⠀⠈⠉
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣻⣿⡃⠀⠈⣿⣏⣟⢿⣽⣿⣿⣿⣤⡸⣿⣿⡟⠋⠁
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠁⢀⣼⣿⣻⡻⣈⠻⣽⣿⣿⣷⣿⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⣿⣿⣿⣿⣧⠈⠻⣇⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠉⠙⠛⢋⣡⣭⣼⣿⠯⢛⣿⣿⣿⣿⣷⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠘⢿⡷⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⠿⠿⠿⠟⠃⠉⠉
⠀⠀⠀⠀⠀⢸⣿⣇⣿⡏⢠⠀⠀⠀⠀⠀⠀⢀⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢠⣤⣽⣿⣿⣷⣿⣾⣷⠞⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠦⠀⠀⠠⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠿⠟⠛⠻⠿⠿⠿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⢿⣿⢿⡿⢿⣿⢿⢿⡿⢿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣏⣷⢗⡚⣷⡝⣷⡝⣏⣯⡗⣿⢏⣯⡷⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⣁⣽⣷⣾⡋⠛⠁⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⠏⢤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⣰⣄⣠⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⢹⣿⣿⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣆⡘⠠⢀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⢀⣠⡤⠀⣤⣟⢧⠼⠛⠲⢦⣈⠢⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⠄⠤⠤⠤⣯⡍⢻⡿⠎⡣⡀⠑⡀⠀⠀⢹⠑⢄⠑⡄⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁⠀⠀⠀⠀⠀⢈⡡⠾⡱⣃⠵⠀⡇⢀⡠⠿⠀⠀⠱⡈⢂⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠈⠱⠀⠀⠀⠀⠀⠘⢄⡠⠁⠓⢆⠀⠑⠊⠀⠀⠀⠀⠀⡰⡄⢃⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠁⡀⣆⠺⠆⠀⠀⠀⠀⠀⠐⢷⡼⢷⠘⡀⠘
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠇⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣔⣚⡀⠃⠀⡄
⠀⠀⠀⠀⠀⠀⢸⢀⠖⠒⠒⠒⣦⠈⠀⠀⠀⠹⢆⠀⡎⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠈⠇⠀⠀⠇
⠀⠀⠀⠀⠴⡃⠉⠈⠁⠀⠀⠈⠉⠈⠁⠸⢄⠀⠀⠉⠙⠻⣆⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣸⠀⠇
⠀⠀⠀⢠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⢨⠁⠀⠀⠈⠐⠤⢀⡀⠀⠀⠀⠀⠀⢀⠏⡸⠀⣐⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡤⡀
⠀⠀⠀⠸⠀⠃⠀⣤⠀⠀⠀⠀⢀⡄⠀⡃⠀⡄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢚⠐⠛⠒⠒⠒⠒⠒⠺⠚⠋⠛⠉⠩⢋⣭⣍⣍⠢⡀⠀⠀⠀⠀⢱⢃
⠀⠀⠀⡇⠀⠈⠒⣿⠀⠀⠀⠀⢸⡷⠊⠀⠀⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠴⢘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⡻⣁⠎⢹⡇⢀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢡⣀⠀⠀⠀⠀⠀⢸⠀⡜⠁⠀⡖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⠘⠣⠶⠛⠁⡀⠀⠀⠀⠀⠀⡅⡂
⠀⣀⣸⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⢸⣧⣉⡐⠂⠤⠄⠸⠴⠠⠤⠐⣣⠇⣈⠁⢀⡄⠒⢀⣻⠈⠁⠀⠀⢣⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠄
⡀⡀⠀⠀⠀⠃⣀⣀⣀⣀⣀⣀⣀⣀⣀⢁⠀⠀⡄⡈⣃⠉⠐⠀⠐⠒⠀⠂⠈⣩⢨⠁⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠱⡀⠀⣬⠤⠤⠤⠄⠒⠂⠉⢰
⡗⠂⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⠉⠈⠉⢱⠀⠀⠈⠙⠁⠈⡰⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⣊⡙⣤⢣⠀⠀⠀⠀⠀⠀⠀⠇
⡇⢀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⢸⠈⢂⡴⠥⠈⢹⡟⠻⡆⠀⠀⠀⠀⠀⠀⠃
⠑⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠔⠁⡌⠉⠉⠉⠉⠉⠉⠉⠁⠘⢠⠀⠀⠀⠀⠀⣀⠨⠖⠉⠀⠀⠀⠈⠁⣀⣄⣀⣀⣀⣀⣀⣀⣸
⣀⣀⣱⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣃⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣁⣈⣬⣯⣿⣶⣿⣷⣶⣶⣷⣶⣶⣒⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠚⣷⡂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⠻⡀⣸⣆⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠌⠀⠀⠁⡄⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣒⡀⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠸⠗⢋⠀⣘⠛⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⢀⠘⠦⠟⢻⠛⠋⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⣾⠓⣿⢋⣴⣬⡐⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⠤⠀⢡⠀⠀⣐⡀⠀⠀⡶⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣰⣁⠉⠁⡤⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⢁⡁⠀⠀⢀⠃
⠀⠀⠀⠀⠠⠀⠀⠈⠀⠈⠒⠀⠠⢆⠀⠉⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠋⠉⠙⠂⣼⠀⠀⠀⠀⠀⠀⠀⢀⡔⣆⡀⠛⠁⠀⡠⠊⠠⡤⢤⣀⢀
⡀⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠜⢉⠒⠀⠰⠊⣵⠀⠀⠀⡏⠉⠉⠉⠈⠁⠉⠉⠉⡛⠙⠉⣋⡴⢀⢀⠉⡆
⠇⠠⠄⠇⠀⠀⢀⡀⢤⠴⠄⠀⡐⠀⠀⠀⠀⠀⠀⢀⢠⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇⠀⠀⠁⠐⠄⠀⠀⠀⡇⠈⠀⠀⠉⠉⠉⠁⡇
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡈⠆⠎⠾⠁⠀⠀⠀⠀⣰⡖⣀⣄⣀⢀⠀⠀⢰⠇⠀⠀⠀⠀⢡⠀⠂⠀⡤⠠⠐⠒⠒⠁⠀⠀⠀⠀⠀⢤⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠆⠀⠀⠀⠀⠀⠀⢈⠀⠀⠄⠀⠀⠀⠀⣈⠣⢄⢀⠀⣄⠀⠀⣰⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠁⠂⠀⠀⡀⠀⠀⠈⠛⠁⠀⠀⠀⠰⠀⡗⣒⠋⠸⣿⡿⠀⣞⠒⠤⡆⢀⠀⠀⢠⡊⢨⣽⠀⠀⡀⠀⠄⠀⠸⢀⠄⢀⠄⠌⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠀⠀⠀⢈⠂⠀⠃⠀⠂⠀⢤⠃⣍⠭⠀⠈⠀⠀⢲⠀⢐⡞⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠁⠀⠀⠀⠈⠙⠒⠠⠤⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠒⡖⠋⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡄⠠⠼⠒⠒⠒⠒⠒⠲⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠒⠤⢀⣀⠀⠀⠀⠀⣀⠠⢸⠀⠀⡐⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠐⠒⠆⠀⠀⠀⠠⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⡀⠀⢀⣀⣀⡤⠔⠊⠀⠐⠦⣀⡀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⣀⠀⠀⡀⠀⠳⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⡟⠉⢹⠉⠁⠇⠀⠀⠀⠀⠀⠈⠈⢱⠒⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠘⠒⠖⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠸⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡍⠈⢙⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆⠀⠀⠀⠀⢠⠦⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡌⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⠃⠀⠀⠀⢰⢀⡇⠀⠀⠀⠀⠤⡀⠈⠀⠁⠀⠀⠀⠀⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠞⠈⡇⠀⡰⠍⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠂⠸⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⠆⠼⡀⠀⠀⡀⠄⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣠⡀⠜⠁⠀⠀⠀⠀⠀⡞⢐⡐⡘⡒⡄⠀⠀⠀⠀⠄⡀⠀⠀⠂⡠⡀⢠⠀⠸⠀⠀⠀⢀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⣙⡣⠼⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⢂⣾⡆⠀⠀⠀⠀⣀⣘⣓⣩⡴⣾⢛⣇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣾⠗⣋⠜⠱⠀⠀⠀⠀⠉⠉⣏⣰⠐⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⣤⣾⡃⠀⠀⣈⠀⠀⠀⠀⠀⢹⣥⣤⣀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣛⠁⠀⣀⡅⠀⠀⠀⠀⣰⣯⣤⠤⠭⡗⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠽⠿⠾⣧⣶⠀⣠⠶⠚⠋⠉⠀⠀⠀⠀⠈⠉⠉⠓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠰⢬⣦⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⡀⠈⠳⣾⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣤⣞⣿⣤⣴⣄⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⢧⣄⠒⠃⢸⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠷⠄⣿⢀⣴⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡀⠀⠸⡇⠰⣦
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠸⠀⠀⠀⠀⢀⣠⣿⠈⠉⡞⠷⠀⠀⠀⠀⢀⠔⣩⠞⠁⣧⢻⡀⠀⢙⡖⠻⢿⡆
⠀⠀⠀⠀⠀⣠⣯⠈⠙⠻⡶⠀⠀⠐⠚⠣⠆⢸⣆⠀⣇⠀⠀⣀⣀⣤⡤⠞⠁⠀⠀⢹⣦⣄⣀⣼⠁⠀⢸⡇
⠀⠀⠀⢀⡼⢿⡘⢷⣄⣰⢳⠀⠀⣤⠀⠀⢀⡀⣮⠓⣿⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⠈⡿⢻⠃⡀⡀⠈⣧
⠀⠀⢠⣾⡇⢸⡇⢸⣏⡏⣼⠀⠀⠈⠉⠉⠉⠁⢹⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠆⣿⠀⡇⡇⠀⣿
⠀⠀⢸⣿⣧⠘⣧⠘⣿⣧⡟⠀⠀⠀⠀⠀⠀⣰⡂⢻⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⡿⢸⡇⢡⠀⢸⡆
⠀⠀⠀⠻⣿⡄⢻⡆⠀⢸⠷⠤⠤⠴⠶⠖⠛⣻⠉⠁⣀⣇⢀⣀⣀⣀⣠⣤⣤⣴⣶⣾⣯⠄⡇⢸⡇⢸⡀⢘⡇
⠀⠀⠀⠀⠈⠛⠶⢬⠀⣾⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⠋⠋⠩⢍⣉⡀⠀⠀⠀⠠⡆⢠⡇⢸⡇⠀⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣼⡄⠀⠀⠶⣤⠭⠽⠦⠤⠄⣧⢸⠁⢸⡇⠀⢿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠙⡷⠆⠀⠀⢳⠀⠀⠀⠀⠀⣿⠘⡆⠸⡇⠀⢸⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⢷⠀⠀⠀⠈⣆⠀⣀⠀⠀⢹⡀⠖⠺⡇⠀⠈⡗⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⢸⡀⠀⢀⡌⠀⠀⠀⣠⡼⠫⠟⠁⠀⠸⡇⠀⠀⣷⣀⠔⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⢀⡤⠞⠁⡿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⠄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠢⣄⢫⡽⣄⠘⠆⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⣂⠙⣽⠃⠹⠤⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣤⢠⠀⣦⣄⠙⡶⠀⠚⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⠧⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣀⠴⠒⠒⠒⣶⣤⠄⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣬⡖⡖⢉⣉⠙⠲⢄⠀⠀⠘⣤⠚⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣗⠁⡴⠊⠡⠙⢢⡀⠀⠑⢄⠀⠀⠀⢀⠘⢣⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡋⠀⢐⡀⠔⠁⠀⠐⡀⠀⠀⢢⡄⠂⠈⠆⠂⡇⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢖⠈⠀⠠⣀⠀⠀⠀⠐⢆⠁⠀⠱⡀⠀⠀⠂⢹⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣄⠤⠄⠛⣉⣀⠀⠀⠀⢦⡀⠄⠛⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⢀⠀⠀⠉⣏⠀⠀⠀⠀⢀⡀⠄⠆⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠄⠀⠙⢄⠀⠈⠰⠤⠀⠀⢀⠇⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⢤⣀⣉⣠⣄⣀⣹⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢉⣤⡐⢊⡠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠴⠚⠁⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢛⠉⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠫⠅⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⡴⢚⠿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠐⠀⠀⠀⠀⣀⣀⡤⠴⣒⠋⠍⣀⠴⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡋⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⣐⣠⠥⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡚⠋⢀⣠⡤⠶⠶⠛⠛⠉⢁⣀⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢀⣠⢞⣫⣡⠤⠖⠪⣉⣁⣤⡤⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣴⣟⣒⣉⣡⣤⠤⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⢠⢂⡐⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢈⣌⡠⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠌⡀⢀⠜⠜⠀⠀⠀⠀⠀⠰⠃⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠃⠠⣀⡡⠊⠀⠀⠀⠀⠀⠂⠀⠑⠊⠠⠂⠀⠀⠀⠀⠈⠢⡱⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠘⠀⠤⠂


⠀⠀⠀⠀⠀⢀⡴⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⢀⠥⠀⠆⠠⠅⠀⠀⠀⠀⠀⠰⠌⠉⠉⠉⠁⠀⠀⠀⠀⠈⠀⡈⠐⠡⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠃
⠀⠀⠀⠀⢐⡄⢀⣄⠀⡌⠀⠀⠀⠀⠀⢀⣠⣔⣦⡖⠀⠀⠀⠀⠀⠠⢔⠁⠒⡈⠄⠀⠀⠀⠀⠀⠀⣠⠤⢤⡄
⠀⠀⠀⠀⠈⠛⠋⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠃⣶⢲⡄⠂⠀⠀⠀⠀⠀⣾⡆⠉⠁⣿⠆⠀⠀⠀⠀⠀⢗⢄⠠⢪⢆⠀⠀⠀⠀⠀⠀⠀⠛⠘⢆
⠀⠀⠀⠀⠀⠇⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⢰⠐⠙⠀⠀⠀⠀⠀⠀⢀⢕⠕⢈⠁⠀⠀⠀⠀⠀⢖⠑⡢⠀⠚⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠂⠀⠘⠛⠀⠀⠀⠀⠀⠀⠓⠀⠀⠒⠁⠀⠀⠀⠀⠀⠐⠉⠃⠒⠂⠁


⠀⠀⠀⠀⠀⠠⠒⠘⠢⠀⠀⠀⠀⠀⠀⠒⠀⣀⣠⡀⠀⠀⠀⠀⠀⠠⠽⢄⠀⡸⣀⠀⠀⠀⠀⠀⠠⣄⠓⠚⡦⠄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⠸⠀⢸⠀⠀⠀⠀⠀⠀⠚⡐⠆⠘
⠀⠀⠀⠀⠀⠠⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠃⠙⠛⠇⠀⠀⠀⠀⠀⣄⠀⠈⢰⠊⠀⠀⠀⠀⠀⠤⠚⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠄⢀⡄⣠⣄⠀⣰⠏⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⢰⡴⢱⡷⢁⡟⢰⡟⠔⣶⠋⣽⢂⣴⢋⡿⢁⣴⡓⣀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠃⠘⠁⣸⠃⠿⠁⣼⠇⠸⠏⠀⠋⠸⡇⠸⠥⢺⠏⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠔⠊⠉⠈⠀⠀⠙⠀⠀⣀⣠⠤⡤⢠⢀⠤⠄⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠃⡟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢠⠒⢠⡁⠀⠀⠃⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⢈⣀⠧⣤⢨⣎⢡⡟⣰⡶⠀⡜⣠⠆⣀⣴⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣿⠐⢸⣇⠀⠛⢸⠏⠘⠁⠛⢀⡞⠸⠇⠠⡿⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡿⢀⠀⠁⠀⢀⣀⣠⠤⠖⠒⠚⠃⠀⠀⢀⡠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠄⠄⢀
⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠀⠀⠀⢀⠠⠀⠒⢦⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⢀⡀⠊⠀⠀⠀⠀⠠⠀⠐⠀⠈⠉⠀⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⡰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡄⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠰⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡔⠙⠂⠀⠀⢀⠀⠀⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠙⠀⠠⠀⠀⠀⠀⠰⡆⠀⠑⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠃⠀⠀⠀⢀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠆⠋⢁⠀⢒⠀⢦⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠧⡙⢆⠀⠀⠣⠀⠙⠆⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠦⠠⡀⠠⡀⠰⠒⠀⠳⢌⢳⡀⠀⠀⣴⠦⠀⠀⠀⠀⠀⠀⢠⣾⠿⣲⢶⠯⡖⠈⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⢤⠀⠀⠁⠌⠂⡘⣕⠀⠈⠙⠒⢒⣤⠴⠒⠉⠀⠚⠋⠋⠈⠁⠀⣼⡧⢃⠁⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⢀⠀⠀⠀⠜⠐⡬⠗⣋⠥⠚⠉⠀⠢⠗⠄⠀⣠⠶⠶⣄⠀⠠⣿⠀⠀⠡⢦⡼⠇⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⢀⠀⡨⠀⠀⠖⡊⠄⠀⠙⢌⠦⠀⠀⠀⠀⢀⡀⢁⢻⣄⠠⣟⢀⣴⡿⡦⠒⠁⠀⠄⢋⣼⡿⠀⠠⠀⡀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠉⠀⠀⠀⠀⠘⣿⢀⠗⢀⣀⠴⠞⠊⣽⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⣦⣋⠁⠀⡀⢴⡟⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⡹⠀⠚⠉⡛⠙⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠴⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠒⠒⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠁


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

⠀⠀⠀⠀⢹⠁⣯⢢⣷⢰⡔⣸⠁⡆⠀⢦⠆⡏⢰⢉⠘⠋⡎⡧⣯⡆⢸⠱⡋⢰⣙⢖⢢⡐⢡⠀⠺⡄⡏⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠈⠀⠈
⠀⠀⠀⠀⡏⠉⢯⣭⣩⡉⠉⢹⠀⢸⠋⠉⠉⢩⢉⡉⠉⢳⠀⢰⠉⣉⡉⢉⣩⠍⠙⠂⠀⣼⠉⠉⠉⠉⠉⡩⣽⡆
⠀⠀⠀⠀⡇⢖⣏⡉⢩⡻⠦⢸⠀⢸⠀⢀⣀⣼⣒⣋⠀⢸⠀⠈⡔⠿⣏⣹⣏⡆⠰⡇⠀⣸⠀⣴⡻⠄⠚⣱⢹⠇
⠀⠀⠀⠀⡇⣌⢉⡠⢔⣂⢼⢸⠀⢸⠀⣨⣆⣀⡀⠨⣁⢸⠀⢀⠁⠀⢹⢀⡇⡇⠈⡁⠀⣿⡔⣉⡶⠉⣙⣳⢾⠂
⠀⠀⠀⠀⣧⣈⣉⣉⣉⣉⣀⡼⠀⠸⣄⣐⣢⣤⣔⣂⣀⣼⠀⠸⣄⢀⣀⠓⠗⠃⠠⠇⠀⢹⣉⣁⣀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⡁⣀⠔⡉⣈⠢⡌⢹⠀⠈⡄⢀⡔⠉⠲⣧⠀⡇⠀⢸⢤⣀⡼⠤⢤⡴⠋⡇⠀⢸⢁⡴⠦⠤⣤⠤⡈⡇
⠀⠀⠀⠘⡟⡋⡏⠀⠈⡗⠟⣧⠀⠀⣷⣋⡀⣠⡤⢬⡷⡇⠀⢸⠠⡏⠀⠀⠀⢣⣤⡇⠀⢸⠼⢧⣾⣷⡉⠁⣿⡇
⠀⠀⠀⠈⣧⡁⠙⠒⠒⢁⡠⢾⠀⠀⡇⢸⡀⣯⣇⣸⠀⠇⠀⢸⠖⠣⣀⣀⡠⡏⠀⡇⠀⣾⡞⢆⣻⣭⣤⣴⡏⡇
⠀⠀⠀⠀⠧⠿⠂⠒⠖⠻⠤⠞⠀⠀⠧⠌⠉⠉⠉⠛⠒⠂⠀⠘⠤⠤⠾⠤⠤⠼⠷⠇⠀⠻⠭⠭⠤⠿⠯⠿⠶⠇
⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⣄⠀⢀⡤⠤⢤⡤⣤⠤⠤⢤⠀⢠⡄⠠⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⡇⠀⡤⣒⢒⣢⠀⢸⠀⠈⣶⣾⣥⣤⣤⣽⣷⣾⠀⢸⣴⠒⠒⠫⣒⢦⠀⡇⠀⢸⠀⡠⠒⣖⠲⣆⢸⡇
⠀⠀⠀⠀⣇⡔⠁⠉⠈⠉⠳⣼⠀⠀⡄⣿⠀⡙⡇⣸⡇⢹⠀⢸⠈⣷⣏⠀⠘⡏⠀⡇⠀⢸⠰⡗⢲⠿⡔⠉⡾⡇
⠀⠀⠀⠀⡏⢻⡵⠒⠒⠮⠟⢹⠀⠀⡟⣿⣟⣟⣛⣻⡟⢹⠀⢸⠀⠈⠛⠋⠉⢯⠗⡇⠀⢸⠀⠑⠾⣄⣭⠟⢱⡄
⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠋⠀⠀⠛⠓⠛⠛⠒⠒⠓⠊⠀⠈⠓⠒⠒⠒⠒⠒⠚⠁⠀⠈⠒⠊⠋⠉⠉⠉⠉
⠀⠀⠀⠀⡏⢩⠍⢭⣩⢯⡉⢱⠀⠰⡗⣍⢉⠁⠈⠉⠉⡇⠀⢸⠃⠉⠉⢉⡉⠉⠙⡆⠀⠸⢉⣽⣿⣯⡟⣫⣽⠆
⠀⠀⠀⠀⡧⡏⣴⠚⡦⠠⣟⢸⠀⢀⡷⣏⠉⣹⠲⣄⠀⡇⠀⢸⠖⠙⣦⡋⠙⣄⠀⡇⠀⢻⠙⣿⣿⡽⣯⡅⠀⡇
⠀⠀⠀⢠⠐⠭⣽⣦⣗⣀⣯⢸⠀⢨⠿⡉⠙⠈⠀⣀⡽⡇⠀⢸⣠⠞⠉⠙⠚⠙⢳⡇⠀⢸⠀⠀⡏⢓⣿⠀⢰⠁
⠀⠀⠀⠀⣆⣀⡛⠁⣈⣃⡀⠼⠀⢸⣄⣙⣚⣙⣛⣁⣀⡷⠀⠸⣇⣀⣀⣀⣀⣀⣠⠇⠀⠿⠤⣤⣿⣭⣼⢇⣼⠂


⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠠⠀⠉⠉⠩⠀⠀⠂⠠⠂⠀⢠⢀⡁⠀⠈⡇⠀⢤⣀⡄
⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠈⠲⠚⡈⢀⠀⠀⠀⠆⠐⠈⠂⠀⠄⠀⠐⠿⢄⠀⠀⡇⠀⠀⢁⣠
⠀⠀⠀⠀⠀⠀⠰⢀⡀⠴⠉⢉⡠⠌⠀⡈⠥⠀⠘⠎⠤⠴⠅⠀⠀⠴⢾⡞⣤⠡⠀⠙⠳
⠀⠀⠀⠀⠀⠠⠂⠈⠩⠌⠠⠞⠤⠄⡀⠀⠶⠤⠬⠠⠠⠥⠄⠀⢤⡶⠐⠂⢠⣢⠄⣠⡤⣤⣤⠀⠐⡀
⠀⠀⠀⠀⠁⠀⠁⠈⡠⠤⠄⠀⢈⠃⢩⠈⢈⠀⡀⡉⡀⡀⢉⠀⠘⠁⠘⢠⠯⣎⢇⠩⣅⣤⣄⠀⠸⠀⠠⡅⠘⢶⣥
⠀⠀⠀⠈⡆⠐⠀⠀⡀⠴⡖⠓⠈⠠⣂⠀⢀⠀⠀⣦⡄⠀⠀⠀⠀⢔⡀⡟⢀⡍⣦⠁⠀⠀⢌⠂⠀⢀
⠀⠀⠰⠀⠘⢦⣈⡀⠀⠐⢓⠐⡂⠂⠀⠀⠀⣔⡂⠁⠀⣈⠀⠀⣀⡄⠀⡄⠠⠀⠣⠀⣡⡀⠈⢆⠠⠈⠄⠈⡀
⠀⠀⠀⢐⠀⠄⠀⠠⠸⢉⡹⣿⣉⠀⣨⠉⡍⡅⢠⢈⢻⡉⢀⢀⢉⠉⡭⠠⠆⠀⠀⠐⣰⠔⣸⠆⠉⠁⢀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢀⢀⠀⠀⠀⡥⠀⠎⠬⠄⢧⠠⡄⠘⠀⠍⠰⡆⠀⠠⢲⠅⠈⢈⣢⣬⡜⠆⡄
⠀⠀⠀⣀⠠⠀⠀⠀⠂⠘⠆⠐⠠⣀⠾⠄⠀⢰⠀⠄⠢⠘⠆⢤⠐⠀⡁⠂⠀⢂⡈⡆⠰⠆⠞⠛⢉⣀⣟⣇
⠀⠀⢰⢣⠈⠆⠀⠘⠀⠀⠀⠀⢀⠇⠀⠀⠀⠛⠓⢆⢀⠀⠀⡸⡤⠈⢀⡠⢤⡈⢷⡀⠠⢨⡐⠴⡉⠀⠉⠉⡆
⠀⠀⡆⠀⠀⣸⠂⢀⢲⠌⠼⡐⢊⠀⠀⠀⠀⠀⠀⠀⠁⠨⠘⠃⠓⢌⣿⡜⠏⡻⠀⢷⡀⠤⠈⠀⠙⠒⣤⠔
⠀⠀⠀⠀⠀⠘⠀⠯⣅⡩⢂⣙⢈⡀⠀⡀⠀⠀⠠⠘⠀⠀⠀⠀⠠⠒⠈⠋⠊⠁⠀⠀⠳⡄⢀⠐⢒⠖⡀⢠
⠀⠀⠀⠐⠀⠀⠀⠘⠆⠈⠼⠏⠙⢃⢶⠗⢻⠂⠀⡀⠢⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⠘⠔⡏⡛⢹⢣⠏
⠀⠀⠀⠠⠀⠐⠀⣤⠤⢀⠤⢤⠞⠐⣿⠃⠚⠀⠀⠀⠀⠘⠙⠠⠀⠀⡀⠠⠴⠖⠞⠋⠉⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠉⢧⠴⠃⠈⡀⢄⡠⣏⢠⣀⠀⠀⠀⠠⠀⠒⠑⠀⠀⠀⠠⣄⣘⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⡀⠀⠘⠗⠁⠀⠀⠐⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⢠⡆⠁⠀⠒⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠓⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠅⢿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠊
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢆
⠀⠀⢀⣀⠀⠂⢤⡴⡄⠀⠀⠀⢀⣠⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠐⠻⠻⠖⢲⠞⡓⢻⣒⢶⠞⠧⠙⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠉⠉
⠁⠀⢀⡀⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠐⠂⠒⠤⠀⠐⠒⠂⠒⠀⠂⠠⣶⣴⠖⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠐⡊⠀⠠⡀⠀⡤⡀⠀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠂⠀⣤⣀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠠⠀⠀⠄⠀⠀⢸⢳⡎⡃⢀⠀⠀⠀⠉⠀⠀⠀⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠸⡄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⢸⡓⠽⢁⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⡆
⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠠⠤⡄⠠⠀⠐⠈⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠯⠎⠀⠀⠀⠀⠈⠀⡀⠀⠙⠃⠀⠀⡀
⠀⠈⠀⠀⠈⠀⠈⡂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠋⠁⠉⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⢀⠐⠀⠠⠡⠄⠀⠀⣠⠤⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠜⠆⠀⠀⠀⠀⠀⠀⣀⠂⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠠⣾⣶⠀⠀⠀⣶⠐⠲⠶⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠂⠂⠚⠚⠙⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠻⠤⠤⣤⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠈
⠀⠀⠀⢀⠠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠐⠀⠒⠢⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠑⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠠⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠿⠿⠛⠋⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠟⠛⠉⠁⠀⠀⠀⠀⣀⠠⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠁⠀⠀⠀⢀⡀⠤⠐⠂⠈⠁⠀⠀⢀⣸⣿⣦⣶⣶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⡀⠤⠐⠈⠉⠀⠀⠀⢀⣠⣤⣶⣾⠿⠟⠛⠉⠉⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⢀⣶⡿⠟⣿⡆⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠉⠁⠀⢀⣤⠤⠖⠒⠃⠀⠀⢿⣇⠀⡀
⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⣿⡀⠀⢰⣿⠟⠋⠁⣀⣤⠄⠖⠛⠉⣉⣤⠠⠶⣒⣋⣤⣶⣾⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢻⣧⠀⠘⣿⡆⠀⠀⠉⣠⡤⠆⢛⣋⣥⣶⣾⠿⠟⠛⣉⣁⠀⢳⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠈⣿⣆⠀⢹⣷⠀⠀⠀⣤⣶⡿⠿⡟⢉⣡⠄⠲⠂⠉⢉⣁⣤⣴⣷⣾⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⣿⡄⠈⣿⡇⠀⠈⣿⣇⠀⠀⢳⣈⣀⣤⣴⣶⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠹⣿⡀⢸⣿⡀⠀⣸⣿⣶⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢻⣧⣤⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⠟⠉⣧⢀⣉⠷⣼⠿⢶⡄⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣾⠖⠒⠻⡏⠀⠀⠘⣆⢀⣻⡆⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⣀⣠⢷⠔⠒⠋⢻⠁⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢿⡖⠛⢯⠁⠀⠈⣧⠀⠀⣸⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠈⢷⣄⣈⣷⣤⡶⠻⡟⢹⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⢶⡟⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣾⠻⣮⣿⣤⣿⠀⣿⡀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢼⣟⡁⢻⣾⠟⢿⣄⣿⠸⡯⠙⠇⠈⠁⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⣠⡴⣤⢸⣿⣆⠻⠶⣦⡉⣹⡆⠻⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢹⣦⡾⠈⣿⠛⠇⠘⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠻⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⣿⡟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠿⣛⣋⡭⣽⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣷⠿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣶⣶⡾⠿⠟⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠈⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠔⠒⠒⠒⠒⠦⣄⠕
⠀⠀⠀⠀⠀⣀⣀⢠⠴⠶⣒⡶⠶⣬⣱⡿⠖⢂⣰⣿⣦⠀⢀⣀⣤⣤⣿⣤⣤⡴⠦⣀⣒⠶⠦⠤⠤⠴⠤⠄⢄
⠀⠀⠀⠀⠀⡁⠀⢀⡠⠎⠉⠀⠘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣼⠋⠀⢂⠀⠀⢀⠁⠆⡁⢸
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠐⠀⠐⠃⠀⠀⠈⢄⠉⠁⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⢛⠀⠀⠀⠑⢤⠚⠁⢰⡇⢸
⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠈⠉⠉⡇⠀⠀⠠⠀⠀⠠⠉⠀⠄⠀⠀⠀⠀⡈⠁⠀⣿⠀⠀⠀⠀⠀⡑⠄⠜⢣⠸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⡀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠑⠤⠊⠀⠀⠀⠀⠠⢰⡌⠁⢰⢸⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠆⢸⠘⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠙⠂⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠀⠵⡠⠀⡉⠏⠀⡇⢸
⠀⠀⠀⠀⠀⠧⠀⠀⠀⠠⡀⠀⠀⡇⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠁⠛⠀⠀⠁⢸
⠀⠀⠀⠀⠀⡄⢈⠢⠐⠈⠁⠀⠀⢡⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢂⢀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠢⡇⢸
⠀⠀⠀⠀⠀⠧⠬⠤⣰⠤⠤⠄⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⣧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠓⠒⠒⠤⠤⢭⡤⠎⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠈⠉⠉⠉⠉⠁⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠋⠉⠁⠈⠉⠉⠉⢀⡰⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠛⠻⠷⣶⣶⣦⣛⠃⠉⠉⢉⣩⣭⣉⢋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⢀⣤⣽⣿⣿⠛⠛⠀⠚⠉⡈⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⣠⣾⣿⣿⣿⠀⠀⠐⠋⠁⠀⢀⣀⠀⠀⠀⠀⣿⣆⢱⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣯⡌⠦⠀⠀⠀⣿⣟⡰⠃⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢋⡶⣶⣍⠻⠃⠀⠀⠀⠀⠘⢿⣇⠖⠀⠀⠀⠈⣻⡧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠟⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⣛⡀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠮⠹⣶⣶⠟⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢹⣆⠀⠀⠀⠀⠀⠀⠀⠙⠠⠤⠜⠋⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠒⠊⠉⠉⠁⠀⠀⢸⡇⠀⠀⠉⠒⠢⢤⣤⣀⢤⣤⡄⠚⠁
⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⣶⣤⠙⢦
⠀⠀⢀⡜⠃⠀⠀⠀⠀⢀⣴⣶⣶⡶⡏⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣷⢦⢷⣴⣿⣦
⠀⢠⠎⠀⠀⠀⢀⡴⠊⠙⢿⣿⣿⣷⡇⠀⠀⠘⢿⣿⣿⣿⡗⠶⠄⠰⠖⠉⣿⣿⠈⢦⠹⣿⣿⣷⢦⡀
⢀⡛⠀⠀⠀⡰⠋⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⠀⠈⢣⢻⣿⣿⣇⠙⢆
⠸⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⢸⣿⡇⠀⠀⢻⣿⣿⣿⡀⠈⢧
⡆⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠈⣿⠇⠀⠀⢀⣿⣿⣿⡇⠀⠈⢣
⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⣿⠀⢀⡴⠋⠈⣿⣿⡇⠀⠀⠈⡆
⡇⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠉⠉⠉⠐⠒⠒⢠⡄⠀⢻⣿⡀⠀⣿⡀⣿⡀⠀⠀⢻⣿⡇⠀⠀⠀⢰
⠇⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣆⡠⠤⠜⢻⣿⡚⠿⠥⠼⠳⡄⠀⢸⣿⡇⠀⠀⠀⠈⡄
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠶⠋⣠⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⢡⠀⢸⣿⡇⠀⠀⠀⠀⢿
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⣷⠀⢃⠛⠉⠁⠀⣠⣶⣶⣶⡀⠀⢸⠀⢸⣿⠀⠀⠀⠀⠀⢀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢨⡄⢸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣦⠞⠀⢸⡟
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣷⣀⣀⠤⢿⣿⠟⠁⠀⠙⣷⠀⢸⠃
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡿⠀⡌
⣇⡀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⡇
⠈⠙⣷⠂⠤⠤⠄⠒⡟⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠠⠤⠤⠐⡞⠋
⠀⠀⣿⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⠀⠀⠀⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠃
⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠠⣇⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣄⣀⣀⣀⣤⡁⢈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⣥⣀⣀⣀⣀⡇
⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣠⣀⣀⣠⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣁⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠡⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠈⢁⠀⠠⠰⠀⠄⠀⢀⠈⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠂⠀⠀⠀⣾⣤⠀⠀⠀⠀⠃
⠀⠀⠰⠀⠀⠀⣀⠂⢠⡄⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠘⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠄⠀⠀⠉⠀⠈⠀⢂⠀⠀⢸⠀⠘⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⡀⠈⠀⢸⣿⣯⡀
⠀⠀⠀⠴⢈⣁⠀⠠⠆⠀⠀⢣⠀⢸⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠀⠀⡈⠀⠙⢿⣦⣤⣶⠿⠂
⠀⠀⠀⠀⢸⡅⠀⠨⠀⠐⢠⠀⠀⡈⠠⠀⠀⠠⠀⠀⢠⠀⢠⢠⣤⡀⣦⠠⡆⢰⣦⠀⢀⠀⠀⠸⡟⠀⠀⢀⠀⠀⠆⠀⠀⠉⠋
⠀⠀⠀⠀⢸⠀⢀⠀⠂⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣶⣿⢸⠘⡇⣿⠀⡇⢸⣿⡆⢀⣀⠠⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⠀⠀⣿⡇⢸⣸⠇⣿⡆⣇⢸⣿⠃⢀⠄⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⢸⡃⠀⢠⡄⠀⢠⠀⠀⣤⠑⠀⠄⠀⠁⡀⠀⠀⡀⠀⠀⠀⠈⢀⡉⠀⣁⠀⢀⠀⠀⣴⣷⠀⠀⠀⢐⡄⠃⠀⠶⠖⠒⠊⠉⠘
⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠈⠀⠀⠉⠀⠀⠀⠀⠐⠒⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⠀⠈⠈⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈
⠀⠀⠀⠀⠺⠄⠀⠸⠃⠀⠀⠀⢃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⢀⡀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢆⠀⡐
⠀⠀⠀⠀⠀⠒⠀⠠⠠⠀⡀⠀⠈⠀⡆⠀⠀⠀⡇⠀⡲⠀⠀⢰⢁⡄⠀⢰⠀⡼⠀⠀⠅⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠪⠈⠙⠉⠉
⠀⢀⣄⠀⠀⠀⠀⠤⠀⢆⠀⠀⠀⠀⡇⠀⠀⠀⡇⠰⡄⠀⠀⡏⠈⢡⠀⠈⡄⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠑⠀⠈⠁⠀⠈⠁⡀⠁⡀⠀⠀⠘⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⣦⠀⠲⣶⡶⢰⣶⡄⣴⢶⠆⣖⣦⢸⡗⢺⡇⡴⢲⡐⣶⢶⠀⠀⠀⠀⠀⠲⠛⠙⠾⡉⠙⡃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢉⣀⠀⠀⠀⠀⠙⠀⠘⠛⠃⠙⠋⠀⠛⠛⠀⠓⠘⠃⠈⠋⠐⠛⢘⠃⠀⠀⠀⠀⠈⠒⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠠⢀⡤⠼⠋⠙⠳⠒⢶⠐⠀⠈⢳⠘⠀⠀⠾⡀⢰⡆⡆⠀⠀⠀⢠⡟⠀⢠⣟⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠸⠋⠀⡄⡅⠰⠈⠀⠀⠹⠀⢰⠏⠀⠀⠀⡷⠇⠀⢷⡇⠀⠀⠀⠈⠳⠀⠀⠙⠃⠀⢀⠃⠃⠐⠒⠀⠈⠉⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇⠀⠀⠠⡇⠀⠀⡀⠘⠀⠀⠦⠀⠃⠸⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠂⠀⠈⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⡃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠄⠂⠀⠚⠋⠁⠀⠀⠀⢀⣴⣷⡌
⠀⠀⠀⠀⠂⠀⠐⠒⠒⠓⠀⠀⢀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢦⡜⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌⠆⠀⠀⠀⠀⠐⠀⠐⠒⠀⠂⠀⠠⠴⠂⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠠⢀⢔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡖⠊⠉⠦⠒⠞⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⢀⣤⠤⢤⣤⠂⠁⠈⠀⠐⠃⠀⠀⠀⠀⠀⠢⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢨⡏⠀⠀⠀⢹⡆⠀⠀⢀⠀⣎⠀⠀⠀⠀⠀⢢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢧⣀⠀⢀⣼⠧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⡖⠚⠛⠹⠉⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠢⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠢⢄⠀⠀⢀⠴⠒⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠥⠰⡃⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⡰⠉⠉⠱⣄⠀⠀⠀⠀⢀⡜⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠉⠒⠒⠚⠁⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⣤⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡄
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡤⠀⠀⠀⢠⠀⠀⠀⠀⠿⠿⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠿⠷⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣶⡆⢰⣶
⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠸⠡⢤⠀⢰⣶⠀⢰⡖⠂⠀⣶⡆⠀⣾⣷⢴⡄⢀⠀⠀⢀⠀⢁⡀⠀⠀⠀⠀⠉⠀⠿⠟⠈⠉
⠀⠀⠀⢸⣿⠀⣿⡇⠀⢀⣠⠀⢚⣿⠇⢸⡿⠀⠒⠀⠙⠀⠈⠉⠀⠈⠉⠁⠀⠉⠁⠀⢹⣷⢰⡇⠰⡂⣠⣦⡰⣿⣿⣷⠀⠀⠀⣶⠀⢴⡆⢰⣦
⠀⠀⠀⠤⠤⠤⠤⠥⠄⢈⣿⠁⠸⡏⠀⠈⠀⠀⠰⠀⠀⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢾⡗⢸⠇⠈⠀⠿⣿⣻⣿⣿⠛⠃⠀⠀⠉⠀⠈⠁⠈⠉
⠀⠀⠀⣤⣤⣤⣠⣤⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠰⠀⠠⠀⠀⠁⠀⢤⡀⣄⠀⠀⠁⠃⠂⢠⣿⣿⣿⠇⠐⠀⠀⣿⡇⢰⠂⣿⡇
⠀⠀⠀⠿⠿⠿⠿⠿⠠⢤⣧⣤⣀⣠⡹⠿⠆⠀⠀⠀⢀⡀⠀⠂⠚⡤⠀⠀⠀⢀⡀⠾⠇⠀⠀⠀⠒⠀⠀⢺⣿⣿⠿⠂⠀⠀⠀⠛⠃⠘⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠐⣷⣾⣾⣿⣿⠁⠀⠀⠆⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⡇⠀⠀⣿⣿⢹⣿⡟⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠸⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⡀⠄⠀⠘⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⣩⣭⢭⣭⣭⣭⣭⣉⣉⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⣷⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠽⠉⠓⠒⠒⣒⣻⠿⠿⠿⢿⣿⣗⣒⣶⠶⠦⠤⢾⣼⣥⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣤⣤⠤⠤⠤⣤⣤⣤⣀⣀⣀⡈⠉⠁⠒⠒⠲⠮⠭⢭⣙⣓⣒⣶⣤⣌⠉⣓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠞⣠⡏⠀⣠⣤⣤⣤⣄⣀⠉⠉⠉⠙⠛⠛⠶⠶⢦⣤⣄⣀⣀⠀⢀⣽⡟⢿⠙⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠚⠉⠀⠘⠓⠲⠶⠶⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡏⢿⢻⡏⠀⠃⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⣹⡇⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⢸⠀⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠂⠀⠤⣾⠛⢻⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠒⠒⢿⣀⣼⠧⣄⣀⣀⣀⠈⠉⠉⠁⠒⣾⠋⠙⣧⠤⠤⢀⣀⣸⡇⠀⡇⣼⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠻⣤⡼⠧⠤⠤⢄⣀⣸⡇⠀⡇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⠄⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⡇⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠤⠄⢼⡇⠈⣿⣀⠈⠁⠀⠐⠒⠀⠠⠤⢠⣴⢶⣄⣀⡀⠀⠀⠀⣿⠃⢸⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠷⠾⠋⠀⠀⠈⠉⠁⠀⠒⠀⠀⢼⡇⠀⣿⠄⣀⣈⠉⠀⣿⠀⢸⢰⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⢸⣿⠀⢸⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠤⡄⠀⠀⠀⢸⣿⠀⣼⢸⠁⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢝⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠉⣰⠃⠀⠀⠀⢸⡟⠀⡏⢸⠀⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣣⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣀⣸⡇⠀⡇⢸⠀⢸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⠛⢟⠛⣻⠟⠛⠒⠒⠶⠤⣤⣄⣀⡀⢀⡴⢋⡭⢼⡇⢠⠁⢸⠀⢈⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⢾⣀⣯⡉⣹⠗⠳⠦⢼⣄⣸⣀⣼⠶⢿⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⡶⣶⢶⢶⢶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⡶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⡔⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣤⡄⣤⢠⢄⡠⣄⣤⣠⣄⣤⡄⣤⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡿⢻⣿⣈⣢⣙⣾⡟⢻⣾⡗⡇⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠠⡤⠚⡏⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡰⣃⠀⠀⣠⠊⠀⠀⢈⠿⠷⠈⢣⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢰⡷⠛⢄⡸⣅⣀⠀⠀⠘⡄⠀⠀⠀⢃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⢜⠀⠀⠓⢢⠀⠈⠉⡆⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠘⡿⡀⠀⠈⢦⠀⡰⠋⠀⠀⢸⠀⢀⠎⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠘⢗⢄⡀⠘⣴⠁⠀⠀⠀⣳⣿⠎⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠫⢶⣶⣀⣴⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢒⣲⣒⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⣿⣍⢏⠷⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠬⠽⠭⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⢀⠤⣤⢖⣑⠦⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣴⠄⠠⠖⡶⠶⠶⠶⠦⣴⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⣷⡄
⠀⠀⠀⠛⠒⠁⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⣅⣀⣮⠇⠀⠀⠸⣇⣀⣀⡀⣀⣿⠇⠀⠀⡴⠋⢉⠓⢦⠔⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡤⠒⠈⢰⠂⢄⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠙⠿⠿⠤⠟⠀⠀⠘⠖⢺⡇⢺⡠⠀⠈⢸⠀⠀⠀⡀⠐⠠⠆⢀⠤⣠
⠀⠀⠀⠀⠀⠾⣤⣐⡴⠧⢀⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⣇⡼⠧⢄⣁⣀⡶⠟⠀⠀⠨⠗⣟⠀⣶⢤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⣈⠗⢶⡎⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡚⠛⡳⢾⡆⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠠⡀⠙⠲⣼⡇⢀⠊⠀⠀⠀⠤⠤⣄⣀⠀⠀⢀⡞⠁⢰⣶⠈⠺⡅⠀⠀⠀⠀⠀⢠⣤⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠁⢀⣀⠤⠚⡁⠀⠀⠨⠃⠀⡸⡄⠀⠀⢀⠀⢸⡇⠀⠀⢀⠠⢴⡏⡈⢁⣦⠬⡑⠲⣦⡀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠒⠁⠁⢄⡐⠁⠀⠀⠃⡷⠀⠠⠀⢸⢚⠀⠀⢠⣅⠴⠋⠐⠀⢘⣧⣀⠝⠈⠋⠀⠀⠀⠀⠘⠇⢃⡟
⠀⠀⠀⡤⠶⣤⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠈⠀⠀⠀⠀⠑⠀⠀⠀⠐⠊⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⡇⠀⡏⠀⠄⠂⠐⠂⠤⡄⠀⠀⠔⠒⠂⢤⡀⠀⠀⠀⢀⠤⡄⠀⠀⠀⢀⣤⡀⠀⡤⢤⠀⠀⢀⠤⠤⢤⠀⠀⠀⠀⡤⢤
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡖⠈⠀⠀⠀⠀⢊⠀⡄⡑⠀⠀⠀⠀⣴⠰⡀⠀⠀⠘⡀⢳⡀⠀⡎⠀⠀⠸⠐⡆⠉⠀⠀⠀⠀⠀⢸⠀⠀⠴⠶⠶⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⠀⢰⠁⠀⠀⠀⠀⡙⡀⢃⠀⠀⠀⠐⠀⠃⢸⠃⠀⠀⠀⠈⡉⠵⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡈⠁⡀⢃⠀⠀⢀⠸⠁⠡⣘⠆⠀⠀⠀⢂⢀⡇⠀⠀⠀⠀⠠⠇⢤⠀⠀⠀⠀⡀⠘⠃⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠽⣆⠈⠁⠀⠈⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢆⠲⢸⠂⠀⠀⠀⠰⡏⠉⣹⣦⣤⡔⠀⠀⠀⠀⠀⠀⠉⢉⣢⡀⠀⠀⠀⠀⠀⢠⠉⠃⠒⠂⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⢋⡁⣀⡘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢛⡈⣡⣼⠩⠶⠀⠀⠀⠰⣤⣤⣀⡤⠛⢃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⠀⠀⠀⠀⠀⢠⠰⢖⡄⠀⠀⠀⠘⠂⠐⠚⠀⠀⠀⠀⠀⠀⠀⠑⠐⠛⠃⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠉⠻⠆
⠀⠀⠀⠀⠀⠀⠙⠛⣁⠀⠀⠀⠀⠀⠀⢾⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠯⠷⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⡐⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠤⠀⡀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⢀⡉⠉⠀⠀⠀⠀⠀⣄⣾⣿⠟⢉⣗⠀⠀⠀⠀⠀⠄⠁⠀⠀⠠⡀⠂⡀⠀⠀⠀⠀⠈⡠⢔⠁
⠀⠀⠀⠀⠀⡤⠦⣧⠀⠀⠀⠀⡄⠀⠈⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⠃⠀⠀⣀⣀⠀⢀⠀⠀⠀⠈⢱⣄⠘⠂⠀⠀⠀⠈⠁⠀⠃
⠀⠀⠀⠠⢬⡅⠀⡟⠀⠀⠀⠀⣵⡟⠛⠛⢿⡆⠃⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨⣿⣿⠄⣀⡴⣦⡀⠀⠀⠉⠂⠨
⠀⠀⢰⡎⠘⢯⠉⠀⠀⠀⠀⠀⣿⡦⠀⠊⢸⣧⣠⠀⠀⠀⢀⠀⠀⠐⡄⢨⠄⠀⠀⠀⡇⢸⠀⠀⠨⠗⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣰⣀⣠
⠀⠀⠀⠑⠄⠘⠀⠀⠀⠀⠀⠀⠘⠃⠓⠒⠟⠉⠉⠀⠀⠀⠘⡆⠀⠠⠥⠘⠃⠀⠀⠀⢹⣽⡗⢰⣛⣦⠂⠀⠀⠀⠀⠀⣴⣰⣂⣴⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠤⣄⠀⢠⣆⠀⢠⡖⠦⠀⡴⠶⠀⡖⠒⣦⢠⠖⢲⡀⡟⠙⣦⠘⠛⡟⠛⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⢈⡇⣸⠙⡆⠀⠳⢦⡀⠙⢦⡀⣧⠤⠞⡏⠀⠀⡇⣧⡤⠟⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠛⠋⠀⡟⠉⢻⡀⣀⣠⠇⢠⣠⠇⡇⠀⠀⠳⣄⡼⠃⡟⢣⡀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢒⡶⢶⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯⣄⣀⡞⠀⠀⢳⡀⢈⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣽⠉⠉⠉⠉⣏⠉⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⢻⡟⠒⠲⠶⠦⣿⠤⠤⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⣇⣀⣀⡀⢀⡟⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡋⠉⢯⠉⠉⠉⣹⠓⢦⣄⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⢧⣤⣴⣧⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⡇

⠀⠀⠀⠀⠀⠀⣤⠄⣀⣀⣀⣀⡀⣀⠀⣠⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⠛⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⢸⠀⣿⢦⡾⣇⠀⣧⢀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡆⢹⠀⠀⢻⡆⣿⠉
⠀⠀⠀⠀⠀⠐⠛⠗⠀⠀⠉⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠘⠃⠀⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠕⠈⠉⠉⠓⢌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡤⠤⡤⠤⡮⠀⠀⠀⠠⠀⠬⣮⣇⣤⡤⢄⡠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⠔⠁⢀⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣆⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢮⠥⡽⠀⠀⠀⠀⠀⠀⠀⠀⠮⡅⡽⠂⠈⠢⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⣄⢾⣼⡷⠀⠀⠀⠀⠀⠀⠀⠰⣞⣐⡳⠀⠠⠔⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⡎⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⡰⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛⠛⠒⠒⠒⠂⠀⠀⠀⠐⠓⠓⠒⠓⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⣿⠙⢱⡎⢹⡆⠀⠀⠀⠀⠐⠒⡶⠒⠂⢶⢲⠀⠀⢀⣶⡀⢰⡀⢰⡇⢺⠉⠀⣴
⠀⠀⠀⠀⠀⠀⢿⠀⠸⣇⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⣄⠀⢼⠗⢷⠀⢳⣼⠁⢸⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠈⠀⠛⠀⠈⠀⠀⠋⠀⠘⠋⠁⠉⠛⠁

⠀⠀⠀⢀⣠⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⣀
⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢸⢀⣀⣀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠣⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⢂
⠀⠀⠀⠋⠉⠙⠉⠉⠁⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣴⣿⣶⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠛⡋⠀⢘⡄⠀⣤⢄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⡡⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⣷⠀⠀⢀⣀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠊
⠀⠀⠀⡀⠀⠀⠀⠀⠠⣿⠀⠀⡇⠀⠀⡀⠀⠀⠀⣄⠀⠀⠐
⠀⠁⠊⠀⠀⠀⠀⠀⢸⡟⠀⠀⣷⠦⠶⢂⣄⣁⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠂⠀⢰⢀
⠀⠀⠀⠒⠀⠀⠀⠐⠃⠀⠀⠀⠈⠉⠛⠛⠛⠓⠚⠁⠀⠐⠛⠙⠋⠀⠀⠙⠙⠋⠂⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠄⢤⠤⢴⠶⡶⠄⠼⢰⠆⠐⠚⠛⠛⠛⠧⠇
⠀⠀⠁⠀⠀⠀⣀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀
⠀⠈⠉⠀⠀⠀⠀⠉⠙⠊⠀⠀⠀⠀⠀⠐⠒⠶⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⢀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠂⠀⠀⠀⠄⠈⠀⠀⠀⠀⠠⠀⣀⠀⠀⠸⠁⡇
⠀⠀⠀⠀⠀⠉⠉⡏⠉⣆⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣀⣀⣁⣉⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠳⣆⢤⣠⠤⢔⢂⣰⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠠⠀⡀⢀⠠⣄⣠⣤⣿⡚⡟⢁⡰⡎⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡡⠒⠉⢈⠹⠎⠉⠀⠀⠙⢾⣥⣹⡀
⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢢⣴⠒⠒⠿⠋⠑⠄⠂⠙⣿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠤⠄⢢⡀⠇⠀⡰⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠉⡆
⠀⠀⠀⡀⢠⠔⠚⠒⠒⠒⠒⠻⠟⠀⠘⠷⠯⠤⢒⠷⢾⣶⣦⠢⣑⡀⠀⠴⠀⠐⠄⠀⠀⠈⣴⡠
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠄⠀⢈⠏⠀⠀⠀⠀⠀⠐⣄⠀⡔⠜⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢸⡄⠀⠀⠐⠒⠖⠙⠐⡥⠤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢸⠄⠀⠀⠀⠀⠀⠀⢆⠸⡐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠸⠀⡀⢀⢀⠀⢀⠠⢸⢐⠌
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣷⠶⠤⠤⠬⠠⠄⣊⡜⠋
⠀⠀⠀⠿⠦⢤⠤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢀⢒⠂⢄⣔⣵⣷⣭⠨⠤⠴⠚⠉⠀⣀⣠⡠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠃⠒⠒⠻⠚⠛⠋⠋⠁⠀⠠⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⠉⠉⠉⠁⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡠⠤⠄⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠄⢀⣀⡀⠀⢰⣄
⠀⠀⠀⠀⠀⡜⠀⢸⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣬⠀⠳
⠀⠀⠀⠀⠀⢡⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡔
⠀⠀⠀⠀⠀⠀⠟⠋⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣤⢀⣀⡀⢤⠒⠉⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⡇⠀⠀⠀⢸⠉⠉⠲⣄⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡆⠀⠀⠑⣄⠀⣠⠎⠀⠀⠀⡏⢢⠀⢨
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠑⣤
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⣌⠀⠀⣠⠞⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⢦⡀⢀⠱⡄
⠀⠀⠀⠀⠀⡄⠉⡟⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠹⡄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠐⡀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠱⡀⢡
⠀⠤⢀⡀⢠⠂⠘⢢⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⢠⡞⠁⠈⢢
⢰⣄⠀⠘⣷⠀⠀⠀⡿⢶⠚⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣾⣾⣅⠀⢀⣬⡀
⢸⣿⣿⣾⠁⣷⣶⣎⡀⠙⠀⠀⣀⢀⡀⣠⣀⣄⣀⣀⠀⢀⣬⣀⣀⣾⣟⣁⣈⣁⣉⣹⣿⣄⠀⠀⠀⠀⣀⣀⣀
⢈⠀⠉⠓⠸⠿⠿⢿⠇⠀⠀⠀⡧⠤⢤⡬⣷⣤⡤⠤⠤⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠐⣿⣿⣿
⣼⣿⣷⡎⢠⣤⣤⣤⢰⡇⠀⠀⡇⠀⢰⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⣼⠋⠀⠈⠻⣆⠀⠀⠙⢿⣿
⠧⣉⠛⠃⠸⠿⠿⠿⠀⠀⠀⢀⠀⠀⢸⠀⠨⠀⡇⠀⠀⠀⠠⣞⠉⣀⡿⠆⠀⠀⢻⣄⠀⢀⣰⠏
⠀⠀⠉⠁⠒⠒⠒⠒⠚⠒⠂⠙⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇⠀⠙⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢠⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⣸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⢽⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠘⠿⡇⠀⣧⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠚⠂⠚⣄⠀⢠⠓⠐⠛⠐⠒⠠⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣶⣦⣶⣶⣦⣤⣬⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⠠⠒⠙⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠙⠀⡀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠅⢠⠂⠀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠄⠀⡄⠄⠀⠀⠈⠡
⠀⠀⠈⠉⠁⠀⠀⢠⠄⠐⠀⠐⠐⠧⠀⠀⠉⠢⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠅⠉⠒⢤⡀⠀⠀⠀⠀⠀⡀⡀⠀⠃⠁⠀⠀⠀⠀⠈⠁⣀⠀⠀⠃
⠀⠀⠀⣤⠀⠀⠀⠀⠑⢄⠀⠀⢠⠠⠤⠄⡝⢂⠈⡆⡠⡀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠢⡀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⠠⣀⠀⢀⡤⢋⡴⠋⣦⣀⠔⠉⠀⠉⠐⠢⠤⢀⢀⡀⠀⠈⠆⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠆⠰⠥⠐⡚⢡⠏⣠⠎⡔⠁⠀⠊⠉⠑⡀⠀⠀⣰⣏⡿⠢⣀⢰⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⢹⣁⡏⣰⢃⠎⠀⠀⠀⠢⠠⠰⠁⢠⣾⡽⠋⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠘⡀
⠀⠈⠀⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠃⢀⢔⡶⢢⢄⠀⠀⣰⣧⠝⠁⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⢡⠀⠀⠀⠀⡄⠀⠀⠀⠄
⠀⠀⠀⢀⢀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⢃⡞⡰⢃⠊⠀⣴⣭⠋⠀⢀⣠⣴⣲⣶⣶⣢⣤⡀⠀⠈⠢⡀⠀⠀⠀⠈⡅⢀⠒⠂⠀⠈⠀⠍⣈⠂⠑
⠀⠀⠀⠑⠂⠀⠀⠀⠀⠐⠒⠠⣀⠀⠀⠀⠀⠀⠎⠀⡄⡞⣰⢃⠂⠀⣸⣛⠋⢀⣴⡿⠊⣉⠀⠀⠠⢉⠙⢾⣷⡀⠀⠈⠲⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⣀⠠⠐⠂⠀⠁⠐⡒⢄⡛⢹⠃⣦⢴⠀⠀⠴⣇⡏⡈⠀⢰⠛⡏⠀⣾⡎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠹⣾⡄⠀⠀⠘⢄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⣁⠀⠀⠀⠰⢂⠉⠉⠁⠀⠃⡏⢠⠇⡄⠀⠀⠀⠀⠈⠀⠀⡾⡿⠀⢰⣼⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠑⠢⢤⣀⠀⢈⣹⡡⠸⠀⡇⢸⠀⠁⠀⠀⡀⡀⠀⠀⢰⣷⡆⠀⠘⣻⡀⠰⡀⠀⠚⠀⠘⠃⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠤⠚⠧⠧⠘⠺⠀⠀⠊⠀⠈⠀⠀⢸⣬⠁⠀⠀⠹⢷⡀⠀⠀⠀⠀⠀⠂⠀⢉⢾⡟⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠀⠒⠀⠀⢸⣹⠀⠀⠀⠀⠈⠻⢳⣦⣤⢤⣤⣤⣺⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜
⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠺⣾⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠈
⢈⠁⡐⠂⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋⠉⠉⠀⠀⠀⠀⠀⠈⢉⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠁⠀⠀⠀⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠣⠄⣀⡀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠔⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⢀⠭⠤⠤⡄⠒⠒⠂⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠃⠠⠀⠂⠒⠺⠈⠈⡀⠥⠤⠤⠄⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠒⢲⠀⠀⠀⣀⠀⠀⢘⣉⣙⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠂⠒⠂⠀⠈⠉⠉⠉⠉⠭⢭⣤⡤⢀⠀⣀⠠⠬⣉⣁⡒⠤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠊⠁⢲⢡⠨⠭⠋⠑⠒⠄⠀⠏⠠⢊⠄⠀⠠⣔⠅⠂⠐⡔⠆⢠⡔⠒⠤⠄⠈⠑⡌⢢
⠀⠀⠀⠀⠀⠈⠉⠆⣗⠀⠔⠁⢉⢰⠖⡜⠀⡄⡡⠔⠀⠒⠼⠤⠶⢦⡧⠼⠀⣃⠄⠂⠁⠐⠈⠘⡀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣼⣅⠹⡁⡠⡇⠠⡌⠀⠐⠆⢚⠔⠀⠀⢀⡗⢚⡄⠁⠀⠋⠰⣢⠊⠄⣦⠴⢤⡄
⠀⠀⠀⠀⠀⢀⠸⠀⠒⠸⠡⠤⠤⢎⣌⡇⠀⡏⣲⠊⠀⠈⠐⠦⠀⠀⠈⡄⡇⣈⣀⣔⡊⢐⡖⢒⣩⠐⠀⠓⠒⠀⠈⠁⢢
⠀⠀⡀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠛⡔⠀⠄⠐⠒⠈⠉⠨⢅⠈⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠸⠉⡩⡉⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠑⠒⠊⠀⢠⠀⠀⠀⠀⠀⢀⠠⢖⣒⠠⢄⠀⠀⠀⠀⡇
⠀⠀⢣⣊⣱⠰⠀⠀⠀⠐⡪⠑⣼⠀⠀⠀⠀⠀⡠⣶⠶⠓⠚⠶⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠊⠉⠀⠉⠲⡐⣄⠤⠠⠄⡀
⠀⠀⠈⡀⠁⠐⠀⠀⠀⠀⠁⠝⢸⠀⠀⠀⠀⢎⡞⠁⠀⢀⣀⠀⠀⠱⣵⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠊⠙⡆⠀⢡⡇⠀⠀⠀⠄
⠀⠀⠰⠉⠉⠁⠒⠀⠤⠄⠀⣀⠀⠧⠄⠀⢸⣸⠀⠀⠎⠀⠀⠃⠀⠀⡇⣃⣀⣀⣄⣀⠀⠤⣿⠀⠘⠦⠴⠃⠀⡼⠳⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠐⠒⠈⠀⠀⣰⡟⠀⠀⣀⣀⣀⠀⠠⠴⠓⢄⣀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠒⠃⠠⠤⠄⠒⠈⠁⠑⠤⣄⣀⣀⡠⠔⠁⠉

⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⠴⠖⠒⠦⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣁⣠⠤⠦⠤⣤⣀⣙⡆⠪⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⢔⢄⣠⣤⣴⡶⡟⣷⠾⣛⣽⡿⠶⢖⣿⣷⠲⠶⢶⣶⣾⣿⣬⡶⠮⣁⣾⣶⠶⠶⠴⠶⡶⢦⡀⢠
⠀⠀⠀⠀⠀⡁⣿⣀⠀⡠⠜⠉⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢰⠏⠁⢂⠀⠈⠉⢐⣐⠀⣷⢀
⠀⠀⠀⠀⠀⠀⣗⢠⠋⠀⠀⢐⣀⣘⡃⠀⠀⠡⣈⠁⠀⠀⠀⠀⠀⠀⠀⣂⣀⣘⡇⠀⠀⠑⢄⠊⠈⣿⠐⡏⢸
⠀⠀⠀⠀⠀⠃⣼⠁⠀⠀⠀⠈⠀⢸⡇⠀⠀⠂⠀⠀⢊⠀⠀⠀⠀⠀⠠⠁⠀⡸⠄⠀⠀⠀⠀⣑⠰⠹⠀⣿⢸
⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢱⠈⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡆⡇⠀⠈⠶⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⢑⡀⢀⠀⢤⠂⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡂⢻⠄⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠂⠀⠈⠑⠲⠆⠀⠀⢀⡇⢸
⠀⠀⠀⠀⠀⡃⣧⠀⠢⡀⠐⠃⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⢀⠀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠈⣷⢸
⠀⠀⠀⠀⠀⠃⢿⣐⣡⣈⣦⣤⣄⣀⣧⣀⡀⠀⠀⠀⠀⠀⠚⠃⠈⠁⠀⢸⠀⠀⠆⠀⠀⠀⠀⢀⠀⣹⣤⡟⢸
⠀⠀⠀⠀⠀⠠⠲⠠⠄⠘⠐⠀⠉⠘⠅⠐⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠺⠦⠴⠗⠒⠶⣤⣤⣥⡼⠋⠁⠖⢸
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠀⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⢀⣴⡆⣀⡐⣞⣇⣀⡀⣠⣤⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢆
⠄⠀⠉⠉⠤⠋⠖⠘⠚⠙⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⣀⡀⡀⣄⠉⠠⠠⠀⢀⣀⣤⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠠⠤⠀⢀⠀⠀⣈⠉⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣀⡀⠀⠀⢀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡑⠀⠀⠀⠁⠀⠀⠈⠈⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢹⡐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡪⡟⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄
⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠄⠤⠂⠂⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠀⢀⣀⡀⠀⠈⠛
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠉⠁⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠁⠀⠀⢠⡎⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣤⠀⠀⠀⢠⠀⢶⠴⣶⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⠂⠀⠀⡇⠠⢤⣄⣀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠦⠴⠶⠾⠶⠦⠀⠚⠓⠚⠛⠛⠋⠉⠁⠀⠀⠧⠤⣄⣀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣔⣒⣓⡖⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣉⢀⠉⠁⠐⠒⠀⠀⠀⠠⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠁⠀⠀⠠⠁⠀⠀⡈⠒⠀⠀⠀⠁⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠒⠒⠀⠒⠂⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿