Veterinarian Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠄⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢀⣔⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡠⢋⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⡌⠁⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢃⠔⠣⡀⠊⠐⠀⠀⠀⡐⢘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⠖⠀⣤⠠⠐⠀⡌⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⡔⠀⠀⠄⠈⠀⡀⠀⠀⠀⠀⢀⠆⢀⠈⠀⠱⡀⠰⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠈⣇⠀⠀⠀⢠⠊⠀⠀⠀⡶⠖⠃⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢠
⠀⢀⠀⢠⡄⠋⠣⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠐⡁⠀⠑⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠆
⠀⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠀⠀⠀⠀⢀
⠀⠐⠤⡀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠈⡄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠈⡀
⠀⠀⠀⠈⢂⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠁⡀⢀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡐⠒⠒⠀⡐⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣒⠤⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢀⠠⠀⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢳⠀⠂⠀⠀⠠⠄⠠⠤⠄
⠠⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢆⠠⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠋⡠⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⢼⣀⠀⠀⠀⠀⡃
⠀⠈⠢⣈⠁⢀⣁⢄⠀⠀⠀⠀⠀⡠⠁⠈⠥⠤⠄⢀⡄⢀⠀⠀⠁⠀⢀⠀⠀⠉⠈⠉⣉⡉⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠅⠀⠤⠄⠒⠒⢂⠤⠊⠁⠀⠈⠀⠀⠀⠠⠥⠤⠤⠤⠠⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢌⠀⠀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠀⠈⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⣀⠀⠀⠀⠙⠆⠖⠃⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣶⡦⠛⠀⠀⣄⣀⣠⣴⣾⣿⣿⣿⣿⣷⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠛⢠⠎⠂⠀⠿⠿⠿⠛⠋⠉⠈⠉⠻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⣠⡂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⠷⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⠀⠀⠁⠁⠀⠉⠈⠁⠀⠠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⣢⠂⠐⠂⠀⠀⠒⢠⡆⢀⡖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⢈⠁⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣛⠉⠐⣶⠀⠈⠿⠢⠙⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠂⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡆⠀⠀⢀⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢒⡁⢤⠗⢲⠛⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠒⠢⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⠀⠈⠀⠀⠀⠀⢠⠱⡀
⠀⠀⠀⠀⢀⡤⠚⡀⠀⠀⠀⢀⠟⠳⣟⠄⠀⠀⠀⠀⠀⢀⠎⠁⢰⠀⠀⠀⠀⠀⠀⢨⠀⢣
⠀⠀⠀⢠⠊⠀⢠⠁⠄⠀⠠⠄⣧⠀⠈⢊⡱⠂⠄⡀⢠⠂⠀⢰⠀⢃⢀⠀⠀⠀⠀⢸⠀⠀⠃
⠀⠀⠀⡌⠀⠀⠸⣆⠀⣤⡄⢠⡏⠀⠀⠈⡦⡀⠀⠀⠉⢆⠀⡸⡄⠀⠓⢀⣤⢀⣀⣸⠀⠀⠘⡀
⠀⠀⠀⢣⠀⠀⢸⠎⠣⣈⡰⠁⢹⠀⠀⢠⠁⠈⠲⢄⠀⢀⡕⠁⢡⢀⠔⠁⠀⠀⢀⡔⠀⠀⠀⠇
⠀⠀⠀⠀⠑⠒⠺⠀⠀⠀⠀⠀⠈⠒⢖⠁⠀⣀⣀⣀⣉⣁⣀⡀⠜⢅⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡏⠩⢀⣤⣭⠋⠀⡠⠚⡅⠀⠀⡎⠉⠁⠉⠉⡇⢀
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⣜⣈⣉⣿⣶⡞⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⠀⠀⡇⢀⡀⠀⠳⡀⢸⠀⠀⠀⠘⢘⠁⠀⠀⠱⡀⠀⠀⡠⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⢸⠀⠀⠃⢸⠀⠀⠀⠁⢸⠀⠀⠀⡆⠸⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠉⣦⡀⠘⠀⢠⠀⠈⢆⠀⠀⡄⢸⠀⠀⢀⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠒⠂⠈⠁⠐⠒⠦⢠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⡝⠜⢄⡀⠸⠀⠀⠈⡄⠀⡃⡸⢔⡺⡛⠘⠤⠤⠀⠀⠠⣤⠄⠒⠂⠁⠀⠀⠀⠀⠀⢀⡀⠄⡷⢺
⠀⠀⠀⠀⠀⠀⢀⠆⠀⣷⢃⡸⠃⢰⠆⠀⡶⠗⢀⣛⣈⣏⣉⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠂⠈⠉⠁⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠁⠁⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣠⡴⠶⠚⠛⠛⠛⠒⠲⢤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢷⠀⡞⠁⠀⠤⠶⢤⡀⠀⠀⠀⠀⠈⠳⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠧⣾⠸⠟⠃⠀⢠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣎⣉⠀⠀⠀⠀⢯⣴⣶⡿⠀⠀⠀⢀⣈⡙⠆⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⢹⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⣤⡟⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⣀⡼⣇⠀⠀⠀⢀⠀⠀⢤⣀⣀⡆⠈⢉⡾⠁
⠀⠀⠀⠀⠀⣀⣠⣴⣶⠟⠛⣻⡇⠏⣽⠃⠘⣦⡀⠀⠈⠑⠒⠤⠍⠉⠀⣠⡞⠁
⠀⠀⠀⢠⡾⠋⠉⠉⢿⡀⣰⠏⢷⠸⣿⡀⠀⠈⠻⢦⣤⣀⣀⣀⣤⡴⢺⠏
⠀⠀⠀⣿⠃⠀⠀⠀⢸⣿⠋⠀⠈⢧⡙⢷⡄⠀⠀⠀⠀⣼⡿⢉⡿⡡⠋⠙⢦⣀
⠀⠀⢀⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⣯⣙⠓⠶⠶⣿⠽⢟⣩⠞⢷⡀⢀⣠⠿⠷⠤⣤⣀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⣦⣄⡀⠀⠀⢹⡈⠙⢦⠀⢀⣴⠋⢀⡤⡾⠛⠁⠀⠀⠀⠀⠀⢈⣳⣄
⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠉⢻⠆⠀⠸⡇⠀⠈⣿⢿⢸⠆⠎⡜⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠙⢦⡤⢤⣀
⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⣰⠋⠀⠀⠀⣇⠀⠀⣿⢸⢸⠂⡞⠀⠁⠀⠀⠘⠛⠀⠀⠘⡇⠀⠀⠀⢱⡈⠏⠱
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡀⣇⠀⠀⠀⠀⣿⠀⠀⣿⢻⢨⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣷⠾⢤⣇
⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡇⠹⣷⡀⠀⠀⣿⠀⠀⣿⢺⠸⣿⡿⠟⠀⠀⠀⠀⠀⢀⡞⢸⣇⠀⠀⠀⢠⠏⠓⠦⣼⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⢹⠀⠀⢿⢸⠀⣿⠳⣤⣄⣀⣀⣤⢴⠟⡰⠃⠘⠦⣄⣠⠞⠀⠀⠀⠈⠙⢦⡀
⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠻⡄⢺⠀⠀⢸⡘⡆⢸⢠⠇⠀⣠⠟⠁⢶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠾⢻⣆⣀⠀⠹⣾⠀⠀⠈⣇⠻⣼⣿⠴⢋⡴⢻⣄⣨⢷⡀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣧⠀⢠⢶⡄⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠊⠁⠀⠈⠀⠉⠓⠦⢿⣄⣀⠀⠘⠶⢤⡴⠚⠁⣀⡼⠅⠤⣤⣷⣸⠃⠀⢀⡆⠀⡜⠁⠀⠀⠀⠀⠀⢻⣤⠏⣸⠇⠀⠀⢸
⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢷⡶⠞⠉⠀⠴⠖⠦⣌⣹⠆⠀⢸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠸⣧⠾⠋⠀⠀⠀⢸
⠀⠀⠀⢸⡏⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠚⠐⠒⢤⣸⡆⠀⢸⣀⣸⡀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⠀⠀⠀⠀⣉⣳⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⠐⠾⣻⢗⡶⠃⠀⠀⡎⠉⠉⣹⠶⠂⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⣸⣤⡴⠶⠚⠛⠉⠁⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⠀⣿⢁⡼⠯⣌⣙⣶⠬⣹⠶⠀⠀⢀⡇⣰⠟⠁⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠷⠊⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⠾⠑⠧⣄⣀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⢤⣤⣤⠤⣤⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠒⠊⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠤⢤⠔⠉⠠⠔⠂⠘⢦⣀⡴⠛⢦⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡖⢩⡅⠀⠀⠾⠂⠀⠀⠀⠁⣠⡾⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⡎⢮⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣬⡁⠀⠀⠀⢀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢄⣤⠀⡙⠀⠀⣀⠴⠛⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠳⢍⡠⠴⡊⠁⣀⣷⢵⣤⣤⣄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡟⣻⠋⢠⠎⠀⠀⠈⢷⡄⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡞⠳⠃⠀⢸⠀⠀⠀⠀⢸⢡⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢰⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠈⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢡⠀⠘⡄
⠀⠀⠀⠀⢀⠴⠊⢩⡯⠉⠓⢀⡀⠀⠀⠀⠀⠀⢀⢷⡙⠢⡄⠀⠀⠈⠀⠀⠀⠀⢸⠀⠘⡄⠀⡇
⠀⠀⣀⠔⠉⣆⡀⡼⢸⠀⣀⡞⠑⢄⡀⠀⠀⣀⣾⢄⣙⠒⡇⠀⠀⢸⡀⠀⠀⠀⣸⠀⠀⢧⠒⠁
⢀⠞⠁⠀⠀⡏⣹⠃⠈⣆⠉⣷⠀⠀⠙⢯⠉⠀⠀⠀⠀⢹⠁⠀⣀⠜⠋⠉⠉⢉⡏⠀⠀⢸⡄
⡎⠀⠀⠀⢸⢠⠏⠀⠀⠘⢆⢸⠀⠀⠀⠈⣧⠤⠐⠒⠊⣏⠴⠊⠁⠀⢀⡠⠔⠋⠀⠀⠀⠀⠳⡀
⡇⠀⠀⠀⢸⡇⠀⣶⣶⣦⠈⢿⡀⠀⠀⠀⣇⢀⣀⣠⠾⣅⠀⢀⡠⠖⠉⢀⣀⣀⣀⣀⣀⣀⡀⠱⡀
⡇⠀⠀⠀⢸⣇⠀⠭⡿⠅⢀⣿⡀⠀⠀⢈⣷⠷⠀⠀⢀⡨⠟⠉⠀⠀⠀⣏⣀⣀⣀⣀⣀⣀⣹⠀⠹⡄
⢱⠀⠀⠀⣸⡌⠓⠒⠒⠒⢺⠹⡇⠀⠘⣷⣾⢄⠀⣰⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡀
⠘⢄⡀⢀⡟⡇⠀⠀⠀⠀⡜⠀⢇⠀⣀⠽⣛⣿⡋⠈⢢⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠙⡆
⠀⠀⠉⠉⡏⠀⠀⠀⠀⠀⣇⠀⠈⢹⠁⠀⢀⠤⠵⣄⠀⡟⢦⡀⠀⠀⠀⠈⢦⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢹⠀⠀⡜⠀⣰⠁⠀⠀⠘⣆⡇⠀⠙⠢⣄⠀⠀⠀⠉⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢸⢣⡀⠀⠀⠀⢸⢀⡴⡇⠀⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⣀⣀
⠀⠀⠀⠀⢸⠀⠱⣄⠀⠀⢸⠁⠀⡇⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⣀⣤⠀⠀⢨⡍⠓⠲⠤⢤⣤⣤⣤⣤⠤⠴⠒⠊⠁⠀⠀⠀⠉⢹⠒
⠀⠀⠀⠀⢸⠀⠀⡟⡗⡄⢸⠀⠀⡇⠀⠀⠘⡄⠀⢀⡯⠤⢶⣏⣁⠞⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢼⡤
⠀⠀⠀⠀⢀⣀⣀⣇⣸⠘⣼⣀⡀⣧⡀⠀⠀⢱⣀⣸⠦⠐⠒⠉⠁⠀⠀⠀⠀⠙⠢⠤⢀⣤⣀⣀⣀⣀⣤⡀⠤⠤⠔⠒⠊⠉⠀⡾
⠀⠀⠀⠠⠯⠥⠬⢿⠤⠿⠭⠤⠭⠷⠿⠶⠏⠭⠭⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠄⠤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠞⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠠⠀⠂⠉⠀⠀⠀⠈⠂⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⢀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⡄⡨⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⠰⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠊⠁⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠈⠴⠁⠀⠀⠀⠀⠀⠁⠀⠀⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠐⢶⢰⣶⠖⠠⣂⠀⠐⠀⠀⠘⢏⠁⠀⠀⡲⠊⠉⠁⢀⡀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢠⠁⠀⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⢰⡷⠀⠀⠀⢰⡷⠀⠀⠀⠀⠠⠁⠀⡤⠑⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠰⡷⠀⠀⠰⡷⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⣇⠀⠰⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠂⠀⠀⠀⡸⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⡈⠠⢄⠀⠀⠈⠀⠀⢀⣠⡀⠀⠐⠀⠨⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⣀⡀⡤⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠉⠛⠙⠓⠋⠁⠀⠈⠀⠤⣀⣀⠄⠁
⠀⠀⠀⠀⠀⢀⢠⠄⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠂⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠶⢀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠸⠃⠀⠸⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡸⠀⠀⠀⠃⠀⠀⢰⠀⠀⠀⠀⠁⠀⠁
⠄⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠁⢥⢠⡄⠠⠇⠀⠀⠈⠑⠾⠖⠂⠀⠀⠠⡀
⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠂⠀⠈⠉⠉⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠀⠂⠄⠀⠀⠠⠄⠐⠂⠄⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⢀⠐⡀⠇⠀⠀⠀⢀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⡀⠀⠀⠀⢀⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠢⡈⠁⠀⠉⡠⠃⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡒⢄⣀⠀⠁⠀⠁⢀⢠⣴⠨⠄⠀⠤⠤⠤⠤⠤⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠂⡠⠂⢃⠀⠈⠉⠀⢠⡠⠁⢀⠔⣡⣄⠀⠀⠀⣠⣌⠲⡀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡐⠁⡼⠁⡈⠀⠢⠀⠀⡠⠋⠀⠀⠃⠀⢐⡂⠀⠀⠀⢐⡂⠀⠘⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⡀⠀⠀⠀⠂⠀⠀⢰⡃⠀⠃⠀⠀⢐⠊⠀⠀⠀⢠⠔⠁⠈⠍⠉⠉⠉⠫⠁⠈⠢⡄⠀⠀⠀⠑
⠀⠀⠀⠀⢠⠂⠂⣰⢂⡄⣀⢀⡀⡖⡂⠅⠀⠌⠀⢠⡴⠋⠳⣤⠀⠀⠀⠘⡀⠀⠀⠀⣴⠀⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⢦
⠀⠀⠀⠀⠬⣨⠄⠨⠁⠃⠏⠂⠡⠁⢅⡠⠬⢀⠀⣸⠁⠀⠀⠘⡄⠀⠀⠀⠀⠢⠤⠔⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠣⠀⠔⠈
⡀⠀⠁⠀⠀⠁⠈⠈⠉⠁⠉⠉⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢾⠟⠀⡀⠀⠀⠈⠀⠀⢀⠀⠳⡀
⡇⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠐⠒⠂⠀⠁⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⢂⠀⠑⠄⠀⠀⠀⠀⠀⣆⡄⡄⢾⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⡇⠀⠀⠀⠀⢸⠀⠀⠀⢶⢷⠆⠀⡆⠀⠀⠀⠀⠀⠀⡧⠀⠀⠠⠀⠀⠀⠀⠀⡌⠠⠄⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠
⡇⠀⠀⠀⠀⠈⠄⠀⠐⠉⠈⡂⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠐⣄⠀⠀⡄⠀⠀⠀⠠⠀⠀⣠⠂
⡇⠀⠀⠀⠀⠀⠈⠂⠄⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠼⠀⡀⡀⠀⠀⠀⠀⢀⠀⠧⡀⠀⠄
⣧⣤⣄⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣂⣀⣀⣘⣂⣀⣀⣀⣐⣃⣀⣀⣐⣀⣂⣀⣀
⣿⣿⠉⡉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡾⠁⠀⢠⡆⠀⠈⢷⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⡇⠀⠒⢺⡗⠒⠂⢸⣂⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣿⠉⠉⠉⠹⣄⡀⠘⠃⢀⣠⠏⠉⠉⠉⣿⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⣄⣀⣀⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠿⠀⠀⠀⠀⠀⠸⢁⡞⠁⠀⠀⠀⠹⡌⢷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢺⠒⠶⠶⠶⠖⣶⢸⡇⡉⢀⡀⢉⡀⡇⢸⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠀⠆⢀⠰⠀⣿⠈⡟⠁⢯⡽⠃⢻⠗⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣦⣈⣉⣁⣴⠋⢠⠟⠲⠚⠙⠶⠛⢧⠀⢤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢦⠀⣰⠃⠀⠉⠀⠈⣧⠘⠀⣦⠀⡆⢠⡄⠘⣇⢸⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⡏⠀⡆⢰⢰⡆⢸⠀⠀⡟⠀⡇⠘⡇⠀⢻⢸⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣄⣧⠀⡇⢸⢸⡇⣸⠀⠀⡇⠀⡇⠀⡇⢀⣾⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⣤⣬⣤⣤⣤⣭⣿⣧⣼⣤⣿⣥⣤⣯⣥⣤⣧⣤⣭⣿⣥⣤⣤⣤⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡶⠞⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠿⡆
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢠⡿⢻⡆⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⢀⡿⣠⡤⠀⠀⠀⠀⣠⡟⠁⠀⢻⣄⠀⣿⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣼⠿⣿⠃⠀⠀⢀⣴⠏⠀⠀⠀⠀⠹⣦⣿⠀⠙⢷⣄⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣿⠀⠀⣠⡾⠡⠶⠞⠗⠀⠀⠀⠈⠿⠆⠐⠿⠿⢷⣄⠀⠀⠀⢸⡏
⠀⠀⠀⠀⢿⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⢾⡏⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠈⢹⡿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠹⣆⠀⠀⠀⣼⠋⠻⣆
⠀⠀⢰⡏⠀⣷⠀⠀⠀⠀⠀⠈⠁⢠⣄⡀⢀⣠⡤⠀⠉⠀⠀⠀⠀⠀⣸⠇⢸⡇⠀⠀⠀⠀⠀⠀⣾⢃⣤⡀⢿⡄⠀⣸⠇⣠⣄⢻⡄
⠀⠀⠈⢷⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣼⠃⠀⠀⠀⠀⠀⣸⠇⣾⠉⣷⠸⣇⢠⡟⣰⡏⢻⡌⣷
⠀⠀⠀⠘⣧⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⠀⢠⡟⢰⡏⠀⢹⡆⣿⣼⢃⡿⠀⢸⡇⢹⡆
⠀⠀⠀⠀⢻⡄⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃⣸⠇⠀⠘⣧⢹⡿⣸⠇⠀⠘⣇⠸⣧
⠀⠀⠀⠀⠘⣧⠸⣯⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣹⡇⣸⡇⠀⠀⠀⠀⠀⢠⣿⣠⡿⠶⠶⠞⠛⠻⠷⠿⣤⣄⡀⣿⠀⣿
⠀⠀⠀⠀⠀⢹⡆⢻⡆⠀⠙⠳⢦⣤⣀⣀⣀⣀⣠⣴⠾⠋⠁⢀⡿⢠⡿⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠀⢹⡆
⠀⠀⠀⠀⠀⠈⢿⡀⢿⡀⠀⠀⠀⣿⠉⠉⠉⠉⢹⡇⠀⠀⠀⣾⠁⣾⠁⠀⠀⠀⠀⠀⢸⣏⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠘⣷⠘⣷⡀⣀⣤⣿⠀⠀⠀⠀⢸⣧⣀⠀⣼⠇⣼⠇⠀⠀⠀⠀⠀⠀⢸⣿⠉⢹⡇⠀⠀⠀⠀⣿⠉⢹⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⢿⡋⠀⢿⡀⠀⠀⢀⣾⠁⢉⣿⠋⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠁⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⡌⠻⣦⣈⠻⠦⠴⠞⢁⣤⠾⢁⣼⠋⠻⣦⡀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢸⡇
⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠙⢷⣌⣉⠛⠛⠛⠛⢋⣡⡴⠟⠁⠀⠀⠈⠻⣆⠀⠀⢸⡿⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢾⡟⢸⡇
⠀⠀⠀⣰⠟⠀⠀⣄⡀⠀⠀⠀⠈⠙⣿⠀⠀⣺⡋⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⢸⡿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣼⠃
⠀⠀⣰⠏⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⣿⣤⣤⣾⠄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⢷⡜⢷⣿⡀⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠋⠁⢀⠀⠀⠀⣿
⠀⢠⡟⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣿⠈⢿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢿⡀⠉⠛⣿⠛⣛⣩⣅⣀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⣿
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣆⠘⢷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣷⠀⠀⣿⠟⣉⣥⣬⣉⠻⣦⠀⠀⢀⡀⣼⠇⢻⡆⢻⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣦⡈⠻⣦⡀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣼⣧⣼⣧⣼⣏⠀⠀⠙⣧⢸⡇⢀⡾⢿⠏⡀⢸⡇⠈⢷⡀
⠀⣿⠀⠀⠀⠀⣀⣀⣀⣀⣹⡆⠀⠀⠀⠀⠀⠈⠳⣦⡈⠛⠶⣤⣿⣀⡴⠛⠁⢀⣤⣤⣤⣤⣤⣤⣽⡃⢀⣰⡟⢰⡿⠟⠁⠀⣸⢿⡿⠀⠀⠈⢻⣄
⠀⣿⣤⡶⠛⠛⠉⠉⠉⠉⠙⠻⣆⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⡽⠋⠀⠀⠀⣀⣀⣀⣹⡏⠻⣦⣉⣛⣛⣉⣴⠟⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠈⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠉⠉⠉⢹⡆⠀⠀⠉⠙⠋⠉⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠂⠈⠉⠉⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡐⠁⠀⠀⠉⠐⠂⠐⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠀⠀⠠⠖⡒⠦⠀⠀⠀⠀⠠⢖⠲⠆⠀⠀⠈⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡀⠠⠀⠀⠀⠀⡆⢈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠐⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⣘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡔⠁⠀⠀⠀⠀⣈⡐⢠⠀⢀⠀⠀⢢⠀⠀⠀⠀⠰⠠⠄⠀⠀⠠⠄⢲⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠊⠀⢀⠴⡀⠃⢰⠂⠰⠈⡄⠙⠣⡀⠀⠑⢄⠀⠑⢄⠀⠀⠈⠂⠄⠀⠀⠠⠔⠁⠀⠀⡠⠊
⠀⠀⠀⢀⠄⠁⠀⠠⠁⠀⠐⡚⠁⠈⠁⠈⠀⡐⠀⠈⠂⠀⠈⠂⠀⠀⠈⠶⣤⡄⣀⣀⣀⣀⠀⣤⠶⣮⣀⠀⠀⡀
⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⢈⣐⠀⠀⠀⠀⢐⣸⠀⠀⠀⠆⠀⠀⠀⠐⢤⠋⠙⡀⠀⠀⠀⠀⢀⠋⠄⠙⣆⠀⠀⠀⠑⢄
⠠⠁⠀⠀⠀⠀⢠⠔⠀⠉⠁⡐⠉⠉⠉⠉⠣⠀⠉⠁⠂⡄⠀⠀⠀⠀⠀⢲⠀⠑⠄⠀⠀⢀⠊⠀⠀⠀⠘⡆⠀⠀⠀⠀⠡
⡇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢄⡀⠠⠤⢀⣀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⡈⢂⡍⠀⠢⠔⡁⠀⠀⠈⠀⠀⣧⠀⢰⡀⠀⠀⠡
⠐⢄⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠐⡀⢾⡄⠺⡌⢂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠇⠀⠀⠀⠁
⠀⠀⠁⠂⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣠⠁⡟⠓⠀⠚⠙⢦⡙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⢇⠀⠀⠈⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⢀⡞⠠⢉⠈⠁⠀⠀⠐⠀⠈⠁⢈⠅⠳⣼⡇⠀⠀⠀⠐⣦⠁⠀⠀⠀⢀⠠⠆⡀⠀⣦⠴⢾⡄⠸⠀⢠⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⡌⣇⠀⠀⠀⠀⡇⠀⠠⡠⠐⠁⠀⠀⠈⠘⠻⢤⣼⡇⡄⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢙⠀⠀⠀⠀⡇⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠀⠀⠀⢀
⠀⠀⢀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠠⡀⡤⢼⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀
⠀⠀⠆⠑⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠂⠀⠠⡤⠤⠤⠤⠄
⠀⠀⠐⡀⠀⠀⠀⢸⠀⠀⠀⡀⢀⣀⣀⣀⠀⡀⠀⠀⢀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠈⢂⣄⣀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀
⠀⠀⠀⠰⠁⠀⠐⠈⠁⠐⢠⠀⠀⠀⠀⠀⠀⣀⠐⠈⠉⠢⡀⠀⡁
⣶⣶⡶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠃⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠏⠤⠺⠒⣿⣿⣿⡇⠀⠌⠉⠉⠁⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢇⢹⣿⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣏⠐⠠⠃⠀⠀⠀⠈⡆⢿⠃⢀⠞⠀⠀⠀⠀⠓⢤⣤⣤⣤⠀⠘⠿⠿⠆⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣠⣿⣧⣾⣄⡀⠠⠀⠀⠸⡌⢀⠞⠀⠀⡆⠀⠀⠀⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣿⡆⠀⠀⠀⢹⠎⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠉⠙⠿⠀⠀⢀⡀
⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⠀⠿⠇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣀⣀⣠⣀⣄⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠉⠙⠉⣉⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⢠⣾⡽⣷⣹⠗⠒⡄⢀⣠⣞⣵⣆⣽⣿⡇
⠋⢹⣇⢸⣿⣿⡇⢸⡇⢀⣿⣿⣿⡇⡀⢿⠏⠘⣿⣿⣿⣿⡘⢷⣾⣿⡎⢳⡾⢶⣟⣿⣿⣹⠏⣺⣿⡇⢈
⣤⡄⠁⢸⣿⣿⣇⣥⣴⣿⣿⣿⣿⠇⠶⢤⣤⠄⠻⣿⣿⣿⣿⣿⠿⢷⣾⣿⣻⣿⢋⣽⣿⣿⡾⣿⣿⡇⢿
⠐⠂⠀⠸⠿⠿⠛⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠀⠹⠗⠛⠉⠿⠿⠛⠁⠋⠐⠿⠿⠇⠈
⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⠶⣿⠿⠷⢿⣿⡾⠾⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⣰⣶
⠀⠀⢀⣴⣿⡏⣄⣿⣷⣦⠀⠀⠀⠀⢻⣿⣿⣶⣴⣦⣾⣿⣿⠟⠀⠀⠀⢀⣀⣤⣶⣿⣷⣺⣸⣿⣷⣦⣀⣀⠀⠀⠀⠈⣿⣷⣄⡀⡆⣀⣼⣿⠇
⠀⣴⠿⠟⠉⠤⡗⠨⡉⠿⢷⡦⠀⠀⠀⠈⠙⣛⣿⣿⡛⠉⠁⠀⠀⠀⠀⠘⠻⠿⠋⡥⠝⢻⠛⢳⡉⠻⠿⠛⠀⠀⠀⠀⠈⠿⢋⣉⡿⢝⠻⠋
⠀⠀⠀⠀⡖⠀⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⢿⠆⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⠘
⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⢀⣀⠀⠀⣀⣀⡄⣀⡀⠀⢀⣀⠀⢠⡀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣀⣤⣄⡀⢴⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⡀⣤⣀
⠈⠻⢿⡿⣿⡿⡿⢿⡿⣿⠿⠋⠀⠈⠿⣷⣶⣿⢾⠿⣿⣶⡾⠿⠀⠀⠀⠉⠛⠛⠻⠿⠿⢿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠹⢿⣿⡿⠿⡿⢿⣿⡿⠟
⠀⠀⠀⠀⠠⠖⠟⣳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢺⠉⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢺⠒⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⡏⠙⣦
⠀⠀⠀⠀⢠⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⡏⢈⡁
⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠁


⠠⣤⣤⣄⡀⠀⡀⠀⣀⣤⣤⡤⠀⠀⢀⡐⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣆⢀⡄⢠⣶⣶⡄
⠀⠈⠻⣿⣿⣶⣷⣾⣿⡿⠋⠀⠀⢠⣿⣿⣶⣶⣾⣷⣶⣶⣿⣿⠄⠀⠲⣦⣤⣶⣾⣿⠿⢿⡿⢿⣿⣷⣶⣴⡶⠃⠀⠚⠛⠛⠿⢿⣿⠿⠟⠛⠛
⠀⠀⠀⠀⠡⠖⡗⢢⡍⠀⠀⠀⠀⠀⠙⠿⠿⣋⣹⣍⡙⠿⠿⠋⠀⠀⠀⠀⠈⠉⠉⠀⠚⢻⠉⢳⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠶⣚⡟⢷
⠀⠀⠀⠀⠲⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢹⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠏⣠
⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣄⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠉⠉⠀⠀⠀⠀⣀⣄⠀⠈⠙⠁⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⢄⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣾⣿⡎⠛⣃⡈⠉⢾⣿⡇⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠘⠛⣡⣼⣿⣿⣦⡀⠉⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣄⠀⠀⠈⠁⠀⠀⠉⠀⠀⢀⣤⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣦⣀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠰⣿⡷⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠬⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣮⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣼⣿⡿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⣶⣶⣬⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣠⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⣿⣿⡇⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠄⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢴⣦⣴⣤⣤⣤⣤⣴⠶⠆⠀⠻⣿⣿⣷⣮⣝⠃⠀⠀⠀⠐⠶⣦⣤⣤⣤⣤⣴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⢿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣶⡝⣿⣿⡇⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣦⣿⣇⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⠿⠁⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⡆⠀⠀⢸⡿⡟⠙⣿⡋⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣆⡀⠀⠈⠻⣿⣶⣝⡁⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⡄⠀⠀⠀⢙⠛⢿⣆⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣷⡀⠀⠀⢸⣷⣸⣯⢀⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⡀⠀⠀⣿⠟⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡃⠘⠃⡏⢀⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣿⣦⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⣿⣷⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣦⡸⣿⣿⡿⠸⣿⣿⡿⣠⣶⣄⠀⢀⣴⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⣿⡇⢀⣡⣶⣶⣦⣅⡀⣿⣿⣿⠀⢸⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣷⡌⠉⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣌⠛⠛⢻⣿⡿⠃⠀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⣾⣧⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⢸⣿⡇⢸⡇⠀⠺⢿⣿⣿⡿⠇⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡇⢸⡇⠀⠀⠀⠻⠏⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⡇⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣾⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⣿⣿⣦
⠀⠀⢀⣠⠴⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⢷⣶⣟⣝⣿⣿⣿⣍⠉⠉⠛⠛⠃
⠀⣴⡏⠀⢠⠆⠀⠈⣳⡄⠀⠀⠀⠀⠀⠈⠓⠤⢄⣘⣿⣿⣿⣧⣴⣿⣿⣿⣛⠲⠦⢤⡀
⠀⣿⣿⣆⠀⠒⠷⠀⢿⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣏⠳⣮⣷⡗
⠀⠹⣯⠿⠂⠀⠀⠀⠀⠿⣷⠀⠀⠀⠀⣀⢤⠆⠀⢀⣾⢗⣿⣿⣿⠿⢿⣿⣿⣷⣤⡉
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠛⣻⣀⣤⣴⠾⠊⠁⣴⣭⠟⠛⠛⠛⢿⢷⠾⠛⠉⢻⣿⣿⣿⣦
⠀⠀⠀⢀⣿⡷⠦⣤⣤⣴⡏⢑⠭⡏⠀⠀⠀⠍⠅⠀⠀⠀⠀⢸⠈⠒⠁⠀⡄⢿⣿⣿⣿⣷⡀
⠀⣠⡴⠟⢣⡙⠦⣤⣿⣧⣇⠐⣗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠀⠀⠀⣇⠘⣿⣿⣿⣿⣿⣄
⢸⠋⠢⡄⠀⠱⡄⠙⢿⣿⣾⢀⣿⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾⢷⡀⠀⣿⢰⡏⣿⣿⣿⣿⣿⣆
⢸⠀⠀⠹⣆⠀⠘⣆⣼⠟⠘⢯⣻⡎⣻⡀⠀⠀⠀⠀⠀⠀⢰⢧⡇⠈⣧⠘⡿⢸⣿⠏⠁⠉⠙⢿⣿⡀⠀⠀⡰
⢸⡄⠀⠀⠙⢆⣠⡿⠋⠀⢀⣼⣿⡇⠹⣧⠀⠀⠀⠀⠀⠀⢸⢸⠇⣴⠻⣿⡇⢸⣿⡆⠀⠀⠢⠈⣿⡇⠀⡼⢡
⢸⣿⡄⠀⠀⠈⠟⠁⢀⣸⣿⣿⠹⡇⠀⢿⡄⠀⠀⠀⠀⠀⣸⢸⠀⢸⡷⣾⡇⣾⡻⣷⡀⠀⠀⢠⣿⣃⣼⣴⠟
⢸⡉⢿⣄⣠⢀⣀⢀⣿⣿⠋⢹⠀⣧⠀⠸⣇⠀⠀⠀⠀⠀⡿⣸⠀⠈⣧⣿⠃⣿⣧⣿⣧⠀⠀⢚⣿⣿⠟⠁
⢸⡇⢈⣿⣿⣾⣿⣿⣟⣹⣆⣸⣧⣿⣤⣀⣿⣀⣀⣠⣀⣰⣗⣙⣻⣷⣾⣋⣄⣿⣯⣭⣭⣤⣭⣿⣿⣥⣤⣤⣤
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣼⡟⡶⠒⢲⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⡀⠀⠀⠀⠀⠀⣀⠀⠴⠉⠷⠄⢀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣾⡇⣠⡀
⠀⠀⠀⠀⠀⠀⠛⢻⠀⣀⡁⢛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠁⠀⠀⠀⠀⠀⡇⠀⣀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣥⣮⡘⢛⣥
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠾⠟⡸⠀⠀⠀⠀⠀⠀⠐⣏⣠⣾⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠆⠛⠇⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋


⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠤⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠
⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡈⠀⣁⠃⠀⠀⠀⠀⠀⡰⢾⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠙⣇
⠀⠀⠀⠀⠀⠀⢿⣭⣟⣿⣻⣭⡿⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⢿⣆⡴⣤⢶⣶⣿⠀⠀⠀⠀⠀⠀⣀⠘⣍⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠢⡀⠂⠤⠤⠐⡩⠂⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠆⣰⣖⣦⠀⠀⠀⠀⠀⠀⠀⢞⠉⣿⣿⡇⡏⢹⠆
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⡠⠒⠘⠀⠀⠀⠀⠀⠀⣴⢞⣿⠿⣯⣿⣦⠀⠀⠀⠀⠀⠀⣇⣀⢸⠸⡿⠇⢇⠀⠀⠀⠀⠀⠀⠈⠓⠿⣿⡷⠗⠁
⠀⠀⠀⠀⠀⠀⢆⡈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⡨⠀⠳⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠼⠃


⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡖⡀⡍⢠⢩⢡⢲⠀⠀⠀⠀⠀⠀⢀⡶⢅⠩⡌⠱⡆⠀⠀⠀⠀⠀⠀⠑⠜⣲⠾⣯⠤⠆⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣶⠄⠀⠀⠀⠀⢀⠇⠈⠉⠉⠉⠉⠈⡆⠀⠀⠀⠀⠀⠀⠯⠝⠀⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠿⠼⠿⠿⠧⢧⠿⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠤⠟⠀⠀⠀⠀⠀⠰⠶⠞⠋⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣍⣩⣥⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⢖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠂
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣀⣠⢤⠤⠖⠒⠒⠒⠋⠉⠉⠉⠉⠙⠓⠒⠒⠒⠦⢤⢄⣀⡀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠄⠀⠀⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠀⠀⠀⠤⣀
⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠓⠲⢄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢀⣤⣄⠀⠀⣠⢤⡀⠀⠈⢢⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠸⣄⣸⠃⠘⣇⣠⠇⠀⠀⠀⠹⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⣀⡀⠈⠁⣀⣀⠈⠁⢀⣀⡀⠀⠀⢱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠷⠃⣴⠋⠉⠉⠙⣦⠘⠾⠃⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡴⠖⠋⠀⠀⠀⠀⠙⠲⢦⠀⠀⠀⣸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⣀⣀⣀⣀⠀⣾⣾⣶⠀⣠⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠛⠚⠋⠉⠁⠉⣭⣿⣿⣿⣿⣴⣧⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⣀⣀⣀⣿⣿⣿⣿⣿⠿⠿⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻⣿⣿
⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⠉⠛⠿⣷⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣴⣾⠟⠋⠉⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⠘⢿⡿⠃⠻⣿⠿⢁⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⣴⣿⣷⡄⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⢋⣤⣾⣿⣿⣿⣿⣦⡈⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠙⠻⠿⠿⠟⠻⠿⠿⠟⠁⠀⢀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣀⠀⠀⣠⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣶⣶⡆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠻⠿⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣛⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠸⣃⣍⠉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⣀⢀⠀⠢⣀⡀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠟⢁⠄⠀⠀⠈⠙⠦⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠋⠐⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡇⠀⠀⠀⠀⠀⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⡛⢹⡳⢄⠈⢦⣈⢱⠛⠅
⠀⠀⠀⠀⠀⢀⠴⢊⠉⠀⠀⡎⠀⢈⠹⡆⠐⠄⡤⠓⢀⡆
⠀⠀⠀⠀⢠⠏⠀⠀⠡⠀⠀⡸⠃⠠⠂⠉⢆⠑⠠⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠀⠀⠱⡄⡀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠑⣄⣀⠀⠘⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠐⠀⠀⠀⠀⠣⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡄⠀⠀⠀⠀⠀⠳⡀⠀⢰⡀
⠀⠀⠀⡀⠀⠀⠀⠀⡎⠠⠅⠐⠛⣷⠀⠆⠀⠂⠀⢀⠛⢧⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠇⠀⢀⠀⠀⠀⠀⠈⡞⠊
⠀⠀⢀⠁⠀⠀⢀⣰⣁⣀⣀⡀⢀⠸⠇⠀⠀⠀⠀⢸⣀⣄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠿⠟⠃⠀⠀⠉⠀⠀⠀⠀⠀⠇
⠀⠀⢘⠀⠀⠈⠈⠁⠀⠀⠁⠀⠉⣽⠈⣯⡕⠠⢀⣿⠈⠀⠁⠒⠁⡀⠀⠀⠀⠀⠀⠀⢇⣠⡀⠀⠀⠀⣀⠀⠀⠀⠀⠘
⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠴⠤⠀⣽⣠⠿⠀⠀⠀⠉⢢⡀⠀⠀⠀⡌⡙⠷⠂⠤⣄⠀⠈⠙⠬⠿⠿⣟⠉⠀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠛⠀⢀⡈⢲⠄⢠⡿⠋⠠⠀⣼⣤⣅⠈⢢⣀⠚⣧⠀⠀⠀⠀⠞⠉⠓⠒⠤⢼⠶⡧
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⡏⠀⠀⠀⠀⠀⠀⡈⠓⠠⢬⡷⠼⡦⠀⠀⠀⠀⠀⠀⠀⠄⠈⠚⠁⢣⠤⠤⠤
⠀⠀⠀⠀⠐⠛⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠛⠓⠒⠦⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠧⠄⡀
⠀⠀⠀⠀⠰⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⢸⡄⠀⠄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⣠⠝⠲⣄⡔⠊⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠂⠈⠀⠀⡠⠖⠉⢀⣤⠤⣄⠀⠀⠀⢀⠀⣠⡾⠂⠂⣼⣶⣡⡄⠀⢉⠟⢻⣤⡔⠊
⠀⠀⠀⠀⣦⡀⠀⠀⢀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⢷⣦⣼⣗⠀⠀⠀⠀⠀⢠⡀⠉⣡⠀⠉⠳⢤⣌⡘⢁⠞⣩⠶
⠀⠀⠀⠰⠀⠀⠈⠉⠁⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠉⠉⠙⠓⠖⠊⠀⠀⠀⠀⠈⠑⠪⢰⠧⠜⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠓⠉⠁
⠀⠀⠀⠈⠐⠀⠤⢀⠀⠀⠀⠀⠀⠈⠱⠚⢣⣶⣒⣠⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⣤⡄⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⠿⠿⠟⢟⠙⡟⠛⠛⢻⠛⢛⠃⠀⠀⠤⠒⠒⠚⢀⣀⣀⠀⢠⣤⠀⠀⠈⠛⢠⠆⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢉⠀⢸⠀⠀⢸⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠀⢀⣀⣀⣀⠁⠀⠈⠛⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠁⣄⡀⠀⠈⠁⠀⠉⠀⠐⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠛⠚⠓⠓⠠⢀⡀⠀⠙⠢⡀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠘⡥⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⡘⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠟⣛⣛⣛⣉⣩⣥⣴⣾⣿⣿⣿⣦⣍⣙⠻⣿⡀
⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣦⠙⣿⣿⣦⣿⣿⣿⣿⣿⣿⣼⣿⣿⢉⣴⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣙⣉⣿⣿⣿⠟⣰⠟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠻⠿⠿⠛⡋⢡⠾⢡⠾⣿⣿⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠤⢰⣶⣿⣶⣿⡘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣤⠰⣶⣦⠹⣿⣿⣿⣿⣧⡐⢿⣿⣿⣿⣿⣷⣌⠻⠿⠇
⠀⠀⠀⠀⠀⣰⣿⣿⠀⢿⣿⣧⡘⠿⠿⠿⠿⢃⣶⣤⡤⠈⣿⣿⣿⣿⣶⣿⡆⢠⣤⣄
⠀⠀⠀⠀⢀⣿⣿⣿⣷⣶⡄⢹⣷⡀⢶⡶⢠⣾⡏⢤⣶⡀⣿⣿⣿⣿⣿⣿⣇⠻⠿⠟⢀
⠀⠀⠀⠀⢸⣿⣿⣿⡏⣹⣅⠻⣿⣿⡌⢡⣿⡿⠗⣸⣇⠀⢹⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣸⣿⣿⣿⢰⣿⣿⣷⣦⡙⠃⠘⣉⣴⣿⣿⣿⡄⣄⢻⣿⣿⣿⣿⡿⢋⣭⣤⣭⣿⣿⣿⣦
⠀⠀⠀⠀⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠁⠛⠂⠙⠻⢿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣽⣿⣿⣿⡇⢸⣿⣿⣿⣯⠀⠀⠀⠀⣾⠃⣾⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⢠⡟⢸⣿⣷⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢀
⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⢀⡼⢁⣿⣿⠃⠀⠀⠙⣿⣿⣿⣿⣿⠟⠁⠈⢳⡄
⠀⠀⠀⠸⠿⠿⠿⠃⠀⠀⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠀⠾⠏⠰⠾⠿⠃⠀⠀⠾⠿⠿⠿⠿⠿⠇⣀⣀⣀⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣄⠀⡀⣠⣤⢀⣤⣤⢠⣤⡄⣠⣄⠀⡄⣠⡀⣀⠀⣠⡀⢀⣤⣄⢀⡀⢀⣄⠀⣀⠀⣀
⠀⠀⠀⠀⠀⢹⣼⠃⣿⠒⠀⢸⠀⢸⡖⠂⡷⢾⠁⡇⣿⢳⣿⢠⡯⣷⢸⡷⣟⢸⡇⣾⢽⡄⣿⢳⣿
⣶⣶⡶⣶⠶⢶⣿⣶⣿⣿⣷⣾⣶⣾⣿⣷⣷⣾⣷⣷⣿⣶⣿⣾⣶⣾⣿⣷⣿⣾⣿⣷⣾⣷⣿⣶⣿⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣽⣿⣿⣿⣿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⠀⠀⢸⠀⠀⢸⠿⢿⣿⡿⣋⣥⣬⣭⣭⣭⣭⣭⣭⣭⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣷⠖⠛⠓⠶⣏⠀⠈⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⠁⠀⠀⠀⠀⠘⣷⣾⣿⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣄⣀⡀⠀⢀⣿⣿⣿⢸⣿⣿⢸⣿⣿⡟⢻⣿⣿⣷⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣬⣉⣁⣤⣾⣿⣿⣿⢸⣿⣿⢸⣿⣉⠁⠀⣉⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⢸⣿⣿⢸⣿⣿⣧⣼⣿⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠟⠁⠀⠘⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠃⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃

⠀⣠⣤⢀⡀⣤⣤⠀⠀⢀⠀⢠⢀⠀⠀⡀⡄⠀⢀⠀⠀⢀⠀⣀⢀⢀⠀⠀⣀⠀⠀⢠
⠀⢛⠋⢊⡄⣛⡛⠀⠘⠈⠀⠈⠘⠀⠁⠀⠀⠃⠉⠈⠁⠀⠀⠈⠀⠐⠀⠀⠉⠑⠀⠀⠘
⠀⣔⣈⠉⢤⡄⣠⠀⠐⠀⠈⠚⠑⠠
⠀⠛⠛⠐⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤⡈⠀⠒⢀⠄⠀⠀⠀⢠⡶⠆
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠐⠚⠃⠀⠐
⠀⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⢄⠀⠋⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣄⠀⠀⠀⠀⠀⠀⠠⠐⠢⡀
⠀⠀⠀⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⡀⠀⠀⠀⠀⠀⠰⣀⢠⠁
⠀⠀⠀⠀⡐⠉⠀⠈⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⠐⠒
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⣀⢠
⠀⠀⠀⢀⡅⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠄⠀⠀⠄⠀⠀⠁⠉⠀⠀⠉⠈

⢤⣤⣤⣶⣶⣤⡐⠿⢂⣤⣶⣶⣤⣤⣤
⠈⠻⠿⠿⣿⣿⡿⣿⢾⣿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣶⣶
⠀⠀⠀⠀⠀⠽⠶⣿⠦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠿⠿⣿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⢥⣿⠋⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠏⠱⣿⠎⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣇⠀⠀⢸⣿⣿⣿⡇⠀⡟⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠸⡄⠙⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣷⣤⣾⠄⠀⠀⠀⠀⠀⢀⣴⣷⡻⣿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⢈⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣵⢟⣻⠻
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⠚⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⣻⣿⣿⣿⡃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣯⣽⣧⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣿⣦⠀⠀⠀⠐⠒⠛⠛⠛⠶⠶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿
⠀⠀⠈⠿⣦⣤⣤⣤⣄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢰⣶⡆⠀⠶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⠐⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣦⡀
⠀⠀⢀⡼⠁⢧⡀⣴⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡦⠞⠱⠒⢦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆
⠀⠀⢸⣷⣶⣶⡇⣿⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⠴⠲⡘⢆⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉
⠀⠀⢸⡿⠿⠿⡇⣿⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠏⠉⠻⠇⠀⠀⠀⠀⠀⠀⢠⣶⣧⣀⠴⠁⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠘⠧⠤⠴⠇⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⣤⠤⠤⢄⣀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡄⡜⠉⠠⠤⢄⠀⠀⠀⠙⢢⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢓⡷⠛⠁⢀⠖⣲⡄⠀⠀⠀⢄⠀⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢶⠀⠀⠀⠛⠛⠁⠀⠀⣖⣦⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⢻⣀⡼⡄⠀⠀⡀⠀⣄⣀⡆⠉⡽⠁
⠀⠀⠀⣠⡴⢶⡟⠉⣽⡌⣼⠁⠹⣄⠀⠈⠁⠒⠀⣠⡞⠁
⠀⠀⣼⠃⠀⠀⢿⡞⠁⢳⡻⣆⠀⠈⠙⢳⡶⢺⠏⠜⢤⡀
⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠙⣯⣓⠲⠶⠯⣓⠽⢻⣀⡠⠿⠦⠤⣄⡀
⠀⢀⡇⠀⠀⠀⢸⠛⠶⣄⠀⢹⠈⠳⣤⢾⡇⣔⠟⠁⠀⠀⠀⠀⡤⠿⡄
⠀⢸⠃⠀⠀⠀⢸⡀⣠⠋⠀⢸⡀⠀⡏⠈⣇⡎⠃⠀⠀⠶⠀⠀⡇⠀⠈⢋⢳⠢
⠀⢸⠀⠀⠀⠀⢸⡇⣇⠀⠀⠈⡇⠀⣟⣧⣯⣤⡀⠀⠀⠀⠀⣀⡇⠀⠀⠀⣶⠦⢆
⠀⢸⠀⠀⠀⠀⠀⣷⠘⢷⡀⠀⡇⠀⡏⡇⣿⣏⠁⠀⠀⣀⡼⡱⢣⡀⠀⡼⠀⠙⠺⣄
⠀⢸⠀⠀⠀⠀⠀⢹⠀⠀⢳⡀⡇⠀⢇⣇⢹⡸⠉⣹⠟⢩⠞⠁⠀⠈⠉⠀⠀⠀⠀⠀⢣⡤⠤⠤⠤⠤⣤
⠀⠸⡇⠀⠀⠀⡠⠞⠻⢤⣀⢹⡇⠀⠸⡜⠾⠗⡫⠖⡧⠼⢣⠀⡆⠀⠀⠀⡠⠀⠀⠀⠈⡇⢠⢶⠄⠀⢸
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢬⣽⣏⣠⠖⢋⣀⣚⢻⡅⠀⡇⢠⠁⠀⠀⠀⠀⢹⣣⠞⠀⠀⢸
⠀⠀⢸⡟⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠒⠠⣉⡆⠀⣇⣨⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢸
⠀⠀⢸⠁⢀⣀⣤⠽⠶⠦⣤⣀⠀⠀⠀⠀⣼⠧⣤⠤⣘⠿⣿⠋⠀⢠⠁⣨⠟⠂⢀⠖⠉⠀⠀⠀⠀⠀⢸
⢀⡶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠳⠶⢤⣯⠞⠉⠓⠚⠉⣏⣁⣀⡼⢼⡁⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣬⣭⣥⣤⣤⢤⣤⠤⠤⡤⣤⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠘⣿⣿⣿⣿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢦⠀⢹⣿⣿⠇⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣶⡀⠻⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀⣀⣤
⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⠀⢸⣶⣶⣶⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣭⣭⡍⠀⠀⠀⣰⡆
⠀⠀⠈⣿⣷⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⠀⢿⡇
⠀⠀⠀⠘⢿⣿⣶⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡘⣷
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⡆⠀⠀⣾⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠉⠙⠿⠟⠁⠀⠀⠙⠿⠟⠉⠉⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⠀⣠⣤⡄⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⢼⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⣿⣎⠻⢟⣁⣙⠿⠋⣾⣷⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠻⠿⢣⣾⣿⣿⣿⣿⣆⠻⠿⠁⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⠆⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⣷⣦⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠀⠘⣿⣇⠀⠈⠻⣿⣿⣶⣤⣤⣤⣤⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣴⠟⢋⣉⠛⢷⡄⠀⠀⢻⣿⠀⠀⠀⠈⠙⠻⠿⠿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢸⡏⢰⣿⣿⣷⠈⣿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣄⡙⠛⣁⣼⠏⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠈⢿⣷⣤⣀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢾⣿⣿⠶⠀⠀⠀⢰⠞⠛⠛⠛⢲⡄⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⡀⣤⡾⠀⠀⠀⢰⡄⠀⠈⠂
⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠈⢻⡷⠷⠛⠛⠀⠀⠀⠀⠁⣂⠀⠀⠀⠀⣨⠠⠌⠀⠀⠀⠀⠡⢌⡲⠞⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠶⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⢿⣿⣀⠀⠀⠀⠀⠀⡄
⠀⠀⠙⠲⢤⣤⣶⣿⣿⣾⡭⠙⠃⠀⠀⢘⠀⠀⠈⠉⠉⠁⠀⠀⡇⠀⠀⠀⡿⠿⠙⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣅⠀⠀⠀⠀⢸⠀⠀⠠⢾⡷⠄⠀⠀⡇⠀⠀⠀⢣⡄⢠⠍⠋⢹⣿⢿⡄
⠀⠀⠀⠀⢾⡋⢿⡁⢸⣿⠃⠀⠀⠀⠀⠨⣀⣀⣀⣈⣁⣀⣀⣀⠇⠀⠀⠀⠈⠇⡆⠀⠀⠀⠙⠚⠹⠆
⠀⠀⠀⠀⠀⠓⠀⠉⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄
⠀⠀⢠⣌⣤⣍⣤⠀⠀⠀⢀⡴⠒⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠴⠋⠑⠒⠊⠱⠆
⠀⠰⡖⢾⠟⢳⠖⡖⠀⠀⠈⠀⠀⢠⡟⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠁⢩⠆⠀⠀⠁⠀⠀⠀⡾⠿⢷
⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠂⠀⠘⠁⠀⠀⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣩⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⡀⢿⣷
⠀⠀⠀⠀⠀⠀⣼⣇⠈⠁⢛⡛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢛⡛⠈⠁⣸⣧
⠀⠀⠀⠀⠀⡀⠻⡿⢰⣿⠟⠁⠀⠀⠀⠀⠀⣼⣿⣿⡄⢠⣿⣿⣧⠀⠀⠀⠀⠀⠈⠻⣿⡆⢿⠟⢀
⠀⠀⠀⠀⠀⣿⣆⠀⣤⡶⠀⠀⠀⠀⢠⣤⣄⠘⢿⣿⠇⠸⣿⡿⠃⣠⣤⡄⠀⠀⠀⠀⣶⣤⠀⣰⣿
⠀⠀⠀⠀⢀⠙⠟⠸⢟⡁⠀⠀⠀⠀⢻⣿⣿⡇⢀⣴⣾⣷⣦⡀⢸⣿⣿⡟⠀⠀⠀⠀⢈⡻⠇⠻⠋⡀
⠀⠀⠀⠀⠸⣷⣄⢠⣿⠇⠀⠀⠀⠀⠀⠉⠉⣠⣾⣿⣿⣿⣿⣷⣄⠉⠉⠀⠀⠀⠀⠀⠸⣿⡄⣠⣾⠇
⠀⠀⠀⠀⢀⡙⠛⠈⢉⣶⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣶⡉⠁⠛⢋⡀
⠀⠀⠀⠀⠀⢻⣷⣄⢸⡿⣀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠿⠿⠿⣿⡿⠟⠀⠀⠀⠀⠀⣀⢿⡇⣠⣾⡟
⠀⠀⠀⠀⠀⠀⣍⡉⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢉⣉
⠀⠀⠀⠀⠀⠀⠙⠿⣷⣈⣛⣐⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣂⣛⣁⣾⠿⠋
⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⣿⡿⣿⢻⢛⣿⡛⣻⣿⢟⣻⡿⣿⣿⣿⢻⣿⡿⣿⣛⣿⣿⣿⣿⢀⣀⣀⣀
⠀⠀⠀⠀⠹⣿⣿⡇⣿⣿⣿⣷⣡⣿⣰⣿⣇⣿⣿⣜⣿⣧⣻⣿⣿⣿⣍⣇⣧⣻⣿⣿⣿⣿⢸⣿⣿⠏
⠀⠀⠀⠀⢠⣿⣿⣇⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣸⣿⣿⡄
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠸⣿⣿⣿⣿⣿⣛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⡇⢰⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡻⣿⣮⡻⣷
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠙⠟⢃⣈⠻⠛⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣝⢿⣿⣮⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣠⣾⡟⠛⣷⣄⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⣌⢳⣼⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠉⠀⠀⠉⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡻⣿⣮⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⡎⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠐⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⠶
⠀⠰⢤⣴⣶⣶⣶⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣿⣿⢀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⣿⣷⣶⣶⣶⡶⠆
⠀⠀⠀⠀⢬⣥⣴⣶⣾⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣶⣦⣤⡤
⠀⠀⠀⠀⠀⠈⠉⣭⣤⣶⡿⠿⣛⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠇⣿⣿⠸⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣮⣙⠿⢿⣶⣦⡬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠱⠿⠋⠼⠟⠹⠟⠙⠛⠁⠉⠁⠀⠀⠀⣿⣿⠀⠀⠀⠈⠉⠈⠛⠃⠻⠏⠻⠧⠙⠿⠎⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣾⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⢶⠀⠀⠀⣿⣿⠀⣀⣀⡖⠒⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠘⣿⣿⡗⣿⣿⣼⣿⣿⠁⠀⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⢻⡛⠃⣿⣿⠉⢩⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣇⠀⠈⣧⠀⣿⣿⠀⡾⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣾⡄⠀⢸⣦⣤⣤⣼⠃⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢧⠀⠀⢿⠛⠛⡟⠀⠀⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸⡆⢸⠃⠀⢰⠃⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⢻⡏⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⣇⠀⠈⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢸⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣤⣶⣾⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⢛⠋⠀⢶⡂⠀⠘⡿⠦⡈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣽⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣀⡀⠐⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢏⠀⠀⠀⡠⠊⢇⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⣹⡤⠴⡞⠊⠟⠉⠉⠺⡆
⠀⠀⠀⠀⢀⠔⠒⠒⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡌⠀⢸⠀⢸⠀⠀⠀⠀⡟⡄
⠀⠀⢀⡤⢇⠀⠀⠀⠀⠀⢸⠿⢦⡿⡀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡇⢇⠀⢸⠀⢸⠀⠀⠀⠀⡇⠸⡀
⠀⡴⠁⠀⡸⠂⠀⠀⠀⠀⠹⡄⠀⠙⣜⠢⣄⡀⠀⠀⠀⡰⠁⠀⡇⠘⡄⢸⠀⢸⠀⠀⠀⠀⡇⠀⢱
⡸⠀⠀⠀⣧⠈⠁⠀⠀⠉⢠⡇⠀⠀⠈⡎⠁⠈⠑⠢⠼⡁⠀⠀⢀⠀⠐⣜⠀⢸⠀⠀⠀⠀⡇⠀⠀⠇
⡇⠀⠀⠀⡏⣦⠀⢿⡗⢠⢿⡇⠀⠀⠀⡝⠢⣄⠀⠀⠀⠑⢄⢠⠛⡀⠀⠈⢁⠜⠒⠒⠒⠲⡇⠀⠀⠸
⢡⡀⠀⠀⣿⠀⠳⠄⠴⠃⠀⢃⠀⠀⢠⠇⠀⠀⠑⢄⡀⢀⡸⠃⠀⢣⣠⠖⠁⠀⠀⠀⣀⠜⠀⠀⠀⠀⡇
⠀⠉⠒⠊⡏⠀⠀⠀⠀⠀⠀⠈⠒⢎⠁⠀⢀⣀⣀⣀⣈⣁⣀⣀⡠⠺⣄⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣿⠉⢏⢉⣉⣉⠶⠂⠀⣠⠜⡏⠁⠀⢀⡂⠉⠉⠉⠉⢙⡄⠇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⡤⠙⠛⣿⣷⣤⡄⠁⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⡁⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⡆⠀⠀⠀⢸⡇⠒⢲⠋⠉⠙⠁⡤⢠⡇⠀⠀⠘⡆⠀⠀⠀⠀⢠⠃⠘⡇
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⡆⠀⠀⠘⡄⢸⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠘⢦⣀⣀⡴⠃⠀⠀⢃
⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⡇⠀⢀⠁⠈⡄⠀⠀⠀⠁⢸⠀⠀⠀⢀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡇⠈⣦⣄⠀⣧⠀⢸⠀⠀⢣⠀⠀⠀⡇⢸⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠓⠈⠉⠉⠉⠉⠐⡶⠶
⠀⠀⠀⠀⠀⡇⠀⡏⠎⢆⠯⠀⢸⠀⠀⠀⢇⠀⢀⠃⢀⡄⢔⡾⡇⠸⢄⣀⣀⣀⣀⣀⣀⡠⠤⠐⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠔
⠀⠀⠀⠀⢀⡇⠀⣇⠼⠈⡷⠀⢸⣄⣀⣀⣼⡄⢸⠯⠵⢖⠓⢲⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⠤⠤⠤⠤⠤⠤⠐⠒⠂⠉⠁⠀⡇
⠀⠀⠀⠀⠺⠤⠤⠽⠒⠺⠤⠤⠼⠀⠀⠪⠤⠤⠜⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿