Sleeping Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠈⠓⠒⠒⠒⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⣀⣤⢤⣤⣀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⣴⣿⣿⣿⠷⠿⠟⣿⣦⣦⣄⠀⡀⠄⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢰⣿⣒⣶⣿⡿⠛⠃⠀⠀⠀⠀⠀⢤⣭⣻⡧⠀⠐⠂⡀
⠀⠀⠀⠀⢀⣀⡀⠀⣠⠤⠒⠠⢌⢀⣄⣿⣿⣿⣿⣯⡇⠀⠀⡄⠑⡄⠀⠀⠈⢹⣯⡧⠔⠚⠉
⠀⠀⠐⠋⠉⠉⠿⣿⣶⣤⡀⠀⠀⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠉⠀⣀⠠⢄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠛⣶⣥⣀⡈⠹⢿⣿⣦⡀⢀⣇⠈⠁⠀⢸⡀⠀⢠⣄⠀⡄⠐⠆⡬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠈⠙⢿⣷⣤⠄⠙⠯⣿⣧⡏⠀⡅⠀⠀⠱⡀⠀⠙⣃⢤⡲⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠈⠻⣶⣤⢂⠈⠛⢷⣤⠀⡘⠛⠿⣦⡁⢠⣴⡾⠟⠉⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠈⠙⣷⣆⠀⠀⠉⠛⠢⢤⣄⣀⠉⠒⠥⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠡⢆⠀⠀⠀⠈⠻⣷⣤⡄⡀⠉⣦⣄⠀⠲⢤⣀⠀⠀⠀⠀⣠⣾⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣀⠀⠙⠻⣷⣄⠠⠌⠻⣷⡄⠀⠈⠑⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⣤⣠⣿⣷⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢿⡇⠀⢠⡀⠀⠀⠀⢀⣠⠀⠀⣄⡀⠀⠀⠀⢀⡄⠀⢸⣿⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠘⣧⠀⠀⠙⠻⠶⠾⠛⠁⠀⠀⠈⠛⠷⠶⠟⠋⠀⠀⣼⠏⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣽⡀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⢀⣯⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠈⢉⡁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠿⠟⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣬⣿⠦⢄⣀⡀⠀⣀⡠⠴⣿⣥⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⢉⠂⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡄⠀⠀⠀⠀⠀⠀⢀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⠦⠤⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠛⠛⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⡀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⢄⢢⠠⠀⠈⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠡⡆⢺⠆⢈⣿⣷⡦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣷⣿⠀⢸⣿⣿⣿⢿⣿⣕⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠤⢆⣹⡏⡀⠀⠙⢿⠟⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠂⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠉⠺⣁⢤⢶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣀⡤⠚⢍⠉⠉⠁⢶⠢⠤⣄⡀⠀⠈⠢⠍⠾⢤
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⡿⠏⢹⠀⠀⠀⠱⡀⠀⢸⠀⠀⠀⠈⠑⠒⠤⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⡆⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠣⡀⠀⠀⢸⡄⠨⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡇⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣠⠾⠗⣸⠋⠁⢀⢫⡟
⠀⠀⠀⠀⠀⠀⢃⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢒⡪⠥⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠮⡑⠒⠤⠤⠤⠄⠒⠛⢛⣢⣴⠞⢉⠽⡓⡂⣁⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠑⠒⠒⠒⠒⠲⢾⠿⠟⣁⢴⠁⠀⠀⠀⢀⡀⠀⢀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⢠⣀⣀⠀⣀⣀⡠⠤⠒⠉⠀⠀⠢⠤⠒⠉⠀⠀⠀⠀⠈⠁

⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⡖⡖⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠶⠒⠒⠆
⠀⠀⠀⠀⡟⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⢸⠘⢲⠚⠒⠚⠛⠛⠛⠛⠓⣧⢰⠀⠀⠀⠐⠂⠐⠒⠐⢰⠄⡘
⠀⠀⠀⠀⢁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⢸⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠆⠀⠀⠀⠀⠸⠀⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢐⡇⢸⠀⠀⢠⠄⠀⠀⠀⠀⡀⠀⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⡈⠀⠀⠀⠡⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸
⠀⠀⠀⠀⠀⠥⠀⠀⠀⣃⡄⠀⠑⠢⠄⠀⠆⠀⠀⠼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⣦
⠀⠀⠀⠀⠀⢠⡀⠀⡠⠃⠀⠀⠀⠉⠉⠀⠈⠂⠀⡘⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢀⣼⠤⢦⡀⠀⠀⢀⡀⠀⠀⠈⠀⡋
⠀⠀⠀⠀⠀⠀⣤⠀⡀⠤⠤⠀⠀⠐⠒⠂⠂⠀⠉⠁⠀⠀⠀⡆⠀⠀⡇⢸⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠐⢥⣴⠖⡇⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠐⠢⠀⠀⢀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⢸⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣧⣤⣄⣤⢸⠀⠀⠀⢸⠀⢼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⣠⠖⢊⣡⡼⠋⠻⠥⣀⠀⠀⠉⠚⢦⣤⠤⢼⣀⣾⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⢰⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡐⢂⠜⠒⠂⢤⣠⠞⠀⢀⠰⠋⠀⠀⠀⠀⠀⠈⠁⠐⠲⠤⢌⢢⣀⠄⠘⠓⢦⣄⣀⣀⣀⣤⡇⢸⠀⠀⠀⠀⠀⠀⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⠃⠀⡠⠴⢾⢃⡤⠊⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⠒⠤⣀⠀⢩⡉⠉⠁⠀⠁⠈⠀⠒⠒⠒⠒⠀⠃⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢿⡤⠏⠀⠀⠈⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠢⣼⠉⠉⢉⡩⠭⠭⠌⣉⠉⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⢀⡤⢾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣄⠀⠀⠁⠀⠀⠏⠐⠠⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡅⠸⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡸⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠈⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢡⠀⢸⠀⡤⡟⠒⠠⠤⠤⠤⠴⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⢸⠀⢸⢐⡇⠀⢱⣦⠶⢶⡖⠈⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡼⠀⠀⠀⠀⠀⢠⠝⠶⠐⠒⠚⠃⠐⠒⠶⠤⢶⣉⣀⠀⠀⠀⠀⠀⢣⡈⢸⠱⠦⠴⠶⠿⠿⠦⠤⠦⠴⠶⠦
⠀⠀⢀⣀⡀⡀⢀⣀⢈⣷⠒⠀⣀⠞⠉⠀⢀⣄⣀⡀⠠⠄⣀⣀⠀⠀⢀⡀⠉⠫⣄⡈⠉⠈⣯⣵⢼⣄⣀⣀⣀⡀⣀⠁⡀⢀⠀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⣰⠁⠀⠀⠰⡿⠏⣀⡀⠤⠄⢀⣀⠉⠑⡾⢬⡇⠀⠘⡇⠀⠀⠈⢁⠛⠋⠘⠛⠙⠛⠛⠟⠋⠙⢻⢾⡃⠉⠀⠉⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢁⣀⣈⣦⣠⠶⠅⡀⣠⠊⢠⠀⢀⠀⠀⢈⠙⠀⢀⠨⠶⣶⣦⢤⣤⣤⠈⣶⡦⠀⣀⣀⣀⠄⠀⣀⣀⢸⡟⠋⠛⠛⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢨⠛⠀⠈⠁⠀⠃⢀⡴⠉⠀⠀⢀⡂⣈⡁⠨⣄⠐⠀⠁⠀⠀⡴⠦⣀⡤⣄⠀⠉⣴⣄⣀⣄⣀⣀⣀⣏⣻⣿⣃⣤⣤⣤⣼⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡃⡆⢀⡔⠀⠄⠀⣭⣠⢀⡀⠀⠀⠀⠀⠀⠁⡌⠀⣤⢤⣰⡄⠈⠆⢸⡡⠖⠀⠀⠈⠅⠀⠀⠀⠀⣀⣀⠠⠀⣀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⡾⠁⠰⢀⣐⣀⠠⡎⠀⠀⡾⠶⠸⢤⣀⡅⣤⣧⡄⠠⠘⡀⠀⠈⠦⠠⢀⠀⠀⠃⠐⠂⠚⡄⠀⠠⢎⠀⠀⡀⣀⠤⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡸⠓⠛⠂⠉⠉⢀⢀⣣⣤⣌⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠸⠦⠴⠆⣀⣀⣀⣈⣉⣉⠈⠀⠙⣄⠀⢀⡄⠛⠛⠁⠒⠓⢠⠀⠀⠀⠈⢆
⠀⠀⠀⢠⠒⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠐⠊⠉⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠑⠒⠐⠒⠒⠂⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠈⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠦⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠶
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠉⠉⠉⠉⠙⠉⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⠀⠠⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⠤⠄⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⣀⡴⠚⠉⠉⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠡⠀⠀⠠⠤⠁⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢠⢤⣀⠀⠓⠈⠙⠛⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣇⠀⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠄⠀⠀⠀⡠⣊⡂⠰⠀⠀⡀⠄⠀⢀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠠⠄⠀⠉⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠈⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠑⠤⣀⡀⠤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠠⠊⣰
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠦⠤⠤⠤⠒⠒⠒⠀⠀⠀⠀⠀⠈⠒⠢⠤⠤⠤⠀⠠⠤⠤⠤⠴⠖⠿⠦⠤⠤⢤⣤⣤⣬⣅⣤⣤⣤⠤⠤⠤⠤⠴⠖⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣴⣷⣶⣾⣿⣶⢠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠠⠀⠀⠀⠆⠀⣿⣄⠀⠘⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢿⡏⠟⠀⢿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣙⣬⡋⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡄⢀⠀⠀⢘⢠⠀⠀⠀⣻⢁⠁⠀⠘⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⢹⣷⢿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣷⢀⢳⢸⠀⠀⠈⢳⣇⠀⠀⣿⢸⣷⢀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠄⣿⠘⡀⠛⠄⠀⣬⠀⣿⠀⠀⣹⣧⣟⡌⠿⣂⠙⡛⠿⢿⣿⢿⡟⠟⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈⡖⠀⣿⡐⣧⠐⢦⡠⠿⠇⠸⢣⡸⣻⡞⢻⣧⣧⠈⠃⠁⡜⡛⠻⠛⠀⠶⠤⢠⣭⣉⣛⡛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡆⣿⣿⣽⣦⠋⠀⠀⠀⠈⠛⣷⣿⣡⠐⠸⡃⠀⡇⠸⢷⣿⣶⣦⡄⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠟⠛⣻⣀⣠⣠⡀⠀⠀⠀⠬⢻⠉⠀⠀⠁⠀⠇⠀⠘⣻⡿⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠻⡛⠛⣂⣴⣿⣿⡟⣿⣿⣿⣦⡀⠀⠀⠈⠀⠃⠀⡆⠀⠁⠀⠰⠃⠘⡇⡀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠰⡤⢼⣿⡿⠉⠉⠛⠿⠛⠈⣿⣷⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡞⢀⠀⠃⠁
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠉⠻⠿⠁⠀⡀⠀⠀⠀⠘⠙⢿⣇⠀⠀⠀⠀⠀⡀⠘⠀⢢⠁⠸⠆
⠀⠀⠀⠂⡔⠁⠀⠀⠀⠀⠀⠀⠑⡀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠚⠀⠈⠀⠀⠀⠰⠐
⠀⠀⠀⠀⠋⠓⠒⣬⠁⠀⠀⠀⠈⣖⢏⡀⠠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡜⠀⣄⢀⠀⠀⠀⠀⢀⣉⠂⠘⣷⡶⠀⠀⠨⣀⢀⠀⠀⠀⠀⠀⠀⡀⠚⠲⠂
⠀⠀⠊⡅⠀⡆⠀⡤⠀⠀⠀⣤⠙⠇⠀⠀⣄⠀⠀⠀⠉⠉⠀⠀⠀⢀⡠⠄⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⢻⠐⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⠀⠁⠀⠀⡁⠀⠀⠇⠀⠠⠱⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡀⠀⠀⠀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣀⠈⠑⡤⢌⠁⠀⠀⠀⠀⣀⠤⠔⠒⠶⣶⠦⠤⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠣⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡘⠛⠕⣢⠀⠀⠉⠀⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠐⢲⠀⠈⠁⠀⠀⠀⠀⡈⠀⠀⠀⠘⡤⢸⠤⢀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⡠⠔⢊⠅⠒⠀⠀⠒⠢⠉⠁⠒⠤⢌⡀⡄⠈⠀⠀⠃⠀⣳⠀⠀⠀⣉⠢⣀⣀⢸⡀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⡠⠊⠀⡰⢋⣰⠆⣠⡄⢴⣈⡙⠄⠀⠀⠀⠀⠁⠂⠤⢀⣠⣶⠟⠀⣐⠁⠀⠀⠀⠀⠈⠉⠓⠤⡀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⢰⠁⠀⠀⠳⣻⠟⠏⠙⢉⠻⢿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢩⡤⠄⠉⠒⠠⠀⠠⠤⠀⠀⠘⠓⠈⠉⠁⠀⠀⠀⢡
⠀⠀⠰⠁⠠⠤⠤⣴⠋⠀⠐⢄⠆⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⢯⢊⠅⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠒⠒⠒⢺⣅⠀⠀⠈⠀⠀⠀⣸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠛⠉⠈⠛⠢⡀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡄⢀⠀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⠉⠉⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢠⣄⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣠⣶⣿⣧⣀⣼⣿⣿⣿⣿⠋⠐⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣴⣷⣶⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡁⢠⣾⣿⠉⢹⠏⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡏⢈⣿⣿⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠿⣿⠿⢷⠀⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⣷⣶⣶⣶⣆⣠⣄⣈⣁⡘⢳⣝⠿⣿⣿⡿⠟⠀⠀⣠⣴⣿⢿⣿⣿⣿⣷⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣿⣿⣿⣿⠋⠉⣹⣿⣿⣿⣬⣇⠀⠶⠶⣤⠴⣶⣾⣿⣿⣶⡿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⠛⣿⣿⣿⣿⣿⣉⣿⣿⣇⣄⣤⣿⣿⡿⢿⣿⣿⣿⣶⣦⠀⠀⠻⠿⢿⣿⣷⣤⡾⠛⠉
⠀⠀⠀⠀⢀⣤⣶⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣿⣷⡘⠀⢩⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠈⠃
⠀⢠⣄⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣤⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣷⣠⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠈⢻⣧⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⢿⣿⣿⣿⣿⣀⡽⣻⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣼⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠠⢤⣴⣶⣿⣿⣿⣷⣦⡤⠤⠄⠒⠒⡄⠀⠀⠀⠀⠀⡀⠠⠤⠄⠠⠔⠁⡥⠀⠀⡀
⠀⣀⠔⠊⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠱⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠸⡥⡤⠔
⢀⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠈⠷⡤⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⣉⠁⠀⢀⡀⠀⠐
⢸⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠻⠀⠀⠁⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⡠
⠈⠀⠀⠉⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣴⣾
⠀⠣⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢢⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢔⣡⣾⠟⠁
⠀⠀⠑⢄⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣴⡯⠛⠁
⠀⠀⠀⠀⡶⠠⠄⠀⠉⢉⡋⠗⡄⡠⣤⠒⢒⠚⠐⠀⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠄⢸⠀⠀⠈⠘⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠐⠦⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⡄⢠⣦⡾⡄⠀⠀⢳⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠊⣀⢴⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠙⠄⠀⠊⣛⡿⣿⣿⣿⣿⣯⣿⡇⠀⣿⣿⠟⢣⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠁⠀⠀⠉⠉⠛⠛⠇⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣻⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⡴⠚⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡰⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣠⠢⠀⢠⢷⣬⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠁⠈⠀⣸⢿⠛⠀⠤⠐⢤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⢀⠀⠠⠔⠒⠀⠐⠲⠦⡈⠀⠑⠂⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠁⠀⠀⢀⡤⠆⣩⠥⢬⢸⢷⣠⠠⡄⢀⠭⠐⠂⠛⠀⠠⠔⡒⠦⢍⣱⡤⠔⠂⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠎⠀⠀⠀⠞⢸⠃⡄⠘⠶⠁⠚⢿⠼⢵⣱⢀⠀⠀⠀⠀⠀⠐⠀⠙⣇⠀⠘⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⢀⠂⢰⠀⠟⠀⠀⡄⠀⠄⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⢦⣲⡀
⠀⠀⠁⠀⠀⠘⠀⠀⠀⢸⡀⠄⢹⣠⣲⣦⡾⠂⠀⠀⠈⠀⠀⡀⠀⠀⡇⠀⣈⠣⡀⠴⠆⠀⠀⠈⢣⡧⢨⢻⠇⡄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢣⡀⢳⢘⡿⣿⠁⢀⠀⡁⠀⠚⠰⠗⠀⢀⣇⠂⣀⡰⠟⠉⠂⠀⠀⠀⢘⣇⡿⣿⣷⠂⢀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠾⠏⠷⠞⠒⠮⣐⠃⠀⠀⢀⠤⠀⠚⠛⠖⠁⠀⠀⠀⠀⠀⢲⣄⡼⡟⠱⢇⠏⢀⠌
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠢⠁⣀⣀⡀⠀⠉⠉⠙⠛⠚⠦⡀⠀⠀⠀⠀⢀⣀⣤⡴⠻⠿⠛⣱⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⡖⠛⠻⠭⣽⠟⣽⡄⠄⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠞⠋⠑⠲⠄⢀⣠⠤⠞⠁⠀⠀⡼⠃⠀⠟⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⡜⠀⢠⣞⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠶⠶⠶⡶⠄⠀⠀⠸⠃⠀⣌⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠂⠀⠀⢰⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⢻⣿⣿⣆⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⢨⣿⡅⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣹⣿⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢿⣿⣿⣿⣦⠀⠀⠀⢃⠀⠀⠆⠀⠀⢸⣿⣆⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣽⣿⡁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠇⠀⠀⠀⠔⠀⠀⣠⣾⣶⡆⢰⣶⣶⣶⣶⣷⡀⠀⠈⢆⠀⠀⠀⠀⠸⣟⡿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠊⠀⢀⣴⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⢢⡀⠈⠔⠀⢠⣾⠟⠛⠻⣶⣶⣶⣶⣄⠀⠉⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠆⠀⡜⠁⠀⠔⠁⢀⣴⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢸⡿⠃⡀⢠⣿⡟⠃⠀⠀⠈⢻⣿⣿⣅⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⢠⡴⡿⠰⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠇⢸⠁⠈⠠⠘⠋⠀⠙⠋⠀⠀⠀⠉⡿⠟⠀⠀⠀⠀⠀⠈⣹⣿⣿⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠒⢻⣶⣶⠀⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⠆⠀⠀⠄⠀⠀⠀⠁⠀⢀⠈⠓⣠⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣞⣀⡤⠤⠤⠴⠤⠿⣿⣤⡟⠛⠛⠉⠉⠉⠉⠩⠍⡉⠛⣿⢿⣤⣀⠰⠀⠀⠈⠀⠀⠀⠀⡡⠄⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠐⠂⡀⠈⢼⡏⠈⠀⢧⠀⠀⠀⢀⡴⠊⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⣁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⠁⠀⠉⣧⡦⢶⡤⠷⣶⡀⠉⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⠈⢳⠚⣳⣞⣛⣭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠙⢅⢀⣀⣀⡙⠃⠄⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠈⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢋⠄⠀⠀⠀⠀⠀⠀⠡⡀⠂⠖⠀⠀⡈⠉⠩⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠛⢥⠄⣀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠉⠀⣀⡂⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⣍⠉⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠉⠐⠄⠀⠀⠀⠀⠀⠠⠮⠄⠀⠀⢀⡤⠔⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠤⠁⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠔⠤⡀⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡌⠀⠀⠀⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠈⠢⢅⡀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠝⣠
⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠤⠤⠤⠤⠒⠘⠦⠤⠤⠤⠤⠭⠤⠤⠤⠤⠤⠤⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⣶⠟⠉⢐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣵⣿⣿⣧⣀⠆⠠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠂⡠⢂⢏⡠⠈⣀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠋⠛⢤⢾⣷⠀⠬⠄⢲⡛⠒⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⠿⠀⠓⠤⠊⠀⠉⠋⠀⠀⠀⠀⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⡀⠀⠄⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠆⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡅⠀⠀⠠⠀⠐⠤⡀⠀⠀⠀⠠⠀⠀⠀⢠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⢀⠀⠀⠈⠑⠢⠄⣀⣀⣀⣀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⢁⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠑⠢⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡤⣀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠰⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠷⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⣀⡄⢀⡞⣧⠀⠀⠀⠀⠀⠀⠀⣤⠊⠥⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⡶⡊⠑⠃⡀⠘⡀⠀⠙⠉⠀⡀⢊⠈⠑⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠧⣤⢦⡀⡀⠀⢰⠠⠂⠀⢰⠀⠈⠫⠬⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⡼⠀⠈⠙⢼⢃⣠⢼⡖⢶⣲⣺⠿⠲⡆⠐⢢⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠃⠀⠚⠿⠿⠿⣯⢴⣯⣾⣿⣿⣿⣿⣷⣿⣷⣿⣿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠧⣈⣳⡀⢠⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠐⢏⡩⠽⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢛⠻⢿⣿⡏⠀⠀⠀⠀⣶⠖⡤⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⣿⡿⠁⠶⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⢠⣿⠃⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡴⠁⢘⢷⡀⠈⢦⣉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡸⠃⠀⠀⠀⠀⠀⣤⡼⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⣿⠏⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⢷⣄⠀⠀⠀⠀⠀⠉⠀⠒⠙⠀⠀⠀⠀⠀⢠⡾⠳⣶⣦⣀
⠀⠀⠀⣀⡴⠖⠲⠞⠉⠀⢀⣀⣀⡾⠉⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡿⠠⣄⡼⠃⢙⢧⡀
⠀⠀⢸⡋⠀⠀⠀⠀⠠⡶⠋⠁⠉⣹⠖⠂⠀⠙⠿⢭⣿⣷⣶⠖⠒⠻⣏⠁⢀⡿⠀⠈⠓⢶⡁⣰⠇
⠀⠀⠀⢿⣀⡀⠀⠀⢀⡟⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡜⠷⠋⠀⠀⣴⠦⠴⠛⠁
⠀⠀⠀⠀⠙⢧⡴⠷⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠶⠞⠁
⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⢸⡦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣠⠞⡱⠋⢹⣆⡀⠘⣇⠀⠈⠉⠙⠛⠶⠦⣤⣄⣀⠀⢀⡟
⠀⣠⠞⡡⢊⡤⣴⠏⠈⠙⢦⣾⡳⣤⣀⠀⠀⠀⠀⠀⢠⠟⠻⣿
⣼⣣⠎⢱⣭⡵⠛⢦⡀⠀⠀⠈⠙⢲⡽⠛⠓⠶⠦⢤⡏⠀⠀⢈⡇
⠈⠛⠛⠋⠁⠀⠀⠀⠙⠶⣤⣤⠴⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢧⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠠⣀⠸⢭⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣅⠢⢍⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡾
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠲⡄⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠄⡔⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⡖⠲⠒⠒⠂⠐⠂⠒⠀⠐⢺⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡀⠀⢰⠀⠃⠀⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⡇⠀⠀⢰⠀⠃⠀⠀⠀⢰⠀⡄⠀⠀⡈⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡇⠀⠈⡀⢰⠀⠀⠀⠀⠀⢁⠀⠀⠀⡇⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡇⠀⠀⡇⢸⠀⠀⠀⠀⡇⠸⠀⠀⠀⠁⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠧⠤⠔⠃⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠒⠒⠚⠒⠒⠚⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠐⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠒⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⠎⣀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⢤⡈⢇
⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡒⠒⠒⠒⢲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠶⠀⢈⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣁⠀⠚⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣷⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣧⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡾⠋⢀⣴⡆⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⠻⣿⣿⣯⠉⠀⠀⠈⠉⠁⠀⣿⣇
⠀⠀⠀⠀⠀⠀⡀⣠⣶⣟⠋⠻⣿⣿⣆⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⣶⡿⠛⠛⠛⠛⠛⠛⠻⢿⣷⡄⠈⢻⣿⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⣴⣿⣿⣆
⠙⣷⣄⠐⢿⡇⠀⠀⠀⠀⠙⠿⠀⠀⠁⠀⠀⠀⠀⠰⢦⡴⠾⠋⠀⠈⠉⣡⣼⣿⡄
⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⢻⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⣿⣿⣷⣄
⠀⠀⠀⢸⡇⠀⠀⠰⣦⣤⡾⠋⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠀⠘⠋⢁⣾⣿⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠀⠀⠀⠀⠚⠛⣩⣿⡄
⠀⠀⠀⠀⠘⣿⣿⡿⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠈⠙⢷⠀⠀⠀⠀⠀⠘⠻⢿⡇
⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡍⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⠿⠳⠶⠶⠶⠶⠶⢶⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣀⣠⣆⣠⣆⣸⣿⣇⣰⣷⣀⣴⣦⣄⣤⣶⣀⣀⣀⣀⣀⣤⣴⣶⣶⣾⣿⣿⠏⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠛⠋⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠋⠙⠉⠉⠉⠁⠀⠀⠉⢿⣦⣤⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠞⠀⠉⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⡿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠘⠟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡈
⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡷⠆⠀⠤⠀⠠⠂⠀⠀⠀⠀⡰⠒⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡇⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠠⠃⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠰⢻⠃⠀⠘
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠈⠙⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⠀⠀⢀⠄
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠃
⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⢠⠑⠤⢀⠌
⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠁⠂⠀⠀⠄⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠁
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡟
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠄⠀⢠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⢄⠀⠀⢀⡈⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠒⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢨⠀⡠⠄⡸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠈⠁⠁⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⠶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢄⣀⣀⡀⠈⠉⠙⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⢀⣀⣈⠉⠑⠒⠦⢤⣀⠀⠈⠙⠛⠶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠖⠛⠛⠓⢊⠔⠉⠀⠀⠀⠢⢄⡀⠀⠉⠑⠢⢄⡀⠘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣟⠋⠀⠀⠈⠑⠒⠴⡃⡀⠀⠀⠀⠀⢀⠀⢀⠉⠡⢄⠀⠀⠀⠀⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠉⠑⠒⠤⢀⠀⠀⠈⠑⠲⠤⣀⣀⡁⠐⠁⢀⣀⠀⡀⠦⢄⡀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢉⣁⠀⠀⠀⠈⠑⡀⣿
⠀⠀⠀⣠⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⣀⠀⠀⠈⠑⠤⠐⠃⠀⡇⣿
⠀⠀⢸⡏⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠝⣦⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⢸⡟⡉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⣰⠁⣿
⠀⠀⢸⡇⢸⠑⠢⠄⡈⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠊⠁⡸⠀⣿
⠀⠀⢸⡇⢠⣍⠀⠀⠀⠁⠂⠄⣀⠉⠒⠤⣄⡤⢔⠂⢀⡄⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⠀⢰⡟
⠀⠀⠈⣧⠐⢤⡙⠢⢄⡈⠐⠠⠀⠉⠒⠤⣀⠃⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣤⠶⠟⠀⠈⠛⠛⠁
⠀⠀⠀⢻⣤⣾⠙⠳⢦⣌⡑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣈⠉⠒⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡇⠀⡄⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠉⢹⠂
⠀⢠⠖⢦⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡛⠛⡇⠀⠀⡞⠉⠰⠿⡄
⣠⠞⠛⠉⠛⡏⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠾⣇⠀⠀⠛⠛⠛⠛⠁
⢷⣄⣠⡤⣴⠥⡴⠃⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠖⣦⠀⠀⠘⠒⠒⠒⠋
⠀⣿⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠴⢧
⠀⣿⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛
⠀⣿⠀⠀⢸⠀⡇⠀⠀⣠⡄⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⣤⣤⣀⡀
⠀⣿⠀⠀⢸⠀⣇⣀⣰⠃⠸⠋⡰⠟⢛⣧⣠⡞⠉⠙⠋⡉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⢦⡀
⠀⣿⠀⠀⢸⢠⠋⠘⠉⠁⠀⠀⠀⠐⠋⢱⡜⠀⠀⠀⡐⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠙⣄
⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⣆
⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠈⢀⠇⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠶⠤⢤⣀
⠀⣿⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⣿⠀⠀⢸⠈⢢⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢠⣞⡀
⠀⢻⠀⠀⢸⢰⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠈⡅⢹
⠀⣿⠀⠀⢸⠸⠤⠤⠤⠤⠤⠤⠤⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢸⠀⠄⠀⡧⠼⢶
⠀⣿⠀⠀⢸⢤⣤⣤⣤⣤⣤⣤⣤⣬⡀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠀⣣⠀⣠
⠀⣿⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠁⠀⠀⠀⢀⣸⣀⣀⣀⣀⣀⣀⡀⠀⠀⣇⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⣿⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇⠀⢸
⠀⠙⢶⡶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⠞
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠿⠿⠿⢶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⣰⡟⠉⠀⢙⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣴⠾⠃⣀⣤⣤⣀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠈⢻⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣧⣀⠀⠀⠀⠀⠀⠘⡇⠀⢀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⣋⣭⣿⣿⣿⠉⠉⠛⠿⢷⣶⣶⣶⡾⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⢁⣠⣾⠿⠋⢹⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⣠⣾⠟⠁⠀⠀⣼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⣾⡿⠁⠀⠀⠀⠀⣿⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢠⣿⠏⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢿⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⡀⠀⠀⢀⣀⣀
⠀⠀⠀⣰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣤⣶⣿⣿⣿⣿⣶⣤⣄⢀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣯⣭⣭⣥⣦⣴⣶⡶⠶⠒⠒
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣯⣥⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠠⠻⠟⠛⠛⠛⢋⣽⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⠄

⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⠀⠀⠀⠀⠀⡤⠖⠃⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⡼⠛⠛⠛⠛⠙⢦⠀⠀⣀⣠⣿⡿⢿⣆⣿⠀⠀⢀⢤⣤⣷⣤⣄⠀⠀⠀⢀⣽⣿⣿⣿⣾⣿
⠀⠀⠀⡇⠀⠔⡀⠢⠀⡸⠀⠀⣿⠀⠀⡾⢻⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⢲⠀⠀⠀⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠘⠦⣀⣉⡠⠔⠁⠀⠀⣏⠀⠸⠃⣠⠚⢂⠀⠀⠈⠻⣿⣿⠿⠋⠁⠀⠀⠀⠈⠉⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⢦⡀⠀⠀⠀⠈⣧⣿⣧⡀
⠀⠀⢠⠀⠀⣰⣷⡀⠀⠀⠀⠀⡯⠐⡖⢀⢠⡄⢹⡀⠀⠀⢰⢿⣿⡏⣧⠀⠀⠀⠀⢰⠉⠉⠉⣿⡂
⠀⠀⢸⣠⣼⣹⣿⣽⣦⣄⡄⠘⢧⣈⠁⠚⠈⠁⡴⠁⠀⠀⠀⢸⡏⣷⠀⠀⠀⠀⡄⣈⠩⢉⡉⢉⢀⡄
⠀⠀⠸⠉⠉⠹⠩⠏⠉⠉⠇⠀⠜⠋⠙⠋⠉⠉⠀⠀⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠁⠉⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠈⠓⠑⠀⠀⠀⠀⠀⠀⢀⡾⣿⣷⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⣋⣻⣷
⠀⠀⠀⣿⣿⢻⢻⣹⡟⢦⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⢰⠀⠠⠏⣰⠪⠇⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⢧⣽⣿⡿⠉⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠻⠿⣿⣿⡏
⠀⠀⠀⠐⠒⠚⠓⠒⠂⠀⠀⠀⠀⠀⠈⠋⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢙⠛⠉
⠀⠀⠀⠀⠀⣠⣦⠀⠀⣤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⣿⣗⡀
⠀⠀⠀⢀⣨⣿⡿⣷⣄⣿⠀⠀⠀⠀⢾⡿⣿⠆⠀⠀⢀⣼⣿⣿⠿⠋⠻⢷⡄⠀⠀⢠⡟⣿⣿⢧
⠀⠀⠀⣿⠀⢀⡾⣻⣿⣿⠀⠀⠀⣠⣤⣿⣷⣤⠀⠀⢸⣏⠀⠤⢀⠠⠄⢸⣿⠀⠀⠈⢠⡟⣿⠈
⠀⠀⠀⣇⠀⠼⠁⡠⠓⣄⠀⠀⢰⡟⣿⣿⣿⣿⠇⠀⠸⠿⠦⣄⣙⣀⡤⠿⠿⠀⠀⠀⠸⡇⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠴⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⢀⠂⠀⠀⠀⡘
⠀⠀⠀⠀⣰⠁⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠁⠌⢀⠔⠁⠀⠁⠀⢃⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠘⠀⢰⠀⢸⠀⠀⠀⠀⢀⠀⢀⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⢘⡀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⢀⡄⢀⠠⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢋⠀⣉⠒⠤⡀⡐⠸⡉⠀⠈⠒⠈⠀⠀⠡⣄⠀⠀⠈⠟⠂⠁⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⠰⡀⠀⠀⠰⠃⠀⠀⠀⠈⢩⣾⣗⠂⠐⠦⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⠀⠀⠀⠀⢤⠁⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡐⠀⠄⠀⠀⡀⣴⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣤⣶⣄⣀⣩⣥⣤⠾⠂⣄⡀⠀⠀⠀⠀⠀⠀⣠⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠋⠀⠁⠘⠃⠂⠘⠉⢙⢻⠿⣿⠿⣒⠒⠶⠦⠚⠉⠉⠙⣧⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⣲⣄⢠⣤⣀⠀⡠⢠⠀⠀⠀⠀⡀⠤⢀⣀⣜⣰⠃⢔⣺⡗⣤⣀⡤⢂⡀⠀⣸⣿
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⠻⠋⠉⡏⢣⡀⣿⣀⣠⠴⢚⡽⣻
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠑⡉⢙⠆⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠀⢉⠤⠈⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉
⠀⠀⠀⠀⠠⠄⠈⢀⡤⠀⠉⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠛⠾⣭⣟⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⡛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠳⢦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⣠⣾⠟⡋⠹⠙⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠙⠳⣬⡻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⡛⠙⠳⣤⣀⠀⠀⠀⣿⣥⠂⠀⠀⠀⠀⠀⠀⠈⠙⡻⣷⣦⡀⠀⠀⠀⠀⠈⢻⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠉⠲⢄⡀⠉⠳⢦⣀⠈⠛⢷⣦⣄⡀⠀⠀⢀⠐⣨⠷⢚⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠉⠛⢦⣄⡈⠙⠻⣶⣴⣠⣟⣥⣶⠟⠋⠉⠛⢦⣄⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠈⠙⠶⣄⡀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⣼⡇⣿⡇
⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⡇⣿⡇
⠀⠀⠀⢸⡿⣥⡀⠀⠀⠀⠀⣴⡟⠙⢀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠈⠛⢦⣄⡀⠀⣠⡴⠛⠉⠀⠀⢀⡿⢹⡇
⠀⠀⠀⢸⡇⠈⠙⢦⣄⠀⠀⢿⡻⣷⢄⡉⠰⣀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣨⣿⡟⠁⠀⠀⢀⣠⠶⠛⠁⢸⡇
⠀⠀⠀⢸⣧⠀⠀⠀⠉⠻⢦⣀⠙⢶⣕⣭⡲⣄⠘⢠⠀⠀⣀⣤⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢻⠁⢸⠇⣀⣤⠾⠋⠁⠀⠀⣀⣼⡇
⠀⠀⠀⢈⣿⣦⣀⠀⠀⠀⠀⠉⠳⣦⡈⠛⢿⣮⣷⣤⣚⡯⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⢸⣠⡼⠟⠋⠀⠀⠀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⣿⠀⠉⠳⢦⣀⠀⠀⠀⠀⠙⠳⣤⡙⠻⠿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⢀⣠⡴⠛⠁⠀⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⢀⣤⠾⠋⠁⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠳⣦⡀⢀⣠⠶⠋⠁⠀⠀⣠⡴⠞⠋⠀⠀⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠈⢻⠋⠁⠀⠀⣠⡴⠛⠉⠀⠀⠀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠈⠛⢦⣄⠀⢸⠀⣠⡴⠛⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠈⠛⢿⠟⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⢸⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣼⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢂⣶⣶⣶⣦⠀⢰⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠛⣻⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠚⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⡃
⠀⠀⠀⠐⠀⠀⢸⠀⠀⣾⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⠀⢀⠀⠀⠀⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠋⠀⠘⠛⠛⠛⠛⠉⠉⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⣾⣿⣿⠿⠟⠟⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⠀⠆⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣶⣖⣀⣀⠿⠿⢶⡐⢠⣄⠔⢘⣁⣀⣼⣿⣿⣿⠃⠀⠀⠀⠁⠋⣿⡀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣴⡎⠁⠀⣿⣿⣿⢀⣀⣸⣿⣿⣈⣢⣼⣋⢱⣿⣿⠿⠿⠀⠀⠀⠀⢀⠀⠞⠁⠀⠀⠀⠀⢀⡔⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣤⠤⠖⣻⡿⢻⣶⣶⣿⠁⠀⢸⣿⣿⡇⠀⢸⣿⣿⡉⣿⣿⣉⣉⡃⠢⡀⠀⠠⠄⠁⠀⠄⠀⠀⠀⣠⠰⠏⠀⣾⣿⡇
⠀⠀⠀⠀⡠⠚⢹⣷⣶⠉⠉⣿⣿⣿⣃⣠⡼⠛⠛⢻⣶⣶⡞⠛⠋⣿⣿⣿⠁⠀⢹⣷⠈⣿⣿⣷⠀⠘⠶⢀⠀⠀⠀⠀⠀⡀⢦⡈⠃⠀⠀⣿⣿⡇
⠀⠀⠀⣴⣷⣶⠋⠉⣿⣿⡟⠉⠁⢸⣿⣿⡇⠀⠀⣸⣿⡿⣇⣀⣀⠿⠿⠿⣧⣤⡼⠛⢶⡏⠉⠉⠃⠀⠀⠀⠀⢤⠤⠶⠮⠧⠥⠀⠐⠂⠀⣿⣿⡇
⠀⢠⣶⠞⠛⣷⣶⡴⠛⠛⣷⣶⣶⡏⠉⠉⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⣿⢿⣿⣆⡘⣧⠴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠰⠛⢻⣤⣴⠛⠛⣧⣤⣴⠛⠛⠻⣦⣤⣤⠿⠟⠛⣷⣶⣶⡏⠉⢹⣿⣿⣿⡧⠀⠀⠀⠈⣷⣶⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⢀⣿⣿⡇
⣥⣤⠿⠿⣧⣀⣠⠿⠿⢿⣀⣀⣠⠟⠛⠛⣤⣤⣤⡟⠛⠛⣧⣤⣼⡛⠛⠛⣧⡀⠀⠀⣠⡇⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⣿⣿⡇
⠛⠛⠀⠀⣿⣿⡟⠀⠀⠘⠛⠛⠛⠂⠀⠀⠛⠙⠋⠃⠀⠀⠉⠉⠙⠃⠀⡀⠀⠉⠛⠉⢉⠉⠀⠈⠁⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠊⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠉⠑⠦⣄⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠒⢴⢧⡀⠀⠀⠀⠀⠀⠀⣨⢷⡉⠀⠀⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⡠⡚⠁⠀⠀⠀⠀⠘⠳⠋⠀⠀⠀⠀⠀⠀⣇⠀⡿⠀⠀⠀⠀⠀⢀⠔⣷⠒⠒⠦⣄
⠀⠀⠀⠀⠀⣼⠑⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢿⡠⠟⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣿⡀⠤⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢠⡞⠓⠒⠃⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⡞⠁⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢰⠇
⠀⠀⠀⠀⠸⡇⠀⠀⢀⡠⢤⡀⠀⠀⠛⠲⠤⠀⠀⠿⠤⠄⠀⠰⢇⠀⢀⡄⢠⠀⢠⠀⠀⠘⠧⢼⡗⠃
⠀⠀⠀⠀⠀⠙⠲⢤⣾⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡞⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠈⣷⠀⠀⠀⢀⡽⢃⡴⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢻⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠾⠥⠠⠔⠊⠁⠀⣼⠀⢀⡰⠋⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠉⠀⠈⠓⠦⠤⠀⠀⠀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⢀⡖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠢⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠄⢀⣀⠀⠄⠀⠢⠤⠄⠤⠄⠐⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠈⠉⠈⠉⠲⢄⠀⠐⠈
⠀⠀⠀⠀⠀⠀⡀⠀⡁⠂⠀⠑⡄
⢀⡂⠀⠀⠀⠘⠟⠀⠏⠀⠀⠀⢱
⢠⠑⡄⠢⠄⣀⠀⠀⠀⡀⠀⠀⠘
⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⡌⠑⠢⢄⣀⢀⠀⡄⠊
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⢄
⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠁
⣶⣶⡶⡶⠶⢶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⢠⡞⠁⣐⣒⣶⠂⠀⠼⠅⠀⠀⠂⠀⠁⢀⣁
⠀⠀⠀⠀⠀⠔⠒⢄⠀⠀⠀⣀⣠⠤⠴⢒⡾⠋⠉⠉⣴⡯⠤⠄⠀⠀⠉⠉⠁⠒⠒⠠⠁⠀⡱
⠀⠀⠀⠀⠀⠣⡀⠀⠒⠊⠉⠀⠀⠀⣰⣟⣤⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⢰⠁⠀⢀⠊⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⡎⠀⠀⢀⠀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⣇⠀⠀⢀⡠⠁⠠⠊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠀⠈⠀⠐⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⣀⠈⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠐⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡖⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⢦⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡴⠃⠈⠉⠛⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠿⠛⠻⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠁⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢸⡇
⠀⢀⣀⣀⣀⡀⠀⢀⣠⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⢠⣿⠋⠉⠙⣷⠀⠀⠀⢸⣿
⣼⣿⣿⡿⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⠇⠀⠀⢸⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣼⠟⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠻⢶⣤⣸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡶⠟⠋⠉⢀⣀⡀⠀⠈⠙⠻⢶⣄
⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠿⢾⣿⣥⣀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣶⣾⣿⣀⡀
⣿⣿⣿⡇⢀⣠⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣶⣤⣶⠾⠟⠛⠉⠁⠀⠀⠈⠉⣛⣷⣦⣀⡀
⣿⣿⣿⡗⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠋⠉⠈⠉⠛⠿⢶⣤⣄⡀
⣿⣿⣿⣿⡿⠟⠻⠷⣶⣤⣤⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀
⣿⣿⣿⣅⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣦⣄⣀
⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⢻
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠟⠛⠉⠀⠀⠀⠀⢸
⠀⢸⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢸⣿⣿⡇⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠛⠉⠁⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⣁⣀⡤⢤⢴⠒⠒⠲⣄⢸⡆
⠀⠀⠀⠀⠀⡴⠊⢁⡠⢴⢺⠉⠁⠀⠀⢼⢸⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⣸⠀⣰⠋⠀⢸⢸⠀⠀⠀⠀⢸⢸⠀⠀⠀⣸⣸⡇
⠀⠀⠀⠀⡏⠀⡏⠀⠀⢸⢸⠀⠀⢀⣀⣼⠼⠖⠛⠛⠛⢮⡑⠤⡀
⠀⠀⠀⠀⡇⠀⡇⢀⣀⣼⣼⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⠓⢤⡀
⠀⠀⠀⠀⡇⢰⣏⠉⠀⠈⢿⡿⡲⣄⠀⠀⠀⠀⠀⣀⡤⢖⣚⡥⠴⠒⠋⠙⠳⢤⡀
⠀⠀⠀⠀⡇⢸⠀⠑⠦⡀⠀⠉⠪⢿⡦⠤⠒⣊⠭⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠸⣄⠀⠀⠈⠳⢄⡀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠀⡇⠑⢦⡀⠀⠀⠙⠺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠷⠒⠋⠉⠉⢲⡀
⠀⠀⠀⠀⢧⣤⠇⠀⠀⠈⠳⢄⡀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⢉⣀⣤⠴⣞⣿⠷⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⢀⡔⠋⢁⣠⡴⣖⣋⣭⡶⢿⡀⡏⣁⣠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠙⠷⣄⡀⠀⡞⠀⣸⡥⠾⡇⣟⢉⣀⡤⢼⡇⡏⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠈⠙⠿⡇⠀⣯⠠⠴⡇⣿⠉⠀⠀⣘⣇⡧⠔⣚⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⡇⠀⡇⠀⢀⣇⡿⠔⢚⣉⠥⠖⠚⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⡇⠀⣟⣉⠥⠼⠒⠉⠁⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄⢀⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠀⠤⠀⠈⠖⠠⠀⠀⠀⠀⢀⠄⠒⠛⠛⠻⢒⣒⣂⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠀⠀⠠⠂⢀⠀⠈⠣⡀⠀⠰⠁⠀⠀⠀⠀⠀⠐⠉⠓⠵⡄⠀⠀⠀⠀⠀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠈⠉⠄⣀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠘⡂⠞⠒⠤⡀⠀⠀⠀⡇⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⠒⢁⣔⠉⠀⠀⠀⢉⣆⡀⠈⠁⠒⠤⢆⠀⠀⠀⠀⢀⡇⠀⢀⠄⠈⠒⠠⠤⢧⣀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⢀⠊⠀⢠⣉⣴⣿⣴⣶⣼⣷⣤⣡⠀⠀⠀⠀⠀⠉⠑⠰⠾⣟⣁⠠⠇⠤⣀⠀⠀⠀⠀⠀⠑⠢⣀⢀⡀⠄⠀⠀⠑⡀
⠀⠀⢀⠌⠀⠀⠀⢡⡟⠉⠀⢠⠀⠉⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠖⡫⠄⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⡀⠀⢐⣯⠀⠀⠈⠎⠀⠀⠈⣗⢀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠉⢣⣄⢡⡤⠄⢤⡐⠒⠂⠀⠤⠤⠤⠤⠤⠄⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣝⠿⠦⠶⠼⢟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠈


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⡇⠀⢰⣿⣟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⡏⠀⢸⣿⣿⢸⡇
⢀⣴⣶⣦⣄⠀⠀⢈⣿⣿⣿⢸⡇⠀⢸⣿⣿⢸⡇
⣸⣿⣿⡏⣿⠀⠀⢺⣿⣿⣿⣸⣇⣀⣼⣿⣿⢸⠁
⢹⣿⣿⡇⣿⠀⠀⠸⣿⣿⣿⡇⣭⣵⣿⣿⣯⠟
⢸⣿⣿⣧⣿⠁⠀⣸⣿⣿⣿⠇⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀
⢸⣿⣿⡟⣿⠀⠀⢈⣿⣿⣿⡆⡇⠀⢀⣾⣿⡿⣦⣀⣠⣶⣿⣿⣿
⢹⣿⣿⣷⣿⠀⠀⢘⣿⣿⣿⢸⡟⠀⢸⣿⣿⣿⣎⢻⣿⣿⣿⣿⡿
⢸⣿⣿⣿⡸⣄⣀⣸⣿⣿⣿⢸⡇⠀⠀⠻⣿⣿⣿⣧⡹⣿⣿⠟
⢨⣿⣿⣿⣿⣶⣯⣿⣿⣿⣿⢸⡏⠀⣾⣷⣜⣿⣿⣿⣷⣌⡻⢷⡀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⠇⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣸⡇⣸⣿⣿⣿⣟⣛⡁⠈⠉⠉⠁⢀⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣅⢿⡆⢠⣾⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⡿⢁⢀⠘⣿⣿⣷⠙⠻⣿⣿⣆⠀⣄⣠⣤⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣼⣿⣿⣿⢸⡏⢿⣿⣷⣮⡻⣿⣿⡟⣴⣿⣿⣷⠹⣿⣿⡎⣷⣌⠻⣿⠃⣿⣿⣿⣿⣱⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣸⡻⢿⣿⣿⠘⣿⣮⡻⣿⣿⣷⣌⡻⠾⣿⣿⣿⣿⣧⡹⣿⡇⣿⣿⠟⠡⣾⣿⣿⣿⣿⣿⠃
⢀⣀⣀⣀⣀⣀⣀⣸⣿⠃⢿⣿⣷⣮⣽⣀⣈⣿⣿⣮⣝⣻⣿⣿⣿⣷⣬⣻⣿⣿⣷⣹⣿⣛⣥⣾⣷⣮⣭⣝⣿⣿⣟⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣶⣬⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⠿⠿⠿⠿⠿⠟⠰⡹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⠇
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠋⠉⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⢀⣤⠤⣤⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠾⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠾⠧⠄⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠠⢦⡀⠀⠀⠀⠛⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⣀⠀⣀⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠚⠁⠉⠠⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⡔⠢⠀⡀⠤⠛⠂⠀⠀⠀⠀⢀⣠⠀⠐⠂⠠⠄⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡸⠀⠀⠂⠀⠀⠀⠶⠀⠀⠀⠀⠉⠙⢳⠀⠀⠈⠄⠀⢃⠀⢀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡠⠎⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠈⠄⠐⣀⠤⠈⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠰⣏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠀⠰⠈⢡⠄⠃⡠⠂⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠳⠐⠉⢦⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠣⡀⠋⣀⠔⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠁⠀⠑⢄⠀⠀⠀⣀⢴⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠐⠃⠀⠀⠀⢠⡆⠀⠀⢠⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠴⠦⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢀⠄⠁⠀⠁⢲⠎⠀⢀⠃⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠢⢄⣈⠑⠠⠀⠀⠀⠀⢀⡹⠒⠒⣊⣁⠀⠀⠀⠠⠋⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠐⠒⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣀⢀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⣀⠀⠤⠤⠶⠒⠃⠀⠤⠄⠀⣀⡀⠀⠀⠀⣀⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣿⣿⡿⠿⣿⡿⢿⠿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠀⠐⠂⠀⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠁⣤⠀⠀⡀⠔⠀⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⠀⡄⠄⠐⠑⠀⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⡘⠀⢈⡄⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠄⠊⠀⠀⠠⠈⡀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠂⠐⠒⠠⠂⠀⠈
⠀⠀⠀⠳⠀⠀⠀⠀⢀⠎⠈⠀⠀⠉⠘⡄⠀⠠⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠎⠑⠂⠀⠀⡀⠀⠀⠀⠀⠀⣀⠄⠄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀⠤⣠⠊⠁⠀⠉⠦⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢠⠊⠁⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢄⠀⡀⠀⠰⠉⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠒⠢⡀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⢲⢀⡔⢦⢠⡖⡄⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⢄⣀⡀⡀⡀⢀⠝
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⡇⠀⠀⠀⠀⠘⠁⠈⠣⠞⠘⠋⠐⠆⠀⠀⠀⠘⠀⠀⢀⠀⠄⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⣀⣀⢀⡀⡸⠀⠀⠀⠀⠀⠀⢠⠛⠀⠠⡆⠰⠗⠰⢒⠀⣂⠀⣖⠀⠠⠀⠆⠀⡜⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⡀⠀⠀⠀⠀⠀⠔⠀⠀⠘⠀⠁
⠀⠀⠀⠀⢠⣀⡀⠀⠈⠀⠀⠀⠀⠀⠈⣄⠀⠑⠂⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠒⠘⠁⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠈⠒⠀⠒⢄⣀⣀⠔⠓⠂⠂⠀⠀⠀⠀⡰⠤⠤⡀⠀⠀⠈⠂⠀⠉⠀⠉⠀⠩
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠐⡁
⠀⠀⢀⠂⠈⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠄⡀⠀⠀⢠⠋⠀⠀⠀⠀⠉⠠⠀⠀⠀⠐⠂⠁⠀⠠⠄⠄⡀⠀⠀⠀⣰⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠱⡀⠀⠀⠀⠀⢀⡪⠀⢀⠄⠐⠐⠀⠂⠠⡀⠀⠀⠀⠉
⠀⠀⠂⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠉⠓⠒⠢⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠑⠂⠅⠉⠀⠀⠀⣴⠀⠀⠀⠀⠈⠢⠀⠀⣀⠄⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡀⠈⠀⢀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⣒⠄⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢻⣛⣟⣙⣛⣟⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢛⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡉⠉⠉⠓⠒⠦⠤⣄⡀⠀⠈⠉⠛⠷⢦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠧⣄⠗⡢⠒⠒⠒⠠⢀⠀⠈⠉⠒⠢⢄⡀⠀⠈⢹⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⠛⠛⠥⢀⡀⣰⠀⠊⠀⠀⠀⠀⠀⠀⠉⠲⠦⠀⠀⠀⠈⠉⠒⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠋⠙⠣⠤⢄⡀⠀⠀⠀⠈⠑⠼⣀⡀⠀⠀⠀⡔⢁⠄⠂⠈⠙⠂⢀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⡀⠀⠀⠉⠑⠒⠦⠧⣨⣤⣤⣤⠤⠤⠈⠉⠒⠤⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⢄⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⣠⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣀⠀⠀⠀⠑⠆⠈⠀⠀⡁⢸⠃
⠀⠀⠐⡏⣉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⢹⡄⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⣿⢉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠁⣸
⠀⠀⠀⣿⠈⡍⠓⠢⢄⠉⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠊⠁⣸⠀⣿
⠀⠀⠀⣿⠀⣍⠐⠀⠀⠈⠐⠠⢄⡈⠉⠒⠤⣄⣀⡤⣒⠀⢀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣷⢶⣟⠁⢀⣿
⠀⠀⠀⣿⠐⢬⡙⠲⢄⡀⠑⠢⢄⠈⠑⠢⢄⡀⠙⠀⢸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⡴⠏⠀⠙⠿⠟⠃
⠀⠀⠀⢸⣇⢰⡟⠷⣦⣈⠑⠢⢄⡀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠉⠛⠶⣤⣈⠙⠲⠤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢸⠀⠀⠀⣀⣠⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣷⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⣀⠀⠄⠐⠀⠀⠀⡀⠀⠀⢀⠛⠁⢂⠀⠀⠀⠤⠜⠉⠀⠀⠀⠈⠀⠀⠂⠀⠉⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠞
⡔⠈⠁⢱⠀⠀⢲⠂⠀⠀⠁⡄⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣌⡀⠀⠀⣄⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠐⠄⣀⣀⣠⢴⠢⢄⠀⠀⠃⠀⠀⠀⠀⠀⢨⠁⠈⠉⠃⠀⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠘⠁⠐⠀⠀⠈⠛⠁⠠⠖⠀⢀⠀⠀⠠⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠃⠈⠀⠆⠀⠀⠀⠀⠀⠁⠀⠒⠢⡀⠀⢄⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⠈⠁
⠀⠀⠀⡤⠯⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡓⠀⠂⠀⠂⠀⠀⠆⠀⠀⠃⠐⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠰⠀⠀⢀⡀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⠀⠀⠀⠀⣀⠀⠘⠻⠿⠿⠆⠈⠛⠳⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⠁⠀⠀⠀⠀⠘⠛⠛⠋⠉⢩⠋⠑⠀⠀⢀⡴⠯⠗⠒⠛⠒⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢰⡄⡀⢀⣀⣀⣀⣠⣴⣧⣀⣂⣤⠖⠁⠀⠀⠀⠀⣀⣠⠶⠶⣮⢳⣄⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡼⠋⠈⠀⠀⠀⠀⠀⢀⣀⣼⣿⣥⣄⣀⣤⣤⠴⠾⡅⠀⠀⠀⠈⠑⢿⣷⣄⣐⣦⣄⡸⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠎⠀⠀⠀⣠⠔⣪⠕⠛⣡⡾⠛⠉⠉⠀⠀⢘⣿⡄⠀⢹⠀⠀⠀⠀⠀⠈⣬⠷⠻⢿⡿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠄⠀⠀⠀⡐⠁⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⢠⠃⠀⠃⠀⣰⠟⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢿⣆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠋⠀⢀⠎⠀⠀⠀⢸⡀⠀⠀⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⢀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⣄⠀⠀⠛⠀⠀⠀⠸⡟⠂⠙⡆⠀⠀⠈⣸⡄⠀⠀⠀⠀⠀⠁⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠀⠀⡀⢸⣧⠀⠀⠈⠃⠙⡇⠀⠀⠀⠀⠀⢈⣿⡀⢀⣧⣤⠮⣨⡾⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠃⠀⢀⣤⣴⣾⣿⣟⠛⠲⠦⣤⡤⠄⠀⠠⢤⣶⣶⡆⠛⠿⠟⣛⣓⡟⠙⠁⠀⠀⢀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠃⠒⠀⠀⠀⠀⠀⡤⠞⠛⠒⣛⣛⠉⠉⠿⣦⠀⠀⠉⠀⠀⠀⠀⠈⠙⠓⠶⢦⣄⡀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡟⠁
⠀⠀⠀⠀⠠⢦⣤⡌⣤⣤⣤⣷⣖⣉⣥⠀⢀⣀⡡⠀⠀⠀⠀⠀⠀⠤⣀⡁⠢⠄⠀⠀⠀⠀⠀⠐⠀⠤⠶⠾⠛⠛⠒⠂⠘⢋⢉⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠪⠭⠭⠌⠉⠉⠉⡥⢣⡄⠁⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠒⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠾⠛⠁⠁
⠀⠀⠀⠠⠖⠶⠦⢄⣤⣀⠀⠀⠀⠀⠀⠊⠀⣠⠑⣄⢠⣀⣀⣀⣀⣀⣤⣐⣢⣤⣤⣤⣤⣉⣥⡖⠁⠀⣴⣶⠀⠖
⠀⠀⠀⢀⠀⠀⠛⢋⡨⠟⠛⠻⠿⠎⠁⠀⠉⠀⠀⠘⠀⠙⠊⡙⠃⠀⠀⠀⠄⠠⠌⠉⠉⠀⠈⠀⠀⠀⠉⠛⠒⣆
⠀⠀⠂⠁⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠉⠩⠙⢋⡀⡈⠉⠉⠩⠰⡒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢄⣠⠀⣠⠖⠋⠉⠀⠀⠀⠀⠉⠙⠲⢌⠀⠣⡀⠉⢙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡤⠊⢀⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠱⡀⠈⡗⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠃⢁⠎⠀⠀⠀⣠⣴⠒⡶⣋⠶⢆⠀⠀⠀⠀⢱⠀⢣⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠖⠂⢸⠀⠀⠀⠘⡄⠓⠀⠓⠉⢁⠎⠀⢀⠀⠂⢈⠀⢀⠕⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣔⠁⡀⢸⠀⠀⠀⡀⢸⡀⠀⠀⠀⡎⠀⠀⠀⠀⠁⡸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⡄⠈⢆⠀⠀⠠⢀⡇⠀⠀⢸⠀⠀⠀⢠⠐⢠⠃⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠴⠎⣀⠀⠈⢦⡀⠀⠀⠛⠀⠀⡃⡀⡄⡆⠀⡰⠃⠀⠀⡔⠋⠁⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠤⠤⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⢱⣠⡄⡉⠢⢄⣸⡀⢑⣇⣠⠤⠔⠋⠀⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠑⠀⢇⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠰⣎⡀⢘⡽⢟⡆⠈⠑⢦⡜⠁⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠀⠠⠔⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣉⣉⣤⡴⢞⡧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡘
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⢠⣀⣴⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡌⠀⡜
⠀⠀⠀⠀⠀⠰⡁⠀⢀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠀⠀⠀⠀⠀⠈⠻⣙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠘⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠰⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡔⠉⠉⠲⡀⠀⠀⠀⢻⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣌⣊⠔⠰⠀⠆⡔⡠⢠⢀⠎⡞⠠⠃⢋⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠑⠂⠄⠊⠀⠀⠀⠀⢸⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠢⠤⠤⠤⠤⠤⠔⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣱⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢣⡸⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⢈⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡴⠆⣨⢔⠵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣷⠆⢐⠵⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠕⡪⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⣂⠅⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣩⣿⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⣻⢹⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢕⡏⢸⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡠⢀⠴⣂⢔⡢⢊⠤⣂⠔⡪⠔⡡⢐⡠⢂⠴⣂⠔⣢⢔⡠⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠥⢻⡰⣛⢕⡾⢳⣄⣿⢔⡠⢂⠄⡢⡤⠔⠔⠠⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣯⠉⠀⠈⠉⠈⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠄⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣈⣓⠀⡖⠀⠀⠀⠀⠀⠀⣰⠋⢠⣾⣏⣹⣆
⠀⠀⠀⠀⠀⣽⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣾⣷⣤⣬⣤⣀⡀⠀⠀⠀⠀⠀⠘⢉⣉⣋⣉⠙⠀⠂⠀⠀⠀⠀⠀⠀⢿⠀⠘⢿⣽⣿⣿
⠀⠀⠀⠀⠀⠯⠤⠤⠴⠦⠤⠤⠗⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⠛⠛⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣨⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠸⠟⠙⠻⠋⠛⢿⠀⠀⠀⠀⠀⢀⣾⡏⠀⣀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⣶⣶⣾⣷⣶⣶⣤⠾⠀⠀⠀⠀⠀⢸⣿⣇⠀⠉⠀⠰⠀⠀⠀⠀⠀⠀⠈⠉⠛⢃⣤⠟⢁⡀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠠⡇⣸⠃
⠀⠀⠀⠀⠀⠟⠉⠛⠛⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠰⠧⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢦⡴⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⡴⠒⠲⣍⠠⠖⠀⠀⠀⠀⠀⠀⢠⣾⠟⢠⡼⢿⣿⡀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠉⠛⣿⠇⠀⠀⠀⠀⠀⠀⣇⠀⠈⢢⡉⢠⠂
⠀⠀⠀⠀⠀⢾⠀⠰⠂⢸⡇⠆⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣅⣻⡼⠗⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣿⣿⣦⡐
⠀⠀⠀⠀⠀⠈⠳⠤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠃



⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠙⣦⣤⡀⠀⠀⠀⠀⠀⢠⣿⡇⢀⡼⠃⡀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠛⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠐⠓⠰⠇⠆
⠀⠀⠀⠀⠈⢧⣀⡀⢀⣀⡿⠶⠛⠀⠀⠀⠀⠀⠸⣿⣧⡀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠈⠑⠈⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⠄⢲⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣠⣞⣁⠀⠀⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠰⠯⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣐⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⣀⠀⠀⠀⢀⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⢀⠁⠀⠁⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠌⠀⠀⠂⠀⣀⠀⠀⠀⠴⢦⡀⠀⢁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡠⠊⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⡀⢃⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⣎⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⢁⠐⢂⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠂⡀⠂⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠢⠈⠀⠈⠁⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠉⠀⢀⡤⠤⠔⠸⠁⠀⠀⣀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠃⠤⠄⣀⠀⠀⠀⠘⠅⡀⠀⠀⠀⢀⠐⠁⠀⢤⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠂⠐⠠⠀⠁⠀⠀⠀⠀⢈⠖⠐⠀⠁⠀⠀⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠐⠚⠙⠒⠂⠀⠀⠠⠤⠀⠤⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠶⠀⠠⠄⠠⣤⠀⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠴⠀⠠⡄⠀⣤⠀⢠⡄⠀⣈⠀⠀⠁⠀⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠶⠀⠰⠆⠀⣤⠀⣠⡄⢀⣀⠀⣈⠁⠀⠛⠀⠘⠃⠀⠖⠀⠰⠄⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠠⡄⠀⣤⠀⢠⣄⣀⣈⣁⣈⡋⠀⠛⠃⠘⠟⠀⠶⠆⢰⡦⠀⣤⠀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠰⠆⠀⣤⠀⣠⡄⢀⣤⠖⠉⠀⠀⠀⠀⠀⠉⠛⢿⡀⢾⡦⢠⣦⠀⣤⡄⢀⣀⠀⢈⠁⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⣤⠀⢀⡄⠀⣈⠀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⠖⠁⠀⠀⠀⠀⠘⣏⠀⠛⠁⠘⠇⠀⠶⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠤⠀⢠⡀⢀⣀⠀⢈⡁⠀⣻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⠀⢶⠆⢠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡩⠊⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠀⠀⠄⣠⡀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠈⠁⠀⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠖⠀⠠
⠀⠀⠀⠀⠀⠛⠀⠰⠆⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠄⢠⡄⠀⣀
⠀⠀⠀⠀⠰⠦⠀⣤⠄⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢠⡄⠀⣀⠀⣈⡉⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⢀⡁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⠀⠙⠁⠘⠟⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢉⣉⠀⢈⠁⠀⠛⠀⠘⠂
⠀⠀⠀⠀⠉⠀⠘⠃⣴⠟⠋⠙⠣⢰⣶⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠛⠀⠛⠃⠐⠗⠀⠰
⠀⠀⠀⠀⠀⠀⠺⢸⣏⠀⠀⠀⠀⣤⣤⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠇⠐⠷⠀⢰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⣦⠀⢻⣦⣤⣤⠖⣉⡁⢈⡛⠻⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠆⢰⡆⠀⣤
⠀⠀⠀⠀⠀⣾⠁⢀⣄⠀⢀⡁⠀⠙⠁⠘⠛⠐⠿⠛⢿⡿⢿⣿⡿⣿⣿⢩⣭⡁⣙⡻⣿⣶⣤⣤⣤⣤⣴⣶⣿⡟⢠⣦⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⠃⠘⠛⠀⠾⠇⢰⣶⠀⣴⡄⣠⣭⢀⣭⡁⢈⣛⠀⠛⠃⠸⠿⠛⢿⠟⢻⣿⠁⣤⠀⢠⡄⠀⣈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠀⠰⠆⠀⣶⠀⣠⡄⢀⣭⠀⣈⡉⠈⡛⠁⠻⠟⠘⠿⠃⢾⡷⢠⣶⠀⣤⡄⢀⣌⠀⢈⠁⠀⠉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣄⠀⣈⠁⢈⡋⠀⠛⠃⠘⠿⠀⠿⠇⢰⡶⠀⣴⡄⢠⣄⠀⣉⠁⠈⠉⠀⠛⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘⠋⠐⠿⠂⠲⠖⠠⣶⠀⣤⡄⢀⣌⠀⢈⡁⠀⠉⠀⠘⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠰⡶⠀⣤⡄⢠⣄⠀⣈⠀⠀⠉⠀⠙⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⣇⢀⠈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⡉⠁⢀⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢹⠀⠀⠰⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠀⡄⠀⠀⠸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠐⡆⢸⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⡆⢠⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⡇⠀⣰⠀⠀⠀⠃⡆⠀⠀⠀⠀⡇⢠⠀⠀⠀⡆⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⠀⣇⠀⢸⠀⠀⢀⡀⣇⠀⠀⠀⢀⡇⢘⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠛⠛⠋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣈⣉⣈⣉⣉⣉⡉⠉⠉⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡰⠁⣀⡠⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠂⠠⠤⠤⢄⡀⠱⡀
⠀⠀⠀⠀⠀⠀⣡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣀⢀⣀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡀⢀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠁




⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⢶⣶⣶⣶⡶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠉⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⠈⠀⠀⠀⠀⡤⠀⠠⠔⠒⠐⠙⠄
⠀⠀⠀⠠⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠊⠀⣈⢵⣂⠢⠀⠐⠈
⠀⠀⠀⠄⢈⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠇⠀⢠⣈⢡⠇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠁⠀⠈⠐⠃⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠢⠤⡀⠀⠀⠀⠐⠂⠑⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠐⡀⠀⠠⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⣀⡀⠀⠀⠀⣀⣀⠀⡈
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠠⠠⠄⡐⠁⡢⠥⠈⡅⢰⢠⡄⢐⠁⠊⠁⠉⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠂⠁⠘⠒⠀⠅⠃⠀⠀⠀⠀⢼⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠡⠀⢘⠚⠀⠠⢀⠔⠉⠉⠑⠄⠀⠸⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⠄⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠉⠉⠚⠒⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠪⢀⣠⠀⣀⣀⣀⡀⠀⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠢⢄⣀⠆⠈⠀⢠⢾⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠂⠄⠀⠀⠀⠈⠲⢇⣀⣄⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠶⣄⠀⠀⢹⡿⡇⠀⡗⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡒⠈⠀⠀⠀⠀⠀⠐⠓⠙⠂⢀⣣⡰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡏⠚⠀⠀⠀⠙⣿⣿⣿⣿⣆⠀⠀⡻⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⢀⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠂⠑⠛⠘⠀⠃⠀⠃⠂⠃⠋⠞⠁⠐⠃⠀⠋⠘⠁⠐⠑⠃⠀⠂⠘

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣗⣠⡀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠤⠶⠖⠒⠒⠂
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠛⢁⡴⠉⠉⠙⠯⣦⠀⢀⡤⠚⠉⢙⠉
⠀⠀⠀⣄⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⠁⢀⡷⠀⠀⠀⠙⢎⠀⠀⢀⡎⢀⡀
⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⡏⠁⣀⠀⣀⠀⠀⠀⠀⢠⠀⠘⣿⡀⠸⡄⠰⡝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣼⠏⢀⡆⠙⠢⠀⠀⡼⡠⠀⢹⠳⡄⠙⢦⡙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣀⣀⣀⣀⠊⠀⠀⢀⡿⡀⠙⣆⠀⠉⠲⣽⣮⡳⢤⡲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠻⠟⠦⠶⠉⠉⠙⠻⢥⣀⣉⣢⡈⣓⣦⣀⣠⣭⡽⠦⠬⠷⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠦⣀⠀⠀⠀⠀⠀⠉⠉⠻⡗⢦⠀⠢⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠖⠚⠓⠒⠺⢮⢳⡀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣠⠖⠉⣠⠔⠁⣼⡡⠖⠚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠘⠋⠀⢀⡞⠁⢠⠞⠉⣀⡤⠤⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⣠⣯⠴⠖⠛⠚⠊⠁⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⡠⠠⢄⡀⠀⠀⢀⣀⣼⠁⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⠄⠠⡄
⠀⠀⠀⠀⠀⠀⠣⠤⠤⠼⠆⠀⣴⠟⠙⣦⠟⠁⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠾⠤⠤⠴⠃
⠀⠀⠀⠀⠀⢠⠤⠤⣤⠀⠀⢰⡇⠀⡜⠁⠀⠀⠀⠸⠟⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⢻⡀⠀⠀⢠⡤⠤⢤
⠀⠀⠀⠀⠀⠘⠶⠚⠁⠀⠀⢺⠏⣸⡇⠀⠀⠀⢠⠖⠋⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⢀⣀⣉⠀⠈⣇⠀⠀⠀⠙⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣇⠀⠀⢠⡏⠀⠀⠀⠀⣀⣹⡆⠀⠀⠆⠀⠀⣿⣁⣈⣳⠀⢿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠖⢻⡀⠀⠈⣷⠖⠚⠋⠛⠋⣼⠀⠀⠀⣦⠀⠀⠣⡌⡩⠋⠀⢸⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆⠀⢧⠀⠀⠘⠦⣤⣀⡤⠞⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣁⣠⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⡴⠋⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡼⣿⣿⣷⣼⠆⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠰⠦⣌⣻⣿⡟⠀⠀⠀⢀⡴⠋⠀⠀⢀⣸⡁⢸⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣄⡀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠙⠁⠀⢀⡴⠋⠀⠀⠀⠀⡏⠀⢈⡇⢀⠎⢙⡆
⠀⠀⠀⢀⣠⠤⠤⠴⠊⣉⠴⠚⠉⠉⠉⣿⣉⠉⢻⡄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢳⠀⠙⠉⠙⡶⠊
⠀⠀⡾⠋⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠈⠉⣻⠇⢛⡗⠶⠦⠤⠴⠚⣏⠙⣦⠀⠀⠀⠀⢀⡰⠋⣠⠖⠀⠁
⠀⠀⠳⡞⠀⠀⠀⡀⢀⠇⠀⠀⠀⠀⠀⠀⢠⡟⠁⠘⠀⠀⠀⠀⠀⢨⢻⡷⠛⢶⣦⣤⣶⡯⠴⠋⠁
⠀⠀⠀⠙⢾⣁⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡀⠀⣸⠇⢰⣦⢀⠘⡇
⠀⠀⠀⠀⠀⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⣀⡈⠃⠐⠾⠃⠐⠀⡇
⠀⠀⠀⠀⠀⠀⣰⠟⡹⣧⠀⠀⠀⠀⢰⡿⠶⣤⣤⣉⣉⠛⠛⠚⠚⠃⢠⡇
⠀⠀⠀⠀⢠⡾⢣⠞⢀⡼⡆⠀⠀⠀⣸⣯⠀⠀⠀⠈⠉⠙⠛⠳⠶⠦⣼⠃
⠀⠀⠀⣴⠟⡴⢁⣶⣿⡔⢻⡄⠀⣾⠉⠙⢦⣀⡀⠀⠀⠀⠰⢤⣤⣴⡋
⠀⣠⡾⣡⢮⠀⢠⡿⠁⠹⡄⠙⣛⡿⠳⡤⠞⠉⠛⠷⢦⣤⣀⣤⣶⣿⣧⣤⣀
⣴⢏⡔⢁⣠⡷⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⢳⡦⠉⡷
⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠯⣴⣿⣶⡶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠢⠤⢤⡬⣉⣀⣀⣰⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠺⠶⠶⠦⣤⣭⣭⣉⣗⣻⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⠿⠟⠛⢋⡋⣙⣛⣟⢛⠿⠿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⠟⡻⠋⣉⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣩⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡃⠀⠀⠀⠀⠀⠀⢀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⢜⠁⠀⠉⠳⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣠⠔⠋⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⣾⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⢿⡄⠀⠀⠀⢀⣤⠴⠶⠦⣄
⠀⠀⠀⠀⠀⠺⣄⣠⠶⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠘⣧⠀⠀⠀⠀⠙⠲⢤⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⣥⣤⣄⣈⣷⠀⢸⣷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⢻⡶⠶⠶⠛⠋⠛⠿⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢉⡽⠃⠀⠸⣧⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠈⢷⣄⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠙⠋⠀⠀⠀⠀⣿⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⣿⣿⣿⠄⠀⠀⠀⠉⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠐⠀⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣐⠒⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠛⠋⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⣍⣻⡆⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡟⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⡾⠛⢻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠘⠛⠶⠶⢿⣿⣿⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠶⣧⣀⣼⠋⠉⢻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⢈⣿⠀⢰⠏⠈⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡶⠟⢋⣡⡴⠾⠛⠛⠛⢿⡿⠛⠗⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⢻⠛⠾⣯⣤⡼⠃
⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠁⢀⡴⠛⠁⠀⠀⠀⠀⠀⠐⠷⣶⣤⣤⣼⢷⣤⣀⠀⠀⠀⠀⠀⣀⣤⠾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⣀⣤⠄⠞⠁
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠈⢛⠿⠿⠿⠿⠟⠋⠱⣦⣼⣿⣦⠀⠀⠄⠠⠖⣀⣴⠞⣁⣴⡾⠋
⠀⠀⠈⢳⣾⠃⠀⠀⠀⠀⠠⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣷⠿⣿⣷⣶⣶⣶⣿⣿⣥⠾⠟⠁
⠀⠀⠀⠀⠻⣦⣴⠃⠀⣾⠗⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡧⠄⠀⠈⠉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠻⢦⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣻⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡿⢁⡾⠁⢘⣷⠀⠀⠀⠀⠀⠀⣿⠗⠀⠈⠉⠙⠛⠛⠷⠶⣦⣤⣄⣀⣀⠀⣸⡇
⠀⠀⠀⠀⠀⣠⣾⠏⣰⠏⠀⣤⡾⢹⣇⠀⠀⠀⣀⣴⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢻⡟
⠀⠀⠀⢀⣴⡟⢁⡼⠁⣸⣿⣿⣷⠋⠹⣆⠀⢸⣿⡅⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠲⠶⣤⣴⣟
⠀⠀⣠⡾⠋⣴⡏⠀⠀⣹⡿⠃⠘⣧⡀⠻⠿⢻⣿⠿⣦⣠⠾⠋⠙⠻⢶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣄⡀
⢀⣴⡟⣡⠞⠁⢱⣆⣼⠟⠀⠀⠀⠘⣷⣤⡶⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠛⠷⢿⣍⡙⠻⢶⣄
⣾⣯⣴⣏⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣼⠏
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣍⣩⣿⣵⣤⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠈⠉⠻⠿⠿⠃⠈⠉⢉⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣍⣙⣛⠒⠲⠖⠲⠤⣤⣤⣤⣯⣀⣀⣀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠶⣶⣶⣦⣼⣤⣭⣉⣙⣉⣻⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀



⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡀⢠⠄⠀⠀⠀⠀⠀⠀⠢⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢼⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠾⠿⣿⠶⠆⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⡌⢀⣀⡉⣢⠀⠀⠀⠀⠀⠄⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⠛⣝⢿⣩⡛⣻⣿⣽⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠⣐⠀⠂⠆⠐⠃⠈⠅⠈⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠔⢀⡀⠀⢀⣶⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠸⠇⠀⠀⠁⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠚⠁⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠙⠃⠒⠒⠁⡠⢎⡇⢠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣘⠈⠙⠒⠒⠒⢲⠊⠁⠀⠀⠹⣌⠕⠀⠀⠠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀⡀⠐⠁⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⡀⠀⡐⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⢀⠀⠙⢌⢦⠀⠀⢐⡀⠈⠀⠸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠁⠉⠉⠁⠒⠚⠒⠛⠳⡄⠱⠀⠀⠀⡇⠌⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠃⠀⠀⠀⡰⠁⠀⠆⠀⠀⠀⠉⣯⣉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⢐⢧⡀⠀⠀⠀⠀⠀⠀⠠⣇⠑
⠀⠀⠀⠀⠀⠀⡀⠒⣄⠀⠀⢀⡀⠤⠒⠀⠀⠉⠒⠤⠬⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⣀⠠⠀⠄⠤⡀⠈⡄⠈⠁⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⡈⠀⠈⢧⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠄⠈⠀⢁⠀⠀⠠⡀⠀⢀⠀⠤⠤⠮⠤⠤⠤⠄⡀
⠀⠀⣀⣠⡔⣀⣀⡀⠀⠠⣄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡁⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⡄⢤⡀⠀⠀⠀⠀⠘⣄⠀⠂⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠅
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠀⠀⠒⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠖⠒⠒⢲⣍⠤⠦⠤⠄⠀⠴⣆⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⡇⢐⣰⠀⢀⠕⠀⡀⠄⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠊⡇
⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⣀⣈⣑⣐⣈⡡⠂⠁⢀⠤⠂⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡡⠋⢀⠎
⠀⠀⠀⠀⡏⡉⠭⠭⠭⠄⠀⠒⠒⠒⠒⡆⣀⠔⣊⠥⠤⠄⠀⠉⠁⠒⠢⡉⠑⠄⠀⠋⢀⡐⠒⢒⠞⠁⠀⡴⡇
⠀⠀⠀⠀⢧⢃⠀⠀⠀⣎⣑⠀⢀⡠⢐⡉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠊⠙⠁
⠀⠀⠀⠀⢸⠸⠤⠤⠤⣤⣴⠾⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠃⢀⠔⠁
⠀⠀⠀⠀⠘⣆⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⡀⣠⢎⠌⠀⡠⠋
⠀⠀⢀⡠⠒⠉⢸⠀⠀⠀⠈⠉⠩⠀⠈⠩⠭⠥⠄⠒⠒⠀⠀⠐⠒⠒⣒⣒⠒⠚⠁⡘⢀⠞
⢠⠞⠥⠤⠀⠀⠀⠛⠒⠒⠒⠒⠒⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠦⠔⡱⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊
⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⢤⠤⠞⠁
⠀⠀⠈⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼
⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠄⠀⠠⠀⠄⡀⠀⠀⠀⢀⡀⠠⠤⠤⠀⢀
⠀⠀⠀⠀⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⣀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠌⠁⠐⢄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠁⠃⠀⢐⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠁⠀⠀⠀⠀⠠⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠁⣀⠠⢄⡀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢐⠀⢰⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠾⣇⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢻⣾⣿⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⠋⠈⠀⠉⠉⠉⡙⠿⣦⣤⡾⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⡟⠃⣶⢨⠉⢿⣿⣶⣦⡄
⠀⠀⢀⣽⣿⡟⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⣾⡇⡆⠈⠀⠀⠙⠣⣿⣇
⠀⠀⣿⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠁⠀⠀⠀⠀⠀⠈⠻⣄
⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⢸⣿⣿⣿⣿⡟⠢⠀⠀⠀⠀⣾⣿⣿⡿⠀⢰⡦⠀⠀⠐⠃⠀⠀⢀⠀⠈⢧⡀⡀⠀⠀⠀⢀⣠⣴⣶⢚⣻⣷
⠀⠈⢿⣿⣿⣿⣿⣇⣰⡀⠀⢸⣿⣇⡾⠋⠀⠀⢹⣷⠸⠇⠀⠀⣶⣿⠁⠀⠈⠻⣎⠒⠤⢞⢋⣵⣿⣿⣿⡟⠉
⠀⠀⠀⠙⢿⡿⡿⠋⢛⠿⠦⠬⣏⣽⣷⠶⢤⠀⠈⠁⠀⠀⠀⣾⣿⠏⣠⣾⠀⢀⣿⢆⠀⠀⠈⠙⢻⡿⠋
⠀⠀⠀⠒⠒⢲⣶⣭⠵⠶⢶⣶⣾⣽⣟⣻⣿⣷⣆⠠⠀⠀⠀⠟⠁⠠⡟⠋⣰⣾⣡⡏⣠⡶⢂⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠛⠛⠛⠉⠉⠉⠻⠿⠿⠿⣶⣤⣄⣀⠀⢤⣄⣘⣿⣿⣯⣾⣿⣴⠿⠿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣻⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠁





⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣻⣿⣛⣻⣻⣟⣿⣛⣛⣛⣿⣿⣿⣻⣿⣟⣛⣿⣟⣛⣿⣟⣻⣿⣿⣿⣿⣟⣻⣿⣿⣛⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣾⣷⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢟⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⡋⠉⠳⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠙⠓⠲⠾⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢾⣉⣀⣨⡽⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠙⣿⣿⣿⣿⣿⡟⠀⢀⣠⠤⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠐⠲⢦⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣿⣿⣿⣿⡿⠁⠀⠙⠷⢤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠦⣤⠀⢸⣿⣿⣿⣿⠃⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠟⠀⠺⠿⣿⡿⠁⠀⠀⠹⣍⠙⠳⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠉⠁⠀⠀⡈⢐⣿⠀⠀⠀⠀⠀⠙⠳⠴⠋
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠁
⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠁⣀⣠⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⣉⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⠉⢹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠙⢯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⡴⠟⠛⠿⠛⠉⠀⠀⠀⣀⣀⢠⡿⠀⠉⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⡟⠀⢦⣠⡼⠃⠀⣸⣿⡄
⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠙⠛⢷⣶⢤⠀⠈⠻⢿⣟⣛⠷⠶⢶⣦⣤⣦⡶⢶⣾⠛⠉⠀⢸⣧⠀⠀⠻⢧⣠⡞⠋⢀⡿
⠀⠀⠀⠸⣷⡆⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⡀⠀⠙⣧⡀⣠⡾⠁⠀⠀⠀⠀⠈⢳⣴⠟⠁
⠀⠀⠀⠀⠹⣧⣀⡄⠀⢀⡄⢀⣾⠃⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣴⠟⠛⠁⠀⠀⠀⣰⡟⠛⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠻⣦⣄⣼⠷⠟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣤⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄⠀⠀⠀⠀⣿⡶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢀⣴⠟⢁⠖⠙⢷⣄⠀⠀⢸⣇⠀⠀⠉⠙⠛⠛⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣠⡾⢁⡔⠁⠀⢠⡾⠛⢷⣄⡀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢷⣶⣦⡾⠃
⠀⣠⡾⢋⣴⢋⣠⡏⢲⡟⠀⠀⠀⠉⠻⠿⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⣴⠋⡠⠋⠉⣞⣀⡹⠊⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠛⠶⢶⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠙⠿⢷⡴⠾⠛⠉⠀⠀⠀⠈⠻⣦⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠷⣦⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠣⣄⡀⠀⣾⣉⡽⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣌⡑⠢⢄⡙⢲⠾⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣙⠳⢄⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⣿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠤⣉⡑⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠓⠒⠲⠤⢌⡉⠒⠢⢬⣉⡒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢴⡯⣄⡀⠀⠀⠀⠀⢀⣨⡷⠤⠤⠤⣉⡉⠒⠤⢍⣙⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠈⠙⠺⠷⣦⣤⣠⣿⠋⠀⠀⠀⠀⠀⠈⢓⣤⣀⠀⠙⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠭⣖⣤⣄⣀⣴⣊⠥⢖⣫⠽⠲⡇⢸
⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣥⡔⠊⠁⠀⢀⣠⠇⢸
⠀⠀⠀⢰⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣇⡠⠔⠚⠉⠀⠀⢸
⠀⠀⠀⠈⡦⢄⡀⠀⠉⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡅⠀⠈⠑⠢⢄⡀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠈⠉⠒⠶⠚⠉⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⣀⣸⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⡀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣏⣽⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡿⠃⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠈⠀⣸⣿⡄⢁⣴⠀⠀⠀⣀⠀⠀⣶⡄⠀⢀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠁⢠⣾⠯⣄⡀⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣾⡇⠀⢀⣿⣿⡇⢸⣿⡆⠀⢠⣿⡇⣸⣿⡇⢠⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣷⠶⠶⢿⣻⡶⠂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣷⣿⣿⡇⠀⣾⣿⣧⣿⣿⡇⣼⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣷⣦⢞⣫⠋⣰⠿⡴⣿⣶⣶⣶⠿⠋⠀⠀⠉⠙⠛⠋⠀⠨⡙⢿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⠀⠀⠀⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⠇⠸⣿⢁⣽⣶⡿⠛⣹⣏⠁⠀⡀⠐⠒⠄⡀⠀⢺⣯⣶⣦⠘⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣧⠀⠀⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣀⣴⡿⠿⠛⠁⠀⣞⣄⡈⢀⣀⣀⣀⡀⠀⠈⠂⣈⣿⣷⣾⣵⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣀⣠⡶⠛⠉⠀⠀⠀⠠⡞⣙⠋⠠⠝⠋⣉⣍⡉⠛⡷⠳⣦⣽⣿⠉⢹⣿⠿⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠐⣟⣋⡠⠂⠀⠠⣄⠀⠀⢟⣉⡶⠀⣿⣤⣉⣈⣁⡀⣰⡟⠉⢀⠀⠠⠀⡝⢶⣴⣾⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠟⠁⠀⠀⠲⠦⢤⡁⣾⣷⡏⠀⠀⣠⠌⡅⣼⣿⣿⣏⣰⣤⣼⠀⠀⠀⠀⡀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣙⣿⣥⣤⡶⠷⣄⠀⠛⠙⠛⢿⡁⠠⠄⠀⠀⠀⠀⡇⠀⢹⣷⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠯⡝⢲⣦⣼⠀⢻⡇⢩⣤⠆⠙⠒⢦⡄⠀⣼⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈⢿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠊⠀⡟⠀⢀⠃⢀⣤⠀⠠⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⣿⣿⡇
⠀⠀⠀⢰⣶⡦⣀⠀⠀⠀⠀⠀⣏⠀⢠⡇⠀⠘⣴⡟⢿⣀⠠⢁⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠿⣿⡍⠹⣿⢿⣿⣿⣿⣿⣿⣿⠄⠀⠘⣿⣿⡇
⠀⠀⠀⢸⣿⣷⣌⡓⠀⠀⡀⢀⠈⣠⡜⠁⠀⣰⣿⡟⢀⣯⠕⠊⠉⠉⠉⠉⠁⠒⠚⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣼⣤⢋⡔⠏⢀⣴⠚⠁⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⢀⠀⠀⠀⠘⣿
⠀⠀⠀⠘⠓⠉⠿⣿⢿⣿⣠⡟⠀⢠⣿⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⠈⢠⣌⠂⢀⡏
⠀⠀⠀⠀⠀⢠⣴⢋⣉⣤⢏⠃⢀⡿⠃⠀⢠⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⠀⠀⢈⠀⠈⡇
⠀⠀⠀⢠⡆⠘⣿⣤⠀⣿⠈⠀⢸⡇⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠿⡛⠂⠀⠁⠀⠀⠈⠀⠀⡄
⠀⠀⠀⣿⣿⣀⠈⠋⢠⡏⠀⠀⣸⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⣠⡦⣖⡦⠀⣠⣤⣤⣤⡴⠻⠟⢏⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⣿⣿⣧⣆⣠⠈⣇⠀⣰⣿⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⢋⡔⢋⣴⢟⣿⡿⣿⡗⠀⠀⣤⣄⠀⠠⠀⠄⠐⠀⠀⠀⠀⠘⣵⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣀⣿⡟⣿⣷⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠞⠙⣿⣄⠉⢿⣿⠂⠀⢀⠠⠎⠀⠀⠀⠀⠀⠀⣠⠰⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣹⣿⡟⠈⢿⣷⣀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠒⠚⠉⣠⣴⡁⣤⣾⣟⡁⣀⣈⣿⡲⠛⠉⠀⠀⠀⠠⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀
⠀⠀⠀⣿⠟⠛⠿⣿⣿⣿⠁⣿⡅⠀⠂⣹⣿⣷⣿⣦⣤⣄⣀⣀⡀⠀⣀⣤⣞⣿⠧⣀⣿⣿⠃⠀⠀⠉⢿⠀⡌⠀⠀⠀⠀⠀⠀⢰⣄⣼⣿⣿⣿⢿⣿⡇
⠀⠀⠀⣿⡀⠀⣰⣿⣿⡟⡎⢻⣆⠠⠀⣽⣅⣧⡀⠀⡄⠈⠉⠛⠃⢹⢟⡿⠋⠀⠀⠈⣿⡇⠀⠀⠀⢠⡾⠀⠀⠀⠈⠀⠀⢀⢰⣾⣿⣿⠋⠁⡁⢸⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣏⣿⡇⢹⣿⣿⣾⣯⠿⠿⠻⣥⠀⠀⠁⠀⠰⠄⠀⢸⠁⠘⠀⢀⣼⠟⢳⣤⣤⠖⠋⠐⠀⡀⣀⡇⣀⠛⠛⢿⣿⣿⣿⣀⡀⠀⣸⣿⡇
⠀⠀⠀⢿⣿⢻⣿⢏⡿⢧⣾⣿⣿⡿⠈⠀⠀⠘⣿⣀⣰⣞⠀⠀⠀⠀⠈⠳⠶⡶⠞⠁⠀⠀⠄⢀⡀⣀⣰⣆⣿⣿⡟⠁⠈⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠛⢛⣿⣷⣠⣿⣾⣿⣿⣿⣷⣦⣀⣤⣴⣿⣿⣿⣾⣼⣆⣆⢀⠀⠀⢠⡀⠂⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣷⣦⣮⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⢁⡾⠁⣀⣒⣲⠆⠀⡱⠯⠀⠀⠐⠀⠈⠀⣈⡀
⠀⠀⠀⠀⠀⡄⠒⢤⠀⠀⠀⣀⣀⡤⠴⠒⣲⠟⠉⠉⢡⣿⣥⠄⠀⠈⠉⠉⠙⠒⠒⠠⠎⠀⢨⠆
⠀⠀⠀⠀⠀⠣⡀⠀⠓⠒⠉⠁⠀⠀⣠⣞⣡⣤⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠌⢢⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⡜⠀⠀⢈⠔⢀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢧⠀⠀⢀⠠⠀⢀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡀⠀⠈⠄⠀⠁⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢀⠔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠢⣀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡠⠋⠈⠉⠓⠒⠒⠶⠶⠖⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⣿⣄⣿⣿⣿⣿⠃⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠉⠁⢹⣿⣿⣄⣸⣿⣿⣿⣿⣿⡿⠟⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⠛⠋⠙⣿⡿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠸⠿⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠊⠉⠀⣷⠀⠀⠀⠀⠀⠀⠀⡼⠲⣄⣠⠴⠚
⠀⠀⠀⠀⡇⣀⣠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄
⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⠊⠉⠉⣓⠦⠖⠚⠉⠉⠓⠒⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⢴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄
⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⢀⣀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡤⢤⣀⡠⣄⡠⠖⠚⠉⠉⢽⣋⣀⣠⢾⡇⠀⠈⢧⡀
⠓⠶⢞⣉⠁⠀⣀⠤⠖⠚⠉⠉⠉⠀⠉⠉⠓⠲⢤⡀⢀⣀⣀⡀⠀⢰⡃⢾⠀⠀⠋⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠉⠉⠉⠉⠛⢷⡀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠘⣷⡀⠀⠀⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⠀⢠⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡞⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠸⡇⠀⠈⢳⠙⣄⠀⠀⠸⠀⠀⠀⣠⢏⡟⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠀⠀⠘⠊⠁⠀⠀⠀⣀⠤⠚⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⠲⢄⡀⠀⠀⢠⠶⣾⠗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⢄⡈⠙⠋⢙⣎⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠑⠲⠾⡷⠚⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠆⠀⠀⠀⠀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⠧⠤⠴⠋⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠒⠒⠉⠑⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢈⣿⣿⡿⠛⠁⣠⡄⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⡾⠀⣸⣿⣿⣦⣤⣾⣿⡇⠀⢻⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠟⠁⣠⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⣿⡿⠀⠘⠛⢉⣠⣼⣿⣿⣿⣧⠀⠈⠁⣠⣾⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⡟⢀⣼⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣉⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠉⠛⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠉⠛⠛⠋⠁⠀⠈⠻⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⣤⣤⣤⡀⠒⠂⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⢨⣾⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⢸⡏⠛⠫⠙⠻⠟⣻⣿⣿⣄⡠⠄⠀⠈⠢⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠂⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣅⣒⣠⣤⣹⣿⡏⠀⠀⠀⠙⠢⡀⣀⣈⣂⣀⠀⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⢠⣄⣤⠀⠀⠂⢻⣿⣿⣿⠹⣿⠀⠀⠀⢀⠗⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⣿⠋⠉⠑⡄⡀⠀⠙⠻⣯⠆⢨⢀⠠⠒⠁⠀⠀⠀⢀⡀⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠢⡊⠀⠀⠈⠁⠂⣼⠷⠊⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢈⡢⠄⠀⠈⠁⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⠊⠁⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⡞⠉⣧⣤⠤⠤⠤⠤⠤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣇⡀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⢸⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡀⠀⠀⣸⡀⠀⣸⡀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢳⢤⠗⠒⢚⡡⠝⠒⠒⠓⠞⠓⠚⠓⠛⠿⣇⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣻⠒⣦⠀⠀⠸⠀⠀⠛⠁⠀⠘⠃⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠓⠚⠳⡤⠜⠀⠀⠠⡂⢀⠀⢀⡀⠄⠑⠄⠀⠀⠀⢀⡤⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠈⠉⠀⠀⢀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⠔⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠺⠤⠼⠶⠃⠀⠀⠀⢀⡠⠞⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣴⠃⠀⠀⠀⡀⡸⠧⣀⡀⠠⠤⠀⣀⣀⣀⣤⠤⠤⠖⠚⠉⢰⡦⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠘⠧⣤⡤⠞⡿⠁⠀⠀⠉⠙⠓⠒⠒⡧⣤⣤⡤⠶⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⠴⠒⠒⡆⡖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢱⡀⠀⠀⣧⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢣⠀⠀⢸⡄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⢇⠀⠧⢤⡀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⡠⠄⠒⠳⣄⣉⣹⣏⣉⣙⣻⢩⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣾⣥⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠁⣸⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣤⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠴⣴⣶⣶⠂⠀⠀⠀⢈⠝⠂⠀⠀⢀⣤⣴⠟⠉⠁⠀⢠⢀⠄⠂⠀⡄
⠀⢠⣾⠃⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⣯⡀⠀⠐⣤⠈⠋⢩⢻⣶⡾⠟⠃⠀⠀⠀⠀⠘⠀⢴⣧⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠘⠻⠂⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠘⠿⠿⠊⠒⢳⣀⣀⣾⡟⠀⠀⠀⠀⠀⠀⢐⡦⠀⠠⣿⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨⣅⠀⢀⣿⠄⠀⠀⣀
⠀⠀⠀⠀⠈⠧⣀⣀⡀⡀⢰⠂⠀⠀⢀⠀⢀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠢⠄⡀⠀⠠⡷⠣⠀⠼⠟⠀⠀⠀⠈⣆
⠀⠀⠀⠰⠋⣶⠀⠈⠃⠀⢰⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⢿⣀⣀
⠀⠀⠀⣰⢠⡇⠀⣸⣦⡀⢠⡂⢠⡀⠀⠀⠀⢸⡆⢠⢄⣯⡄⢰⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠄⠀⡽
⠀⠀⢀⡸⢸⠇⢀⡿⣻⡇⢸⡇⠸⡳⡀⠀⠀⠀⠘⠒⠠⠤⠠⠄⠤⠤⠔⠋⠀⠀⠀⢀⠂⠀⢢⣄⠀⠀⢉⣀⡄⠚⠁
⠀⠀⠀⢀⠸⠄⣰⡇⢸⡇⠈⣧⠀⠙⠙⠄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢠⠆⢀⠀⠘⠆⠀⠘⠁⠀⠀⠈⠁⠀⢀⠀⠀⡐
⠀⠀⠀⠺⠀⠀⢹⡇⢸⡇⠀⠈⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⠀⢸⠃⠄⠀⢸⣀⡟⠠⠀⠈⠒⠠⠔⠠⡄⠀⠀⠀⠀⡗⠉
⠀⠀⠀⠀⠀⠀⠘⠇⠈⠁⠀⠠⠀⡀⠀⢢⠇⠀⠀⠀⠀⢸⡆⢸⡤⣤⣶⠿⢽⡁⠀⢀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁⠀⢸⡀⠀⢼⢠⠶⠊⢇⠘⠃⠀⢻⠀⠀⠑⠂⠀⠀⠀⠀⠀⢰⣢⣄⣤⣄⣳⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠂⠀⠀⠒⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⠏⠿⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠳⣄⠀⠀⠀⠀⢀⢢⣴⠾⠟⠉⠉⠛⠀⠀⢰⣷⣶⡶⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠳⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐
⠀⠀⠀⠠⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⡇⢀⣀⣠⡴
⠀⢀⠃⠀⠠⠐⠄⣡⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠶⠿⠟⠛⠉⠁
⠀⠈⠁⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠒⠒⠒⠀⠄⠊⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⢀⣄⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠈⠻⣦⡈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⢀⡀⠀⣀⠀⣀⡀⡀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠶⠤⢤⡞⠁⢠⣄⠀⡶⣄⠀⠈⠑⣤⠶⠒⠒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣶⡯⠀⣠⠟⠊⠉⠃⠈⠙⠒⢦⡈⣷⡀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⡴⠊⠉⠀⣧⡞⠑⠦⠖⠀⠀⠐⠦⠔⠀⡇⣸⠈⠑⢆⣀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠈⢳⢹⡇⠀⠀⠀⢤⡤⠄⠀⠀⠀⡿⢙⡏⠀⢸⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⢦⡀⠈⠓⠳⣀⡀⠀⠀⠀⠀⠀⢀⡰⠗⠋⠀⢀⡜⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⣀⡀⠀⠀⠙⢦⡀⠀⠀⢹⡻⠃⠀⢿⡏⠉⠀⠀⢀⡴⠋⢀⣀⣀⡤⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠉⠙⠓⠒⠲⠿⡦⠀⠀⠈⠉⠉⠉⠀⠀⠀⡖⠋⠉⠉⠉⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⣠⣤⠤⢦⠀⠀⢀⡜⣡⢴⣒⣚⣫⣩⣭⣩⣍⣙⣒⣤⣱⡀⠀⠀⡴⠲⣄⣄⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡖⢯⠳⠼⡀⢸⠀⠀⢘⡾⠉⠁⠀⠀⢸⣾⠻⣾⠀⠀⠈⠉⠳⡗⠀⠀⣿⠀⠟⢜⡹⣦⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢏⠂⠀⠀⠀⢸⡀⢀⠞⠀⠀⠀⠀⠀⠉⢸⢸⡏⠀⠀⠀⠀⠀⠙⣄⢠⠏⠀⠀⠀⠘⡹⠃⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣷⠋⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢳⡀⠀⠀⠀⠀⢀⡴⠋⠈⠳⣄⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢧⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠱⣄⠀⠀⣾⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣠⣞⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠻⣄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⣤⣀⣀⣈⣙⣒⣋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣙⣒⣋⣁⣀⣠⣤⡤⠤⠤⠴⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉