Whiny Emojis & Symbols

⠀⠀⠀⣠⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠒⠂⠀⢀⠖⡂⠀⠀⠀⠀⠀⠀⠈⣈⢢⠀⢠⢂⡀
⠀⠀⠀⠀⢈⠁⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⠠⣈⡜⠀⠸⣈⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠤⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⣀⡄⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠂
⠀⠀⠀⠠⡴⡄⠀⡔⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠈⠀⠀⠠⢘⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢄⡀
⠀⠀⠀⠐⠊⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠐⡊⠒⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠤⠄⠀⠀⠠⠤⠆⠀⠀⠀⠀⠀⠀⠐⡂⠄⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠀⠀⠀⢁⠈⡆⠀⠀⠀⠀⠀⠀⠙⡀⠁⠀⡶⡀
⠀⠀⠀⠠⡠⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠄⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⠄⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⡀⡀⠄
⠀⠀⠀⢀⡀⠄⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠈⠠⢱⠀⠀⠀⠀⠀⠀⠀⡦⣤⠁⠀⢠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠀⢀
⠀⠀⠀⠠⢠⠆⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠁⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠐⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⠄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠒⠒⣒⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢚⣯⠴⠚⠉⠀⠀⠀⠀⠠⠞⠒⠒⠒⠒⠂⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠠⢤⣀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠂⠉⠀⠀⢀⡴⠢⢄⣀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠰⠀⠀⠀⢀⠎⠀⠀⠀⠀⠉⠩⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⠠⠮⣀⠀⠀⠀⠠⠃⠀⠁⠀⠙⢦⠀⣤⠀⠀⠀⠀⡇⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⡥⠀⠀⠀⠀⠀⠀⠨⡷⠀⠀⠀⠀⠀⠀⠀⢀⣄⢻⢾⡇⠀⠀⢠⢣⠋⠙⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣌⢀⡀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠐⡀⠀⠀⠈⠁⣼⡀⠀⣀⠴⠃⠀⢀⠴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⢧⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠂⠤⠄⡺⠋⠀⠉⠀⠒⠉⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠔⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠉⠀⠀⢀⣠⣀⠀⠀⢠⣂⡧⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠈⣩⠔⠋⠀⠀⠉⠑⠚⠓⠶⠶⠶⠶⠶⢀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣀⠼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠧⣀⡋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠠⠒⠋⢧⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠑⠂⠁⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⢰⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢄⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠃⠘⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠑⠒⠒⠒⢲⠒⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢻⠁⢰⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⡀⣤⣤⠞⠒⣾⣧⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠲⠶⠞⠿⠻⠿⠛⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡤⠤⠖⠒⠛⠉⣉⠽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⣽⠴⠚⠉⠁⠀⠀⠀⠀⠀⠚⠓⠒⠒⠒⠒⠒⢲⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠠⣄⡉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⠀⢢⣄⡀⠉⠁⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⣶⠀⠀⠀⠀⡰⠋⠀⠉⠙⠒⠲⡤⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢰⠇⢀⠧⠤⢴⡁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠃⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠋⠀⡜⠀⠀⠀⠙⣦⡒⣆⠀⠀⠀⢠⠀⣠⢄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢛⡖⠀⠀⠀⠀⠀⠀⠀⠐⢞⠃⠀⠀⢀⡜⠀⠀⠀⢠⣶⢸⠻⠟⠀⠀⢀⡞⡜⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠳⣀⠀⠀⠀⠀⣼⢤⣀⣠⠴⠋⡀⠁⠤⠞⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣄⠀⠀⠀⠀⣀⣀⣀⣸⡀⠀⠀⠀⠈⠓⠒⣒⡿⠋⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠞⢉⡡⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠋⠙⠛⠉⢀⣀⣄⠀⠀⠀⣰⢚⡯⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⢚⡭⠟⠉⠀⠉⠑⠒⠺⠥⠤⠤⠤⠤⠤⣖⡒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⠀⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣀⠀⡖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣈⠥⠶⣣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠦⡴⠳⠬⢁⠃⠎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢧⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢼⢀⣇⣸⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠦⠵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⡠⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⢀⣇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⣹⠀⢀⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠤⠤⠤⢤⣤⡶⢏⠙⣻⣵⣤⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠛⠶⠯⠝⠻⠏⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣗⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁



⣿⣿⠟⠿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⣂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢩⠯⠒⠉⠁⠀⠀⠀⠀⠚⠒⠒⠒⠒⢒⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠈⠓⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠠⠊⠀⠉⠑⠒⠆⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⢠⡊⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣀⠀⠀⠀⢘⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⢴⡉⠀⠀⠀⠀⠀⠈⣵⠄⠀⠀⠀⠀⠀⠀⣀⢱⣿⡇⠀⠀⢰⠰⠋⢦⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⢸⣀⠀⣀⠔⡁⠁⡀⠞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢧⠀⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠐⠆⠀⠉⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠤⢀⣀⣮⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠰⣏⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⡆⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠓⣊⣭⣆⡀⠀⠀⠀⠀⠀⠀⠀⡦⣄⠈⢍⡒⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡸⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠒⠒⠀⠠⡔⠶⠒⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠓⡖⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⢠⣤⡴⠓⢲⣣⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠟⠛⠛⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠙⠳⣄⣀⣠⣤⠶⠶⠶⠶⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⢰⡶⠲⠶⢤⣀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠸⣷⣤⡴⠶⠋⠁⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⢶⡄⣼⡇⠀⠀⠀⠀⠀⣼⣦
⣠⡴⠶⢶⣶⠂⠀⠀⠀⠀⣀⣠⣤⣤⣿⠁⠉⠙⠳⣦⣀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣴⢷⣿⠀⠀⠀⠀⠀⠀⢿⡟
⠻⣤⣤⠞⠁⠀⣀⣴⠾⠛⠋⠉⠀⠀⣿⠀⠀⠀⠀⠀⠙⠳⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⠷⠞⠛⠛⠛⠶⣦⡀⠀⠘
⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⠀⠀⠀⣀⣰⣿⣷⠄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⠙⠛⠛⠋⣹⡿⣿⡛⠃⠀⠀⠀⠀⢀⣾⣏
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢹⡇⠙⠿⣶⣦⣤⣴⣾⣿⠋⠹⣦
⠀⢰⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⢈⣿⡄⠀⠀⠈⠣⠀⠀⠀⠀⢀⡼⠋⣽⠀⠀⠘⣧
⠀⢸⡇⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⡾⠟⠀⠀⣰⢷⡀⠀⠀⠀⣠⡟⠁⢠⡟⠀⠀⠀⠘⣇
⠀⠀⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠀⠀⣼⠏⠀⢠⡿⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⢀⣾⠋⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢠⡾⠃⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣼⠃
⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢠⡄⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠀⠈⣿⡀⠀⠀⢸⣠⡴⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⡟⠹⡆⠀⠀⠉⠛⠒⠶⠶⠛⠛⠉
⠀⠀⠀⠀⠹⣧⠀⠀⢸⣧⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠘⢧⣠⠏
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⣠⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢰⠏⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⢠⣿⣤⣤⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡀⠀⣀⡿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠈⠳⠶⣦⣀⣙⣻⠏⠀⠀⣠⣿⠛⢦⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠈⣽⣷⣦⣤⣄⣀⣀⣀⣀⡭⠉⠁⠀⣴⠟⠁⠈⠳⣤⡉⠛⠶⢦⣤⣤⡤⢤⣄
⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠛⠒⠿⠄⠉⢻⣯⣭⡭⣭⣿⣇⠀⠀⠀⢻⣄⡀⠀⠀⠈⠻⢦⣄⣀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⢿⣄⣀⡶⠋⠁⢀⣀⠀⠀⠀⣰⠏⢁⡀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⠴⣿⣤⣀⣤⣤⡿⣤⣿⣀⣠⡖⠋⠁⠀⠀⠀⠀⣀⣠⡼⠃

⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠀⢤⠀⠀⠀⠠⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠆⠐⠲⠃⠐⠂⠤⡀
⠀⡄⠀⠠⠄⠀⠀⠀⠀⡄⠁⢠⡀⠀⠀⠀⢁⠀⠍⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡄⠊⠀⠈⡁⠀⠀⠠⠀⠀⠸⠀⠀⠀⠈⠁⠀⠂⠘⠀⠀⠀⠀⠀⠰⠀⠀⠠⠁⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠
⠀⠃⠀⠀⠀⠂⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠁⠈⢀⡂⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠁⠈⠠⠀⠌
⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠈⢀⠔⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⡇⠀⠀⠆⠆⢀⠔⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡠⢀⠀⠀⠡⣤⠀⣤⠅⠀⠀⡄⡀
⠀⠠⠈⠂⠀⠉⠀⠀⠁⠀⠊⡄⠀⠀⠀⠐⢘⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠢⡀⠠⠤⠔⠟⠀⠐⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠈⠐⠄⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⡀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠨⠄⠀⠀⡀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⡂⠀⠀⡀
⠀⠀⠀⠀⢁⡁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠠⢀⠀⠁⠀⠀⠀⠀⠁⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⢀⠀⠀⠀⠀⣈⠁⠀⠌
⠀⠀⠀⠢⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⣀⡀⠠⠊
⣀⣀⣀⣀⣀⣁⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢲⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠶⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⣤⣤⣀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢈⣉⠛⡀⠘⢛⣩⣀⣂⣤⣅⣀⣡⡀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠘⢿⣿⣿⣿⣿⣿⠟⠁⠈⣾⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⣠⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⢀⣘⣀⣃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣠⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠄⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠠⡐⣷⡄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⢼⡟
⠀⠀⠀⠀⠀⠈⠁⠀⠘⢰⡟⠿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁




⡥⢶⠶⡦⢶⠀⠲⠶⢺⢷⣸⣰⢦⣇⡶⣦⣾⡀⠀⡶⡖⠶⡲⢶⠲⡖⠐⡶⠖⢿⡲⡦⢶⠂⢸⢰⡲⣴⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠛⠟⠿⠳⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣼⢤⣤⣶⠲⢶⠦⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣻⣀⠀⣿⣀⡠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⢿⠁⣀⡤⠤⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣾⡧⠀⣀⣀⣤⣀⣔⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣏⠻⡾⢽⠋⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁⠐⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣆⢀
⠀⠀⠀⠀⢸⣿⣿⣷⢟⡿⣿⣿⣿⡟⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠻⡄
⠀⠀⠀⠀⢸⣿⣿⣟⡠⡿⣷⣿⣿⠿⠖⠂⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⣀⠘⢮⣶⡆
⠀⠀⠀⠀⢸⣿⡿⣍⠃⠀⠀⢿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢸⣿⡇⠈⠁⠈⣿⣷
⠀⠀⠀⠀⢸⠲⠛⠳⠿⡳⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣘⠒⠶⠤⡀⠐⣿⠿⣁⣀⣀⠀⠀⠹⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠐⣤⣤⡿⣯⣍⡀⢢⠾⢠⣬⠀⠀⢘⡶⣬⣁⠒⠐⡤⢺⡆⠈⠉⠀⠃⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣰⠁⠀⠀⠁⠐⠀⢄⠀⠶⣤⣽⠳⢭⣤⣶⣡⠞⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡀⠀⠀⠀⢀⡙⢌⣤⠀⠀⠈⠐⠀⠻⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠂⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠉⠭⢭⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⣨⠑⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣰⣸⠋⠓⠃⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⣠⢧⠤⢄⡀⢠⢒⣈⣉⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⢘⠆⠀⠀⠀⢸⠁⠸⡄⠀⣨⠿⡋⢀⣠⣃⡤⠔⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠠⢾⡇⠀⠙⠮⣀⠀⢹⠉⠿⢅⣤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡔⣂⣓⠀⠀⠀⠀⠉⠉⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⡎⡇⢠⢈⡁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡿⣤⢰⡀⣀⠉⠉⠉⡰⠁⢀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠳⡝⢿⣲⡯⠖⠁⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢹⢦⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⣀⡀⢀⡴⠋⢀⠔⠀⣮⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⡯⡤⣰⠧⣀⠀⢡⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⣲⣾⣾⡗⠀⢠⠟⣶⣾⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⡇⠨⠩⠿⢒⣦⠎⡘⠅⢻⢧⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢶⠒⣏⡁⠰⣏⡉⢀⡾⢶⢧⠆⠈⢣⠳⢇⢱⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡾⢓⢋⢭⣅⢀⣷⣾⢷⣬⣭⣭⠭⠞⠀⠀⠸⡤⢾⠺⣌⠆
⠀⠀⠀⠀⠄⡴⡱⢃⣐⠻⣣⣿⣿⣿⠟⠁⢠⣾⡟⠁⠀⠀⠀⠀⠀⠘⠦⠓⠃
⠀⠀⠀⠀⢰⣱⠁⠀⡠⠓⠃⠀⠉⡁⣀⢰⣿⡟
⠀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⢠⡔⠻⠥⠾⣿⠿⡯⠑⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠩⠭⠤⠖⠒⠷⠾⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀⡀⡀
⠀⠀⠐⣀⠀⣠⠀⢸⢹⡇⠀⣿⢸⡇⣿⡄⠀⣿⢰⣶⣦⡄⣤⠑⠀⠀⠀⠀⠀⢀⡠⠚⠳⠟⣋⢉⠙⠂⡀
⠀⠀⠀⣿⠀⣿⠀⣿⢸⣧⣤⣿⢸⡇⣿⣷⠀⡇⢸⠀⠀⠀⡿⠀⢰⠀⠀⠀⢀⢨⠄⢰⠀⠐⠃⠚⠀⠀⠀⠠⡀
⠀⠀⠀⢸⣴⡿⣇⡇⢸⡏⠉⣿⢸⠃⡇⠸⣦⡇⣼⠛⠛⢠⡇⠀⠸⠀⠀⢀⡆⢸⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣿⠀⣿⠇⢸⡇⠀⡿⢸⠀⡇⠀⢿⡇⣿⣀⠀⠸⠃⠀⡄⠀⢠⠊⠁⠀⢳⠀⡇⠀⡐⣀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠟⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠛⠾⠀⡐⠀⠀⡎⠀⠀⠀⢨⣇⣧⡐⠊⠀⣨⡟⠒⠄⢄⣨⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⢸⡄⠀⡀⢠⡎⠻⣿⣡⠀⠰⣟⢼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠑⡀⣤⠏⠀⢸⣇⠱⠀⠀⠉⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⠀⠹⢌⠀⣠⠂⠈⠋⠀⠀⠀⠀⠛⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⠀⡠⠖⠋⠛⠶⡄⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠞⢉⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢠⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠼⠀⠀⠁⢀⣆⠀⣀⠀⠀⠀⠀⠀⢴⡒⣳⣄⠦⠀⠀⠀⠀⠀⠈⣳⣦⠀⠀⠀⢀⣀⣸⣥⣼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠛⠉⠛⠓⠖⠺⠿⠟⠛⠛⠋⠉

⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠃⠀⠀⢰⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⣩⣶⣿⢟⣻⣭⠿⢛⣛⣻⣿⣿⣛⣻⣿⣿⣿⣷⣶⣦⣬⣽⣿⣷⣶⣶⣶⡶⠿⣿⣿⡿⠋⢻⡆⠙⢦⡄⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡿⠋⣴⠟⢉⣴⠿⠛⠛⣉⣉⣉⣉⣛⣛⣛⣛⣉⣙⣛⣿⣿⣿⡿⠿⢛⣩⣴⡾⠛⠁⠀⠀⣼⣿⠀⠀⠹⣦⠹⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠀⣼⠃⣴⠏⢁⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⣉⣁⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⠹⣷⣹⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⠃⣾⠃⣴⣿⡿⠛⣁⣤⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠛⠋⠉⠘⣆⠀⠀⠀⠀⠀⠐⠛⠁⢸⣧⠀⠀⠀⢻⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣧⣼⠃⣼⣿⢏⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠈⠀⠀⠀⠀⣴⣢⣶⣿⠿⣿⡁⠀⠀⠸⣿⣾⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠏⠀⠀⠀⠀⠀⠀⢰⣿⠻⢏⣼⠞⢿⠀⠀⠀⠀⣿⡏⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣿⣿⣿⢸⡟⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⡿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠭⠜⠁⠀⢸⣇⠀⠀⠀⣿⣇⠸⡆⠻⣿⣿⣿⣿⣿⣿⣿
⠇⣿⡏⣿⢸⡇⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢿⡄⠀⠀⢹⣿⣦⣷⡀⠹⣿⣿⣿⣿⣿⣿
⣾⣿⢣⡟⣸⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⢿⣿⡟⣯⢉⣤⡹⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⣧⠀⣴⣸⠇⢻⣿⢷⡀⢻⣿⣿⣿⣿⣿
⢻⡟⣼⢃⡟⠀⠀⠀⠀⠀⠀⠀⠉⠹⢥⣄⠙⢪⡭⠵⠟⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣿⣶⡟⣿⠀⠀⢿⡞⣧⠸⣿⣿⣿⣿⣿
⠘⣿⢏⣾⠻⣦⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠈⡀⠀⣿⣿⡗⢿⣆⠀⢸⣧⢻⡀⣿⣿⣿⣿⣿
⡆⢹⣾⣷⡀⢹⡆⣠⡴⠖⠛⠉⠉⠁⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣿⠋⠀⠀⢹⣇⠈⣿⣼⡇⣿⣿⣿⣿⣿
⣷⠈⣇⢹⣇⣼⠟⠁⠀⢀⣀⣀⣠⣤⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠀⠰⠇⠀⢰⣿⠀⠀⠀⠀⣿⡀⣿⣿⡇⣿⣿⣿⣿⣿
⣿⠀⣿⡸⣫⢋⣀⡤⠖⠋⠉⠀⠀⠈⣷⡄⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢸⣇⣿⣿⠇⣿⣿⣿⣿⣿
⣿⠀⣸⢉⣿⠏⣵⠛⠛⠲⣤⣴⠟⠛⠛⠛⠶⠶⠦⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣺⠃⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⢠⣿⣿⣿⣿⣿
⣿⠀⣿⣾⣇⠀⠸⣆⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⣀⡤⢞⣡⣾⡟⢻⡄⣿⠀⠀⠀⢀⢠⣿⠏⣼⡇⣼⣿⣿⣿⣿⣿
⠇⢰⠋⠈⢿⣷⣄⣈⡿⠋⠀⠀⠀⣠⣶⣶⣶⣶⣶⠶⠶⠶⠀⠀⢹⡤⣤⣶⡾⠵⠞⠋⠉⠁⢀⣾⠃⣿⢀⣄⣖⡞⣿⡟⢰⣿⢁⣿⣿⣿⣿⣿⣿
⢠⣿⣆⠀⠀⠹⣿⡿⠁⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣇⠀⠉⠛⠻⠶⢶⡶⠾⠟⠁⠀⢸⣿⡿⣼⣽⣿⠁⣼⡟⠸⠟⠉⠀⠀⠉⠙
⡿⢿⣿⣦⡀⠀⢸⠃⠀⠀⣾⡿⠁⠀⠀⢀⣀⣤⡴⠾⠛⠁⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⣷⣿⠇⠀⣿⡇⢠⣴⡶⠶⣶⣄
⠃⠀⠙⢿⣿⣷⡏⠀⠀⣰⣿⠃⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠙⢻⣿⠀⠀⣿⡇⠸⠏⠀⠀⠈⣿⠆
⠀⠀⠀⠀⠙⢿⠹⠀⣰⢿⡇⠀⠀⣰⡏⠀⠀⢀⣤⣴⡶⠛⠁⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⣿⠀⠀⣿⣧⠀⠀⠀⠀⣰⠟⢠
⣶⣄⡀⠀⠀⢹⠶⢾⣧⣸⡇⠀⠀⣿⠃⠀⠀⣼⠑⢿⠀⠀⠀⠀⠀⠀⠀⣿⡟⡿⠛⠛⠛⢿⣿⡀⠀⠀⠀⠀⠘⣿⣆⠀⠘⢿⣷⣤⣀⣀⣠⡴⠋
⠛⢿⣿⣷⣦⡀⠀⠀⠙⢿⣇⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⡶⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⡀⠀⠙⢿⣦⣀⠀⠀⠀⠘⠿⣷⣤⣤⣍⣩⣭⡭⠖⣢⠄
⣷⣦⣈⠙⢿⣿⡄⠀⠀⢸⢻⢀⣾⠘⣇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡄⠀⠈⠉⠙⠃⠀⠀⠀⠀⠉⠉⠉⠉⣁⡴⢟⡥⢃
⠀⠉⠻⢷⣄⠙⣿⡄⢠⣤⣾⠋⠙⣷⣿⠦⣀⡏⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠴⢞⣛⡭⠖⣫⡴⠋
⠀⠀⠀⠀⠙⣧⠘⣿⡌⢿⣿⣷⡀⠈⣿⠐⠏⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠃⠁⠀⠀⠀⠉⠉⠩⠭⠭⢷⣖⣒⣫⣭⠵⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⢠⠔⠢⣄⣲⣶⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠉⠉⠈⠑⢿⡌⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠻⣼⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢠⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡤⠦⣼⠀⠉⠀⠀⢠⠞⠁⠈⢳⠀⠀⠀⠀⢠⠤⢤⠱⠏⣽⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⢠⠶⡌⠀⠀⠀⠀⡏⠀⢰⣯⣿⠀⠀⠀⢰⠃⢀⣀⡇⢸⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡈⢦⡇⠀⠀⠀⠀⠉⡉⠛⠛⠃⠀⠀⠀⠸⠤⣼⣾⠃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⢦⠁⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡀⠀⢀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡞⡇⠀⠀⠀⣤⠶⠶⣖⣲⣄⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣇⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠔⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠺⡅⠀⠸⡌⠉⠙⠒⠒⠒⠒⠒⢲⠻⣅⠀⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠒⠦⣀⠱⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⢸⠀⢸⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡝⢆⠀⠘⠦⣀⠀⠀⠀⢀⠞⠀⢸⠃⢧⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠑⢦⣀⠈⠙⠒⠚⠁⢀⡠⠋⠀⠘⡆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣈⣉⣓⣒⣒⣋⣉⣀⣀⣀⣀⣇⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⡀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢳
⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠁⢉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⡆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢈⣿⣿⣿⠧⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⡿⢰⣿⡆
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⣿⣿⡿⣧⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⡏⣸⡏⠀⠀⣽⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡟⠉⠿⠀⠀⢠⣿⣷⠈⠙⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇⠀⠀⢿⣇⠀⠀⣄⡆⢹⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣽⡀⠀⠸⠀⠀⠀⢸⣿⣷⡀⠉⠁⢸⣿⣿⣇⠀⠹⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡀⠀⠀⢸⡏⣿⣷⠀⠀⢸⣿⣿⣿⡖⠈⢿⠿⣿⣿⣿⣿⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠇⠀⠀⠸⣷⢿⡏⠀⠀⢸⣿⢿⡏⠛⣠⣦⠀⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠆⠀⠀⣠⣿⣿⠆⠀⠀⠘⠀⠈⠃⢠⣿⣷⣾⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡆⢰⡀⠀⣿⣿⣿⣧⡀⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠂⠂⢏⠁⢸⠀⣿⠀⠈⠀⠁⠰⠂⣠⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠈⢧⡀⢧⣰⣼⣤⣼⣤⣿⣤⣧⣾⣤⣢⣾⣁⣨⠟⠀⡰⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢄⠢⣘⢦⣌⠲⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣟⣁⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢦⣀⠠⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣔⡪
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠲⣭⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⠿⣿⣿⠻⣿⣧⣤⠔⣀
⠀⠀⠀⠀⢀⣀⠀⠉⠲⢦⣤⣬⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⣿⣿⠀⠈⠛⢿⣿⣅⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⢿⣿⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⢌⠋⡉⢀⣿⡏⠀⠀⠀⠈⣿⣿⣿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣦⡙⢿⣿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣤⣴⣿⣿⣿⣿⣿⣿⠟⢧⠠⡀⣠⣾⡟⠀⠀⠀⠀⣠⣿⣿⡿⢁⠉⢉⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⣛⣿⣦⡙⠻⢦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣹⣿⢠⢨⠘⢠⣼⣿⣿⡿⠋⠀⠀⣀⡤⢾⣿⠿⠛⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠩⢛⣷⣤⣉⠓⠦⣤⣀⡀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣾⠿⢟⣋⡤⠔⣒⣿⢵⡚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢀⠔⠛⣻⣶⣦⣌⣉⣙⠒⠒⠒⠀⠀⠀⢀⣐⣂⣬⣵⠶⡞⠻⡏⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠉⠀⡼⠋⢹⠋⠹⠏⠙⠋⢻⠟⠉⢻⠁⠈⠏⠇⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⡯⠟⠲⡲⠤⠕⢸⠍⠻⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⢠⡴⡿⠗⠈⠠⢄⠀⠀⠂⡀⠀⠀⠰⢯⣔⡩⡻⣿⣿⣿⣄
⠀⠀⠀⢀⣾⠿⠃⡂⣒⠊⠉⠀⠀⠀⠀⠀⠀⠐⠢⢐⠌⠋⠪⡹⣿⣿⣿⣧
⠀⠀⢠⣿⢋⡂⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠪⢌⠢⣨⣿⣿⣿⡇
⠀⠀⣾⣂⡂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢢⠀⠘⣾⣿⣿⣿⣯⠀⠀⠀⠀⡟⢦⣀
⠀⢰⣯⣙⢀⢀⠀⠀⠀⠀⠀⠤⣤⣰⢄⠀⠀⠀⠈⢐⠨⡢⠱⣎⢦⣯⣿⣿⣏⠀⠀⢀⠴⠃⠀⠙⣷⣦⡀
⠀⢸⣿⡋⠈⠩⠀⠀⠀⠀⠀⠘⠻⢄⡀⠂⠀⢀⠈⢒⢍⡪⣢⣜⣿⣿⣿⣿⢯⣧⠀⣿⣦⡀⠀⣰⣿⣿⡇
⠀⠈⣿⢀⢎⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠊⡾⣿⣿⣻⠟⣽⣿⣿⣷⡟⠙⠻⠿⠿⣿⡟
⠀⠀⢿⣳⣷⡡⡀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢤⣨⣶⣿⣿⠋⢁⣾⣿⣿⣿⡿⣧⣔⣀⣶⣽⣿⡿
⠀⠀⠘⣯⣿⡆⢢⠈⠨⡂⠀⠠⠀⠀⠀⠀⢄⡨⢑⡭⣛⣿⣟⣿⢲⣾⢿⣽⢿⣿⠈⠈⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠙⣿⣿⣐⢅⢄⢀⠀⡀⠀⠁⠀⠀⡴⡫⣐⠟⣯⣿⣟⣷⣿⣟⣿⣧⣾⠧⣆⡑⣼⣿⠋
⠀⠀⠀⠀⠈⠻⣝⣵⣕⠤⣨⣖⣵⣤⣴⣽⡾⣟⣾⣿⣏⣻⣿⠟⠁⠈⠻⣿⣿⢺⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣏⡳⢺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣣⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⠀⠀⠀⠀⢰⡟⣴⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⣀⣀⣀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⡇⢀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣼⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⡇
⢴⣂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢟⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠘⣿⣧⡀⠠⡀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⡤⠀⠀⠀⠈⡨⠄⣉⠀⠀⢠⡶⠂⠀⠀⠀⠀⠉⠙⠂⠀⠘⠿⣿⣷⣷⠧⠼⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠀⠙⠦⡽⢂⡀⠈⣿⣹⡗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⡠⢀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠙⡄⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⡴⣡⣿⣿⣌⢦⠀⠀⠀⢀⡤⠶⢖⠗⠀⣠⠃⠀⠀⠀⢀⣉⣤⣾⣿⣿⣿⠳⡀⠱⢌⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣽⣒⠋⠉⠑⠢⠤⠠⠘⠁⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⢒⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠎⠀⠀⠀⠀⠀⠀⠈⠘⠿⠻⠿⢿⣿⢿⡟⠰⡀⣈⠖⠋⢀⡞⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣠⠄⣀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⠁⡄⠐⠋⠀⠀⠀⡄⠉⠉⠛⠛⠋⠉⠋
⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡐⠀⠀⠉⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡰⠃⠀⠚⠃⠀⠀⠀⣶⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣀⠀⣸⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⢈⡽⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⠀⢇⠀⢀⡤⠖⠒⠦⢄⡤⠄⠛⠚⠒⠘⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⣀⡤⠖⠀⠀⢲⡀⣀⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣭⣥⣤⣤⣤⣤⣼⣷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⢀⢳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠂⢁⣀⣀⠀⠀⠀⠀⢻⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢁⡤⠂⠉⠈⠉⠀⠀⣠⠤⢄⠀⠺⠾⢄
⠀⠀⠀⠀⠀⠀⢠⠊⢀⣀⡀⠀⠀⠀⡜⠀⠀⠀⠙⢄⠐⠺⣄⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⡷⠚⡽⠁⠀⢀⠊⠉⠀⠀⠀⠀⠉⠂⢣⠀⢈⣧⠀⠀⠀⢠⠞⣁⢤⡑⣄⠤⡒⠈⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠇⣠⠄⠈⠀⠀⡀⠀⢀⣠⠒⠐⠂⡡⢠⠊⠀⠀⡰⠁⠎⠀⢀⣵⠜⠋⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠋⣃⡀⠀⠀⠋⠀⠀⠀⠉⠁⠀⠀⡇⠸⢆⢀⠜⣠⠁⢀⡤⠼⡀⠀⠀⡀⠀⠀⠀⠣
⠀⠀⠀⠀⡤⠒⠒⠠⠄⣀⠈⠢⣠⠡⡀⠀⢀⡾⠠⠀⠴⠃⠀⠙⢋⣜⠤⠓⠁⠀⠀⠈⢻⢁⡀⠀⢀⣠⠀⠁
⢀⡠⠤⢤⡄⠀⡞⠓⠒⠦⠬⣈⡛⠀⠀⠀⡀⠀⠀⠀⠀⠁⢄⣠⠉⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜⠀⠀⡄⠀⢂
⡇⠀⠀⠉⠉⠙⠓⢤⠤⠠⢀⠠⠍⠙⢰⣶⠁⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠱⠊⢀⣀⡀⠰⠀⠘⡀
⠐⡀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣀⣤⣴⡾⠿⠿⠿⣀⠀⠀⠀⠀⠀⠀⡇⡥⠚⣉⣀⠈⠖⠁⢠⠇
⠀⢃⠀⠀⠀⣠⣇⣘⢄⠀⠀⠀⠀⠀⠘⢿⡿⠛⠉⠉⠉⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡸⢀⠀⠀⠁⢀⡴⢁⠔⠁
⠀⠸⡀⢲⠒⠢⡀⠈⣏⠢⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠤⣄⣀⣤⠎⣀⠠⠤⠄⡴⢁⠌⠐⡤⠔⠊⡴⠋
⠀⠀⢃⠀⣆⠀⠑⣔⣉⣂⡙⠦⡀⠀⣀⡈⣦⢄⡴⠋⠀⠀⠀⠈⠉⣒⠒⠤⠔⠊⢀⢎⠔⠉⢀⠔⠋⠀⢀
⠀⠀⠘⡀⠸⢤⡏⠀⡄⡬⠅⢀⡈⠁⠨⠤⠔⠋⡠⠎⣀⣀⣀⠠⡄⠊⠉⢑⠖⠈⠉⢂⡠⠂⠁⠀⠀⠈
⠀⠀⠀⠑⠄⡀⠑⠄⡁⠀⢀⡜⠉⠑⠒⠒⠒⠉⠀⠀⠀⠀⣣⠀⠘⣎⠑⠋⠀⠀⠀⠀⢣⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠉⠐⠐⠠⠍⡉⠙⠒⠒⠀⡴⠉⠈⠉⠒⠋⠐⠓⠒⠁⠀⠀⠀⠀⠠⠞⠁⠀⠀⢠⠃⠀⠈⢦⢦⠲⣉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣄⣠⠃⠀⠀⠀⣿⢸⠤⠇⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠍⠀⠀⠀⠀⣿⣼⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⣄⣟⡇⠀⢠⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⡠⡄⢺⠁⠀⠀⠀⣠⠞⢱⡀⣿⣿⠁⢠⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠒⠒⠂⠈⠉⠀⠀⠰⡀⢣⠀⣠⠔⠁⠀⠀⠳⢨⠏⡰⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢵⠴⡏⠀⠀⠀⠀⠀⠀⠛⢎⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡶⣤⣤⣤⣤⣶⣮⠵⡺⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢹⠮⣙⠓⠲⠿⠽⠽⣭⣭⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡐⠒⠓⠒⠒⠐⢀⡀⠀⠉⠉⠁⠤⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣔⣤⣀⡀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠐⠋⠙⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠔⣻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣶⣦⣤⣶⣷⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣰⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⡟⡇⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⡠⠁⠀⠉⠀⠈⠀⠈⠁⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠄⠀⠀⠐⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣤⣶⣿⣷⣿⣿⣿⣶⣶⣾⣿⣷⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠿⠿⠿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣴⣶⣾⣷⣦⡀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠉⠉⠀⠙⣿⣧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢸⣿⡇⠀⣀⣤⣶⣿⠿⠿⢿⣷⣦⠀⠀⠀⣽⣿⣶⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡿⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣴⣿⡿⠟⠉⠀⠀⠀⠀⠹⣿⣇⠀⣴⣿⡿⠋⠁⠈⠛⣿⣷⡄⠀⠀⠀⠀⠈⠛⠛⠋⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠸⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⡿⠋⠀⠀⢀⣴⣾⡿⠟⠁⠀⠀⠀⠀⣤⣶⣶⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⠉
⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢀⣀⣤⣶⣶⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⣶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠈⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠘⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣤⣤⣄⣤⣤⣾⣿⠂⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⣴⣾⣶
⠀⠀⠀⠀⢶⡦⠀⠀⢠⢴⡶⢦⠀⠀⠀⠈⢏⠉⠀⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄⣶⠎⠋⣁⠀⠀⢶⡆
⠀⠀⠀⢰⣿⣿⠆⠀⠈⢻⣿⡏⠀⠀⠀⠀⠈⠋⠙⣿⣿⡆⠀⠀⣠⣄⠀⠀⠀⠀⠠⠤⠶⢾⣿⡏⠁⠀⣴⣿⣷⡆
⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡿⣿⠿⠐⢶⣬⣯⣄⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠿⣿⣿⠷
⠀⠀⠀⢰⡏⣿⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⠀⠀⠀⢈⣿⠆⠀⠀⠀⠀⢀⡿⢸⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠘⠃⠙⠁⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠚⠁⠘⠃⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀
⠀⠀⣿⣿⣛⣃⠀⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⣚⣛⠀⣄⡐⣿⣂⡀⠀⠀⠀⠀⠀⢘⣿⡃⠀⣿⣝⢻⣏⡤⠴⠂
⠀⠀⠉⢸⣿⡿⣧⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠉⣿⣿⣽⠀⠀⠀⠀⢠⣿⡟⣿⡆⠉⠉⠈
⠀⠀⠀⢸⡟⣿⠈⠀⡀⡀⠘⣿⡆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⢸⣿⣿⡟⠃⠀⢸⣿⣿⡀
⠀⠀⠀⢸⡇⣿⠀⠀⣿⡇⣼⠟⣷⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⡏⢸⡇⠀⠀⠀⠀⠈⢹⣿⡇⠀⠀⣾⡟⣿⡇
⠀⠀⡀⡈⣀⣈⠀⡀⠉⡁⣁⠀⣉⡀⠀⠀⢀⠀⡉⡈⠀⠀⠉⠀⡈⠀⢀⠀⠀⠀⡀⡈⠉⡁⠀⠀⡈⠀⢈⡀


⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⢰⣶⠀⢀⣴⣦⠀⠀⠀⠀⠀⢾⡧⠰⣿⠀⠀⠀⠀⠀⢿⠆
⠀⢀⣀⣾⣿⣿⣄⡀⠀⠀⢰⣿⣿⣷⡴⠀⠀⠀⣿⣿⡇⠛⣿⣿⣧⠀⠀⠀⣼⣇⠀⠀⣼⣿⠀⠤⠴⣿⣿⢷⣀
⠀⣈⡁⢸⣿⡇⢈⣁⠀⠐⠋⣿⣿⡇⠲⠖⠀⠀⣾⣿⡇⠀⣿⣿⠿⠀⠀⠀⠹⣏⠓⠋⢽⡟⠀⠀⢀⡿⢿⡀⠈
⠀⠈⠁⢸⣿⡇⠀⠉⠀⠓⠂⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⢀⣿⠀⠀⢸⡇⠀⠀⣼⠇⢸
⠀⠀⠀⠘⠋⠃⠀⠀⠀⠀⠀⠙⠙⠁⠀⠀⠀⠀⠙⠙⠁⠀⠙⠙⠀⠀⠀⠀⠈⠃⠀⠀⠈⠃⠀⠀⠋⠀⠘
⠀⠀⠀⠉⠉⠀⠉⠀⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠉⠀⠀⠈⠉⠁⠉⠀⠁⠈⠀⠀⠀⠀⠉⠁⠈⠀⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⡤⢤⣄⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⢿⡕⢦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡶⠄
⠀⠀⠀⠀⠀⠀⠰⢾⡏⠀⢀⠂⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠒⢀⠤⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠒⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠈⢻⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠁⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⢿⣻⡃⠀⠀⠀⠀⡄⠐⠒⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣢⣀⢀⠀⠠⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠠⡔⠢⢄⡀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠙⠲⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⢘⡣⠀⠀⢣⣈⣉⠉⣉⣀⠔⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠃⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠄⠀⠀⠠⡠⠳⠈⠉⡐⠀⠀⠀⠀⠀⢠⠂⠈⢢⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⠊⠀⠈⠢⠠⠜⠀⠀⠀⠀⠀⠘⢄⣀⠜⠀⠈⠑⢄⠀⠀⠀⠀⠈⠀⠈⠓⣄
⠀⠀⠀⠀⣀⢀⠀⣠⠞⠒⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠶⢤⠀⢀⠀⠀⢀⢺⡄
⠀⠀⠴⠛⠁⠨⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢬⡉⠁⠉⠒⠶⠋
⠀⢸⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⣄⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠠⠀⣀⣤⠞⠛⠓⠦⣤⣀⣀⡀⣀⣀⣠⠶⣄⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠙⠦⣄⡀⠀⣨⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⣇⠀⠇⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⢀⣀⠠⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢀⣠⡴⠖⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⢠⠿⠋⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠹⣶⠞⠛⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⣧⠀⣴⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢙⡿⠖⢀⢎⡤⠤⢼⣀⣶⠀⠀⠀⠀⠀⢸⢶⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠴⠀⠀⠀⢀⡠⠞⠉⠀⠀⢰⠏⠀⠀⢀⣹⡆⠀⠀⠀⠀⣠⠟⠈⠃⠴⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣿⠀⠀⠀⠘⣻⡟⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠘⠷⠤⠴⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠒⠋⠀⣷⣄⠀⠀⠀⠀⢀⣠⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣧⣿⡀⠀⠀⣠⠴⠲⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⣠⠖⠋⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣿⢁⣴⡶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣈⣀⣀⡤⢾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣼⠀⢈⠉⠓⠒⡶⠶⠶⠶⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⠀⠀⠀⢳⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣤⣤⣤⡼⠇⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣀⣀⣿⠋⢧⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡿⠶⠦⠉⠁⠘⣦⣤⣤⡤⠴⠖⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠒⠲⣮⣤⠞⠁⡼⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠺⢧⣀⠀⠀⠀⠠⠤⠾⡵⠷⠒⢀⣠⢟⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣈⣿⡓⠛⣛⣓⣶⠶⣶⣾⠷⣖⣚⣉⣓⣋⣽⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠭⠭⠭⠔⠒⠋⠁⠈⠉⠒⠒⠫⠍⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⠀⠀⠀⠀⠀⠀⠀⢰⠆⢾⡷⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⢸⣿⣻⠆
⠀⠀⠀⢰⣾⣿⣿⣦⠀⠀⠀⠀⠀⣠⢶⣿⣿⡷⣄⠀⠀⠀⠀⠀⠿⠶⣿⣿⡷⠿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣷⠄⠀⠀⠀⠀⣿⣿⣷⡄
⠀⠀⠀⠀⢽⣿⣿⠁⠀⠀⠀⠀⠛⠁⢸⣿⣿⡇⠈⠛⠁⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣿⠙⠳⣤⠀⠀⠀⠀⣿⣿⡏⡇
⠀⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡇⠀⠀⠀⠀⠃⢀⣤⣼⣿⣷⡼⡇⠀⠀⠀⠀⠀⠀⣿⣿⡏⠃
⠀⠀⠀⠀⣿⡇⣿⡆⠀⠀⠀⠀⠀⠀⢸⡟⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣧⠀⠀⠀⠀⠀⠈⠉⢩⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠿⠀⠻⠃⠀⠀⠀⠀⠀⠀⠸⠇⠘⠟⠀⠀⠀⠀⠀⠀⠀⠸⠇⠘⠟⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠇

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⡀⠀⠻⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣄
⠀⠀⠀⣄⠘⢿⣃⣤⠾⠋⠀⠀⠠⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣣⡴⠞⠃⠀⠀⣀⣠⣼⡛⣶⠂
⠀⠀⠀⣿⠞⣿⣿⣧⠀⠀⠀⠀⠀⣠⣿⣽⣄⠀⠀⠀⠀⠀⣴⣶⣞⡷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠞⢻⣿⣿⡀⠀⠀⠀⠸⣧⣽⣷⣿⠃⡀
⠀⠀⠀⠁⠀⣿⣿⣿⠀⠀⠀⠀⠰⢿⣿⣿⡿⠇⠀⠀⠀⢾⣽⣷⣿⣧⣀⣰⣶⣶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⢀⣿⠁⣿⠀⠀⠀⠀⣠⣼⠿⠿⣷⣤⠀⠀⠀⠀⣬⠻⣿⢿⣿⣏⠙⡿⣧⠉⠈⡇⠀⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⢠⣴⡿⠿⠷⣶⣄
⠀⠀⠀⢀⣾⠏⢀⣿⠀⠀⠀⢀⣿⠁⠀⠀⠀⢿⡇⠀⠀⣴⣿⣦⠘⢾⡡⠘⠻⡇⠀⠀⠀⡇⠀⠀⣰⡿⠁⣼⡇⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿
⠀⠀⠀⠈⠉⠀⠈⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠘⠃⠀⠀⠙⠛⠉⠀⠈⠃⠀⠈⠁⠀⠀⠀⠁⠀⠀⠉⠁⠀⠙⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⢴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣶⣦⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⣤⣽⣭⣄⠀⠀⠀⠀⠀⠀⠀⢐⣅⣤⡀⠀⠄⠀⠀⠀⢀⣿⣿⣄⠀⣰⡄⣦⠀⠀⠀⠀⠾⢷⣦⣥⣍⣿⠀⠀⠀⠀⠀⣬⣿⣅
⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠚⣻⣿⣽⣿⡆⠀⠀⠀⠀⢾⣿⣿⣿⠗⢸⠏⣿⠀⠀⠀⠀⠀⣼⣿⣿⠉⠛⠃⠀⠀⠀⢸⣇⠂⣹⡆
⠀⠀⠀⠀⢸⡿⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠀⠀⠀⠀⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⣿⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⣾⠏⢸⡟⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⣩⣷⣶⣶⣶⣶⣶⣯⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠻⠿⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣐⣒⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡉⠙⠛⠉⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⣿⣿⣿⠿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣿⣿⡿⢻⣿⡟⠉⠈⠹⣿⣿⠻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣀⣺⣿⣇⠀⠀⢀⣿⣿⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⡴⠋⠳⢦⡀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡷⠶⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢡⣦⢹⡏⠀⠀⠀⠀⢹⠡⣶⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠴⠊⠀⠀⠀⠀⠀⠈⠳⠴⠞⠁
⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢤⣤⣀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢾⣿⣿⡧
⠀⠀⠀⢸⣿⠈⠁⠉⠈⡇⢸⠀⠉⠈⠅⢹⠀⠍⠈⠁⢹⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠁
⠀⠀⠀⢸⣿⢀⠀⣀⠀⡇⢸⠀⣀⠀⡃⢸⠀⡃⢀⡀⢸⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠁⠀⢩⠉⠁⠀⠀⠀⣿
⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⠀⢠⣤⡄⠀⠀⢀⣠⣄⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⠿⠃⠐⣾⡆⠈⠋⠀⠀⣦⠸⢿⠿⠀⠀⠀⠀⠉
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣛⡿⠟⠻⢿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣆⠉⣷⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⣶⣶⣶⢤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⣿⣛⣛⣛⣛⣛⣛⠾⠿⠿⣺⡿⢿⡻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⢿⣳⣚⣛⡛⠛⠛⠛⣚⢓⣒⡂⠉⢭⣛⡲⢍⣓⢬⣓⢯⡻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣟⣛⡓⠬⠥⢤⠄⠒⣒⣀⣲⠦⠀⠃⠰⠘⠣⢔⣢⢍⡓⠮⣝⠮⣟⢿⣻⣻⣿⣆
⠀⠀⠀⠀⢀⣴⣿⣿⠈⠡⠀⣒⠲⠤⠄⠒⣓⡂⠀⠄⠀⠉⢠⠀⣉⡐⠢⣌⠑⠭⡳⢌⠑⢮⡷⣝⣿⢯⣿⣷⡀
⠀⠀⠀⣠⣿⡿⠿⠖⣈⡍⠭⡭⠁⠒⠀⠐⠂⠀⠉⠁⠀⠀⢀⠑⠒⠉⠑⠢⢍⠳⢌⡲⢙⠦⡙⢾⣿⣿⣷⣿⣿⡀
⠀⠀⣰⣿⣛⣠⣌⣁⡀⠙⠃⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⠢⠉⠲⣝⠮⡳⣌⢢⣱⣷⡽⣿⣿⣷
⠀⣰⣟⣛⠐⠶⠤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⡈⠢⡑⢌⢬⠣⣿⣹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣄
⢀⣿⢛⣈⡍⢬⣉⠂⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⣌⡓⢬⡳⣌⢦⡡⡱⡝⣽⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠙⣷⣀⡀
⢸⡟⢯⣫⡉⡑⠬⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠑⠲⢄⡙⠦⡈⢶⣠⡙⣌⢿⡟⣾⣿⣿⣿⠇⠀⠀⠀⠀⢀⣰⠇⠀⠀⠻⢿⣶⣄
⢼⢿⣧⢳⠰⣌⢤⡀⠀⠀⠀⠀⠀⠀⠈⢹⣛⣷⠶⠟⢲⠄⠀⠀⠀⠠⣌⡓⠦⣌⠲⣌⠢⡹⣷⣌⣾⣻⣿⣿⣿⣿⣦⡀⠀⠀⣴⠟⠁⠀⠀⠀⠘⢢⢻⣿⣷
⣹⣮⣏⢃⠑⡌⢦⠁⠀⠀⠀⠀⠀⠀⠀⠘⠫⢿⣀⢀⣐⠇⠀⠀⢀⡒⠤⠉⠳⢌⡓⢬⡳⣜⣝⣮⣷⣿⣿⣿⣿⠿⣼⣿⡀⠀⣿⢿⢤⣀⠀⠀⡀⣦⣿⣿⣿
⢸⣿⠟⠦⡑⢆⢀⡀⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠙⠆⠀⣙⠢⣝⠲⣝⠮⣹⣎⢿⣿⣿⡿⢻⣿⣿⣿⢷⡄⡽⠿⢾⣿⣼⣴⣼⣿⣿⣿⡿
⢸⡟⡆⢶⡹⣄⠀⡙⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⣑⠢⢑⣮⡙⢮⣿⣧⡿⠋⣤⣿⣿⡿⣿⣾⣿⡟⡤⠀⠈⠙⡟⣛⢛⣿⣿⡁
⠈⣿⡹⡼⡷⣌⢣⡀⣄⠠⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡑⠢⢍⡒⠬⣓⡶⢭⣛⣶⠟⠁⠀⣿⣿⢿⣿⣿⣿⣿⢿⣳⣠⡞⡘⣸⢱⣣⣿⣼⣿⡇
⠀⠸⡳⡹⣜⢮⠃⡱⢌⠳⠘⢦⡀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠒⠮⣝⠲⢿⣛⡿⢿⣿⣮⢿⡀⣀⣾⣿⣿⣳⣿⣽⡿⡟⣸⢹⢧⣿⣧⣿⣿⣿⣾⣿⡿⠁
⠀⠀⢻⣜⣾⢮⡣⠙⢎⠳⡌⠢⣝⠂⢀⡒⠀⣀⠂⢄⡀⠀⠒⢤⣉⡒⠦⣝⡒⣮⣭⣽⠿⢨⣿⢉⣿⣟⡿⣷⢷⢟⣷⣿⠇⡇⡌⡼⣹⢻⣿⣿⠿⠿⠋
⠀⠀⠀⢻⣮⢣⡱⡔⢦⡓⢌⠲⡈⠰⠀⠄⠀⠌⢑⠢⢌⡀⢄⡐⠮⢭⣑⣶⢾⣏⣻⡶⡿⡷⣿⢼⣿⡮⣝⣾⣏⣾⡿⣹⢸⢠⢣⢃⣧⣿⡿⠋
⠀⠀⠀⠀⠻⣷⣝⢮⡳⣝⢮⡳⢌⠳⢌⡲⢬⣓⠮⢑⡲⢬⣐⠮⣭⣒⠶⠦⣶⡖⢶⣛⣿⣿⣿⡾⠛⢿⣮⣿⣿⣽⡇⡌⣼⣸⣼⣸⣿⣷⠃
⠀⠀⠀⠀⠀⠈⢻⣦⣙⢮⡳⣝⠢⣅⡲⢬⣓⠮⢝⣶⢭⣷⣮⣟⣚⣛⣿⡽⣷⣚⢽⡳⣫⡿⠁⠀⠀⠀⠙⢿⣵⣿⡇⡏⣏⣯⣇⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠮⣷⣿⡾⣝⡲⣭⣟⣳⠿⣷⣾⣿⣗⣿⣿⣿⣟⣚⣽⣻⢵⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⡇⡿⢸⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣽⣛⣷⢿⣿⣿⣿⣟⣿⣟⣾⣟⣩⣖⣫⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⡇⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠇⢹⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⢸⣟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡄⢘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠃⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣜⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠴⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠉⠒⠉⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠉⠉⠉⠉⣀⡴⠀⠀⠀⢦⣄⡀⠳⣄⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡠⢂⣠⡴⠶⠟⠋⠀⠀⠀⠀⠀⠙⠿⣷⣮⣕⣦⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠃⠐⠙⡋⠐⠉⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⢤⣉⠉⠛⠓⠐⡆⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢀⠂⠀⢠⠦⡇⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡤⠀⡤⠤⡀⠀⢳
⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢏⠁⠉⠿⠟⠁⠀⠀⠀⠀⠀⠈⠁⠈⠹⠿⢣⠀⢀⠀⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠀⢣⠀⢀⠀⠈⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠋⠀⢘⠀⠀⠰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠳⠨⡄⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⢀⠐⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢣⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠃⠀⠀⠀⢀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠚⠓⠒⠚⠛⠂⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠣⢀⠄⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠤⣈⠢
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⣀⡠⠖⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⠎⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠦⢄⣀⠀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⣤⠤⠶⠂⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⠁⠒⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠈⠑⠢⢄

⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⡀
⠀⠀⠀⠀⠀⢀⢾⡳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠰⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⢀⠁⠀⠀⠀⡄⠀⠀⠉⢃⡸⠀⡀⠀⠐⠰⢤⡀⠲⠼⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠙⢢⣼⣯⣧⣠⡔⠋⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢱⡄⠀⠀⠀⠀⠀⠰⠞⢱⠛⠋⠠⠟⢑⡆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠛⠺⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠦⠆
⠀⠀⠀⣀⢀⠀⠀⢀⠀⠐⣤⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠠⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣄
⠀⠀⠀⢰⠊⢀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠒⢢⠀⠀⠀⠀⠀⠀⠀⠐⢌⠳⠚⢁⠀⡀⠀⠈⡃⢨⠇⠀⠀⠀⠀⠀⠠⢖⣴⣤⡀
⠀⠀⠀⠈⠁⡘⠀⠀⢠⠀⠈⠃⠶⢠⠄⠀⠀⠛⠀⠀⠀⠠⢠⠱⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⣠⠠
⠀⠴⣤⠄⠀⠘⠀⠀⠠⡄⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢘⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⢀⠆⠀⠀⡡⠀⣠⢤⡜⠀⠀⠙⠠⣶⣄⠀⠀⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠘⠆⠁⠈⠁⠐⠛⠛⠁⠈⠁⠈⠀⠉⠉⠀⠀⠀⠈⠁⡈⠐⠂⠀⠀⠉⠀⠀⠀⠀⠑⠒⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⡿⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠠⣀⠠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠃⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠐⣇⠀⣠⢦⡀⠀⢀⡼⠂⠀⠀⠀⠘⠀⠀⠀⢿⡀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠂⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⢀⣠⢻⣿⠾⢃⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢷⢴⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠊⠀⠑⠊⠥⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⢀⠄⠐⣆⣀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠉⠉⠉⠉⠁⠀⠄
⠀⠀⠀⠐⠀⠀⠠⢄⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠐⣶⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠖⠋⡀⢀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠈⠀⠠⠄
⠀⠀⠀⠐⠀⠀⠤⠀⠀⢲⠀⠠⢤⠴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⠀⢀⠠⠀⠀⠀⠘⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠷⠀⣲⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⣰⣸⠏⠀⠀⠀⠈⠍⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣾⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣗⣲⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣾⣿⣿⣽⣿⣿⣿⣭⣭⣽⣾⣷⣿⣯⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠀⠐⠒⠚⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠀⠀⢀⣀⣤⡴⠖⠚⠛⠛⠒⠲⢤⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠗⠒⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⠏
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠈⢳⡀⠞⡥⠄⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡞⠁⠀⠀⠀⣠⠏
⠀⠀⠀⠐⠉⠁⠀⠀⠀⣩⠿⠓⢦⠀⠀⠙⡆⠐⠚⠁⠀⠀⠀⠀⠀⠀⢧⠀⢰⠏⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠏
⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠢⡀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠶⣾⠇⠀⠀⠀⠀⠀⠀⠘⠀⢰⠃⠀⠀⠀⠀⠀⣀⡀
⠹⣄⠀⠈⢄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⣁⠀⠀⢀⠔⠊⠲⣄⠀⡞⠀⠀⠀⣠⠾⠋⠁
⠀⠈⠢⠀⠈⠑⠄⠀⠀⠀⠀⠀⠠⠤⠀⢉⡀⠀⠀⠀⠀⠈⠉⣨⡀⡀⠀⠀⠘⡆⠇⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠀⡴⠚⠡⠋⡜⢀⠀⠀⢁⠐⠀⣸⠁
⠀⠀⢰⠉⠋⠙⢢⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠈⠓⡾⠀⠀⠀⠘⣋⣽⠃⠀⠀⠀⠀⡟
⠀⡞⠃⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⠢⡈⠀⠀⢀⡠⠚⠀⠀⠀⣀⡤⠥⠚⠀⠀⠀⠀⠀⠁
⢀⠇⠀⠀⠀⠀⠀⢟⢦⡀⠀⠀⠀⠀⠘⠒⠊⠁⠀⠀⠀⡰⠋⠈⠇
⠘⡄⠀⠀⠀⠀⠀⠘⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠴⠚⠁
⠀⠀⠑⠤⣀
⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣷⣴⣾⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⢸⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣽⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠛⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⠋⢰⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣽⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣾⣬⣏⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠉⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠈⠛⠿⠿⣿⣿⣿⣿⣿⡿⠛⠉⡁⠈⠀⠀⠀⢀⠀⢣⣀
⠀⠀⠀⢀⠔⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠙⢳⠄⠤⠀⠀⠀⣆⣮⣿
⠀⠀⠀⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣤⡈⢫⡄⠙⢶⣾⣽⣿⣿
⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⣷⣶⡷⣼⣿⣦⣿
⠀⡌⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⣤⠄⢺⣽⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠄⠀⣀⣀⢀⡤⠴⠀⠒⠛⠶⠿⠟⠙⠛⠛⠿⠋
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒⠒⢒⢐⠒⢖⣋⣹⣿⣿⣉⣉⣩⣭⣃⣞⣛⣛⣛⣋⣙⣭⡭
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣀⣤⡤⠒⠃⠀⠀⠀⠀⡀⢀⢀⣤⣶⣧⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⢻⣿⣿⣿⣿⣿⣟⡿⢿⣿⡿⠿⠁⢰⡀⠒⠉⠀⠀⢀⣀⣀⠀⠀⠀⠉⢁⣈⢘⠛⠛⠉⠉⠉⠛⠉⠈⣉⠉⠿⢛⠛⠛⠛⠛⠛⠻⠟⠛⠉⠈⠁
⠀⠈⠻⢿⣿⣿⣿⣿⡿⠿⡷⠤⣄⣀⣁⠀⣀⠈⠀⢴⡚⢻⣿⣶⣶⠒⣶⡖⠚⠋⠁⠀⠈⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⣤⡘⢋⣉⠁⠈⠉⣹⠟⠀⠀⠄⠁⠴⠖⠂⠀⠀⠀⠠
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣶⣦⣾⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣟⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣶⠈⣶⡼⠀⣀⣀⡀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠋⠙⠄⠻⣿⣼⣿⣾⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠉⠉⠀⢀⣾⣿⣿⣿⣿⠟⠛⢷⡀⢆⠉⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⠋⠀⣀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣦⣐⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠
⠀⠀⢀⣀⣀⣀⣀⣤⠀⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⡀⠀⣠⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⢀⣄
⠀⠀⠈⣿⣿⣽⡇⣿⠶⣿⣿⢰⡿⣧⡇⢸⡷⡁⡷⣾⠁⠀⢸⣿⣿⡿⡁⣿⣎⣿⣽⠃⢸⣏⢻⢸⠆
⠀⠀⠀⠸⠟⠿⠃⠛⠀⠛⠛⠙⠛⠙⠃⠛⠛⠛⠛⠛⠂⠀⠾⠿⠋⠛⠉⠉⠉⠛⠛⠂⠈⠋⠈⠛⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⣿⠋⠁⠀⠉⠻⣷⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⢀⣀⣀⣀⠉⠛⠛⠻⠧⠀⠀⠀⢠⡾⠟⣿⣆⣠⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣦⣤⣴⠶⠾⠇⠀⠀⠀⢰⠿⠟⠛⠁
⠀⠀⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠙⢷⣦⠀⠀⠀⠈⠙⠛⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⠃⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢶⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⡇
⠀⠀⠀⠀⠀⠐⢻⣿⣿⡀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢸⣧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠁⠀⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⠇⠀⣀⣀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⡾⠋⣠⣾⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣄⣠⣤⣤⣄⠈⢷⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣁⣀⣀⣀⣠⣤⡾⢛⣡⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠙⢿⣷⣄⡉⠛⠶⢤⣤⣤⣤⡴⠾⠛⠛⠉⠉⠉⢉⣩⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⡴⢶⣾⣿⡿⠿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⠿⠿⠿⠿⠶⠞⠋⠁⠀⢀⣀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣤⡤⠴⠶⠾⠟⠛⣉⣀⣉⣉⣉⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣥⠴⠶⠶⠚⠛⢋⣉⣉⣭⣭⣭⣭⠿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠓⠒⠛⣛⢉⣉⣁⣀⣀⣤⣤⣤⣬⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡟⠛⣷⡶⠶⠖⠛⠛⣉⣉⣉⣭⣭⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠘⣷⡶⠟⠛⠛⠉⣉⣁⣀⣀⣀⣀⣤⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣈⣹⣿⠿⠿⠟⠛⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣯⣥⣤⣴⠏⠁⠙⠋⠉⠉⠙⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣤⣤⣤⣤⣤⣴⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣄⠀⠀⣰⠃⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠏⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠹⣷⡄⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢿⣷⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⢀⡴⠋⠁
⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠛⠉⢁⡄⠀⢠⡟⠁
⠙⠿⢧⣄⠀⠈⠉⠉⠙⠛⠿⣍⡉⠛⠲⢦⣀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢹⠀⠀⣠⠶⠛⠋⠉⠀⠀⠀⣠⠔⠉⠀⢀⡿
⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠈⢻⣦⣿⡀⣄⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣧⠾⣧⡀⣯⣇⡴⢦⡀⠀⠀⠉⠁⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢠⡀⢀⠲⣤⣽⣿⣿⣿⡿⠀⠈⢻⣏⡟⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣦⣤⣷⣼⣟⣵⣷⣿⣿⣿⠃⠀⠀⠘⣿⡇⠀⠀⠘⣧⡀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢿⣿⣹⣟⡹⣦⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⢘⣷⣦⠃⢀⡞⠁⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⣿⣶⠟⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣻⣿⣿⣿⣿⣇⠀⠀⢀⣀⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⡷⣞⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠻⢿⣿⣷⢾⣟⣃⣿⣯⡛⠿⣿⣿⣿⣿⠿⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣍⠻⡍⠛⠉⠉⠛⠛⠛⣛⣭⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣦⠀⠀⣰⠆⣴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢽⠀⠀⠿⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣱⢾⣿⠟⢽⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⢉⡁⢾⠇⣀⠀⢁⢨⡷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⠀⠉⠈⠈⠉⠀⠀⠀⠠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠠⠄⠀⠀⠀⣤⡄⠀⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠛⠂⠀⠈⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⠁⠀⠄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⢀⢴⠏⠀⠀⠀⠀⠘⠓⢍⢹⣄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡘⠀⠀⠀⠙⠆⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⡀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠁⡅⣀⠀⠀⢛⠀⡆⠐⣯⣤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣈⠁⠀⠀⠀⢠⠃⠀⣀⢔⠜⠁⠀⠠⡀⠀⢀⠁⡄⢉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⢻⡿⠋⠀⠀⠀⠀⢿⣿⣿⣥⡘⠀⠀⠀⠀⢰⡀⠃⣼⣽⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣇⠀⠀⠀⢠⠘⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠿⠛⠛⠛⠛⠋⠀⠑⠀⠀⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⣛⡛⢻⡻⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢄⠀⠀⡃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⡠⠞⡠⠐⠋⠂⣤⡀⠀⠈⠡⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡒⠂⠜⢡⠎⠀⣤⣼⣼⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠌⢀⣷⣾⣿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⢿⣶⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⠘⠏⠁⢀⠀⢀⢀⣀⠸⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠈⠀⠀⠂⠉⠠⠀⠉⣩⠄⠋⠀⠀⠀⠀⡠⠀⢄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠅⣁⣀⡠⠀⠐⠪⢥⠄⠀⠀⢂⡉⠠⠄⠧⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠺⠤⠗⠀⠀⠐⣶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠄⢀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡀⠠⠒⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠢⡀⡄⠀⡁⢡⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⠃⣷⠑⢦⠼⡏⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠂⠀⢆⠀⠘⠀⢸⠀⠀⠀⡀⠆⢀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠁⣇⡡⢀⠀⠠⡢⡤⠀⣧⠖⠋⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣠⠀⠀⡖⠘⡀⠀⠘⣷⣊⣁⠈⠀⠤⠠⢴⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠊⠀⡠⠑⢤⢔⡃⠉⠉⠢⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⢡⠈⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠊
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀
⠀⠀⠀⠐⢮⡓⣶⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠈⠪⣝⠮⣼⡟⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢮⣻⠿⣦⠈⠑⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠢⢀⢈⣱⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠐⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⠠⢴⣾⣿⣿⣶⣦⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠐⠒⠒⠒⠛⠛⠛⣛⣛⣟⡛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠷⢦⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⢦⡰⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡘⠃⠀⠀⢤⣠⠤⠂⠉⠀⠀⠈⠀⠀⠉⠉⠛⠛⠻⠶⠒⠌⣷⣦⣤⣾⣿⣿⣿⣟⣿⣿⣿⣿⣟⣦⠈⠉⠉⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣈⠀⠀⣴⠀⠀⠀⢀⡐⠀⠈⠀⠀⠀⣀⣍⣬⢯⠿⠿⣿⣿⡿⠿⡿⢉⢿⣿⡿⠿⠛⢿⣿⣿⡟⠻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠛⠁⠀⠀⠀⠨⠁⢐⠀⠀⣀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠐⠀⣱⠟⠋⠀⠀⠀⠀⣿⣯⡄⠸⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⢈⣁⣤⣥⣶⣶⣾⣟⣛⡿⢯⡟⠉⣠⠴⢺⣧⣤⣤⣤⣤⣴⣾⣿⣯⠀⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣯⣭⣾⣿⣿⡾⠀⡐⠂⠛⠡⠜⢢⡜⢋⢛⣋⣽⠿⣫⠩⢆⡉⣠⠆
⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣤⡴⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠾⢓⡋⢼⡿⣄⡀⣺⠀⠿⠩⠃⢴⡀⣡⣴⠦⣼⣥⠏
⠀⠀⠀⠀⠀⠀⠘⠒⠿⠏⣫⡭⢠⣽⠿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢛⡵⣤⣴⡴⠦⣐⡀⣒⢐⡃⠩⢍⡻⣷⢾⡟⠋
⠀⠀⠀⠀⠀⢀⣀⣠⣴⠬⢶⣾⣿⣶⣶⣦⣭⣭⣭⣉⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣻⣛⢿⣇⣠⡿⠆⣥⢤⣄⣶⢜⣣⣟⠋
⠀⠀⠀⠂⠉⠉⢉⣡⣤⣴⣾⣿⠿⠟⠛⠻⠉⡍⠉⣹⣻⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣼⣿⣽⡯⠋
⠀⠀⠀⣀⣤⣺⠿⠟⠛⠉⠁⢀⠀⠀⠀⢲⠑⠃⠀⠛⢳⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠙⠛⠿⢿⣿⢿⡟⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣤⣤⣤⣠⣄⣠⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⢸⣿⡇⠀⠀⠀⣠⣤⣖⣄⠠⠀⠀⢈⣉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⣿⣿⣿⣽⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⢸⣿⣇⣴⣶⣼⣿⣿⢋⣿⣻⣧⢶⣾⣿⣧⠀⠀⠀⣻⣿⣿⣿⣿⢟⣚⣻⣿⢭⡿⣿⣗⣿⣿⣿⢸⣿⣿⣾⣶⣆
⠀⠀⠀⠀⢠⣔⣴⣿⣿⣿⣿⣿⢸⣿⡇⠛⡻⠟⡟⣉⣿⣿⣿⣿⣿⣿⡌⣿⠇⠀⢀⠀⣖⠊⣿⣿⣶⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠨⣿⣗⣿⢿⡄⣷⡿⣟⣥⠿⣿⢿⣟⣴⠛⣦⡶⣾⠿⠷⠾⣵⣿⣿⣟⣿⣿⣮⠙⣿⣼⣿⣿⣿⡾⣿⣿⣿⣣⣶
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⠁⣿⡀⢫⠶⣯⠹⠎⣿⡿⢁⡿⠹⡄⢡⡀⠀⢺⡟⠉⠙⠿⣿⠟⢡⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣤⣠⣾⡄
⠀⠀⣠⣟⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣏⢿⣤⡩⣴⣾⢟⡿⢀⡾⠀⠀⠁⠀⣵⠀⢸⡆⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁
⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢨⢹⡇⠀⣷⡟⠀⠛⠁⠀⠀⠀⠀⠸⠄⣸⡅⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⠁⠄
⣠⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⠘⠷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡙⠁⠀⠀⠀⡸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣶
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢁⢾⣿⣦⣤⠀⠀⢠⡀⠀⣠⣠⣄⣶⣇⠀⠀⠀⢰⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⡇⢿⣾⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣯
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣇⢿⣾⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⡿⣿⣿⡿⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠁⠀⢀⣼⣿⣿⣿⣡⣤⣿⣿⡿⠃⣿⣿⣿⣿⣿⠉⢉⣿⣿⡟⠀⣿⣿⣿⣛⣛⠙⣿⣿⣿⣿⢾⣾⡀⠒⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠽⠟⠋⠀⠀⠀⣴⠿⣿⢿⣿⣿⠋⠉⠸⠿⠾⣴⣿⣿⣿⣿⣿⠐⠿⠿⠿⣧⣾⣿⣿⣿⡇⠀⠂⠹⣿⣿⣿⣎⢻⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠙⠋⠛⠙⠿⠀⠀⠀⠀⠸⠿⠿⠿⢿⣿⡀⠀⠀⠹⣿⢿⣿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤⢻⣴⣒⡡⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠫⠿⠛⠁⠀⣠⡼⠗
⠀⠀⠀⠰⣄⠀⠀⠱⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠰⠆⠀⠀⠠⠆⠁⠀⠀⠀⠀⢀⣄⠀⠀⠀⠄
⠀⠀⠀⠀⠈⢷⡱⠀⠙⣇⠀⣀⠀⠀⠀⠀⠀⠀⠈⠹⠆⣄⡤⠒⠁⠀⠐⠾⠀⠀⢠⣼⣿⣿⣴⠈
⠀⠀⠀⠀⠀⠐⠛⣆⠠⣿⣆⡙⣦⢠⡀⠀⠀⠀⠈⠛⠀⣏⢀⣄⡀⠀⠀⢀⠀⠸⡞⣿⣿⣟⣿⣿⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠑⠷⣼⡇⢸⣾⣧⣾⠄⠀⠀⠘⠄⢿⠛⠉⠁⠀⠀⠀⠃⠀⢰⣿⣷⣿⣀⣹⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣿⢾⣽⣾⡟⠤⢀⠀⢀⣠⢠⣆⣀⠀⢁⠀⢤⢠⣀⣼⢳⣿⣿⣿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⡙⢿⣷⠀⠌⠁⠐⢺⣩⢋⡱⠀⢸⣆⢹⣬⡟⠁⣀⣠⡤⠆
⠀⠀⠀⢤⡞⢱⣧⡄⠀⠀⠀⠀⡈⠀⠱⠟⠷⡀⡴⡀⠦⣝⣻⣧⠀⢸⠁⣸⣟⡛⠋⠉⠃⠀⠀⠀⠀⢰⡖⣤⡄
⠀⠀⠀⠐⠸⢿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⣧⡄⠀⠀⠘⠁⠀⢸⡶⣓⡚⠛⠛⠶⠀⠀⠀⠀⠀⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢉⣶⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠹⠟⠳⡄⠀⠀⡠⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⡏
⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣤⠄⣀⡀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢿⡆⠀⠀⠀⠁⠀⢙⣾⡇⠀⠀⡰⠟⢳⡄
⠀⡠⠠⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⠇⠀⠠⡀⠀⣿⡿⠀⠀⢦⣠⣴⣾⣿⠇⢰⠁⠀⠀⠈⠘⡄
⠀⠹⠟⣳⡟⠀⠀⠀⡆⠾⠀⠀⠀⠀⠀⠀⠀⢀⡬⠏⠀⠀⠀⠀⠀⡟⠁⠀⠀⠈⠉⠉⡟⠁⠀⠈⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠑⠀⠀⠐⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠐⠲⣤⣀⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠃⠙⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠄⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⠛⣦⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠖⣋⣁⣤⠾⠃
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠛⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠠⠤⠬⠭⠭⠶⠶⠶⠤⠄⢸⡿⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⡠⠴⠶⠶⠶⠖⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⣼⡇⠀⠈⠉⠒⠲⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⣤
⠀⠀⠀⣀⣀⣤⡤⠀⠀⠀⠀⠀⣼⠟⢉⠛⠦⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠉⠾⠿⡛⠓⠀⠀⠀⠀⠀⠀⣘⡛⠛⠷⠶⢦⡀
⠲⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠻⠦⠀⠀⣀⠠⠶⠛⠁⠀⠀⠀⠀⠀⠀⣤⣰⡇⠀⣰⠖⢠⡞⠋⢁⡀⠀⠀⠀⠻⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠋⠀⠀⠉⠁⠿⢠⡾⠋⡁⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⠋⠀⠀⠀⠀⠀⠀⣴⠇⠉⣿⣉⡵⠁⠀⣠⣶⣶⣦⣄⠀⠹⣄⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠈⠁⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⢰⡟⠓⢤⣄⣀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣼⢿⣦⣄⠀⠀⠀⠀⠀⢸⠿⠿⢿⡿⠁⠀⠀⠀⣀⣴⠟⠁⢸⡇⠀⠀⠈⠉⠙⠛⢛⣓⣴⡿⠋
⠀⠀⠀⠀⢀⡴⢚⣽⠟⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⣿⠻⠿⣶⣄⣀⠀⠈⠀⠔⠋⣀⣠⣤⠶⠟⠛⠁⠀⠀⠈⠃⠀⢀⣀⣠⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠘⠷⠋⠁⠀⠀⠸⣇⠀⠀⠃⠀⠀⠀⣰⠏⢀⣿⡇⠀⠀⠀⠀⠉⠉⠒⠒⠂⠈⠉⠀⠀⣠⣴⣦⣠⣤⣤⡴⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢀⣠⠾⠋⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡤⠀⠀⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⡴⠀⣷⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⠃⠈⠉⠛⠛⢿⡁⠀⠴⢶⣶⠶⠶⠶⠶⠿⠛⠋⠁⠀⠀⠀⢠⡿⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣀⡀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣼⠇
⠀⠀⠀⢠⡾⠛⠙⠷⠚⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠉⠛⠶⢦⣄⡀⠀⠀⠀⣸⡟⠀⣀⣴⠟⢣⡄
⠀⠀⠀⢿⡇⠀⠀⣠⡶⠟⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⣄⠀⠀⠀⠈⠛⠷⠆⢠⣿⡷⠞⠋⠀⠀⠀⠻⣆
⠀⠀⠀⠘⣧⠀⢸⣿⠀⠀⠀⠻⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⣤⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠘⢷⡈⢿⣇⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡘⠋⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠹⣦⣨⡻⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣮⠙⢿⣦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠙⢷⣄⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣬⣙⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣄⣈⣀⣀⣀⣠⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠙⠛⠶⢦⣤⣀⣀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣶⣾⣿⣾⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠙⠛⠋⠛⠛⠛⠛⠻⠿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠠⠴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣠⡿⠀⠀⠀⠀⢿⣤⣴⡟⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠖⢒⠆⠀⠉⠉⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡷⠶⠶⠀⠀⠀⠀⠀⠀⢠⣿⢡⡖⠓⣦⢹⡆⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⢹⠾⡿⣾⠃⠀⠀⢀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠟⠿⢶⣦⣤⣄⣀⣀⣀⣸⠇⣾⣛⡇⣿⣤⣴⣶⣿⣯⡁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⡄⠻⠿⢣⡟⠋⠉⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣼⢋⡉⢻⣄⠀⠀⣀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⢀⣼⠟⢉⡻⣆
⢀⡴⢛⣿⣻⣧⠀⠙⠷⠿⢿⣳⡶⢶⣿⣁⠀⠀⢀⡞⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠈⣷⠀⠀⢀⣹⣷⠶⠶⠿⠿⠿⠿⠁⠀⣾⣛⣿⠳⣦
⢾⣇⣻⣭⠌⣿⡀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢬⣽⣇⣼
⣾⣿⠶⣛⡧⠈⣛⣀⡀⠀⢸⣿⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠠⢽⣓⠾⣽
⠹⣷⣫⣵⠾⠛⠉⠉⢹⣿⣿⣿⠷⠶⠶⠶⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⢷⣶⣶⣶⣶⣿⠿⠟⠛⠉⠙⠛⠶⣬⣳⡾
⠀⠉⠉⠁⠀⠀⠀⠀⢸⣿⣽⣿⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠀⠀⣀⣀⣀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢃⣠⣤⣤⣤⣤⣴⠟⣉⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠶⠄⠀⣀⣀⣀⣤⣠⣾⠋⠉⠉⠉⠁⠀⠀⠐⣿⣿⠛⠳⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠿⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣤⣤⣽⠟⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣰⣿⠀⠀⠀⠀⠐⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠿⠿⠿⠿⠶⠶⢤⡄⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡍⠁⢀⣾⠛⠷⣤⣤⣤⡶⠿⢿⣶⣀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣼⡿⠯⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣧⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣠⢟⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣉⠉⢉⠉⠉⠙⠛⠛⠛⠛⠻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠁⠘⠻⠀⠤⠟⠿⠃⠧⠿⠀⣿⣏⣠⣿
⢀⣀⣀⣀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠷⡿⡷⡟⠇⡌⣶⡂⠀⠀⣿⡋⢙⣿
⣽⣗⡿⠿⠟⠛⠿⢿⣷⣤⣄⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⠠⢰⢰⢠⠢⣤⣤⡄⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣷⣶⠴⠤⣄⣉⠙⠛⠛⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠈⠈⡈⡈⢀⡀⠈⠉⠁⠀⠀⣿⡏⢹⡟
⠈⠻⣿⣿⡟⠀⠀⠀⠀⠉⠓⠢⢤⣤⡴⠿⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣧⣀⣀⣀⣈⣁⡑⠀⠁⠀⠀⠀⠀⢠⣿⠅⢸⡇
⠀⠀⠙⠛⠁⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣦⣾⣇⠀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡾⠥⠤⠍⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⢉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡖⡂⠁⠈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⣀⣴⡴⠟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣶⣶⡶⠚
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠀⠀⠀⢠
⠿⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠬⣷⡶⢶⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡄⠀⠀⠤⠶⠖⠲⣻⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠓⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣐⣒⣶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡁⠈⣹⣿⣿⣧⣧⠬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢷⣾⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡯⣅⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟
⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠟⢋⣽⣿⣿⣿⣿⣿⣿⡃
⠀⠀⢀⣿⣿⣿⣿⣿⠛⠉⠀⣠⣿⡿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⣿⣾⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠁⠀⠀⠠⠤
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⠿⣿⣿⡏⠀⠀⠒⠤⣄⢀⠴⠲
⢀⣀⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⣾⣿⣿⣿⢶⣭⡿⢿⣿⡿⣟⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⡄⠀⠙⠋⠛⠿⠿
⡟⣷⠿⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⠟⠀⡀⢡⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⣠⣤⣿⣿⠟⢠⠰⠀⠰⢰⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠛⠛⠛⣻⡿⠛⠁⠀⠀⢀⠈⢀⠈⠀⠐⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣴⣶⣶⣦⣶⣶⣶⣶⣶⣶⣦⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⣤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢦⣄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠘⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⡄⠀⢀⣇⠤⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠁⠀⠘⣧⢰⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀⡀⠀⣽⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠳⣄⠀⠀⠀⠘⠒⢦⣤⢤⣤⣤⠞⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠎⠓⠦⣄⣀⡀⠀⠉⠛⠛⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠠⣄⠀⠈⠉⢹⠏⠻⣟⠉⣁⠀⠀⠀⢀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠞⠁⠀⠀⠀⠀⠈⠑⠦⢤⣸⣀⣤⠞⠉⠉⣹⡀⡠⢇⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠉⣩⣋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠸⣑⠄⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⡀⠀⠉⠚⢵⣒⠲⠶⠶⠴⠶⠒⢳⠤⢦⣀⣏⡀⠀⠀⠙⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠶⠶⠾⠷⠒⠃⠙⡍⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠒⠋⠑⣆⡤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠶⠉⠫⢒⡆⠀⢀⡴⠂⠙⠆⠀⠋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢵⣄⣀⡀⠀⠀⠀⠀⡀⠀⠀⢸⡤⠴⠫⠄⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⢿⣿⣿⣿⠿⠿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⣿⡟⠀⢀⣾⣿⣿⣏⠀⠀⠀⠀⠈⠙⣿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⢰⣿⠀⠀⢸⣿⣿⣿⣿⣶⣤⣴⡷⠀⠀⣿⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⢸⣿⡀⠀⠘⣿⡉⢻⣿⣿⣿⣿⠃⠀⢀⣿⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠛⠻⠿⠟⠋⠁⠀⢀⣾⠏⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄⢠⣶⠿⠿⠿⠿⣷⣦⣀⡀⠀⠀⠀⢀⣀⣴⣿⡿⠶⠶⣶⣄⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣧⡄⢀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⢀⣠⣼⣿⢿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣿⣧⠰⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡟⠛⢿⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢻⣧⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠹⡷⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⣛⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣿⠻⣿⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠛⠛⠛⣻⣿⣟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⢿⠿⢿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢠⡞⠉⠉⠉⢻⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣤⣼⣴⣼⣬⣦⣥⣺⣵⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢸⡤⠴⠒⠢⢤⡿⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⡇⠀⠀⠈⣻⣦⣤⣴⣟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⢠⣿⣿⡇⠉⢹⣿⣿⡆⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿
⣿⣿⣿⡇⠀⣾⣿⣿⣷⠀⣼⣿⣿⣿⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⡇⠀⣿⡃⣿⣿⣿⣿⣿⠉⣿⠇⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⡇⠀⢹⣷⣿⣿⣿⣿⣿⣾⡟⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠃⠀⠀⠀⠀⣀⡀⠀⣄⣀⠀⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡞⠀⠉⠙⠛⠋⠑⢽⡗⢤⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣀⠀⡞⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢠⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡏⠈⣿⠁⠀⠀⢀⠴⠚⢳⡄⠀⠀⠀⢀⡀⠘⣿⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠻⠀⠀⠀⡏⠀⠀⢿⡇⠀⠀⣰⢋⢽⡆⡇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠻⡕⢶⠀⠀⠀⠀⠉⢹⡟⠚⠁⠀⠀⣇⡈⢺⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠞⠁⠀⠀⠀⢀⣀⡈⠻⡄⠀⠀⠀⣶⠈⠁⠀⠀⠀⠀⢸⡯⣁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⡏⠀⠀⠀⢀⡜⠁⠀⠈⢳⡹⣄⠀⠀⠀⣶⣤⡶⣾⣲⣤⣠⡀⢛⡞
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢫⠳⣧⣀⡈⠀⠀⠀⠀⠀⣙⡷⢫⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⣇⠀⠀⠀⡼⠀⠀⠀⠀⠀⡇⠀⢳⣞⠒⠛⣩⠟⠛⡿⢏⠁⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢠⠏⠈⠦⡀⠘⠧⣤⠤⢤⡤⣤⠟⠀⠈⠉⠉⠉⠁⢀⣼⣁⡼⠐⠿
⠀⠀⠀⠀⠀⠀⠀⢘⡄⢸⠀⠀⠀⠈⠲⣄⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠔⠋⠀⢸
⠀⠀⠀⠀⠀⠀⡴⠉⠙⢾⡄⠀⠀⠀⠀⠈⢻⡀⠀⠀⠸⡄⠀⠀⠀⣰⡻⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠹⡖⠛⠉⠀⢳⠳⡀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢹⢀⣀⣀⠈⠀⠀⠀⠀⠀⠀⡼⣷⣄⠀⠀⠈⠉⠓⢦⡼⠀⠹⣄⠀⠀⠈⠛⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠓⠤⣄⣀⣠⠴⠊⠀⠀⠉⠓⠤⠤⣤⣤⠴⠃⠀⠀⠈⠳⣼⡷⣄⣄⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠀⠉⠀⠀⠀⠀⠈⠉⠂⢄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠀⠀⠀⢣⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣧⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠈⠳⡀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⡀
⠀⠀⠀⠀⡠⠂⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣆⠔⠁⠈⠠⡄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠱⠀⠀⠀⢀⠃⢀⠠⡄⠀⠁⠀⠰⠅
⠀⠀⠀⠀⠱⡀⠀⠀⠀⡇⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠥⠐⠀⠀⢀⠬⠐⠋⠀⠱⠄⢠⠒⠁
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠱⣌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠉⠉⠉⠢⢄⣀⣀⣀⣀⣀⣀⡠⠤⠀⠀⠁⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠔⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠈⢣⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡲⠀⠊⠐⡐⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠠⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠢⠀⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣡⠄⠂⠁⠀⠀⡄⠀⠀⠀⢠⠂⠀⠀⠇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠒⠚⢢⣀⠀⠘⠀⠀⠰⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠄⠒⠁⠈⠑⠤⠤⠔⠁


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠳⠌⣉⡹⠦⣘⣀⣁⣬⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠒⢬⢤⣠⣤⡷⠾⠟⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠈⠀⢈⠁⡆⢃⣴⠎⠀⠉⠻⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠀⠈⣿⠁⠀⠀⠀⠀⠈⣷⣿⠛⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⢻⣿⣿⣷⣾⣧⣄⠀⠀⢈⠀⢠⣛⠽⠶⢠⠃⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠒⠺⢈⠹⣿⣿⠛⢏⡋⠱⠙⢻⠗⡼⡀⢁⠴⠀⠀⠀⠀⠀⠀⠀⣌⣠⡾⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢙⡍⠙⢷⣌⠓⠀⡀⠇⠀⠣⡀⠁⣴⠉⠀⢤⡄⡰⣤⠏⣽⡏⠀⠲⣴⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢤⡀⠀⠀⢠⠚⠾⠀⠀⠙⢧⣀⠀⠀⠀⠀⡇⠀⡌⠙⠧⣼⡋⢠⡄⠀⠙⢷⣬⣙⢋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⠄⠀⠀⣀⣱⠀⡔⣠⢠⣿⡤⠂⠉⠈⢿⠀⠈⠁⡤⠃⠀⠃⠀⠀⠈⠙⠿⣧⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢕⢧⠀⠒⠀⠹⡟⠛⢅⡀⠛⢿⣷⠀⠀⠀⠀⠁⠀⡔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⣴⣷⡖⢁⣀⡇⣠⠊⠀⠀⢀⣿⣤⡄⠤⠤⠤⠀⠰⢾⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠻⠟⠚⢋⡰⠃⠀⠄⠘⢋⡙⢿⡀⠀⢀⡤⢀⡴⠛⠙⣦⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⢸⠸⠂⠈⠉⢹⠋⠁⠀⣄⢤⣿⣆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⢔⠁⣿⣄⠀⠀⣿⠀⠀⢀⣽⣾⡷⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡮⠟⠁⠀⠀⠙⣿⣶⢿⠀⢀⡼⣿⣿⣧⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠠⢻⠇⠈⠁⠁⠀⡞⠉⠀⠀⠠⡀⠀⠀⡴⠀⠐⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠐⢠⠂⠀⠶⣐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠴⣟⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢣⣌⡴⠀⠀⠀⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠩⡃⠀⠈⠑⢀⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⢆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⣠⠬⣦⡀⢀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠸⠊⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⡴⠙⣢⡼⠋⡟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⣏⠀⠐⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢠⠞⢁⣴⠋⢀⣜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠲⠄⠚⠘⠡⣄⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠀⠀⢠⠋⣠⠟⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣂⣤⠤⠊⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢧⣀⠀⠈⢦⣀⠴
⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠛⠁
⠀⠀⠀⠀⠀⠾⢷⣾⠏⠀⠀⣀⠠⠀⢀⠀⡙⠁
⠀⠀⠀⠀⠀⢠⣟⢈⠉⠭⠍⢀⡉⠢⠍⢄⠁
⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠉⡶⠸⢾
⠀⠀⠀⠀⠀⢯⣤⣤⢀⣀⠀⣀⣠⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣀⡒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡀⠀⠀⣀⣤⣶⣶⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣝⣯⣌⣉⣛⣿⡿⠿⠛⠋⠙⠛⠻⠻⠯⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢟⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⠇⠀⠀⠀⠉⠳⠦⠀⠀⠀⣀⣤⠖⠂⠀⠀⠈⢻⡿⢚⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡎⠻⠄⢀⡠⠶⠒⠒⠢⠀⠀⠀⠈⠴⠛⠛⠳⠀⠀⠘⢳⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠐⠠⠟⠸⠆⠲⢀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠎⣠⣔⠒⠐⣦⣄⠈⠂⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⣿⠿⣿⣿⣟⢿⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠈⠈⠁⠂⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡠⠔⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⡍⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠘⢦⠀⠀⠀⠀⠀⣰⠏⠀⢰⣤⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣿⣿⣿⣧⠀⠀⠀⠑⢄⠀⢀⠜⠁⠀⢀⣾⣿⣿⣿⣶⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⣾⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠟⠁⠛⠋⠋⠇⠃⠈⠉⠉⠙⠛⠛⠻⠛⠻⠟⠀⠀⠀⠀⠇

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⢶⢶⣤⠖⢦⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⣇⠀⠁⠀⠈⠀⠀⠀⡸⠛⠛⠓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠊⠉⠉⠉⠑⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢧⢠⠞⠉⠛⠀⢀⡜⢡⠋⢉⠦⣄⠀⠀⠀⠀⠀⠀⣠⢤⡴⢤⣀⡀⣇⣠⠖⠲⡄⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⢀⡠⠋⡠⠊⢀⠎⠀⡜⠋⠀⠀⠀⠀⠛⣇⠀⡇⠀⡇⠹⡌⠁⠀⢀⡇⢸⠁
⠀⠀⠀⠀⠀⠀⡜⠀⣸⣃⠏⠀⠊⠀⠔⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⡄⠀⠀⠹⡞⢉⠿⡄⢸
⠀⠀⠀⠀⢀⣀⡇⢸⠁⢹⠀⠀⠀⠀⠀⣰⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⢱⡎⢴⢃⡞⠲⣄
⠀⠀⣤⠚⠉⠉⠹⣄⢓⣼⠀⠀⠀⠀⢰⠇⡀⠂⠀⢀⠀⠀⢀⠅⠀⠴⠀⡣⠀⠀⠀⠀⠀⡇⢸⡏⠀⠀⠈⢳⡀
⠀⢸⠁⠀⠀⠀⠤⡹⢺⠁⠀⠀⠀⢀⡾⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡧⣼⡗⠂⠀⠀⠀⡇
⠀⢹⠀⠀⠀⢀⣴⠃⢸⠀⠀⣠⠖⢻⡇⠠⢢⠀⠀⠀⠐⠂⠀⠂⠀⠀⠘⡷⣀⠀⠀⠀⢺⠃⠀⠙⢆⠀⠀⢀⡇
⠀⠸⡄⠀⠀⠀⠀⠀⠸⣄⡴⠃⠀⣼⡀⠈⣈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠷⡈⠳⣄⣠⠋⠀⠀⠀⠀⠀⠀⡞
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠻⡀⠀⣰⠃⠉⠉⠉⠉⠓⠒⠤⠤⠤⠒⠚⠉⠀⠀⢙⣤⡼⠃⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠳⣄⡀⠀⠀⠀⣀⡽⠶⣇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠙⠓⠦⣤⣀⣀⣀⣠⡞⠁
⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⣨⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⡯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠀⢳⠈⣟⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⣸⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⠓⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⠓⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠈⢓⡶⠤⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⡠⠴⠚⠉⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠒⡖⠂⠀⠀⠐⠂⠁⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣤⣤⣶⠀⠀⠐⠲⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾
⠀⠀⠀⠀⠀⠀⠒⠛⠿⠿⠷⠆⠙⠛⠌⠱⠀⠀⠒⠒⠘⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⣀⡤⠀⢀⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣾⣶⣇⠀⠋⠀⠀⢨⣌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣼⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠚⠉⠀⠀⢀⣤⡯⠻⣿⣿⣆⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⣿⣿⣿⣿⣿⢿⡷⢚⡒⠂⠀⠴⠒⠂⠀⠈⠀⠀⠄⠐⢤⣄⢸⣿⡛⠀⠀⣠⡶⡄
⠀⠀⠀⠀⠀⠀⠠⠶⠿⠃⢀⣿⣟⣷⡼⠻⢏⡀⡈⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⢤⣠⣔⡿⣿⠷⠀⠼⢻⡤⠁
⠀⠀⠀⠀⠀⠀⢀⠤⢖⣿⠖⠀⠀⠁⠶⡷⢢⠌⢇⣈⣿⠀⢐⠆⢀⣄⠈⢀⡀⠄⢀⢆⣬⠛⢉⣥⡄⠃⢺⠇
⠀⠀⠀⠀⠀⠀⠀⣐⣉⠁⢀⡀⢀⣴⡀⠤⠉⠃⠀⠀⠛⠀⠈⠁⠈⠁⠀⠀⠁⠀⠀⠂⣀⣰⣾⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠈⢶⣿⣿⣿⡿⠿⠿⠿⠆⠈⠀⠀⠀⠀⡀⢀⠀⠀⠀⣤⠒⠒⣞⣻⠟⠀⠀⠀⠀⠘⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠎⣼⠋⠀⠀⠀⣀⣄⡄⣠⠀⢠⣶⡆⡿⢷⡟⠀⠟⢲⠏⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⡏⢹⡁⠀⣬⣿⢧⣱⣼⡧⡏⠷⣸⣥⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣨⠴⠿⠤⠶⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⣲⣶⣦⣤⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⣠⠴⠖⠚⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⠟⠛⢻⣧⠀⠀⡤⠀⠀⠀⠴⠒⠲⣄⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣤⡤⠿⢬⣀⡀⣨⠏⠳⣄⠙⠦⠤⠀⠀⠀⠀⠸⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡞⠁⠀⠀⠀⠈⠉⠁⢠⠖⠛⢷⣦⣄⣀⣀⣀⣀⣀⡤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢧⣀⠙⠛⢯⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢃⣼⣀⠀⢀⡴⠚⠛⠓⠶⣄⢨⢷⡄⠀⠈⣷⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⠀⠈⠛⠋⠀⠀⠀⢀⠀⠘⡿⣆⠀⠀⠀⢛⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⢀⣠⣀⣀⣠⠞⠀⣰⠃⠈⣻⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠯⣭⣀⣀⣈⣡⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿