Dew Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡴⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⢳⡀⠀⢀⣤⣴⠞⠖⠋⠉⠉⠀⢀⡴⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⣷⠐⠋⠀⠀⠀⢀⡖⠀⢀⣴⠟⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡄⣸⠀⢰⡇⠀⠀⢸⣇⡴⠋⠉⠉⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⢚⣱⠏⠀⢸⡇⢀⣠⣞⣋⣀⣀⡀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⡋⠁⠀⢀⣸⠷⠋⠉⠉⠉⠉⠉⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡤⠖⠻⠧⣤⣄⣀⣀⡀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢚⣫⠝⢷⣄⠀⠀⠀⠀⠀⢀⣀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠞⠋⠀⠀⠀⠈⠙⠛⠓⠒⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⢰⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠘⣿⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⢻⣧⡘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡙⠻⠷⠶⠶⠾⠇⣠⣴⠿⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⡈⠛⠿⣶⣤⣤⣤⣴⣶⠆⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣈⣉⣉⣁⣠⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠰⠒⠒⠒⠂⠡⠁⡉⠑⠂⠤⠀⠀⢀⡀⢤⣀⣀⣀⠒⠦⠶⠶⠶⠤⢬⠁⣁⠪⡓⣍⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠒⠉⠀⠀⠴⢤⣀⡀⢀⡀⠁⠚⠲⣦⣂⠄⠈⢋⣑⣠⠀⢑⠋⠉⠀⠀⠀⠀⠀⠀⡀⢐⡦⠔⠉⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠘⠠⠦⣤⣋⢐⠀⠀⠙⠲⣤⠀⢁⡀⠀⣀⡶⠺⠀⠁⡆⠀⠆⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠈⠁⠠⠤⠍⡤⣀⠀⢤⠙⠓⣠⠶⣾⡖⢤⡐⠋⢠⠁⠀⠠⠁⠀⢸⠁⣐⠀⠔⠀⠀⠈⡉⠀⠢
⠀⠀⠀⠀⡅⠠⢀⣴⡾⢎⡍⠓⡅⠠⢀⠊⠤⠋⠁⠀⡀⢱⠀⣸⠀⠀⠀⡂⠀⠀⢠⢃⠠⠚⢁⡤⠨⣄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠂⠃⢊⣁⡶⣂⡞⢰⠀⠑⡢⠤⠭⠔⠖⠃⠀⢻⠀⠀⠀⠀⡀⠞⠃⣀⠀⠀⠋⠀⠀⠘⣆⠀⢘
⠀⠀⠀⠈⢂⠔⠀⡠⠼⠗⠋⠁⠀⠆⠀⠀⡇⠀⠀⠀⡆⠀⠀⠊⠀⣠⡤⠮⠤⠖⠋⠀⠐⠁⠘⠆⠀⠀⠘⠀⢨
⠀⠀⠀⠀⠀⠀⢠⢰⠀⠒⠦⠀⢀⡀⠀⠀⠃⣀⠀⠀⡀⠠⣄⢔⡈⠀⠀⠀⠬⠁⡤⠊⠀⠔⣉⣹⠏⢢⡀⠀⢸
⠀⠀⠀⠀⠠⠀⢸⠀⠂⠀⠀⠀⠀⠈⠉⠁⠀⡨⠋⠅⢐⡀⠀⠀⠠⠤⠤⠤⢀⡜⠁⢐⠘⠃⠀⢀⢔⡼⠀⠀⡄
⠀⠀⠀⠀⠀⢂⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠀⠀⠀⠠⠤⠔⢀⣀⠄⠀⢀⡁⣀⠀⠣⢤⣬⠑⠊⠠⠀⠘
⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠤⠠⢀⣴⡖⣄⠀⠉⠀⡀⡵⠊⡨⠶⠙⡆⠈⡅⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣸⢉⠆⠀⠀⠀⠀⠀⠀⠀⠈⠇⠠⠅⠘⢥⠖⠃⡀⠀⠀⡀⠑⠚⠀⡠⢢⠏⠀⠹⡄⠀⢰⠃
⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⠀⠀⠀⠀⢀⡀⠑⢄⣀⢨⡔⢋⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⡀⠀⠼⠀⠀⠈⠙⠋⠀⠀⠇⠐⠄⠀⠘⠁
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣉⡀⠀⠈⡄⠀⠀⠘⡂⢂⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣫⠗⢨⠆⠀⠹⡄⠠⡀⠐⠄⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢔⡼⠀⠰⠐⠐⠄⠀⢄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢇⠀⢂⠑⠀⡀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠠⢀⠀⣀⣀⢀
⠀⠀⠀⠀⠐⠈⠂⠀⠀⠌⠀⠀⠁⢀⠀⠐⠠⠀⠠⠐⠠⠐⠨⠐⠡⠀⠄⠂⠁⠂⠀⠂⠀⠂⠁⠊

⠀⠀⠀⡄⠘⢣⠋⡀⡇⡀⠀⠀⠀⠀⠀⠠⢊⡥⠦⡄⠁⠠⢀⠀⠀⠀⠀⣠⠴⢄⡋⠙⣆⠤⣄⠀⠀⠀⠀⠀⢀⢄⠸⠑⠘⠂⣠⡄
⠀⠀⠓⣒⠌⣁⣄⡀⠡⢀⠤⠀⠀⠀⠄⠀⣸⣜⣱⣼⡡⡙⣆⠂⠀⠀⢀⡹⣄⣀⣣⣴⠃⣀⣼⡀⠀⠀⠀⠐⠍⠀⠱⣄⣤⠎⠁⠱⠄
⠀⠀⣫⠄⡀⢿⣼⡇⠨⠍⠒⠀⠀⠀⠀⡞⡩⢹⣿⣿⢶⡵⠋⡀⠀⠀⠸⣀⣀⠬⢯⣿⠯⣀⡀⣸⠀⠀⠐⣇⠀⠚⢻⣿⢿⡋⠐⢒⠦
⠀⠈⠁⡌⠴⡤⢠⠠⢙⡘⠃⠀⠀⠀⢁⡳⢬⠽⣏⢤⣦⠆⡀⠀⠀⠀⠀⢞⠁⢀⡎⠘⣆⠀⣹⠀⠀⠀⠀⠛⠀⡠⠀⢸⠀⠙⡀⠼
⠀⠀⠀⠀⠋⠀⠂⠱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠈⠉⠁⠊⠀⠀⠀⠀⠀⠀⠉⠁⠣⠤⠇⠉⠁⠀⠀⠀⠀⠀⠀⠓⠳⠎⠒⠋⠁
⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢠⣾⣶⠻⣿⢷⣾⣲⠀⠀⠀⠀⠀⡖⡃⡆⠆⠆⡥⡓⡆⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⢆⠀⠀⠀⠀⠀⠀⠀⡏⢠⠙⡆⢀⣀
⠀⢀⣼⣏⣻⡶⡻⣾⣋⣽⣦⠀⠀⠀⡸⣰⠉⣞⣿⣿⣮⢐⡚⡇⠀⠀⠀⡾⠀⠀⢀⢤⠀⠀⠈⣧⠀⠀⠀⡎⣉⡒⢇⠉⣆⠗⣋⠍⡇
⠀⠘⠾⣟⣹⣿⣵⢿⣉⣻⠞⠁⠀⠀⢇⠼⡊⢿⣿⣿⡿⡒⢇⡇⠀⠀⠐⣗⠀⠀⠈⠚⠀⠀⠠⡟⠀⠀⠀⠑⠌⢙⢳⣶⣷⢚⡁⠔⠁
⠀⠀⠸⣿⡿⣴⣷⣬⣿⡿⠃⠀⠀⠀⠘⢪⣙⢰⢩⠱⣔⣩⠜⠀⠀⠀⠀⠘⢧⣄⣀⢀⢀⣤⠟⠁⠀⠀⠀⠀⢾⠠⠾⣻⡙⠳⢈⠆
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁
⠀⠀⠀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⢞⠁⠈⡷⠁⠀⡱⠀⠀⠀⠀⠀⣾⠟⠻⡇⢠⡟⠻⣳⠀⠀⠀⠀⣯⡖⠓⣿⣴⣿⠚⣲⣽⠀⠀⠀⠠⣎⠙⢿⡄⢸⠟⠉⡦
⠀⢠⠞⠛⠃⣴⣶⡄⠚⠉⢳⠀⠀⠀⣴⡺⠳⠦⣽⣾⡴⠞⠻⣦⠀⠀⠀⠙⠯⣶⣳⢿⣜⣶⠿⠃⠀⠀⠀⡶⠛⠳⢬⣷⣯⠶⠛⠓⡄
⠀⠘⠧⣤⠖⠛⣿⠋⠲⡤⠞⠀⠀⠀⠘⣳⠖⠋⡿⢻⡙⠳⣶⠛⠀⠀⠀⣴⡿⠻⣟⣿⣹⠟⣿⣆⠀⠀⠀⠙⡶⠛⢋⡟⣯⠙⠶⡖⠃
⠀⠀⠀⢧⣀⡠⢻⣀⣠⠇⠀⠀⠀⠀⠀⠳⠷⠾⡇⡨⡷⠼⠞⠀⠀⠀⠀⣯⣳⣖⡿⠙⢿⣲⣞⡽⠀⠀⠀⠈⠳⠴⢻⡇⢸⠷⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠠⠀⣘⠃⢠⠛⢂⠡⠄⠀⠀⠀⢀⡐⡏⠈⣦⠀⢈⠀⠦⡄⠀⠀⠀⠀⢶⠄⣀⠋⣀⠤⠖⠀⠀⠀⠀⠀⣶⣫⠽⠞⠶⣭⢳⡆
⠀⠠⠘⢁⠈⣦⣷⡔⠊⠝⢠⠀⠀⠀⣏⠀⠈⢢⣼⣶⡁⠀⣠⠃⠀⠀⠀⣀⠤⠷⣼⣶⣧⠤⠤⣀⠀⠀⠀⣼⢽⠃⢀⣤⡄⠈⢻⢽⡄
⠀⠀⢠⣄⡠⠝⡿⢇⠀⢐⠔⠀⠀⠀⣤⠀⠀⢹⠿⠿⢏⠠⠈⡧⠀⠀⠀⠈⢉⠝⢻⠿⢟⠫⠀⠀⠀⠀⠀⢿⡽⣄⠈⠛⠃⢀⣸⣹⠇
⠀⠀⠐⠀⢐⡠⠁⢄⠇⡔⠂⠀⠀⠀⠙⠦⢔⠁⠀⠄⠄⡡⠒⠁⠀⠀⠀⠀⠚⠀⠈⡀⠀⠁⠒⠀⠀⠀⠀⠈⠻⣽⣓⡶⣖⣯⡷⠋
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣾⣿⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠻⢷⣄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⢋⣽⢿⣻⣿⠟⠛⣿⠿⢿⣄⣄⠀⠈⣷⡄⠀⠀⠀⠀⢹⣷⣀⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢯⣿⣿⣿⢿⣿⡉⠉⠁⠀⢻⣷⢫⠶⣧⡀⠈⢻⡀⠀⠀⠀⠀⠘⣿⣶⢾⣯⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢐⣮⡙⣏⣧⣦⣼⣧⡀⠀⠀⢸⡿⠃⠀⣿⣿⡀⠈⣀⣀⣄⡀⠀⠀⢹⣿⣿⣿⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣾⣿⣿⣿⣿⡿⣧⡀⣠⣿⡀⠀⠀⣸⠟⠀⠀⢸⣿⡿⠁⢠⠀⠀⠙⠿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣴⣿⣿⣿⣿⣄⠹⡿⣿⢿⣷⠿⣷⣿⠜⠁⠀⠀⢀⣰⠇⠀⠈⡿⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠙⣿⢱⣿⣿⣿⣷⣿⣤⡾⢛⣷⢿⡿⠀⣰⡆⠀⣿⡏⠀⠀⣼⠅⠀⣸⠅
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢹⣿⢋⣈⡙⣿⣿⣍⣿⣯⣵⣿⣧⣼⠏⠀⣠⣿⣷⣤⣶⠟⠀⢰⣿⣴⡀⢘⠂⠀⠁
⠀⠀⠀⠀⠀⢀⣀⠀⢠⣤⣀⠀⠀⡉⠈⢻⠿⠷⣟⡻⣟⠋⠙⣿⣿⡏⣵⣾⣿⣿⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⡋
⠀⠀⠀⠀⡖⢀⣭⡆⢈⡛⢝⠀⠀⠀⠀⠉⠙⠻⣮⡟⠿⢿⡛⠉⣩⡶⡟⠉⠿⢿⡄⠀⢀⠀⢀⠴⠛⢿⣿⣿⠛⠓
⠀⠀⠀⠘⢇⠘⠾⠛⢀⠃⠀⠐⠄⠀⠀⠈⠛⠀⢸⣿⠷⠢⠷⠾⠿⠒⠀⠀⠀⠸⡦⢤⣴⡟⠁⠀⠀⢸⣿⣿⡇⢰⠀⢀⡠⠀⢀
⠀⠀⠀⠐⠚⠃⢰⣴⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⣍⠛⣦⡸⠀⣉⠳⣔⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⣤⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠁⠀⢸⣁⣷⠔⠀⢈⡤⣼⡙⡿⠿
⠀⠀⠀⠀⠀⠀⠀⡀⠙⢻⠏⠀⠀⡀⠄⠰⢿⣿⡀⠉⠉⢻⣿⣶⡀⠀⠀⠀⠀⢠⣾⣻⣾⡉⠀⠀⠀⠀⠞⠋⠛⠳⠀⠲⠄⠀⠁⠁
⠀⠀⠀⠀⠀⠊⠠⠍⣈⣧⠀⠀⣄⠀⢀⡠⢀⠉⠁⠀⠀⣀⠀⠉⣿⠀⠀⠀⠀⡺⠛⠃⠛⠁⠀⠀⠀⠀⠀⡇⠈⡻⠁⠠⠄⢠⣄⢛⣿
⠀⠀⠀⠀⠐⢀⡀⠀⠿⠟⠀⢰⡷⡀⠀⣤⣷⡀⠀⠀⡜⠗⠀⣿⣿⣶⡜⣣⣠⡗⣶⣴⡟⠀⠀⠀⠀⣤⣶⣿⡋⠑⠄⠠⡦⠈⣻⠛⠛⢠⣤
⠀⠀⠀⠀⣾⡯⢴⣿⠶⠂⠀⠀⠛⢿⣿⠝⣧⣈⣿⣶⡷⠛⡤⢞⡹⠑⠄⢹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⣼⠦⠀⠀⠇⠠⢠⠈⠉
⠀⠀⠀⠠⠿⣷⠿⠿⠄⡀⠀⠀⠀⠀⡄⠀⠉⣿⠏⣯⣡⣿⡀⠌⢐⢀⣄⣼⡏⢀⡀⠘⣿⡆⠐⣦⡀⠀⠘⣾⣯⣀⣈⠳⠶⠂⠀⢠⡴
⠀⠀⠀⢠⣴⣿⣿⣠⠎⣰⠀⣴⣷⣬⣁⢸⠏⡟⠠⢃⣽⣿⣧⣴⣾⣿⣿⣿⣷⣿⣿⣦⡉⠓⠸⠉⠿⠶⠿⠿⢿⣿⣷⣄⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠉⠉⠁⠘⠃⠘⠿⠏⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢶⣴⠟⠉⠛⠛⠛⠛⠛⠛⠓⠒⠒⠲⠶⠶⠶⠶⠶⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⣀⡤⡄⠀⡴⢦⠀⠀⠀⠀⣠⡤⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡟⠉⠉⠀⠀⢸⡄⣽⣏⢠⡾⠛⣿⢹⠀⠉⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠹⠴⣆⠀⡟⠉⠁⡇⢸⡞⣇⡀⢹⣿⠀⡶⢤⣨⠏⠀⣖⣛⡆⠀⠀⠀⠁⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢹⣀⣹⠀⠀⠉⠉⠀⠀⠉⠉⠉⠓⠃⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣄⠀⠀⣤⣼⣴⠋⣉⠳⣤⠛⢛⣾⡏⠹⠖⠚⣳⠀⢰⡏⣳⠂⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⢸⠁⠀⢧⡈⢉⣠⢯⡀⠙⣷⠃⠀⠀⣞⠁⠀⢸⣀⡇⢠⣾⠏
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠖⠒⠒⠒⠶⠤⣤⣀⠀⠀⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠀⠘⠳⠶⠞⠀⠀⠀⠉⠉⠁⠀⠉⠛⢻⣀⡿⡄⠈⣧⠀⣠⢯⣴⠟⠁
⠀⠀⠀⢀⡤⠞⠁⠀⣀⠔⠒⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠉⠑⠢⢤⢄⡀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠉⣉⣩⣴⠿⠛⠁
⠀⠀⣠⠎⠀⠀⢠⠎⠁⠀⠀⢠⣄⠀⠀⠀⠀⠑⢦⡀⠈⠣⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⠔⠋⠉⠛⠛⠉⠉⠛⠓⠒⠒⠒⠛⠛⠋⠉
⠀⣰⠃⠀⠀⣰⠃⠀⠀⠀⠀⠘⡘⡆⠀⠀⠀⠀⠀⠙⢄⠀⠈⢄⠀⠀⠀⢀⡼⠁⣠⡴⠏⠁
⢠⠇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢣⢡⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢇⠀⠰⠿⠿⠛⠉
⣼⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⡀⡆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣥⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢷
⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡗⢄⠀⠀⠀⠀⠀⠀⡀⠀⢸
⣇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⠳⡀⠀⠀⠀⠀⡇⠀⡟
⢸⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠀⠀⡸⠀⢰⠇
⠀⢳⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠳⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠈⠢⡀⠀⠀⠈⠓⠤⣀⣀⣀⣀⣀⡀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⠈⠉⢉⣁⣠⠴⠞⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢶⠀⠀⠀⠀⠀⠘⠃⠚⠛⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠯⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡄⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲
⠀⠀⠀⠀⢸⡇⢻⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⡇
⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠘⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡏⠉⠀⠀⠀⢰⣿⣦⡴⠶⠿⠟⠛⣿⣿⠅⠀⠀⠀⠀⢳⡀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠉⢻
⠀⢧⣀⣀⣀⣀⣸⣟⣀⠀⠀⠀⠀⣀⣘⣻⣤⣤⡀⠀⠀⠀⣻⣤⣿⣡⣄⠀⠀⠀⠀⣠⣤⣜⣿⣀⡀⠀⠀⠌
⠀⠀⠀⠀⢠⡟⣿⣿⡏⠳⣤⣠⠞⠉⣹⣿⣿⢷⠈⠲⠴⠊⢹⣻⡿⡉⠀⠙⠲⠴⠟⠀⡬⣹⡿⡏⠉⠉⠛
⠀⠀⠀⠀⠸⣿⡟⠿⠃⠀⠀⠀⠀⠀⠘⢃⣷⣈⠀⠀⠀⠀⢈⣠⣇⡃⠀⠀⠀⠀⠀⠀⣁⣸⣐⢳⡇
⠀⠀⠀⢀⣸⣿⣷⠆⠀⠀⠀⠀⠀⠀⢀⣽⠟⠻⢦⢀⣀⡠⠼⠟⢿⡅⠀⠀⠀⢀⡠⠶⠛⠛⢿⠙⠃
⠀⠀⠀⠈⠀⠀⠉⠃⠀⠀⠀⠀⡤⠒⠉⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⢁⠀⢰⡏⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠚⡇⠀⠀⠀⢀⡰⢁⡼⠁⠀⠀⠀⠀⢸⠆⠀⠁⣰⡒⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⠀⠈⠉⢁⠎⠀⣠⠀⠀⠀⠀⠁⠀⠀⠼⠄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⡇⠀⠀⡇⡷⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡴⠟⠉⠀⢀⣠⡀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋
⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣴⠋⠀⠀⠀⠀⣿⠁⣿⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⢀⣤⣤⣤⣀⣸⠃⠀⢀⣤⢤⣄⠙⠶⠋⣠⣤⣤⡄⠀⠀⢿⣀⣠⣤⣤⣄⠀⠀⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣀⠀⠙⣿⡀⠀⠘⠷⠶⠟⠁⠀⠀⠻⠶⠾⠋⠀⠀⣸⠟⠁⢀⡀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢿⣽⠇⠀⠈⢡⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⠀⠀⠋⠀⠰⣿⣽⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⣀⡿⠀⠀⠀⡀⠀⠀⢀⣀⣤⣤⣤⠶⠦⣤⣤⣄⣀⠀⠀⠀⠀⠀⢻⣄⣠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⠀⣠⡾⢋⣤⠾⠋⠉⠀⠀⠀⡤⠀⠀⠀⠈⠉⠳⢦⣌⠳⣄⠀⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⢋⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣏⠀⠀⠀⡼⢣⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⡄⠀⠀⢸⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢸⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⡄⠀⠀⢀⣤⣠⣤⣤⣤⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡇⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢷⡘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⣴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣦⡙⠷⣤⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣠⡴⢋⣡⠞⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡶⠳⣦⠀⠀⠈⠙⠖⠀⠉⠛⠶⠶⠦⠤⠶⠶⠶⠛⠋⠁⠐⠛⠁⠀⣠⠶⠶⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⠟⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠃⠀⢀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠠⠆⠀⠀⠀⣌⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣶⠀⠀⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⡄⠀⠀⠀⠀⣴⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⠀⠀⠀⢀⣠⡾⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠿⣿⣦⡀⢀⣴⣿⠟⢛⣛⡉⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⢀⣾⣿⡿⠋⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢰⡇⠀⠀⠀⠀⠙⢿⣾⠟⣡⣾⡿⠋⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⠟⢀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⡄⠀⠀⠀⠀⠈⠟⢰⣿⠟⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢸⣿⡟⣹⣿⡇⠘⣡⣴⣿⣿⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⠻⣿⣄⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⢸⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣦⣈⠻⢷⣦⣀⠀⢸⡏⠀⠀⠀⠀⢀⣴⣿⣧⣤⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠉⠛⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣭⣙⢿⣷⣄⠀⣼⣿⠿⠛⠉⣠⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠹⣧⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⡹⣿⣆⢉⣤⣴⣶⣿⣿⣿⣿⡟⠁
⠀⠀⢀⣀⣀⣠⣤⣄⣰⣿⣿⠁⢀⣀⣀⣠⣤⣴⣾⠿⠋⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⡆⠉⣹⣿⣿⣿⡿⣿⣿⡄
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⣛⠛⢛⣋⣡⣴⠂⠀⠀⠀⢸⣿⡄⢶⣤⣀⣀⣀⣀⣠⣴⣾⣿⠛⢉⣾⡿⢋⣥⡶⠀⠈⢻⣿
⠀⠀⠀⠈⠻⣿⣷⣦⣄⣉⡛⠿⠿⠛⠛⠛⠟⠛⢿⣿⠀⠀⠀⠀⢸⣿⡇⢸⡏⢻⣿⡿⠛⠛⠛⠛⠿⣷⣾⡿⢠⣿⡟⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣷⣶⣶⣤⡀⠸⣿⡆⠀⠀⠀⢸⣿⢃⣿⡇⢸⣿⡀⣤⠀⠀⠀⠀⠈⠙⡇⢸⡿⠁⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠟⠋⠉⣀⣤⠀⠹⣿⣆⡀⠀⠿⣋⣾⡟⠀⠈⢿⣇⢻⣷⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣾⡿⢶⣶⣶⣤⣀
⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⢀⣀⣤⣴⣾⣿⠏⢀⡀⠈⠻⣿⣶⣾⡿⠋⠀⠀⠀⠀⠹⣦⡙⠿⣷⣦⣄⡀⠀⢸⡇⠀⣀⣤⣤⣶⣶⣶⣦⣍⡻⣿⣷⣄
⠀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠋⣴⡿⠿⣷⣤⡈⠻⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⠆⠈⠉⠛⠛⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠓⠘⣿⣿
⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⣼⡟⣱⠂⠀⠉⠻⣆⠀⠀⠀⢀⣀⠀⣴⣾⠟⠁⠀⠀⠀⠀⢀⣼⠏⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⢹⣧⡶⢛⣛⣛⣿⣿⠃⠀⠀⠀⠀⣠⣴⡿⠁⠀⠀⠈⣿⣦⠰⣤⣤⣤⣤⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣽⣇⢻⣷⠀⠀⠀⠘⣡⣾⡿⠟⠋⣿⣿⠀⣠⣤⣶⣿⠿⢋⣴⡆⠀⠀⠀⠘⣿⡆⢻⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠉⠀⠹⣧⠀⢀⣴⠟⠁⠀⠀⠀⢿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣇⠀⠀⠀⠀⢿⣿⢸⣿
⠀⠀⠀⠀⠸⣿⣿⣷⣶⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣿⣃⠀⠀⢀⣠⣴⡾⠋⠁⠀⢠⣄⡉⠙⠛⠿⣿⣦⡀⠀⠀⠼⢃⣿⡏
⠀⠀⠀⠀⠀⠹⣿⣮⡙⠿⣿⣿⣮⡻⠿⣷⣶⠶⠶⠟⠛⢹⡏⠉⠛⠷⣶⣬⡙⢷⣄⠀⠀⠘⣿⣿⣷⣶⣤⣌⡙⣿⣷⣦⣴⣿⡟
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣷⣦⣬⡛⠿⢷⣶⣶⡞⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢿⡆⢿⡆⠀⢠⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠛⠛⠓⠀⢀⣿⠃⠀⠀⠀⣾⡇⣶⣄⠀⠀⠀⠀⠙⢸⣿⠀⣿⣷⠈⣿⣿⠙⠛⠻⠿⠿⠿⠿⠿⠿
⠰⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣶⣾⠟⠀⠘⣿⡀⠀⠀⣼⡿⢁⣿⠻⢿⣶⣶⣶⣶⣿⣿⠀⢹⣿⣧⣽⣿
⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⢻⣷⣀⣘⣭⣴⡿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠁⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠙⠀⣰⠉⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⠉⠙⣗⠉⢀⡆⢳⣤⣠⣌⡴⡀⠘⡿⠎⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⡀⢴⢦⣿⡀⢴⡇⠈⣿⣿⣿⢁⣧⠐⣹⡴⠈⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⢢⣿⣼⣏⠈⣻⣿⣷⡀⢘⣿⡟⣿⡯⡶⠉⢀⣾⣿⣦⠔⢐⡊⠀⠈⠣⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠨⣓⣚⣿⣿⣿⣶⣭⡿⣿⣷⢴⠿⢯⣿⣿⢁⣴⣿⣿⣿⣟⠛⠁⠀⠀⠀⢀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢐⢤⡈⠉⠙⠻⢿⡿⡫⠚⠉⠈⠑⢌⢳⡿⡛⣹⡏⣙⣿⣿⡷⠄⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⡀⠪⠁⡀⣉⣶⣤⣄⣼⠕⠀⠐⠈⠀⢢⠀⣾⣿⣷⣿⣿⣉⣀⣹⣆⠘⣁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⡋⢀⣶⡾⢿⣿⣻⣿⣿⣥⠀⠓⡔⡤⠞⢀⣿⣏⠀⠈⠈⠉⠙⠻⠍⠈⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣼⠀⠀⠀⢻⣻⣿⣾⣿⡿⠛⢹⣷⡵⣲⣌⣠⣤⣿⣿⡿⣿⣿⣷⣿⢿⡿⠏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣀⠀⡀⠽⢿⣿⡿⠋⣀⣰⣯⣵⣾⣿⡇⠈⢿⣿⣷⠇⠽⣿⣿⣿⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠝⠒⣠⡞⠛⢩⢾⡿⣿⣿⣷⠀⢸⡟⠻⣿⣦⡼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠠⡟⠀⣁⣀⣼⣿⣿⣿⣿⣿⣦⣸⡿⣄⣸⣿⣍⠛⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⢒⠀⢸⡇⢆⠈⢹⠋⠼⡻⠻⡟⣿⣿⠏⠁⠀⢤⠔⠙⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⡆⠁⣺⠄⠈⠛⠒⠀⠀⠀⠀⠀⠀⡅⠀⠃⠀⠀⠘⠖⠀⣀⠠⠳⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠊⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢄⣀⣤⣤⣄⠀⠀⠓⢤⣀⡤⠤⠞⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⠋⠀⠀⠀⠉⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠉⠱⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡀⠀⠀⠀⠀⠀⠐⡄⠀⠙⠲⣄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠐⠄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡈⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⠦⣤⣄⠀⠀⢀⣀⣤⠞
⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⢶⡖⠒⠒⢉⣠⡤⣤⠶⢄⠀⠀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⡴⠃⠀⠀⠀⡠⠋⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠙⢦⣀⡏⠀⠀⠀⠀⠈⠛⠉⠑⢆
⠀⢀⡞⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠸⡄⣧⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠹⣅⠀⠀⠀⠀⢀⠀⠀⠀⠘⠢⢤⡀
⠀⡼⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢣⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢠⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⠀⠀⠀⠀⠈⠀⠀⠀⡟
⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠸⡇⠀⠀⠀⣀⣀⣠⠞⠁
⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟⠻⠚⠋⠁⠉
⠇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇
⢻⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⢦⠀⠀⠀⠀⢰⠃⠀⣸⠁
⠈⣇⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡇⠀⠀⠀⠋⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠘⣆⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠉⠒⠶⠤⠤⠤⠴⠒⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣄⣀⣀⣀⣀⣤⠴⠖⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡼⠈⢣⣸⠁⢸⡄⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢤⣘⡌⠳⡇⠀⡎⡇⠀⠀⡷⠃⡼⢀⡤⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢳⡀⠘⣴⡁⢰⠀⢸⠃⢠⠟⠉⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⢦⡀⠙⣄⠘⣇⢸⣀⡎⡰⠃⠀⣠⡮⠤⠴⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡶⡎⠙⠢⣄⣀⠙⠢⣌⣶⣿⣿⣿⣿⣷⡴⠊⠁⣀⣤⣾⢥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⡀⡞⠀⢷⠚⠉⢉⣭⢿⠶⣾⣿⣿⣿⣿⣿⣿⣿⡂⠉⠁⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⢶⠲⢤⡤⣄⣇⠀⢿⠃⠀⢀⣤⡞⠋⢀⡾⢴⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡉⠛⠛⠲⠤⣀
⠀⠀⢠⡤⠤⣌⣧⡀⠙⢦⣻⡄⠘⡆⠀⣼⠏⢀⡠⠞⠉⢁⣠⡾⢿⣿⣿⣿⡟⢧⡈⠑⢯⡙⠳⢞⡋⠉
⠀⠀⠀⠳⢄⡀⠈⠙⠦⡀⠙⣿⣶⣷⣶⣿⣴⠋⢀⣠⣴⡫⠵⠷⢾⣼⡇⢹⡟⢆⠈⠢⣄⠈⢢⡤⠽⠂
⠀⠀⠀⠀⠀⠙⢲⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⢀⣠⣴⢋⡟⡇⠀⡿⣌⠳⣄⠈⠳⣤⣹⡄
⠀⠀⣀⡤⠖⠛⠛⠉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣉⠉⠉⠉⢉⣙⣷⠀⡇⠘⢆⠈⢳⠦⢼⣆⠁
⠀⠈⠙⠒⢲⡶⠖⠋⢁⡤⠚⣻⣿⣿⣿⣿⢟⠓⢄⡙⠪⣽⢿⢉⢯⢹⠻⣄⡇⠀⠀⠳⣼
⠀⠀⢀⣴⣋⣠⣤⠞⠁⢀⠜⠁⡌⠀⡇⠘⡌⢦⡀⠙⣤⣈⠙⢿⡚⠛⠀⠛
⠀⠀⠀⠀⠀⣴⢃⣠⠴⡏⠀⣼⠀⠀⡇⠀⢹⡄⠙⢦⡘⡏⢻⡉⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⣇⠜⣿⠀⢠⣇⠀⢸⠙⢦⡀⠙⡟⠶⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠏⢹⡄⡾⠀⠀⠙⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠨⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⢠⡄⢡⣤⡄⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠃⢠⡄⠀⠀⠀⠀⠀⠘⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⠂⠉⠻⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣦
⠀⠀⠀⢀⣾⣿⡿⢁⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢳⣄⠹⣄⠀⠀⠀⠀⠀⣿⢸⣿⡇⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡈⢛⣿⣷⡀
⠀⠀⢀⣾⣿⡟⣠⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⣆⠀⠀⠀⠀⠹⠼⠿⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡄⠙⣿⣷⡀
⠀⢀⣾⣿⡟⢰⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡄⠸⣿⣷
⠀⣸⣿⡟⣠⣿⣿⣿⣿⣿⡿⠁⠀⠰⠦⣤⣀⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⣧⠈⠈⢿⣿⣿⣿⣿⣿⡄⢹⣿⣇
⢀⣿⣿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠶⠀⠀⠀⠈⠣⡀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣻⡵⠚⠉⠀⠀⠀⠘⢿⢿⣿⣿⣿⣿⠈⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⣠⣤⣤⡤⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣶⣶⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⡴⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣶⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡙⠳⢤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⡿⠛⢁⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣭⡛⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⡶⠋⠁⠀⠀⠀⣰⣿⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣼⣯⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣰⠏⠀⠀⠀⢰⡆⢠⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢦⡀⠀⠀⠀⣼⣿⠏⢠⡟⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢀⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣄⠀⢈⠉⠀⡞⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠸⠇⠘⠇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⣃⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣤⡀⠀⣠⣤⣄⡀⠀⢀⣄⠀⠀⢠⠀⠀⠐⢊⣍⠶⠀⠀⡂⠀⠀⠀⢀⣀⠀⠀⢠⣦⡀⠀⣠⣤⣤⡀⠀⢀⣀⠀⠀⢠⠀⠀⠰⢎⣍⠶⠀⠀⡆⡀⠀⠀⢀⣀
⠈⠋⢀⡞⠁⢸⠀⠙⡆⠘⠛⠁⠀⠀⣶⣶⣶⣦⣤⣤⡄⠀⠘⠫⠀⣤⣿⡟⠀⠀⠈⠋⠀⡞⠁⢸⠀⠙⡆⠘⠛⠁⠀⠀⣶⣶⣶⣦⣤⣤⡄⠂⠜⠫⢀⣤⣿⡏
⣀⠀⠘⢧⡔⢻⠳⣤⠇⠀⠀⠀⠀⢸⣿⣯⣿⣿⣽⣿⠃⠀⣀⠀⠀⢹⣿⢿⡷⠆⣀⠀⠈⢧⡔⢻⠓⣤⠇⠠⠀⠀⡃⢰⣿⣯⣿⣿⣽⣿⠇⠀⣀⠀⠀⢩⣿⢿⡷
⣿⡗⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⣛⠛⠛⠛⠛⠛⠀⢠⣿⣿⣇⠀⢀⠀⠀⢲⣿⡗⠀⠈⠙⠛⠛⠁⠀⠀⠈⠀⠀⠈⣛⠛⠛⠛⠛⠛⠀⣠⣿⣿⣇⠀⢀⡀
⠀⢁⡴⠖⠢⢄⠀⢀⣶⣷⣄⣠⡀⠀⠉⢀⡶⣟⠛⠳⣄⠀⠘⠋⠁⠀⡾⣿⠃⠈⠁⢁⡴⠒⠦⣄⠀⢀⣶⣷⣄⣠⡀⠀⠙⢠⡴⣟⠛⠳⣄⠀⠛⠋⠉⠀⡾⣿⠃
⠀⡏⣴⠛⢷⡈⣇⠈⢿⣿⣿⣿⠇⠀⠀⣾⠀⢸⣶⠤⣽⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡏⣴⠛⢷⡈⡇⠀⢿⣿⣿⣿⠇⠀⠀⣿⠀⢹⣶⠤⣿⠀⠀⠀⠀⠀⠀⡀
⠀⢣⡙⠄⠚⣠⠏⠀⠈⠻⠛⠁⠀⠻⠃⠘⠷⣿⣼⡶⠋⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢣⡙⠤⠚⣠⠇⠀⠈⠻⠛⠁⠀⠿⠃⠘⠷⣿⣬⡷⠋⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠉⠛⠛⠁⠀⠙⣀⣤⣴⠶⢿⡀⠀⠀⠀⠀⠀⣰⣧⣤⡀⠀⡶⠆⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠙⣀⣠⣴⠶⢿⡀⠀⠀⠀⠀⠀⣰⣷⣤⡀⠀⡶⠆
⠀⠀⠀⠀⠀⣶⠞⣛⣩⣥⣶⣲⠈⢷⠀⠀⠀⢀⠘⠻⢿⣯⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⢛⣭⣥⣶⣲⠀⢧⠀⠀⠀⢀⠘⠛⣿⣏⠀⠀⢠⣤⡀
⠀⠀⠀⠀⣠⠹⡄⠳⢟⣛⣭⣵⣾⠿⠃⣿⣷⣿⡇⠀⣀⢀⡀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⢹⡄⠳⢞⣛⣭⣴⣶⠿⠂⣿⣷⣿⡇⠀⣀⢀⡀⠀⠻⠿⠟
⠀⠀⡠⠶⣄⠀⢳⡾⠟⠛⠋⠁⠀⢠⣷⠎⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⣄⠀⢿⡾⠿⠛⠋⠁⠀⢠⣷⠊⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀
⣠⡊⠀⢄⣈⠳⣄⡀⠠⠄⢰⣿⣇⣠⡀⠀⠀⢀⠂⠀⠘⠛⠟⠉⠀⠰⠷⠀⠉⠀⣠⡊⠀⣄⣈⠳⣄⠀⠠⠄⢰⣿⣇⣤⠀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠐⠿⠀⠉
⠙⢿⣦⡘⠻⡷⠈⠻⣦⠀⠘⣿⣿⠿⠃⠀⠀⠈⠄⠀⢀⡀⠀⣰⣦⠀⠀⠀⠲⠀⠙⠿⣦⡘⠻⡷⡌⠳⣤⠀⠘⣿⣿⠿⠁⠀⠀⠈⠀⠀⢀⡀⠀⣰⣦⠀⠀⠀⠲
⠀⣀⠈⠻⣦⡈⢀⡴⠋⣤⣤⡁⠀⣤⣤⡄⠀⠀⠀⠃⠙⢿⣿⣿⣇⠀⢀⣀⡄⠀⠀⢀⠉⠻⣦⡀⢀⡴⠃⣤⣤⡉⠀⣠⣤⡄⠀⠀⠀⠃⠸⢿⣿⣿⡇⠀⠠⣀⡄
⠀⠛⠁⠴⠈⠻⠋⠀⠘⠻⠿⠀⠀⠙⠛⠃⠐⠉⡉⠑⠀⠈⠛⠈⠁⠀⠁⠋⠓⠀⠀⠛⠁⠴⠈⠻⠋⠀⠘⠻⠿⠀⠀⠙⠛⠋⠐⠁⡏⠑⡀⠈⠛⠈⠁⠀⠁⠏⠛
⢠⣶⡀⠀⣠⣤⣤⡀⠀⢀⣄⠀⠀⢠⠄⠀⠐⠬⡍⠶⠀⠀⡀⡀⠀⠀⢀⣀⠀⠀⢠⣶⡀⠀⣠⣤⣤⡀⠀⢀⣀⠀⠀⢠⠄⠀⠐⠌⣍⠶⠀⠀⠂⡀⠀⠀⢀⣄
⠈⠉⢀⡞⠀⢸⠀⠙⡆⠘⠛⠀⠀⢀⣶⣶⣶⣦⣤⣤⡄⠀⢜⠃⢀⣤⣿⡟⠀⠀⠈⠉⠀⡞⠀⢸⠀⠙⡆⠘⠛⠀⠀⠀⣶⣶⣶⣦⣤⣤⡄⠂⠙⠫⠀⣤⣿⡏
⣀⠀⠈⢧⡞⢻⠓⣦⠇⠠⠀⠀⠁⢸⣿⣿⣿⣿⣽⣿⠁⠀⣀⠀⠀⢹⡿⠿⡷⠆⣀⠀⠀⢧⡖⢻⠓⣤⠇⠀⠀⠀⡃⢸⣿⣷⣿⣿⣽⣿⠃⠀⣀⠀⠀⢩⡿⠿⡷
⣿⡗⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⣉⠛⠛⠛⠛⠛⠀⣤⣿⣿⣇⠀⢀⡀⠀⢺⣿⡗⠀⠀⠙⠛⠋⠁⠀⠀⠈⠀⠁⠈⣉⠙⠛⠛⠛⠛⠀⢤⣿⣿⣇⠀⢀⡀
⠀⢁⡴⠒⠲⢄⠀⢀⣾⣷⣄⣤⡀⠀⠉⢠⠶⣏⠙⠳⣄⠀⠘⠋⠁⠀⠾⣿⠃⠈⠀⢁⠴⠒⠢⢄⠀⢠⣾⣿⣄⣤⡄⠀⠉⢠⡶⣟⠙⠳⣄⠀⠙⠋⠁⠀⠾⣿⠃
⠀⡏⣴⠛⢷⡈⡇⠈⢿⣿⣿⣿⠇⠀⠀⢿⠀⢸⣶⠦⣾⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡏⡴⠛⢷⡌⡇⠀⢿⣿⣿⣿⠇⠀⠀⣿⠀⢸⣶⠦⣾⠀⠀⠀⠀⠀⢀⣀
⠀⢣⡙⠠⠚⣠⠇⠀⠀⠛⠛⠁⠀⠻⠃⠈⠳⣿⣼⠷⠋⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢣⡙⠀⠚⣠⠇⠀⠈⠻⠋⠁⠀⠻⠃⠈⠳⣿⣼⠷⠋⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠉⠛⠋⠁⠀⢉⣀⣤⡴⠶⢻⡄⠀⠀⠀⠀⠀⣴⣧⣤⡀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⢉⣀⣤⡴⠶⢿⡀⠀⠀⠀⠀⠀⣼⣧⣤⡀⠀⠿⠆
⠀⠀⠀⠀⠀⣶⠞⢛⣭⣵⣶⣱⠈⢷⠀⠀⠀⢀⠘⠻⢿⠧⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⣛⣩⣵⣶⣹⠌⣧⠀⠀⠀⢀⠘⠛⢿⡧⠀⠀⣠⣤⡀
⠀⠀⠀⠀⣤⠸⡄⠁⢛⣋⣭⣴⣾⠿⠃⣿⣷⣿⡇⠀⣀⢀⡄⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⠸⡄⠳⢛⣋⣭⣴⣶⠿⠃⢿⣷⣿⡇⠀⣀⢀⡄⠀⠻⠿⠟
⠀⠀⡠⠶⣄⠀⢳⡾⠟⠛⠉⠁⠀⢠⣷⠊⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀⠀⠀⠀⡰⠶⣄⠀⢳⡿⠟⠛⠉⠁⠀⢠⣷⠂⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀
⣠⡊⠀⢀⣈⠳⣤⡀⠰⠄⢸⣿⣧⣤⡀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠰⠿⠀⠉⠀⣠⡊⠀⢀⣈⠳⣦⡀⠰⠄⢸⣿⣧⣤⡀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠐⠿⠀⠉
⠙⠻⣦⡈⠻⡷⠈⠻⣦⠀⠘⣿⣿⠟⠁⠀⠀⠈⠔⠀⢀⡀⠀⣴⣦⠀⠀⠀⠺⠀⠙⠿⣦⡘⠻⡷⠌⠛⣦⠀⠘⣿⣿⠟⠁⠀⠀⠈⠄⠀⢀⣀⠀⣴⣦⠀⠀⠀⠲
⠀⣀⠈⠻⣦⡀⢀⠔⠁⣴⣤⠀⠀⣤⣦⡄⠀⠀⡐⠃⠘⢿⣿⣿⣇⠀⠰⢀⡤⠀⠀⣀⡈⠻⣦⣄⢀⡴⠁⣶⣤⡀⠀⣤⣦⡄⠀⠀⡐⠃⠘⢿⣿⣿⡇⠀⢐⢠⡄
⠀⠛⠁⠶⠈⠛⠋⠀⠘⠻⠟⠀⠀⠙⠛⠃⠐⠁⡍⠑⠀⠈⠛⠀⠁⠀⠀⠈⠓⠀⠀⠛⠁⠶⠈⠛⠋⠀⠘⠻⠟⠀⠀⠙⠛⠋⠔⠁⡇⠑⠄⠈⠛⠀⠁⠀⠁⠎⠛
⠀⠉⠁⠁
⠀⠐⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⡠⡤⠂⢰⡆⣰⠊⠐⠂⢰⠆⣠⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣄⠀⠀⢹⡀⠈⣇⢻⣄⢀⠀⡾⢿⠀⠀⠀⠀⠀⢀⠙⢷⣄
⠀⠀⠀⠀⣠⡾⠋⢠⡈⡃⠀⠀⠸⣧⡀⠘⠁⠀⠁⠀⠈⠀⠈⠁⠘⠃⠀⠀⠀⠀⢀⡷⢄⠙⢷⣄
⠀⠀⠀⣼⠋⢠⠖⠀⠹⣏⡛⠛⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠶⠋⣠⠴⠒⠄⠙⣦
⠀⢀⣾⠃⠀⢳⣄⠀⣠⠈⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⢇⣀⣠⠏⠀⠘⣷⡀
⠀⣼⠃⠐⠛⠛⢮⠉⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣹⠿⠏⠀⠀⠀⠀⠀⠀⢉⡞⠋⠙⢂⠘⣧
⢰⡏⢀⠘⠶⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⢀⣉⡀⢹
⣾⠁⡘⠲⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡿⠩⣁⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣟⡽⠃
⢿⡀⠠⢄⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⡠⢀
⠸⣇⠀⠶⠛⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠩⠇⣸
⠀⢻⡄⠰⡂⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣍⠙⠆⢠⡟
⠀⠈⢿⡄⠉⠛⢋⡴⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⠀⢈⠇⢠⡿⠁
⠀⠀⠀⢻⣄⠈⢋⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⡿⢦⡈⠁⣠⡟
⠀⠀⠀⠀⠙⢷⡄⠙⠧⠀⠀⠀⠀⠀⢦⠀⣀⠀⣀⠀⠀⢀⣀⠀⢠⡄⠀⠀⠀⠀⠀⠰⠈⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⡘⢷⠇⠈⠈⢳⣰⡇⠈⣷⠀⢷⠀⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠈⠀⠛⠀⠦⣠⠞⠈⠧⠠⠏⠐⠚⠉⣁⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠄⠐⢤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠑⢤⠊⠁⠀⠀⠀⠈⠑⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⡅⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⡃⠀⠀⠀⠀⡄⠀⡄⢀⣇⣀⢰⡀⣰⠀⠀⠀⠰⠃⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⣣⡀⠀⠀⢄⡨⠂⣉⡁⠀⠀⠀⢉⣉⡑⠢⣴⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠉⢲⠎⠀⠙⠛⠁⠀⠀⠀⠈⢙⠉⠀⠈⢣⠒⠁⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⡌⠀⡔⠉⠉⠱⡀⠀⠀⡎⠁⠈⢱⡀⠀⠓⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⡇⠀⡍⢰⣶⣿⠇⡀⠘⣹⣿⡯⢁⠃⠀⠷⠤⠄⣀⠤⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠒⢃⠀⠈⠂⠙⠋⠀⠧⠀⠈⠛⠒⢁⠀⢠⠇⠀⠀⠈⢢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⢀⠤⠂⠙⡄⠀⠑⠤⣀⡀⠀⣀⣀⡠⠔⠁⢠⡊⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢸⠁⠀⠀⠐⠚⣢⣀⠀⠀⠀⠀⠁⠀⠀⣀⡔⠁⠈⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⠁⠌⠉⠲⠒⠒⡖⠒⡏⠁⠈⢆⡀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠙⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⡤⠤⠔⢳⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⣄⡀⠀⠀⢀⡠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢉⣀⣉⠀⠈⡏⢹⠁⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠉⠠⣀⣀⡀⣠⡬⢱⡇⢸⡮⠥⠤⣤⡀⠀⡀⠈⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠀⠀⠀⠒⠈⠁⠀⠒⣁⠔⠊⡇⠀⠈⠢⢄⣀⠈⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠒⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⢀⣀⠠⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⣈⣉⣉⣉⣉⠥⢶⡇⣷⠊⠤⣤⡤⢤⣔⡂⠀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠠⠐⠊⠉⠚⢁⠴⠊⡇⠆⠑⠤⡀⠉⠀⠀⠀⠉⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⣀⡀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⡇⠀⠀⠀⠈⠁⠒⠀⠐⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠐⠀⡀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⢹⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⠀⡀⠹⣦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠁⠈⠀⠀⠊⠉⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠱⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⡠⠔⠁⠀⠀⢀⠀⢹⡆
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠑⠄⡀⠠⠊⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠋⠀⠀⠂⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⡏⠀⠀⠀⡀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⢠⡇⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⢸
⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡼⣥⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⢸
⠀⠀⠀⢸⡇⠀⠁⠈⠢⢤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡟⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠀⢸
⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢣⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠐⠁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠈⢷⡀⠘⠀⠘⠠⠠⠔⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠉⠉⠙⠁⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣠⠮⢄⠀⠀⠀⠀⠀⠉⠀⠀⢑⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢸⠁⠀⠀⠁⠀⠀⠀⠀⠰⠄⠠⠞⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠤⠃⠀⠀⠀⠀⠀⠀⠄⠀⢁⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠉⠁

⠀⠀⠀⠀⣠⠔⠚⠉⣉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⣀⣠⠤⠔⢢⠀⣖⡆⢀⣀⣀⡴⢦⠞⡆
⠀⠀⡠⠊⠀⢀⠔⠁⠀⢀⠀⠀⠀⠀⢄⡀⠑⢄⠀⠀⢳⣀⠀⢠⠬⠖⡞⣆⡟⠁⢿⡇⢀⡘⢲⡄⢀⣤⡀
⠀⡼⠁⠀⢠⠃⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⢄⠀⠳⡀⠀⠉⢇⢸⡄⠀⠓⠋⠈⠒⠚⠳⠼⠙⠊⠀⠘⠒⠃
⢰⠁⠀⢀⠃⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠡⠀⠱⡀⠀⠈⠉
⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢡⠀⢣⠀⠀⠀⢠⠖⠒⠒⠒⢢⢀⣀⣀⠀⣀⣀⣀⣀⠀⣀⠀⠀⣀
⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣋⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠒⡆⠀⡖⠚⡏⠠⠌⣿⠁⣼⡿⠈⠉⡡⠇⢀⡇
⡇⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐⢕⢄⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠰⣥⣤⠇⠀⠙⠶⠚⠙⠦⠼⣇⣴⡄⢳⡀⢘⣗
⢱⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣅⠀⠀⠌⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠘⠛
⠀⢣⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠑⣄⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠑⠢⢄⣀⡀⠉⠐⠒⠂⣀⡤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢉⣡⡀⢠⣄⠀⠀⠀⣠⣀⢤⠀⠉⠉⠉⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢚⠉⠁⢀⡱⠼⢏⣰⠋⣿⡁⠉⠾⣄⠀⢀⡀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⠙⡆⢣⠀⠰⠜⠘⠢⠼⢧⠎⠲⠃⠘⠣⠃⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⢲⢀⣤⣀⢀⣀⣀⡤⡀⣠⡀⢀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠉⠹⠀⡘⠙⡇⠒⢨⡇⠰⣿⠀⠁⡴⠃⢸⢠⠁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠒⠒⠒⠂⠤⢤⣀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠓⠒⠃⠀⠈⠉⠁⠈⠓⠻⡼⢆⣘⡄⢨⣭⠞⠁
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠐⠈⠀⠀⠀⠀⠀⡈⠑⢄⠀⠀⠀⠉⠛⢲⠄⠀⢀⣠⠤⢤⡴⠦⣤⣀⣀⣠⣤⠴⠖⠋⠁
⠀⠀⠀⠀⡰⠁⠀⡐⠁⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠱⡀⠀⠀⣠⠏⣠⠴⠋
⠀⠀⠀⢰⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄⠐⠛⠋⠁
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠐⠀⢣
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠆⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⢀⠀⡜
⠀⠀⠀⠘⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠈⢄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠑⠦⣀⡀⠁⠐⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠛⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⡀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢸⠻⡆⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⢶⣄⣸⠇⠀⢀⡴⠶⢾⡟⠃⣤⠶⣄⠀⠀⠸⣷⢀⣴⠾⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⠛⠛⠛⠀⠀⠛⠛⠋⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠠⣶⡆⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⢸⣻⠆⠀⠀⣿
⠀⠀⣀⣠⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⢷⣄
⠀⠀⣿⠉⠁⣀⣀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡁⠀⠀⣿
⠀⠀⣿⠀⢰⣍⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⡿⠀⠀⣿
⠀⠀⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠉⠉⢉⡉⠉⠉⠑⠒⠢⢄⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡄⢀⠔⠊⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⢢⡀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⣠⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⢳⡄⠀⠀⢠⣿
⠀⢀⣿⠀⠀⠀⠀⡴⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⢿⡄
⢀⣿⠁⠀⠀⠀⠘⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⢻
⣸⡇⢀⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⢰⡀⠸
⣿⠁⢸⡇⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢸⡆⠀⠀⢸⡇
⣿⠀⠈⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⠁
⢻⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢰
⠘⢷⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣠⡾
⠀⠈⢿⡆⠀⠀⠀⠀⢆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⣿⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠈⠢⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣠⠂⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣠⠴⠋⠁⠘⠁⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⢸⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠀⠀⠐⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⡇
⠀⠀⠘⣿⠀⢼⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠿⠀⠀⣿⡇
⠀⠀⠀⣿⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⠇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣻⡟⠉⣹⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠀⣰⠏⠰⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢠⡟⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢰⡟⠀⠀⠀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⢀⡿⠁⠀⠀⠐⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠀⠀⠺⣧
⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠰⣿⠀⠀⠀⢀⣶⣛⡷⠀⠀⠀⣤⢶⡆
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⠾⠃
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠶⢦⡀
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⡴⠾⠋

⠀⠀⢠⡖⠉⠙⣦⡠⣤⣀
⢀⡤⠼⣦⡀⢀⡏⠀⠀⢹
⣿⠀⠀⢘⡟⠉⠙⣶⠶⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣀⣀⡀
⠈⢻⠚⠛⢧⡄⢤⣇⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣇⡀⢹⡏⠀⣹⣤⣄
⠀⠹⣄⣠⣞⠁⠀⢹⡟⠚⠃⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣘⡿⣪⣧⡿⣏⠀⣸
⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⠉⠈⣩⡻⠿⢧⡛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠛⣿⠋⠙⣿⠈⢱⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣆⠉⢿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠙⠲⠾⠉⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡟⠉⠁⠀⠉⠻⣿⠋⠛⣛⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⣁⣀⣼⣷⣄⡀⠀⣀⣴⡛⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣦⡛⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⠿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣇⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣛⣩⣥⣶⣶⣾⣿⣿⣿⣿⣶⣶⣮⣭⣛⠻⢿⣷⣦⡀
⠀⠀⠀⠀⣠⣾⠟⣫⣶⣿⣿⣿⣿⠿⡟⠻⠛⠿⠛⠟⢻⠿⣿⠿⣿⣿⣶⣬⡛⢿⣷⣄
⠀⠀⢠⣾⢟⣵⣿⣿⡿⢿⠉⠃⠈⠀⠀⢰⡆⠶⢶⡄⠀⠀⠀⠀⠀⡌⠙⠿⣿⣦⡙⢿⣷⡀
⠀⣰⡿⣡⣿⣿⠟⠁⠀⠀⢶⡄⣶⠀⠀⢸⡇⣠⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⣿⣆⠹⣿⣄
⣰⡟⡰⣿⡿⠃⠂⠀⠀⠀⢸⠇⢿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠙⣿⣧⠘⣿⡄
⣿⡱⣽⡿⢡⠙⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡄⠠⠘⣿⡆⠘⣿⡄
⣧⢹⣿⠇⠀⠀⣿⣿⢻⣷⣄⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⠀⠂⠸⣷⡀⢹⣧
⡇⢸⣿⠀⠀⠀⠉⠈⠉⠁⠉⠻⣷⣶⣄⣀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿
⠇⣿⣿⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢸⣿⠀⣿⠄
⠀⣿⣿⠐⠈⢳⡿⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠂⣼⣿⠀⣿
⡄⢿⣿⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⣿⢀⡿
⢷⠈⢿⣿⡀⠀⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣸⣿⡏⣼⠃
⠈⢷⡈⢿⣷⣀⡀⠿⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠻⣿⢀⢀⣼⣿⡟⣸⠏
⠀⠈⢷⡈⢻⣿⣦⠀⠀⠀⠀⠠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⠀⢀⣀⡀⣠⣾⣿⠏⣴⠏
⠀⠀⠀⠹⣦⡙⢿⣷⣤⡀⠀⠀⠏⠀⠀⠀⠀⣴⣇⠀⠀⠀⠠⠽⠗⢰⠿⣿⣿⣿⡿⣣⡾⠁
⠀⠀⠀⠀⠈⠻⣯⡻⣿⣿⣶⣥⣀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⢀⣈⣴⣾⣿⣿⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣾⣽⣿⣿⣿⢿⣷⣷⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣾⣭⣭⣭⣭⣿⣶⣴⣶⣿⣿⣿⡟⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⢋⡉⠙⠃⢰⣷⠀⠘⠋⠹⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⡈⠁⠀⣠⣾⣿⣦⠀⠀⠘⠙⣿⣿⡇
⣤⣤⣤⡄⣤⣤⣤⣤⣤⣤⣿⣿⡀⠉⡀⠀⢿⣿⣿⣿⠁⠀⠐⠂⣿⣿⡇
⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡉⢌⠁⢠⠈⢹⡟⠁⣀⠐⢓⣴⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀
⣿⣿⣇⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣶⣦⣼⣥⣤⣼⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣟⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⣻⣿⣿⣿⣿⠋⢻⡿⢻⣿⣿⣿⣿⣿⠋⣩⡉⠻⡏⠛⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⣀⣀⣀⣰⣿⠟⢋⣽⣿⡇⠈⢤⣾⣿⡏⣉⣹⡇⠰⣿⣿⠀⣇⣸⣇⣸⣿⣿⣿⣿⣿⣿⣿⠿⠇⠙⣋⠘⢛⣻⣿⣿⣿⣿
⣿⡿⠁⠀⣴⣾⣿⡿⣿⣿⡭⣿⡀⠿⠿⢿⣷⣀⣶⣤⣿⣿⣿⣿⣷⣀⠻⠟⠀⠉⠉⠈⠉⡻⣿⣿⣿⣿⣿⣿⡿⢂⡈⠛⢠⣉⣻⣿⣿⣿⣿
⣿⡇⠀⢸⣿⣿⣿⣇⠘⢻⣧⠸⣷⣶⡶⠋⠁⠀⠀⠀⠉⢙⠻⣿⣿⠸⢿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣬⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠘⢿⣿⣿⣿⡄⠟⣹⣦⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡙⠀⠀⠀⠀⢀⠀⠀⠀⢰⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣶⣦⣄⠉⠙⢷⣶⣿⣿⣿⣧⢠⠀⠀⠈⠐⢀⠄⡀⠀⠀⠀⠀⢰⡆⢠⠎⠀⣠⠄⡨⠊⠼⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠀⢈⣿⣿⣿⣿⣿⣦⡡⠀⠀⠀⠀⠁⠠⢦⣄⠀⠈⣼⣇⡟⣠⣖⠃⠉⠐⠀⠀⠀⠐⠍⣿⡟⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿
⣿⣿⣿⣿⡿⠟⠁⢀⣾⠟⠁⠙⠻⢿⣿⣿⣦⣑⠠⢀⣀⠀⠀⠈⠑⡮⠁⠍⢙⣇⣡⣄⠀⠠⠤⠤⠀⠀⢸⣸⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠈⢹⣯⣽⣥⠄⠉⠭⠵⠛⢛⡻⢤⣤⠼⣥⡀⠀⠀⠀⠀⠀⠀⡠⣢⣿⣿⣷⣶⣤⣀⠙⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⡟⠀⠀⠀⢀⣄⣀⠀⢠⣿⡿⠋⠄⠀⠀⠀⢤⠾⠋⠀⡴⠹⡆⠌⠀⠀⢡⣔⣂⣂⣭⣶⠟⠛⠛⠙⠻⣿⣿⣿⡄⠀⠈⠻⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠁⠁⠀⡀⠀⠀⠁⠀⢀⢘⡇⠠⢩⠈⠐⣦⣤⣹⣿⣿⣿⣿⠀⠀⢠⡀⠀⠈⣿⣿⡿⠀⠀⠀⢹
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠄⠉⠘⠁⠀⠀⠀⠀⠹⠟⠛⠉⠁⠈⣿⡀⠀⠸⠃⠀⢠⣿⡟⠁⠀⠀⠀⣼
⣿⣿⣿⡟⠀⠀⠀⠀⢀⣄⣀⠀⣼⠁⠉⢹⣦⣀⣀⠀⢠⣤⣶⣇⠑⠓⠀⠀⠀⠇⠀⠀⠀⠀⢰⣶⡿⣿⡇⠀⠀⠀⢰⣿⣿⣇⠀⠀⠀⣼⣿
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣼⣿⠋⠁⠀⠀⠀⠹⡇⠀⠀⣧⡢⠀⠀⠠⠠⢦⠀⠀⠀⠀⣻⡇⠀⠀⣄⠀⠙⣿⣿⡀⣠⣾⣿⡿
⣿⣿⣿⣦⣄⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⣿⡇⠀⠀⢴⡇⠀⠀⡇⠀⠀⠋⠉⢰⡆⠈⠀⣄⠀⠀⢰⣿⣿⢷⣀⣀⣿⣦⣤⣾⣿⣿⣿⣿⠟
⣿⣻⡿⣛⣿⣿⣶⣤⣿⣿⣿⡿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⠁⠀⢰⣿⠀⠀⠀⠁⠀⢘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣰⣿⣷⣦⣤⣤⣴⣿⣇⠀⠀⣼⡀⠀⠀⢀⣿⣿⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⠿⣋⠁
⣿⣿⣿⠿⡛⡍⠐⣶⣴⣖⡆⡄⢀⠈⣉⢙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⡛⣩⣴⡈⢻⡄⠀⠀⠠⡄
⣿⣿⠃⢰⠛⠃⠀⠁⠀⠀⠀⠉⠈⠃⠛⠛⠂⠿⠇⡖⠀⢰⣾⢩⡍⢙⡛⡛⢛⣛⢛⣛⡛⢩⣭⢡⣶⢠⡎⢸⣷⡘⠏⠓⠀⢀⠠⠻⠇
⣿⡇⠀⠀⠀⠀⠂⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠸⠧⠸⣧⡟⢿⣬⠿⡷⣏⢸⣿⠄⠽⠃⠙⡁⢡⡀⠄⠸⠬⠊⠋⠀⠀⠀⢀
⣿⠀⠢⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠑⠚⠈⠀⠀⠀⠀⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠄⠄⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⣿⣧⡀⠀⠀⠀⠀⣤⣰⢠⣤⣤⣤⠀⠀⣄⣀⣀⣀⡀⢀⡀⢠⣀⡀⡀⠀⢠⣤⣀⢠⠀⠀⡀⣀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⣿⣿⣷⣤⡀⠀⢠⡄⠈⣬⢈⣉⡈⡄⠀⢡⡍⡈⡉⢉⠉⠀⡌⠉⡉⠁⠀⡈⠉⢁⡘⢀⠀⠓⢙⠀⣀⠂⡁⠙⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣥⣀⣉⣉⣈⣁⣁⣀⣈⣉⣉⣉⣉⣀⣀⣁⣋⣁⣉⣈⣁⣀⣈⣉⣈⣀⣀⣘⣂⣛⣀⣃⣘⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡤⠖⠚⠉⣉⠉⠉⠉⠛⠒⠦⣄⡀⠀⠀⠀⠀⢀⣀⡠⠤⢲⡀⢴⣲⠀⢀⣀⣀⡴⢦⠞⡦
⠀⠀⢀⠔⠉⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⢄⡀⠙⢦⡀⠀⠀⢇⠀⠀⢀⣀⡇⡾⢣⢰⡏⢹⣿⡇⢀⠘⠣⡄⠀⣀⣀
⠀⢠⠋⠀⠀⡔⠁⠀⠀⠀⠈⢇⠀⠀⠀⠀⠉⢂⠀⠙⢄⠀⠈⠙⡇⠸⡄⠀⠳⠼⠋⠳⠤⠼⢇⣸⠑⠾⠁⠘⠧⠾
⢠⠇⠀⠀⡸⠀⠀⠀⠀⠀⠘⡈⠀⠀⠀⠀⠀⠀⠑⡀⠈⢆⠀⠀⠘⠒⠃
⡼⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢃⢃⠀⠀⠀⠀⠀⠀⠐⡀⠈⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠀⠀⠀⠀⣇⣀⠀⢀⣀⣽⡴⠛⠳⣤⠖⢒⣶⠋⠷⠔⢳⡀⢰⠓
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠓⠚⢦⡀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⡜⠀⢸⠀⠘⣇⣉⣁⢿⡀⠙⣿⠀⠀⢰⡋⠀⢸⣀
⢇⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⢄⠀⠀⠀⡜⠀⡞⠀⠀⠀⠀⠀⠓⠒⠋⠀⠀⠀⠉⠀⠀⠉⠉⢿⣼⢷⣀⣳⡀⣴⣦
⠘⡄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠙⡄⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠢⡀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠓⠦⢄⣀⡀⠉⠉⠉⢉⣁⡤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠯⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⡍⠀⢉⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⣶⣌⣻⣧⠀⠀⠀⠀⠀⣀⠰⣿⣿⡆⢀
⠀⠀⠀⠀⠀⣶⣿⣷⢙⡻⢣⣾⣷⠀⠀⠀⠀⢀⠀⡀⠀⠈⠛⠛⠉⠛⠛⠁⠀⠀⠀⠀⣾⣿⡷⣨⣟⢱⣿⣷
⠀⠀⠀⠀⠀⠛⣫⣥⡻⢟⡸⠿⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⣦⡛⣋⣜⣛⠋
⠀⠀⠀⠀⠀⠀⣿⣿⡗⢿⣿⡿⠂⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠈⢿⣿⠏⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣶⡦⢙⣙⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⡇⠀⠀⠈⣡⡛⢛⣬⡉⠀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⣴⣶⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠘⠿⠃⠈⠻⠃⠀⠀⠀⠸⣿⣷⠀⠀⠀⢠⣼⣿⡿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⡄⢀⠀⠈⠻⢿⣿⣿⣷⣦⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⣰⣶⣶⡄⢀⣀⠀⠀⠀⠀⢿⣿⣿⣅⠀⣸⣿⣯
⠀⠀⠀⢰⣿⡿⠛⠿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣿⣿⡀⠀⠀⣽⣿⠇⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠄⠠⠀⠀⠀⣠⣽⣿⡿⠉⠀⠀⠈⠻⣿⣯⣤⡀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠐⣿⣿⣶⣾⢿⠗⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀⠀⠒⠐⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡤⠖⠻⠒⠢⡤⠈⠳⠦⢄⡀⠀⠀⠉⣹⣿⣷⣄⣀⣀⣠⣾⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⣤⣿⣶⣿⠶⢶⣶⣿⣦⠴⣷⠀⠀⠀⠻⣿⡿⢻⣿⣿⣿⠿⣿⠿⠁⠀⢀⣤⣀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠾⠯⢿⣿⡆⠀⣿⠿⠿⠛⠁⠀⠀⣀⡀⠀⠀⠈⠻⠟⠋⠀⠀⠀⠀⠀⠺⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣰⣷⣾⣿⡟⠀⠀⠀⠀⣿⡇⠀⣇⠀⠀⠀⠀⢀⣾⣿⠃⠀⢀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⢸⣿⠇⠀⢸⠀⠀⠀⠀⠘⠛⠋⠀⠀⠘⠺⠇⢹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⠛⠶⠶⠞⠁⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠄⢼⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⣦⠀⠀⠀⠀⠀⣠⣤⣼⣿⢹⣷⣤⣄⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣤⣿⡧⠀⠀⠀⠀⠀⢿⣯⣍⠁⠈⣉⣽⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣾⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⣏⣴⣦⣹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⢁⣠⣤⠲⠄⢹⣿⣄⣴⢏⠍⠛⠇⠀⣶⣶⢠⣄⡀⠉⠙⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⢀⡀⠀⠉⠀⢿⣿⠀⠀⣿⣸⣿⣿⠀⠀⠀⢠⣿⣾⡋⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠏⣡⠀⠀⠀⠈⢷⣄⠀⠀⠘⣿⣇⠀⠿⣷⠙⠿⠦⠖⠠⢾⣯⢿⣿⡀⠀⠀⠀⠀⠀⠀⠦⣀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣴⣄⣼⠀⠀⠀⠀⠘⣿⣷⣄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⢀⣴⢟⣷⡄⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣠⣿⣿⢟⣡⣄⠀⠻⣿⣿⡿⣷⣶⠀⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣿⡵⢃⣤⣤⣤⡀⠙⢿⣧⡀
⠀⠀⠀⠀⣴⣿⣿⠃⣾⠀⠀⠀⠀⡈⠿⠷⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠈⠉⢰⠟⡿⠋⠀⣿⠀⠈⢿⣷⡄
⠀⠀⠀⣼⣿⡿⠁⠀⠙⣷⣤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⢦⣤⣴⣾⣿⣂⠀⠀⢻⣿⡄
⠀⠀⣰⣿⣿⣱⠚⠛⠻⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡿⠟⠻⣆⠀⢿⣿⡄
⠀⢀⣿⣿⠇⠹⣦⣀⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠀⠀⠠⠛⠀⠘⣿⣿
⠀⣸⣿⡟⡖⠂⠈⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣤⣤⣤⣴⣧⡀⢻⣿
⠀⣿⣿⢧⡟⠿⠷⠶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⣿⣿⠿⣭⠀⠸⣿
⢠⣿⣿⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠉⠀⠈⠁⠀⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⡀⣤⣀⠀⣠⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⢠⠀⢰⣿
⠀⢻⣿⣇⢠⣈⣹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⡄⣼⣿
⠀⠈⣿⣿⡀⠋⠙⠋⠉⠛⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢶⣦⣄⡀⠘⠃⢠⣿⣿
⠀⠀⠸⣿⣧⠀⡟⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣬⡉⠻⠿⢀⣾⣿⡏
⠀⠀⠀⢻⣿⣆⠘⠲⠶⣾⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠙⣿⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠻⣿⣆⠀⢠⣤⣾⡿⠟⠉⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣦⡀⠀⢤⡤⠃⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠙⣿⣧⡀⠙⣼⠀⣠⡾⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⢿⣿⣿⣦⡀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⢿⣮⠁⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠈⠉⢁⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡶⠒⠲⣦⡀⣴⠒⠒⣦⡀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⢀⣀⠔⢻⣿⡟⠀⠀⠀⣿⣿⣿⣖⠀⢸⣿⡆⠸⣿⣀⡄⠀⠀⠀⢀⣠⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣄⡀⠈⠉⠒⠻⠿⠱⣦⣀⣤⠟⠝⠻⣿⣄⡼⠃⠛⠒⠛⠋⠀⣀⣤⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣾⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠻⣧⣤⣤⠀⠀⠀⢠⣦⠀⣼⣿⠛⠛⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⣠⣴⣾⠟⣿⠀⠀⠀⢘⢿⡀⠛⠛⢷⣄⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣴⡟⣻⣦⠶⠞⠛⠛⠛⠛⠛⠛⠿⠿⠷⣾⣿⣷⣄⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣻⠏⠀⠀⠀⠀⠀⢠⡶⣄⠀⠀⠀⠀⠀⠙⢿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⡰⠁⠀⠀⢰⣿⡇⠀⠸⠶⠋⠀⠀⠀⣾⣷⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⠇⢠⠃⠀⢀⡀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡿⠀⣸⠀⠸⣯⡿⠀⠀⠀⠀⠀⣧⢹⡆⢀⣠⣶⡄⠀⣴⣶⠄⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣧⠞⣡⠞⠁⠀⠈⠁⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡇⠀⢹⠀⣶⢶⡆⠀⠀⠀⠀⠀⢸⣟⣿⠞⠁⠀⠀⠀⣾⣛⣻⠄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠘⡇⠀⢸⡆⠙⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣧⠀⠈⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠸⡆⠀⠸⡆⠐⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢻⡄⠀⠻⡄⠀⠀⠀⢠⣄⠀⠀⠀⣀⠀⠀⠀⢰⠟⡦⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠹⣄⠀⠙⢦⣀⠀⠿⠟⠀⠀⢸⣏⣷⠀⠀⠈⠛⣡⡴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣠⡟⠳⢤⣤⣉⡛⠶⠦⣤⣤⣤⣭⣭⣤⠤⠖⣛⣭⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠀⣀⣀⣽⡛⠛⠓⠶⠶⠶⠶⠶⢖⣿⣿⣿⣷⠀⠰⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⠟⠙⠛⠻⠿⢷⣶⣶⣶⣶⠾⠛⠋⠁⠈⠙⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⣶⣶⣦⣶⡆⣴⠆⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢼⢯⢶⡶⣽⣝⣿⡟⣭⣻⣿⣷⠘⣋⡼⡱⠓⠺⣄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⠿⢺⠿⣗⣯⣿⠵⠟⢻⣿⣯⣾⠿⠟⠻⠿⠷⣹⢶⠼⣥⢿⣿⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡳⢟⣗⣶⣿⠣⠛⠁⠀⠀⠀⠨⠿⣞⡛⢿⠇⠀⠀⠀⠉⠙⠹⣟⣷⣼⠨⣿⢷⡆
⠀⠀⠀⠀⠀⠀⢠⣼⣖⢿⣦⣴⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠒⠇⠀⠀⠀⠀⠀⠀⠀⠙⢫⣭⣟⢿⣩⡇⢄
⠀⠀⠀⠀⠀⣠⣿⠛⢹⢺⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣟⠓⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⣻⡞⢻⣿⣤
⠀⠀⠀⠀⣰⢮⣯⣾⣌⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡃⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⡦⣂
⠀⠀⠀⢀⣛⢻⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢯⣝⣛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣭⣔⠿⣸⡂
⠀⠀⠀⢿⣽⠧⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⢺⣿⣿
⠀⠀⠀⣀⣺⣥⢡⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⠳⣮⣾⡄
⠀⠀⠠⠟⣻⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠟⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡹⣜⣫⡅
⠀⠀⢰⣷⠙⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⣿⣿⣿⣧⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⠿⣧⡆
⠀⠀⠀⣟⣲⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣩⣿⣿⣽⣿⣿⣿⡿⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢶⣶⣿⡇
⠀⠀⠀⢿⡭⣿⣻⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣹⣳⣿⣶⣿⣿⠿⣿⣿⡆⢶⡞⣧⢼⣍⣄⠀⠀⠀⠀⠀⠀⠀⣴⣷⡎⣽⡄
⠀⠀⠀⠸⡶⠘⡷⢞⣧⡀⠀⠀⠀⣀⣶⣽⢍⣲⣸⠳⠋⠀⣿⡿⣬⡿⡇⠀⠶⣴⡾⣶⢭⣴⣄⠀⠀⠀⠀⣴⣮⢉⣼⡛⠋
⠀⠀⠀⠀⠠⣾⣿⢨⣛⠡⠀⣠⣼⡻⠻⣿⣧⠋⠓⠀⠀⠰⣶⢄⡼⢤⠀⠀⠀⠛⠿⡛⣝⡻⢫⣷⡄⠀⣐⣩⣟⢿⣿⡿
⠀⠀⠀⠀⠀⠈⣷⠻⣟⡲⣿⡿⡻⣿⡷⡹⠛⠁⠀⠀⠀⢠⣶⣎⠳⢟⠁⠀⠀⠀⠀⠙⠿⣓⣾⢛⣧⣕⣺⣿⡿⣅⠂
⠀⠀⠀⠀⠀⠀⠘⠿⣬⣽⢿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⢀⣭⡊⣚⡾⠆⠀⠀⠀⠀⠀⠀⢙⣿⡿⣿⣿⣤⡃⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣾⣭⣴⢿⣠⡀⠀⠀⠀⠀⢀⡿⡍⣛⣣⡁⠀⠀⠀⣀⣤⡲⢿⠿⣿⣿⣻⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠵⢭⣇⢄⣮⢷⣿⣻⡖⢶⣞⣿⠿⣿⣷⢧⣦⣺⡗⣿⣭⡿⢰⣶⡟⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠅⣈⠉⣯⣷⣻⠿⢿⣾⣿⣿⣻⢴⣟⣻⡇⣩⣰⠎⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠑⠟⠺⠽⠳⠾⠽⠿⠛⠛⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢀⣤⡄⠀⣶⠀⡟⠀⠀⠀⠐⢲⡤⡄⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢟⠁⠀⠀⣀⠀⢰⡇⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⢸⠁⠀⣴⠖⢢⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡿⠁⢀⣤⠈⢻⣆⠘⣧⡀⠀⡀⠸⠧⠈⠷⠆⠀⠀⣿⠀⢸⡇⠀⢰⡇⢀⣀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⡠⢿⣄⠀⠀⠹⣦⡈⠛⠚⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠓⠤⠟⢰⠋⠀⢱⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠁⠀⠙⢧⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣠⡦⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⢤⣀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡾⣿⠒⠶⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⢀⡀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠘⢣⠀⣀⣤⡞⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠠⠷⣦⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠋⠉⠆⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⢀⡀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠆⣿⡇
⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇⠀⠀⣸⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⣦⡀⢸⡇
⠀⠀⠀⠀⠀⣧⣸⣿⣿⡇⠀⠀⠸⣤⣀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡁⣼⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠈⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡀⠈⠁⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⡾⠋⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠟⠻⢣⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⢧⣀⣀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠗⣸⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣷⡀⠀⠀⠉⠉⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡼⣷⡀⠀⢺⣀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣠⠆⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡹⣿⡄⠀⢻⡁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⢲⡄⠠⠏⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⢷⡜⢿⣄⠀⠁⠀⠀⠀⠀⣿⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢷⡀⠀⡻⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⣆⠙⢆⠀⠀⢀⡀⠤⢿⡼⠋⠤⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠀⠹⡆⠛⠛⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⢿⣷⣄⠀⠀⠀⠁⢴⠟⠀⠀⠀⠀⣸⠂⣲⠂⠀⣦⠄⠀⠀⠀⠚⢧⣼⡇⠀⡀⣠⠃⢀⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠻⢷⣄⠀⠀⠀⠀⠸⣆⣀⣴⠟⢠⡏⠀⢀⡟⠀⠀⠀⠀⠀⢀⠍⣿⠀⠉⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣉⠙⠢⠄⠀⠀⠀⠉⠀⠀⠾⠅⢄⣸⣇⡀⠀⠀⠀⠀⠘⠀⣀⣤⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠦⠤⠤⠤⠶⠒⠛⠋⠉⠁