Kimchi Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⡀⠄⠀⠁⠀⠀⠠⡄⡀
⠀⠀⠀⠀⠀⢀⣤⣤⢠⠈⠛⣯⠦⣔⠤⡀⠀⠀⠈⠀⠀⠀⠀⢀⠠⣒⠽⠋⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣴⣿⣿⣏⡀⠢⠄⠀⠱⠪⣛⢦⣆⠀⠀⠀⢀⣤⢞⡵⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⣙⢁⠚⠡⢩⣶⣶⣾⣿⣿⣴⡶⠄⣈⠒⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠈⠣⠈⠁⠛⠛⠛⠛⠉⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠸⠀⠂⠨⠀⠃⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠃⠀⠀⠀⠀⠃⠀⠅⠀⠀⡀⠀⠀⠴⠞⠋
⠀⠀⠀⠀⠀⠀⡀⠄⠄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣒⡶⣤⣄
⠀⠀⠀⠀⠀⣤⣁⠀⣾⠁⠀⠀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⣺⡛⣿⣫⡟
⠀⠀⠀⠀⠀⠙⠻⣎⣁⣘⠆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⢍⣩⣭⣟⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢧⡖⡚⢹⡉⡉⢡⣀⡵⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠚⠉⠉⠛⠍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⡄⠀⣀⡀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⢀⡤⠀⠈⠃⠈⠀⠈⠈⠢⠉⠘⠂⠰⠈⠂⠰⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠
⠀⠀⠀⠘⡙⠒⠷⠄⠢⠀⠤⢤⡄⢄⠀⠲⣄⡟⠀⠁⡀⠐⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄
⠀⠀⠀⠀⢀⣲⡶⠟⠛⠦⠄⠘⠿⠖⠷⣄⣈⣹⣆⣀⡏⠀⠄⠑⠄⠰⢤⠀⢸⡀⠀⣶⠀⠠⡤⠀⠀⢄
⠀⠀⠀⢸⡋⠀⠀⠀⠠⠤⠶⠶⡿⠷⢶⣦⣖⣉⠛⠛⠳⠄⠡⢼⣄⠀⠀⠐⢠⡽⡛⠻⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠘⠾⣇⠻⡔⠀⠀⠀⠈⠀⠂⠀⠬⠉⣋⠛⣐⡂⠄⠀⠀⠀⠀⠉⠃⠁⠀⠀⢁⣄⠻⢤⣀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⣇⠈⡀⢈⡀⢀⡀⠀⠠⢄⣀⣠⠤⣤⠨⠙⠢⣀⡀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠉⠙⠱⣄⢀⡀⢠
⠀⠀⠀⠀⠀⠀⠙⢶⣿⡆⠋⠐⠀⠁⠀⠉⠀⠈⠀⢶⡿⠛⣂⢶⡶⢷⣤⣤⡀⠐⠈⠄⣀⠓⠀⠀⠀⠀⠀⢀⠈⠁⠩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣙⠷⣭⣋⣉⠁⠀⠀⠀⠁⣐⣠⣴⣠⠷⠾⡁⠎⠀⠙⣹⠷⢦⣤⣤⡾⠿⠓⡉⠤⡀⠀⠀⠤⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠩⠹⡆⠀⣀⣠⣿⡿⠿⠋⠉⢀⣠⡢⠞⠓⠉⣀⠐⠞⠋⠁⠀⢀⣡⠴⠾⠁⠀⠈⠓⠀⠀⠀⠈⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡀⣀⢿⣴⣾⡿⠟⠠⢀⡀⠔⠋⡉⣄⡠⠔⠈⠀⠋⢀⡠⠔⠂⠁⣀⡤⠶⠟⣳⣴⣄⠀⠀⠀⠂⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⠶⠟⡟⢀⡤⠞⠋⣠⠴⠊⠡⠀⠀⠀⣠⠄⠀⠈⠀⠀⠀⠈⠉⢀⣲⣟⠛⠀⠉⠛⠢⣤⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡴⢞⠋⠀⠠⠖⠉⠀⠀⠀⡠⠄⠨⠁⠀⠀⢀⠀⡀⠀⣀⣀⠞⣋⠁⠀⠀⠉⠂⢀⠀⣩⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠠⠀⠀⠀⠘⢷⣒⢰⣶⠈⠁⠀⢀⡠⠀⢀⡄⣈⣤⠖⠛⠈⠁⠤⠈⠑⠀⠀⠀⢀⣁⣼⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⢦⣤⣀⡰⣤⣽⠷⣦⣠⠔⠊⢁⣠⣤⡶⠄⠉⠁⠀⠀⠀⠀⠀⠀⢠⣜⣿⣶⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⢮⣿⣷⣿⣿⣃⣈⡁⠀⣀⣠⣦⣤⣀⣰⣾⣿⣿⠿⠿⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠛⠿⠿⠟⠿⠿⠛⠻⠿⠛⠁

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣄⠄⡤⠄⠠⠀⢠⠀⣀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠋⠂⠑⠂⠈⠃⠘⠀⠋⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠉⠒⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠒⠤⠄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣄⣀⠈⠙⠆
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⢀⣀⠀⠈⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠦
⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠑⡌⠀⠀⠀⠀⠀⠌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠱⢤⡀⠤⠄⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠢⣠⣤⣤⡹⣍⡂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⣀⠈⡱⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⢻⡉⢓⣯⠀⠀⠀⠀⠀⠀⠈⠙⠃⡀⠀⠀⠙⢇⡄⠐⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠈
⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠛⠓⠀⠆⠀⠀⠀⠀⠁⠀⠀⡄⢸⡆
⠀⠁⠀⠀⠀⡀⢒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠐⠂⠡⣁⠀⡙⠚⠀⠀⠀⠀⡀⢀⠒⠰⣺⣿⡇
⠀⡇⠀⠂⠘⡁⠀⠀⠤⢈⡃⡄⠀⠀⠀⠀⠀⠀⠀⠴⡶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠘⠒⠁⠀⠀⠀⠀⠀⠀⠚⠷⠴⠟⠋⠀⠀⠀⠀⡀
⠀⠁⠀⡀⢄⠄⠒⡠⠇⠘⠡⡠⠀⠀⠀⠀⠀⣴⣷⠼⣿⣮⣶⠌⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨
⠀⠄⠀⠠⡄⠀⡖⠠⠇⠉⠴⠀⠀⠀⠀⠀⠀⠽⣿⣶⠻⢸⡿⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠤⠔⠀⢤⠀⠀⠀⠀⢀⡀⠈⠁
⣀⡆⠀⠀⠀⠑⠈⠑⠂⠉⠀⠀⠀⢸⠇⠀⠀⠛⣏⣳⡅⢼⣿⣿⠟⠀⠀⠀⠀⠠⣖⢀⠀⠀⠀⠀⢢⠀⠹⣤⡴⠖⢆⠀⠀⠀⠀⣀⡀⠁⠀⣠
⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠉⠀⠓⠉⠀⠀⠀⠀⠀⠀⠸⠯⣿⠇⠀⠀⠀⠀⢾⣴⣧⣀⢠⡟⠀⠀⠀⢀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⣄⡀⣀⢠⠀⣀⣠⡄⣀⣠⢠
⠀⠀⠀⠀⢠⣿⡁⡏⣿⣾⡇⣇⣅⡿⡏⡿
⠀⠀⠀⠀⠈⠀⠁⠁⠁⠈⠀⠉⠀⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⠀⠒⠀⠐⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⡠⠠⢠⡄⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡠⡴⠂⠀⠀⠀⡂⠀⠀⠁⠂⢤⠀⣀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠘⢇⡀⡁⠀⢈⣁⠠⠀⡰⢃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⢱⣶⣄⡼⠯⠤⠾⠁⢼⡄⠀⠀⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠤⠚⣩⣿⠄⠀⠀⠀⠀⠐⢀⣱⠀⢰⡍⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣄⡐⠆⠀⠈⠁⠜⢦⣀⣀⠀⢶⣴⣦⣿⣀⣾⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠋⢸⠃⠀⠀⠀⠀⠟⠛⣯⣱⡦⠟⠛⠀⠈⠛⢠⡆⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡞⠀⣀⡖⠀⠀⣀⣽⠏⠁⠀⠀⠀⠀⠀⣰⢿⣜⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠸⡟⠗⠋⠉⣹⢿⡆⠀⠀⠄⣐⠀⢀⠈⠻⡇⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣛⠻⣦⣐⣃⠬⣿⣶⣔⣀⠀⠉⠲⢾⡿⠁⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣮⠍⠭⢹⣃⡏⠻⠛⠐⠛⠉⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⣒⣋⡉⠁⠀⠐⠊⠉⠩⠄⠒⠒⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡵⠶⣉⣄⣀⣀⣌⡉⠒⢤⡀⠀⠀⠀⠀⠋⠉⠉⠀⡀⠀⡨⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣹⡷⡾⠙⣉⣥⣤⣤⣀⠙⢷⣄⠙⢀⠀⠀⠀⠒⠂⠉⠁⠀⠀⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣌⣻⣿⣿⠟⢋⣁⣀⡈⠘⢷⣄⠹⣷⡈⢇⠀⠀⠠⠒⠂⠉⣉⠠⠤⢀⢂⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⣱⡿⣷⣶⣿⣿⣷⣷⣾⢷⣤⣿⣦⠈⣷⣌⠀⢠⡒⢪⣉⡵⣤⣞⠶⣽⣗⣇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠂⣿⣾⣿⠟⣻⡿⠟⠿⣿⡇⢻⣿⣿⣿⣾⣿⣸⣦⡿⢿⣟⣿⡿⢟⣚⣩⣭⠶⠌⡶⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢸⠇⣶⡿⢻⣿⢣⣿⣦⣶⣶⣌⢿⡌⣿⡿⣷⢿⣯⣿⣲⣿⣯⡵⠾⠛⠛⠈⠁⠀⠀⠀⢹⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢼⠀⣿⡇⣸⡟⣾⣿⢻⣟⣿⣿⣾⣷⠘⣿⣿⡇⠱⣻⠈⠃⠀⠀⣀⡀⠤⠴⠒⠃⠈⠀⢘⡄⠀⠀⠀⠙⢆
⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⢾⢀⢿⡇⣿⡃⣿⣧⣼⣿⣷⣻⣿⣿⣷⣿⡸⣿⠀⢿⠀⢸⠀⠀⢀⡀⠤⠄⠒⠀⠀⠁⢠⠛⡆⠀⠀⠀⠈⢧
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡘⠮⢼⣗⣻⣷⡟⢿⣿⣿⣿⣏⢿⡉⣿⣿⡇⣿⠀⣿⠀⢸⠀⠀⢀⣀⠤⠄⠀⠀⠀⠀⢸⠀⡅⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠉⠛⠻⠿⣽⣿⣿⣸⡇⢸⣿⡇⣾⠀⢹⠁⢸⠀⠀⣁⠠⠀⢀⣀⡤⠶⠚⢉⠜⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠿⠧⣿⣀⣾⠀⠈⢀⣨⠤⠖⠚⠉⢀⣀⠤⠚⠁⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⠤⠄⣀⣀⣀⣀⠀⢀⣈⣉⣙⣉⠩⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢢⠀⠀⠰⠤⢦⣀⡄⠄⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣂⢠⡴⠓⠀⠖⠀⠉⡀⠓⠀⢇⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣔⠻⠻⠏⢀⣢⢤⠖⢒⠛⠁⠀⠀⠀⠘⠆⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⠊⢱⣠⡠⠚⠉⠀⠀⠀⡀⣀⢠⣶⠭⢠⠀⢬⠦⠀⠀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠂⢀⡬⢀⢀⠞⠡⢤⠚⡱⠷⠂⠓⣲⠦⡀⣐⠛⠁⣠⠔⠒⠂⠀⠠⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠰⢤⠂⠤⠧⠀⠐⠳⢏⣐⠀⠐⠋⠃⠀⠉⢀⡠⠎⠁⠀⠀⠀⠀⢠⠟⠃
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡤⡔⠢⢲⠋⠀⠀⠀⢀⣀⠩⠴⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠠⠉⠉⣅⠠⠔⣶⣖⠒⠉⠉⠀⠀⠀⠘⢦⠀⠺⠦⡀⠀⠀⠀⢀⠔⡻⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠣⡀⠓⠡⠐⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠙⠒⢀⡌⠂⠤⠀⠀⡔⠀⠈⢄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠲⠦⢄⡂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠚⠁⣀⣀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠙⢦⢀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠹⠛⡀⡀⣸⣇⠀⣀⣨⢷⡄⣀⠀⠒⣀⠴⠶⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⡐⣒⡒⠭⠥⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⠔⢻⠏
⠀⠀⠀⢀⣀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣿⣷⡄⠂⠁⢀⠁
⠀⠀⠀⢸⠀⠈⢉⠀⠀⢀⡠⠀⣤⠠⠦⠼⠖⣲⡆⢀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠧⠄⠐⠁⠀⠀⠀⠀⢠⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠀⣸⣀⣀⡈⠀⢒⠰⡸⢀⠈⣦⠀⠀⠀⠀⠠⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠑⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢅⡠⠀⠀⠉⢹⡿⣡⣋⣈⣿⣻⡆⠀⠀⢠⣾⠿⠿⣟⣻⣿⠿⠋⠀⢀⣿⢄⢄⢶⡂
⠀⠀⠀⠀⠀⣤⢦⣀⠀⠀⠀⠻⣟⠍⣂⣌⣀⣉⢘⣉⢭⡿⠶⣁⣢⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡞⢿⣼⡏⠸⠀⡀⡀
⠀⠀⢠⣤⣿⣷⣡⡿⡽⠀⠀⠀⠈⠉⠈⠿⠿⠛⠿⠟⠻⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢻⣿⠃⠀⣎⠀⠄
⠀⣠⣽⣿⢛⣉⣹⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣅⢶
⠀⣾⡻⢷⣼⣿⡷⣿⣳⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠁⠋
⠀⢹⣿⣿⣿⣿⣿⣹⣯⡗⠀⠀⠀⠀⣄⠔⠉⠀⠀⠀⠀⢠⣶⣾⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⠰⠃
⠀⢸⡿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠂
⠀⠈⢷⣼⣷⠿⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠇
⠀⠀⠈⠙⠻⠯⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠰⠀⣶⠂⡈⠀⠈⠒
⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠸⡛⠛⠃⠄⠀⠀⡘⠀⠀⠀⣾⠛⠛⠉⢀⣶⠀⠀⠀⠀⠀⠀⠊⡉⢻⣿⣦
⠀⠀⢰⣿⠘⠷⡶⠀⠀⠃⠀⠀⢴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣻⣿⠀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠀⠠
⠀⠀⣶⠿⠁⣶⠉⢠⢃⠀⠀⠀⠘⢆⣠⡰⡀⠲⢀⡀⠀⠀⠀⢸⠿⠷⣿⣶⣽⡏⠀⠀⠀⠀⡔⠀⠀⠖⢓⡺⠀⢄
⠀⠀⣇⣠⡧⣴⢃⠁⠀⠀⠀⠀⢻⣼⡟⠉⢱⠄⠀⠀⠀⠀⠀⡿⠁⢹⣝⠻⣿⡇⠀⠀⠀⢐⠀⣴⠀⠀⢀⡌⠃⠤
⠀⠀⢣⠾⡇⢻⢺⠀⠀⠀⠄⠀⢀⡟⠉⠑⣄⠀⠀⠀⠀⠀⢀⡇⠀⢺⠞⢄⢸⣿⠀⠀⠀⢸⠀⠀⢀⡟⠉⣡⣰⠟⡁
⠀⠀⣟⢀⠛⠉⠀⠀⠀⠀⠀⠀⢨⣧⠀⢠⢫⢳⠀⠁⠀⠀⠸⡇⢇⠘⡄⣷⣿⣿⠀⠀⠀⠀⠀⠀⠺⠥⣶⡘⠇
⠀⠀⠋⢩⠀⣾⢀⠀⠀⠀⠀⠀⠸⡄⣱⣎⣸⢸⠀⠀⠀⠀⠀⠙⢮⣧⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠁⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⠿⠋⠩⠉⠉⠉⠉⢙⠒⠲⢴⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠆⠈⠛⢷⣾⡓⠒⡖⢀⠀⠠⠤⠀⠀⠈⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡷⠍⡏⠐⠀⠀⠀⠈⡡⠁⠕⡄⠨⢢⣶⡾⠞⠓⠊⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡋⠻⠇⠀⣄⡠⠄⠀⢐⣘⣓⣹⣀⡀⠘⠄⠸⣧⢤⣀⠀⠀⠸⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡟⠀⠀⠂⠀⣿⠚⣶⢈⣮⠳⢄⠁⣀⡁⠠⠁⠐⠀⠰⠟⠉⠉⢼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠹⣷⠀⠠⡀⢀⠿⣤⣤⡄⠟⠳⢤⠁⠈⢈⠑⠓⠁⣀⠊⠀⠀⢀⣼⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⢿⣿⣷⣜⠛⠖⠁⠁⠀⠀⠈⠀⠙⠁⠀⠁⠾⢧⣦⣄⡀⠋⠀⣀⣴⡿⣿⣿⣿⣿⠣⠙⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⣿⣿⣿⣷⣶⣄⣀⠐⠤⠄⡀⡀⠀⠎⠀⠤⢀⣀⣥⣴⣤⡾⢟⣫⣾⣿⣿⣿⡿⡂⣰⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣭⣯⣷⣿⣿⣿⣿⣿⡯⢣⡞⡹⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⡿⢿⣿⣿⣿⣿⣻⣿⣿⡿⠿⢾⢿⠿⠿⠿⠛⠛⢋⣠⣼⣿⣿⣏⠡⠄⠘⠁⠃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠑⠘⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⢿⣽⣷⣄⣤⠦⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⠳⣮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣽⠞⣫⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣾⣿⣷⣷⣿⣯⣽⣷⣶⣿⣿⣛⣯⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉




⣿⢿⠿⢿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⡀⡠⠤⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡊⠁⠐⠂⡁⠠⠀⠀⠀⠉⢠⠑⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠁⡀⡁⠂⠒⠄⢓⠒⡌⡁⠀⠰⠉⠀⠰⠄⠄⣀⡀⠀⠉⢐⠠⢀
⠀⠀⠀⠀⠀⠀⠄⠊⠀⢀⢢⠀⠁⠀⠀⡠⠂⡐⠠⠀⠀⠈⠁⠀⠀⠀⠀⠘⠀⠁⠀⡠⠈⠂⠁⠢⡀
⠀⠀⠀⠀⢠⠂⠀⢀⠔⠉⠀⢀⠀⣀⠊⣠⠚⢂⡐⢂⠀⠀⠍⠀⡒⠠⠄⠀⠀⢰⠄⠅⢀⠈⠂⠀⠘⠄
⠀⠀⠀⠀⡆⠀⠠⡑⠁⠀⠎⠁⢀⠂⣰⡲⢄⠀⠐⠀⠀⠀⡀⡐⠀⣼⠒⠦⠠⠚⠉⡀⠀⢸⡅⣒⡲⢸
⠀⠀⠀⠀⠡⡀⠂⡍⠀⢄⢡⡐⠂⠀⠉⠀⡑⠕⢤⢀⠀⠈⠈⢀⠜⠁⢠⠀⠀⠀⠀⢂⠀⢨⠄⡀⠁⠌
⠀⠀⠀⠀⠀⠑⠳⡠⠤⠠⢊⡄⢉⠠⠶⠢⠭⠀⠤⠇⠈⠀⠂⢉⡱⠄⢄⠀⠱⠄⠥⢂⣄⢊⣾⠢⠊
⠀⠀⠀⠀⠀⠀⠀⠈⢚⠢⠄⣀⠈⠢⣀⢁⠤⠄⡠⠥⠀⠀⠰⠂⠁⠐⠴⠀⠡⠒⣢⠫⠅⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⠁⠀⠀⠂⠀⠐⠀⠄⠀⠒⠐⠂⠂⠀⠉⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠒⠒⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠠⡐⡄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⢴⣶⠛⣉⢿⣦⢑⠦⡘⢲⡀⠀⠺⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢉⣤⠖⢶⣶⣶⠤⡀⡉⢆⠀⠝⠘⢧⠀⠀⠈⢀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡋⣵⣓⣲⣾⠟⠈⠁⠀⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⠏⠈⡽⠟⣓⣃⠂⠡⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢢
⠀⠀⠀⠀⣀⡠⠤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⣜⠛⣲⣛⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠅
⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠐⠄⣠⠀⡀⠐⠆
⠀⠀⠘⣷⣸⠙⠁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢨⠟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⠉⠁
⠀⠀⠀⠾⠀⠀⠀⢜⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠈⠛⠲⠂
⠀⠀⠀⡙⠁⣀⠠⠈⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠮⠁⣴⡎⠀⠘
⠀⠀⠀⠓⠀⠜⣦⣤⠠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠲⠐⠶⠦⢤⣼⣇⢠⡯⣤⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡡⠒⠉⢀⠀⢀⢀⡀⢨⢿⢉⠼⡆⢸⢰⡆⠀⠀⠀⠀⠀⢀⡔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠉⠉⠐⠁⣴⢸⣵⡾⠀⠿⢺⡶⣆⠀⠀⠀⡠⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⡬⠤⠀⢀⣾⣿⡾⢾⡷⠒⠀⠈⢸⡆⢳⠀⢀⠄⠀⠀⠤⠠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠀⠰⠒⠉⠉⠦⠀⢨⡯⠽⠽⠓⢛⣫⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣀⣠⡤⢇⣈⢡⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⣬⣻⣶⣦⣤⣄⠀⠀⠐⠀⠀⠀⠀⠀⠾⠊⠀⠀⠀⠐⠀⢀⣴⡾⠛⠛⠉⠁⠟⠁⢰⡀⠀⠻⠃
⠀⠘⢺⣝⣻⠀⠀⢈⡽⠛⣷⣄⣤⢐⡀⠀⢀⠀⠀⠀⡤⠀⠈⠘⠛⠻⠿⠿⡿⠀⢀⣠⣴⣶⣦⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠁⠀⠀⡀⣀⣄⠀⠀⠀⢩⣷⡄
⠀⠀⠱⠙⠶⡿⠾⠿⢷⣾⠿⣷⣶⡁⣰⠀⠀⢀⠀⢶⣦⠄⠀⠂⢓⠀⠀⠀⠔⠛⢿⣿⣿⣿⣿⣤⠀⠀⢐⠀⠈⡀⢀⣿⡄⠀⢠⠋⡠⠠⢨⡳⠀⠀⠁⠀⢸⡀
⠀⠀⠀⠀⡀⠀⠈⠙⠛⠛⠛⢛⡛⠋⠁⠀⠀⣩⡄⠀⡀⠐⠃⠀⠀⠀⢠⠾⣧⣭⣿⣿⣿⣿⣿⣟⠀⠀⡃⠀⢠⠂⢸⣿⠀⠀⡉⢈⠑⠂⠴⢂⣶⡃⠀⠁⣸
⠀⠀⠀⢀⠙⢦⡀⢀⣀⡀⠀⠉⠁⠀⠺⠇⠀⠈⠀⠀⠀⢰⣟⠀⠂⣠⡅⠚⣂⠐⣶⣿⣿⣿⣿⣿⡇⢰⠃⠀⡔⠀⠸⣧⡄⠀⠻⡄⡁⢲⣒⣩⡏⠀⠀⢀⣿
⠀⠀⠀⠊⠀⠠⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠰⠖⠀⡰⠆⠁⡬⡓⢩⣽⣿⠿⠛⠉⠀⠀⢱⠖⠀⠀⠀⠹⣷⣤⡂⠀⡉⠀⠁⠁⠀⠀⣲⣾⠇
⠀⠀⢀⡄⠀⠀⠀⠀⢇⠀⠀⠘⠂⠀⠂⠈⠈⠀⠀⠀⠀⠒⠦⠀⣄⠀⠈⠁⠀⠓⠐⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⣠⡄⠀⠈⠛⢿⣾⣃⢸⣧⣤⣷⠾⠛⠁
⠀⠀⠀⠏⠀⠈⠀⢀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣁⠄⠉⡉⠀⠀⢈⠁⣶⢉⣈⣇⠀⢃⠀⢲⡀⠗⠀⠈⠁⣀⠀⣀⣄⢈⣉⠉⠉⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡀⢀⡈⠁⢀⣶⢂⠰⠀⠀⠀⠀⡀⠀⠀⠀⢠⡉⢠⠀⠇⢈⡄⢀⠐⣋⠨⠄⣿⠠⢘⠁⣂⠀⡇⠀⠀⢸⡯⠀⠀⠀⠀⠉⠁⠲⣄⠀⠠⡀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠉⠁⣀⣤⣤⣄⠀⠀⠀⠀⢀⣬⣀⡐⠁⠀⠉⠀⠘⠀⠉⠀⠀⠉⠁⠚⠀⠉⠈⠁⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⢶⠋⡀⠘⠇⠀⠒
⠀⠀⠀⠣⠤⠤⠖⠀⠀⠀⠀⢐⣿⣿⣿⡟⠂⠘⠟⠀⠀⠀⠈⠋⠂⡄⡇⠀⠒⠀⢸⡅⠀⠀⠀⠚⠃⢈⡱⠂⠀⢀⡀⠐⠂⢀⣀⡀⠀⠀⠀⢤⣀⢈⡗⠀⠘⡃
⠀⠀⠀⠀⠀⠒⠀⣴⡶⠀⠀⠈⠈⠉⢿⡀⠀⢀⠀⠀⢠⡄⠀⠀⡤⠀⠃⠀⠰⡄⢨⡁⢰⠐⢋⢱⠋⠀⠙⢆⠀⠀⠀⠈⠀⠂⠤⠀⠀⠀⠉⠂⠀⠈⠵⠠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡇⠀⢤⠃⠀⠈⠁⣠⠴⠃⠰⠇⠓⠃⠄⠨⠀⠸⠇⠉⠨⠏⠉⠋⠈⠀⠀⠈⠒⠀⠀⠀⠀⠀⢀⡉⡁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⡂⠈⠁⣀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠓⠀⠉⠉⠉⠉⠁⠀⠀⣄⠀⠀⠀⡀
⠀⠀⠀⣠⣄⣤⣤⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠀⠀⣀⣄⣠⣦⣄⠀⠀⠀⢠⡶⡀⠀⠀⡠⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠈⠀⠀⠄
⠀⠀⣞⠛⡿⠻⡅⠀⣴⣶⣶⡌⠙⠛⢶⣤⡄⠈⢂⠘⣟⣴⣼⠧⣾⠟⢖⣌⣈⡁⠀⠀⣰⠗⠀⡀⠤⠀⠈⢁⢢⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠰⣤⡀
⠀⠀⢻⡿⠤⠥⠈⣛⠛⢤⣁⠄⠒⠂⣠⠈⠣⠀⠉⠑⠀⠻⣕⡿⢛⠋⡛⡍⣂⣄⠂⠐⡿⠁⠀⢀⡴⠄⠄⣑⠀⣐⣾⡇⠐⢾⣂⡶⠁⠂⢀⠀⠐⠀⠚⠀⠟⡏
⠀⠀⠀⠑⢄⠀⠀⠈⠃⠘⠓⠀⠡⠰⣼⡿⠃⠀⢀⠀⠀⠁⠈⠳⠒⠿⢃⠏⠉⠡⢠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠙⢸⠗⠀⠘⠏⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠱⠦⠤⡀⣀⣀⡀⠀⠐⠉⠀⠀⠈⣀⡀⠀⠀⠀⣠⡄⢀⣤⠅⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⠐⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⠐⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⣰⠚⠓⠢⠀⠀⡄⠀⠀⠀⢀⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣤⢠⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣽⢳⡀
⠀⠀⠀⠀⠀⠀⣠⣅⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣇⠻⡄⠀⠀⣀
⠀⠂⠑⠀⠀⠀⠀⠙⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⢻⡄⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡒⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠐⠄⠀⡀⠀⠀⠀⡀⢀⠀⠀⢌⠿⣇⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠖⠂⠀⠀⠀⢀⣴⡆⠀⠀⠈⢂⠑⢀⠀⠙⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠆⠉⠉⡷⢀⣀⡀⠀⠀⠀⠀⣰⡾⠻⡉⠂⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⣠⠀⠀⠈⠈⠀⠀⠀⠀⠐⠀⠈⠀⠀⣰⡿⠛⠙⣇⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⣠⠊⠁⠁⠟⢢⠀⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡃⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠋⠀⠀⠀⠀⢀⠀⠀⢦
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡿⠁⠂⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠓
⠀⠀⠀⠀⡘⡧⠀⠀⠀⠀⠀⠃⠀⠀⠜⢠⠀⢐⡀⠀⠀⠠⡀⢨⣥⡟⠀⠀⠈⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢰⠌⠀⢀⠈⠀⠁⠀⠀⠁⠀⠀⠀⠉⠐⠿⣄⡄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢂⠀⠀⠈⠳⢠⣀⡀
⠀⠀⠠⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠤⠄⠁⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⡀⠀⠀⠈⢇⡀⠀⠀⠀⠙⠷⡀
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠦⡀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠀⠀⠠⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠃⠀⠀⠀⠀⠀⠐⡄⠀⠐⡄⠀⠀⠀⠀⠁⢄⠑⠢⣀⢀⡸
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⠤⠀⡉⠀⠀⠀⠀⠄⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠖⠠⣀⠊⠀⡄⠀⠀⠀⠀⢀⡞⠁⠀⠉⡇⠀⠐⠈⠁⢢
⠀⠀⠢⠄⠠⠀⢰⡶⠼⠦⠤⠤⠤⠴⠷⠤⡀⠀⠀⠀⠀⠀⠀⠈⡠⠒⣿⣯⠉⠑⢎⠂⢄⠀⠀⠇⡀⠀⠀⢠⣏⣀⣀⠀⠀⡇⠐⠁⠀⠂⠆⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢴⣂⠂⠀⠀⠀⠀⠀⠀⠐⠐⢈⣢⠀⠀⢀⡲⣀⢰⣁⠀⣨⠓⢤⣀⣤⡀⠀⠈⠒⠰⠜⢒⡤⠯⠤⠭⣍⡛⢶⡇⠄⠠⠂⠒⢀⠀⠠⠂⠁
⠀⠀⢀⠀⠀⠀⢸⠨⡧⢩⡍⣭⢩⡅⢬⠅⠟⠀⠄⠀⠀⠘⠁⠸⣟⠉⠅⠀⠀⠀⣻⠣⡄⠀⠀⢀⣠⣾⠖⠒⡒⠒⠦⣌⠻⡅
⠀⠀⠀⠀⢀⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⡀⠀⢉⣄⠀⣎⣙⣦⣀⡀⣀⣴⠧⠰⠃⠀⠀⠉⠀⢸⡀⠈⠁⠀⠂⢈⣿⣏⠀⣂⠇⠀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣤⣀⠀⠀⢀⣄⡀⢸⠀⠈⠚⠀⢈⠔⠻⡝⣄⣸⠏⠉⠢⡀⠀⠀⢀⡠⣤⢹⡦⣤⢤⠴⠋⠉⡈⠁⢀⣄⡀⠀⡠⠠⠃⠈
⠀⠀⠀⠀⠤⠼⠿⠿⠄⠀⣿⣿⣿⠄⠀⠾⠿⠧⠼⠀⠀⠀⠀⡎⠀⡄⠈⢮⣻⣀⣢⣤⣱⠀⡰⠁⡀⢰⢨⢿⠟⡲⡀⠀⠘⠖⠀⠐⠂⠉⠋⠒⠤⠬⠆
⠀⢠⢤⡄⠀⠤⠄⠤⠤⠤⡄⠀⠀⠀⡀⠀⠔⠐⠀⠀⠀⠀⠀⠑⠚⠒⠤⠄⢿⡠⢿⠷⠇⠀⠓⠮⣀⢸⣐⡶⠋⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⢀
⠀⠈⡎⡇⠰⠀⣀⡀⠠⠀⡇⠀⠀⠀⠁⠀⢂⡠⠀⠀⠀⣤⠀⢀⠄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠧⠤⠆⠐⠂⢠⣘⠐⠀⠀⠃⢘⡄⠹
⠀⠀⢡⢡⠀⣮⣤⣿⠄⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⢷⡆⠰⢃⡇⢔⡰⡛⠖⠖⡠⢾⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠠⠈⡲⠒⠒⢶⠉⡇⠀⠥
⠀⠀⠸⡈⡄⠌⠛⠋⠐⠂⡇⠀⠀⠀⢠⠖⣂⡐⠦⡀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⢇⠘⠋⣠⠛⡇⣠⠂
⠀⠀⠀⡇⢡⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⡀⠿⠟⢀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠓⠂⡀⠀⠈⢸⣣⠈⠉⠉⠉⢠⡇
⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⣈⡛⠂⠉⠀⢰⡟⠿⣻⠟⡻⣿⠛⢿⢟⣛⣿⢟⡻⣿⣷⠀⠀⠋⠉⠉⠉⠃⠀⢠⠚⠉⡏⢹⠹⢩⠍⣿⡆
⠀⠀⠀⢸⢘⡀⠀⠀⠀⠀⡇⠀⠀⠀⣰⣿⠇⠀⠀⠀⢿⡇⡌⢿⠸⠗⣰⢈⢾⡈⣭⣿⢨⣅⢸⣿⠀⢇⠁⠀⠀⠀⠀⠁⠘⠋⡃⠓⠚⠒⠚⠓⠉⠃
⠀⠀⠀⠀⡀⡧⠒⠢⠤⠒⠃⠀⢠⡾⣿⠏⠀⠀⠀⠀⠈⠙⠛⠾⠷⠾⢿⠿⠷⠷⠶⠿⠟⠛⠛⠋⠀⠾⡀⠀⠀⢀⡠⠈⠀⠴⠀⠀⣰⣰⠀⢀⣡⠄
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⣠⣴⢋⣼⠋⠀⠀⠀⠄⢒⠀⠀⠀⠀⠀⢠⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢉⣹⢀⡯⣼⡀
⠀⠀⠀⠀⡇⡇⠀⢀⡤⠚⣡⣶⠟⠁⠀⠀⣀⡤⣦⠾⣶⣶⣶⣶⣶⢿⠁⠀⠀⢮⣁⡴⠚⢦⠀⠀⠀⡠⠤⢄⣘⡆⠀⠈⠉⡇⠀⠀⣶⢼⠈⡏⢹⠅
⠀⠀⠀⠀⠉⠁⠀⠀⠐⠟⠋⠀⠀⣔⠶⢊⠜⣋⠉⠒⠚⠛⠛⠛⠉⢉⠀⠀⠀⠐⠚⢙⣶⢃⠀⡀⠀⠈⠒⠀⠷⠁⠔⡁⠄⡈⣢⡀⢘⠊⠀⣏⣹⠂
⠀⠀⡔⠉⠁⠀⣷⣦⠀⠀⠀⢀⠔⣡⠔⠁⠀⠹⣧⣀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠤⡼⠘⠤⠇⡖⠒⠿⠛⡆⢸⢸⠀⠀⠀⡇⠀⠸⠀⠘⣟⢻⠇
⠀⠀⢃⠀⠀⡀⠈⣮⢷⡀⠀⠸⠾⠶⠖⠲⠟⠿⠿⡿⠷⠶⠶⠶⠿⠿⠟⠛⠋⠀⠀⢰⠛⠋⠛⢻⣷⡀⠀⢀⡇⢸⢸⡀⠀⠀⠧⡆⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠁⠃⠀⠈⢆⠙⣄⠀⠀⠀⢀⡜⠓⣄⠜⠙⠉⠓⠢⢢⠀⠀⠀⠀⠀⠀⠀⠘⡣⠀⠀⢸⠈⠉⠉⠁⠀⢸⠀⢿⡭⡿⢰⠀⠀⠀⠀⡆
⠀⠀⠀⣀⣄⠀⠌⠢⠈⢣⡈⢧⡀⡠⠚⠀⠀⠘⢇⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠾⠃⠀⠀⠀⠁⠚⠛⠓⠈⠀⠀⠀⠀⠁
⠀⠀⡌⠄⠀⢨⠌⢂⢑⡄⠛⠀⠀⠈⠲⠤⣄⣀⡜⠓⡴⠿⠒⠉⠉⢿⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣷⣴⠆
⠀⠀⡆⡀⠢⠌⠀⠀⠛⠉⠠⢤⣀⡤⠒⠉⠉⠀⡱⢲⡓⠦⣤⣀⣀⣸⠔⠀⢲⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣀⣚⣿⣿⣴⡆
⠀⠀⠇⠣⡤⠆⠃⠀⠀⠐⠀⢀⠈⠑⢆⠀⢀⡾⠁⠀⣧⠀⠀⠙⣦⠈⣀⠤⠴⣁⡚⠀⠉⡇⠀⠀⠀⢀⣦⣶⣦⣄⡀⠘⣿⣿⣿⣿⣿⠇⣀⣤⣤⡀⡀
⠀⠀⠆⠤⠀⢼⡆⠀⠀⠀⠀⢀⡀⠈⠻⠒⠁⠷⠤⢄⡊⠣⠤⠊⠀⠐⡄⢀⡞⠘⡎⠙⣂⠁⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠉⠉⠉⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠄⠈⠀⠘⠲⠴⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠁⠊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠂⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⠀⣼⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⣲⣤⢼⠇⠀⠀⠑⢆⠀⠀⠀⠈⠁⠀⠄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢐⠄⠘⢄⠴⠦⠤⠂⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠘⠓⠁⠁⠉⠀⠀⠀⠀⠀⠘⡄⠀⠀⡀⠀⠀⠀⡙⠢⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣆⡠⠇⢀⣀⡄⠀⢀⣤⣶⣿⣿⣿⣶⣄⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠢⣀⠀⠲⠦⣚⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣾⢟⠙⠛⢉⡛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⠈⠂⡀⢰⠀⠉⠲⡄⠐⠨⠭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠠⠀⠀⠀⠀⠉⠀⠄⠀⠀⠆⠈⣛⡷⠀⠀⠀⠀⠀⠀⡐⠀⠈⠉⠀⠀⠀⣈⣢⠄⠀⠀⠀⠘⠢⣣⣈⠢⣀⢑⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠘⣤⠔⠛⢆⠀⠀⠘⢄⠀⠐⠀⢀⣴⣿⡇⠀⠀⠀⣄⠀⠆⠐⠀⢐⣀⠈⠥⠄⠀⠒⢀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠑⠦⣀⡀⣹⠉⠹⠉⡀⣻⣷⡄⠀⠀⠈⠀⠈⢁⣈⠀⠄⠀⠀⠐⠂⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⡰⢋⠔⠀⠀⠉⢿⣿⡆⠀⠀⠀⠁⠀⠀⡂⠀⠈⠁⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣶⠓⠂⠀⠠⠀⠈⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⡀⠄⣠⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡌⡄⠀⠁⠂⡠⢆⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣨⣥⣶⣿⠇⠀⡆
⠀⠀⠀⠀⢀⠤⠀⠀⢄⡀⠀⠀⠀⠀⠀⢇⡇⠀⠒⢀⡓⢄⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁
⠀⠀⠀⠔⠀⠀⠀⠀⠀⢱⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠙⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⣠⡶⠆⠀⢐⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠛⠖⠈⣑⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠠⠢⠝⠃⠲⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⣠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢄⠀⠀⠀⠀⡆⡀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⠠⠔⠘⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠑⠒⠒⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢓⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢄⠀⠀⠰⣉⠁⢀⠌⢀⠂⢀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠴⡫⠞⠀⠈⠁⢈⢀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢆⣀⠀⠀⢸⠀⠀⢀⣀⠼⠖⠋⠀⠀⠀⠀⠀⠀⡠⢞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⢴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠉⠛⠐⠶⠘⠛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢤⣪⠔⠁⠀⠀⠀⠀⠀⢀⠤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣰⣿⣶⣶⣤⣤⣤⣤⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠨⠭⠶⡤⠊⡠⠞⠹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢻⣿⣹⢿⣏⣿⢹⣿⣟⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⠉⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣀⣀⣹⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⡀⠀⣤⣄⣡⠴⠶⢶⣴⠀⠄⠀⠀⠀⠀⠀⠀⠫⠐⠃⠀⣴⣷⣿⣯⠀⢀⠔⠂⠂⢠⠁⠀⠢⡀⠀⠃⠀⡀⡤⣒⡶⢲⣦⡄⠀⠀⠀⠈
⠀⠀⢨⡟⢿⣃⣄⣠⣤⡼⢻⢧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠀⠀⠁⠀⠀⠁⢊⠁⠀⠰⣀⣹⡎⠀⠀⠈⢻⣿⣷⡆
⠀⠀⡀⠀⠈⠛⠛⠓⠘⠋⠁⠀⠀⠀⢀⠐⠏⠱⠁⢠⠀⠋⠀⠖⠀⢠⠄⠀⠀⠀⠀⠀⠀⠔⠁⠈⠄⠀⠙⠻⢧⣄⣠⣤⡾⠟⣹⠃
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠈⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⡰⠤⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠄
⠀⠈⠀⠀⣠⡄⡀⠀⠀⠀⠀⢤⠀⠱⠀⠀⠀⠀⡄⠀⢀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄⠀⠤⠠⠰⠀⡄⠀⠈
⠀⢀⠀⠈⡹⠋⠀⢀⢠⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠁⠀⠀⠀⠀⠀⠂⠤⢄
⠀⠀⠀⠉⠀⠀⠐⠸⠻⣋⠑⠀⠀⠱⡄⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⢀⠈⠠⠄⠀⠂
⠀⢦⡛⠇⠀⠁⠀⠀⢀⣀⡀⠀⣸⠀⠸⠆⠀⠀⠀⠇⢀⠠⣠⣦⣤⢴⢀⠀⠰⠠⠜⠀⠀⣴⡬⢯⠒⡆⢀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠐⠀⡀
⠀⠀⠠⠂⢠⡔⠂⠀⠛⡗⠄⠀⠀⠀⠀⠘⠀⠐⠀⢀⠡⣾⡿⣿⣽⣿⡧⠀⠘⠀⠀⢠⣧⣵⡽⠆⣎⣽⢆⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣤⢨⣃⠀⠀⢠⢊⣶⠁⠀⠀⠀⠀⠠⠂⠀⠼⢿⡏⠃⠘⣷⣿⠗⠀⠀⠀⠀⢼⣿⣿⣷⣶⣋⣻⠇⠂⠀⡔⠀⢀⢢⠀⣰⣶⣻⣷⣴
⠀⠄⠀⠨⡆⠠⣌⣉⢠⠏⡨⠄⠀⠂⠀⠠⠐⠁⠀⠀⠩⠧⣄⠤⣿⡛⠃⠀⠀⠀⠀⠘⠛⢿⣿⣿⡿⠎⠀⠀⠀⢆⠀⠁⠘⠀⠈⠙⠛⠋⡁
⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄
⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⡠⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠓⠀⠀⢀⠂⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢴⣦⣤⣤⠐⠿⣿⣤⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠢⡀⠀⠀⠙⡀⠀⠀⠀⢀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⡀⠀⠀⠐⢈⠉⠀⠀⠠⣾⣯⢨⣿⣦⣾⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠈⡄⠁⢀⠈⠀⠀⠀⠀⠀⠹⣿⠃⠰⣿⣈⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⠀⠄⠀⠀⠀⠀⠈⠉⠹⠉⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠉
⠀⠀⠀⠀⠀⢀⠄⠀⠐⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢈⡡⠀⣈⠤⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢰⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠙⢿⣧⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠋⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠒⢠⠀⣀⠀⠀⠘⠉⣭⣀⠀⠒⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠤⠤⠤⠔⠒⠄⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⡽⢾⢱⠀⠀⠀⠀⡐⣧⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠑⠤⠀⠀⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⢸⣷⣦⠀⠁⣷⠀⢰⣞⠀⠁⣬⠜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡜⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣿⣟⣽⡀⠀⠈⢆⡼⠁⠀⢀⠏⢢⡀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⡞⠀⠀⠀⠀⠀⡰⠁⣠⡟
⠀⢴⣷⠆⠀⠀⠀⠀⠀⣌⠀⠀⡠⠈⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠀⠸⡇⠀⠀⠈⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡳⢄⠀⠀⠀⢠⠛⠛⠋
⠀⠈⠁⠀⠀⠀⠀⣠⠖⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡀⠀⠀⢄⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠘⠋
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠐⠀⠒⠊⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢦⠀⡠⠀⠁⠀⢲⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠂⠀⠄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⣠⠐⠲⠀⢤⡄⢠⡗⠀⠁⠉⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠂⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣴⣦⣀⣤⡀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠂⠁⠈⠈⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠤⢀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣶⣟⠙⣫⡿⢃⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂⠀⠐⠁⠀⠱⡀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⠀⠈⣿⡿⢾⣿⣿⢿⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠒⠉⠱
⠀⠀⠀⠀⠉⠁⠸⣿⣟⢈⣽⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⢰
⠀⠀⢀⣸⡿⢿⣿⠇⠿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠨⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠿⢿⣇⣮⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⣀⣠⣾⠛⠋
⠀⠀⠀⠘⠟⠃⠈⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠋

⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢤⠤⡤⡠⣤⣤⢤⡤⣤⣴⣶⣤⠶⣶⢶⡴⣶⣔⣦⢶⣢⣴⣤⣦
⠨⣷⠛⣹⡏⢻⣷⣹⢿⡛⣏⢾⡭⢿⠓⣿⡛⡽⣏⢺⡏⡿⢹⣍⢹⣯⡿⣿⣻⢿⣻⣌⠻⣏⣻⠍⣿⢠⣗⠾⣭⠷⣭⣐⣿⡀⣻⣧⡌⠻⣆⢺⣯⡜⣿
⢁⡿⣰⣿⠌⣿⣢⣿⢋⣷⣿⠾⣷⡞⣛⣾⢔⣧⠹⣧⣸⠇⣿⣧⡯⢖⣵⢻⣧⢜⣷⣞⣷⡏⢱⣿⢩⣶⡟⠿⢩⣷⠦⠿⢃⣾⣋⣤⣿⣁⣹⣾⠛⣀⣝
⢽⣿⣧⣴⣤⣿⣿⡅⠀⠻⣿⡦⠈⣙⣿⣿⠀⢁⣾⣿⣿⡐⣿⣿⣶⣷⣄⣛⠛⣶⣶⠿⠯⢑⣻⣿⣷⣿⣿⠓⠲⣿⣧⣤⣬⡉⠙⠻⠿⣯⣥⣤⣾⠿⠟
⠀⣥⣼⣿⣿⣦⠤⠀⢺⣿⣿⣟⠂⠙⠻⠿⢶⣿⣿⣏⣉⠵⠿⣿⣿⣿⣿⣤⣾⣿⣟⠒⠀⣬⣭⣽⣿⣿⣿⣧⣤⣄⠈⠛⠛⠛⠛⠛⣣⣾⣿⣿⣿⡇
⣤⣴⣻⣿⣿⣿⣷⠈⠙⢛⣻⣿⣿⣇⣚⠛⠛⢿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⠛⠛⠛⠿⢿⣿⣿⣿⣧⡀
⠉⠉⠉⣿⣿⣿⣿⡀⠉⠉⠻⠟⠟⢉⣭⣥⣴⣿⣻⣿⣿⣧⣤⠄⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⢻⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶⠄⠀⠀⢨⣽⣷⣶⣶
⠾⠿⠿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣠⣤⣴⣾⣿⣿⣉⣿⣿⣧⣤⣤⣄⡀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠻⠿⣿⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠛⠛⣿⣿⣿⣿⣿⣃⣀⡀⠀⠀⠀⣼⡿⠋⠀⢿⣿
⠀⠀⠉⠉⠹⣿⣯⣿⣿⣯⣍⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠉⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠛⠿⠆⠉⠙⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣥⣾⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠓⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢀⣀⠤⠒⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠈⢉⡥⠖⠂⠀⠀⠀⠈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠐⠚⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠦⠄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢢⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠴⣀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣀⠠⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⢈⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠢⡱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡱⡦⠴⠞⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡌⣏⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢹⡄⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠭⠤⠁⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⣤⠤⠛⠤⣤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⡠⢄⡴⠠⣆⡠⢁⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠼⠋⠀⠀⠈⠛⠧⡤⠴⠋

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠒⠒⠂⠀⠐⠒⠒⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠁⢀⣀⡠⠤⠄⠒⠒⡒⠒⠒⠒⠢⠤⢤⣀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢀⡠⠔⠊⠁⠀⠀⢀⣀⣀⠀⠀⠄⡀⠠⡆⠀⡲⠀⣠⠍⠒⠠⣀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣠⠖⠁⠀⠀⠀⠀⠉⠒⠤⣀⢩⢉⡗⠢⢬⣵⡧⢠⡦⠈⠥⠀⠀⠀⠀⠙⠢⡀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⠊⠀⠠⠤⠤⠤⢄⣳⣄⣐⣦⠈⡀⡘⢇⠑⠖⣼⢐⡹⣧⣀⠄⠶⠋⠀⠑⢠⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠇⢸⠠⡌⡀⡀⢆⠙⠃⡧⣐⣀⡀⠀⠀⠀⡀⠀⠀⠀⡈⠣⡀
⠀⠀⠀⠀⠀⡰⠁⢀⡔⠀⠐⠹⡋⠁⠴⠄⠀⠀⠂⠂⠀⠬⢥⠤⠶⠒⠒⠆⣠⢄⡠⠀⠇⠀⠈⠁⠀⠓⡔⠀⠀⢀⠜⡀⠀⠐⠄
⠀⠀⠀⠀⡰⠁⠀⠌⠀⡠⡄⢀⡈⠒⠤⢈⣁⡀⡀⢀⠈⠀⠀⠦⠀⣁⣀⠐⠜⠀⠀⠀⠀⠀⠐⢈⠀⡀⠒⡆⠐⠿⠀⠠⠀⠀⠈⠄⠀⠄
⠀⠀⠀⢰⠃⠀⡌⡀⠄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠘⣀⠤⠖⠈⠓⠉⠁⠁⠀⠀⠀⠀⠀⠀⠘⠦⠙⠯⡛⠤⣅⠀⠙⠠⣤⠮⠆⠀⠈⠀⠈
⠀⠀⠀⡟⠀⢰⠀⠀⠀⠈⠁⠔⠒⢄⡀⠀⠁⠀⠂⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⣣⣀⠈⠻⢞⣤⠀⠀⠀⠀⠀⢠
⠀⠀⢠⠇⠀⡆⠀⠀⠑⠁⠀⠀⠀⠀⠱⣄⠢⠄⠀⠢⠀⠀⠀⠀⠀⠀⠐⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⢿⡮⢈⢳⠲⣞⣀⣳⢀⣀⠀⠀⡄⠐
⠀⠀⢸⠀⢀⡇⡄⠒⠀⠀⠀⠀⠀⡀⠄⠈⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠳⠾⡉⠒⠘⠈⡿⠲⣮⡁⠀⠇⠀⡇
⠀⠀⢸⠀⢸⠃⠰⠀⠀⠀⠀⢀⣀⡰⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠐⠃⣁⣳⢸⣁⣀⣀⠁⠀⠀⠀⡇
⠀⠀⢸⠀⠀⡇⠀⠃⢠⠔⠐⠁⢀⣠⡲⠃⠶⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠚⠛⠚⠋⠉⠁⠁⠈⠉⠃⠀⡆⠀⡇
⠀⠀⠈⡇⠀⡇⠀⠁⠠⡀⠉⠐⠈⠀⡀⠀⠀⡐⠘⣆⠀⠀⠀⠀⠀⠐⠤⢀⣀⡀⠴⠋⠀⠀⠀⠀⠀⠀⢤⣉⣀⠀⠈⠁⠀⠉⠛⠺⠀⠀⢠⠁
⠀⠀⠀⢳⠀⢸⠀⢄⠀⠈⡃⢂⠴⠊⠁⠐⡎⠈⠁⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢉⠉⠁⠲⠦⠤⠴⠃⠀⠀⡜
⠀⠀⠀⠈⡆⠀⢇⠈⠇⡀⠑⡌⠢⡤⠐⢒⢑⡀⠄⠚⣱⠈⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠒⠉⠒⠒⢎⡠⡅⠐⠂⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⡄⠈⢆⠢⡀⠀⠎⡆⠀⠘⠁⠀⣩⠉⢁⠈⠐⠺⠀⢄⠁⠀⠀⢀⡠⠠⠄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⡁⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠘⡄⠀⢣⡀⠅⢘⠤⠠⢆⠀⢀⡇⢈⢶⣀⣀⠤⠐⠊⠀⢹⠀⠄⡠⠀⠈⠀⠀⡀⠀⠀⠀⢆⠀⢃⠐⠊⠤⠉⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⢄⢨⠀⠀⢸⠓⠙⡆⠀⠀⠀⠠⡀⠀⠀⣠⠞⠐⠂⠇⠀⠀⠀⠀⠅⠀⠀⢋⠁⠀⢀⣹⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠐⣀⠀⠉⠀⢨⡇⠀⠀⣁⠀⠙⢪⠉⡉⠀⠀⡀⡘⠆⠀⠀⠀⢃⠀⠂⠊⢠⠢⠊⡠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⠀⡀⠀⠈⠂⠖⠉⡆⠀⣠⠁⠐⠀⠚⠠⠁⢠⠀⠀⠀⠈⡄⠠⠄⣚⠔⠊⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠉⠺⠄⠄⠀⠀⠀⠆⠠⠀⠑⠂⢀⣀⠠⠔⠋⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠈⠁⠐⠂⠀⠄⠤⠄⠄⠀⠐⠒⠈⠁⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⠤⠤⠤⠤⠤⠄⠒⠒⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⣻⢟⢋⠍⡀⡀⢭⢦⡰⢫⢖⠚⡓⢍⢻⡟⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⡁⠀⠀⢿⠸⣘⣪⠷⠜⣠⢃⢇⡠⣵⠔⠋⢜⡜⡙⠀⠀⠙⢻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢃⠀⠀⠀⠑⠲⠬⣭⠭⠒⠁⠀⠉⠒⠚⣶⠓⠊⠀⠀⠀⠀⢸⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⡀⠀⠀⠀⠸⣷⣦⡦⣤⣀⣤⣿⡤⣦⣄⢀⣤⣤⢀⡿⣆⣀⣀⠔⣇⢠⣼⠀⠀⢈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⢢⡀⠀⢀⠃⠻⡉⢎⠉⢹⡎⢿⣮⡛⠸⢮⣿⡟⡁⢽⡻⠑⠀⣻⠁⢸⠀⡐⠁⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⠁⠀⠀⠀⠃⠀⢸⠈⢈⣳⣁⣃⠘⡧⢤⣟⡛⠉⠉⢭⠎⠀⣾⣠⣤⣤⣏⡉⣸⠀⠁⠀⠀⠒⠼⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡁⠄⠀⠀⠀⡄⠀⠨⡞⢉⠋⠉⠉⢫⠙⢦⠵⠦⠤⠤⠶⢥⡊⢡⡁⠀⠈⡃⢈⠗⠀⡇⠀⠀⡐⠂⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣋⡠⢂⠀⠀⡰⠁⠀⠀⠈⠒⠶⠤⠴⠥⠒⠁⢀⠀⠀⠀⣄⠀⠙⠒⠷⠶⠞⠓⠁⠀⠀⠰⡀⠀⢌⠑⢾⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣁⠔⠁⡠⠊⠀⠀⠀⢀⣀⡀⠀⠀⡤⠠⠄⡠⠎⠀⠀⠀⠈⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡦⠔⠊⠀⠀⠀⡠⢊⠔⢦⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡔⠐⠢⢄⡀⠀⠀⠈⠁⢺⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡠⢊⠔⢁⠄⢺⠘⡄⠘⠦⣀⠀⡴⠙⡆⠀⠀⡖⢢⠀⠀⢀⠜⠀⢰⢐⡋⠢⣌⠑⠤⡀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠠⢊⠐⠁⡐⠁⠀⢈⣇⠱⣄⠀⠀⠉⠀⠀⠙⡒⠚⠁⠀⠉⠉⠀⠀⠀⡌⢨⠉⠑⢬⡑⠢⢌⢑⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠐⠁⠀⢠⠃⡠⠊⢡⠊⠑⢤⣙⠢⠤⠤⠤⠊⡑⠤⠀⣀⡀⠀⠤⠄⠊⡠⠻⡒⢄⠀⠑⡀⠀⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠸⡜⠀⠀⢬⡀⡰⡛⠀⢁⣿⣗⢶⣚⣹⠒⢶⡖⡶⣶⡖⠈⠙⣧⠀⠈⡆⠱⣀⠇⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠟⠸⣞⣱⡜⣡⣰⢹⣭⣹⠛⠮⠷⠚⠛⠓⠉⠀⠀⠉⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣖⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣌⡙⢗⠲⡤⡤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠔⢊⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣥⣱⣵⡀⢸⠈⠉⡃⠐⡖⠒⡖⢲⢈⠋⠸⡰⢃⠍⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣦⣧⣀⣆⢀⡇⢠⢁⣆⣂⣰⣯⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⢰⡄⠠⢀⠲⣿⣿⠿⣿⡿⣧⠆⢸⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠙⠟⠲⠶⡦⣤⣶⣦⣤⣤⣤⣤⣤⣤⣀⠀⢀⡿⢁⣰⠂⢴⠊⣴⣿⣾
⣾⡹⣧⣿⣤⣄⢤⣀⣰⠀⢸⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣦⣥⣀⣄⠀⠀⠠⠈⠈⠀⠉⠉⠙⢉⠉⠃⢀⡗⢁⡼⢀⣾⣣⣾⢟⢷⡽
⢽⣷⠹⣿⣿⣿⣿⣿⡟⠀⠸⠀⢸⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣾⣶⡞⠀⣰⢋⢠⠎⡠⡿⢋⣛⣡⣴⠟⢡
⡈⢹⣷⡙⢿⣻⣾⣿⡿⠀⠀⣴⢋⣿⠛⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢈⠅⣡⠎⣀⠞⢁⣫⣾⡟⢁⣤⢟
⣷⣬⢹⣷⡈⣿⣿⡿⢧⣤⠚⣿⠵⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡉⢻⣧⣬⣭⣭⣭⣽⠛⣁⠂⠔⠋⠐⢁⢐⣹⣶⢛⣛⡄⢀⠀⣩⣿
⣿⣷⣦⠘⢻⣌⢹⣷⡈⠀⠐⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣟⣤⣤⣿⣿⣿⡿⢋⡠⠈⠀⠀⠄⡀⣰⣴⡟⢛⣁⠔⢂⣿⠨⠞⣛⣿
⣿⣿⣿⣿⡭⠻⣧⡙⠫⡀⡰⣿⡀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⠷⣿⣷⠿⢛⡠⠔⠉⠤⢀⣀⣤⣾⡿⢻⠃⠀⠚⢁⣴⣿⠋⢻⠃⢿⣿
⣿⣭⣿⣿⣿⣷⡘⠳⣄⢤⠟⣳⠞⢀⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣞⣻⣟⣲⣚⣳⣼⣭⣿⡿⠩⡤⠔⢓⣢⡿⠿⡟⠧⢸⢉⠁⣶⣿
⣿⣿⣷⣞⣻⣿⣿⣦⡙⢷⣌⠷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⠯⢿⣿⣿⣿⣿⠿⠿⠛⡴⠀⣀⣱⣾⡿⣿⣷⢬⣿⣶⠸⣽⣦⣃⡧
⣿⣿⣿⣿⣿⣷⣿⣻⣿⣦⣝⠷⣌⡛⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠉⢹⡷⠒⢍⣠⣶⣟⠻⠇⣠⣭⣶⣿⠻⣷⣶⣿⣿⡿⠓
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠋⠁⠀⢹⣢⣷⣿⣏⣾⣿⣶⣮⠀⠛⠉⢀⠔⢉⠀⢉⠁⣰⣦
⣴⣂⠍⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⠝⢋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣠⠳⢌⣡⣴⣾⣿⣧⣹⡵⠾⡿⢋⡩⣥⠶⠁⢀⣤⣨⣅⣴⣿⣿⣿⣿
⣿⣿⣿⣷⣇⣦⣌⣛⠻⢿⣿⡵⠞⠉⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣦⣶⣾⣿⣾⣿⣿⣿⣿⣿⠿⡙⢿⣷⣨⡠⣶⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣴⣄⠄⠀⠀⢀⣠⣾⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢿⣿⠿⠛⠛⣭⡗⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿
⠻⣿⢿⣿⣿⣿⣿⣿⠿⠿⠋⠁⣀⣤⣶⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣤⠄⠀⠀⣉⢀⡒⠻⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣠⣿⣿⣿⣿⣷
⠷⠶⢼⣅⣍⣉⠙⡿⣤⣴⣶⣶⣿⣿⣿⣿⣿⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠐⠉⠀⠁⠀⢀⣠⣽⣾⣷⡘⢻⣿⣿⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⡆⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠖⠠⠀⠀⠀⠀⠀⠀⣿⣯⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⠤⡀⠀⣀⠀⠀⠀⢀⠈⠛⢿⣿⣿⣿⡏⠹⠛⢿⣿⣧⡚⠿⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣶⣤⣄⡈⠙⠛⠿⣿⡍⠀⢀⣜⠛⡿⢫⡽⠵⠀⠰⢾⣟⢻⢿⣿⣿⡿⡇⠰⠖⠚⠉⠀⠀⠀⠀⠀⠀⣿⢻⣿⣟⣿⡿⡅⠀⣼⣿⢻
⠆⠘⠓⠲⠟⠚⣿⣟⣀⣈⣉⣉⠹⣿⣿⣿⣿⣷⣶⣄⠀⠺⢇⡀⠁⠙⠐⣿⣤⡤⠴⠗⠺⠠⠤⠤⠤⠖⢀⠀⣀⣤⡶⠇⠀⠀⠀⠀⣿⠿⣿⢿⣿⢿⣇⣀⣸⣿⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠦⠘⠉⠉⣉⣽⣽⣯⣅⣀⣀⣉⣛⣋⣉⣩⣴⣶⣦⣶⣤⣶⣦⣴⣦⣤⣚⣿⣿⣿⣾⣿⠀⠀⠀⠀⣿⣤⣿⣿⣿⠙⠋⠉⣩⣯⣹
⠛⠋⠙⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠿⣿⣿⠟⠿⡿⠹⢿⣿⣿⡿⠛⣿⠉⠛⣿⣿⠋⠻⠙⣿⣿⣽⣿⣿⣟⠀⠀⠀⠀⣿⢀⣿⣀⡏⠀⢰⢿⣿⣿⣿
⠀⣦⣤⣄⢄⣐⣂⣸⡿⠟⣿⣿⠿⠽⣻⣿⡿⠀⠀⢐⡆⠽⣶⣿⣾⣾⣇⡻⠀⠀⠁⠀⠀⣿⣿⠀⠐⠶⠶⡗⠶⣿⣿⣿⠀⠀⠀⠀⣏⠉⣿⢻⣷⡄⢸⠀⣿⣿⣼
⣿⣿⣿⠋⠸⣟⣲⣽⠷⠿⣿⣟⠓⢀⣻⣿⡏⠀⢀⡨⠄⢶⢴⠻⠞⠾⠿⣶⣄⠀⠀⠀⠀⠇⠀⠀⠘⠶⠶⡷⠶⣾⣿⣧⠀⠀⠀⠀⡷⠶⠿⠿⢿⡇⢸⣌⣿⣇⣹
⢿⣿⣷⡀⣿⣿⣿⣿⠀⠀⣿⣶⠐⠀⢸⣋⡇⠀⢸⣇⠀⠉⠀⠀⠀⠀⠀⠀⠙⠻⢷⣄⣀⡀⡀⠀⠘⠛⠓⠗⠰⣾⣽⡏⠀⠀⠀⠀⣷⣶⣦⣶⣾⡁⢰⠈⢉⠀⢸
⢸⣿⡏⠁⠈⣿⣼⣧⡀⠀⣿⡋⠀⠂⣿⠛⢓⣠⣿⡟⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣞⠀⠠⢀⠲⢮⣄⣛⠀⠁⠀⣨⣿⣧⣿⣭⣿⣿⣏⠰⣿⡶⣿
⣾⣿⣇⣴⣾⣿⠟⡿⡿⢀⣿⣉⣀⣀⣿⢀⠈⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠤⡀⠙⢲⡌⣧⠀⠀⢀⠙⠁⠀⠀⠀⠐⠛⣿⢠⣿⡇⣿
⠉⣹⡟⠋⠁⡧⣈⣿⡞⠁⣿⣿⣿⣿⣿⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⢠⣼⠀⠓⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⢈⢹⡉⣿
⢸⣿⡃⣀⣦⡟⣣⣿⣿⣶⠏⠉⠈⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⡇⢠⣾⠓⠆⠀⠀⢨⠀⠀⠀⠀⠀⠘⢻⣿⣸⣿⣧⣿
⢸⣿⡇⣿⣿⣿⣿⠿⠛⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⣹⠀⠂⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⢤⡒⠔⣒⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢠⠉⣗⢖⡀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣭⠠⣨⣧⡰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣤⠘⢺⡶⠩⣁⠟⠂⠀⢨⣀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡤⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢷⣽⠇⣈⣁⢮⠁⠽⡆⠒⢇⢌⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣌⡲⣭⡟⢛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⠟⠹⠷⠰⣗⠀⠳⠀⣤⣜⣉⣾⡛⡷⣦⣶⣾⡋⣰⡻⢋⣿⣿⣓⣊⣛⣿⡛⡚⣣⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⢀⠀⠒⠏⣤⡀⠑⣷⣤⣼⣿⣿⣷⢾⣯⣿⣿⢿⠟⠞⣻⢋⣂⣴⢟⣾⡷⠽⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢿⣮⣵⠂⢀⢮⣽⠟⠻⣽⣾⣿⣿⣿⣷⡳⢿⣇⣆⢹⡿⢛⣡⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠦⠤⢀⣀⣉⣉⣉⢉⣱⣶⣾⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁




⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠶⠧⠸⠋⠘⠁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣰⢠⡖⢢⣠⡐⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⣄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠹⠃⠰⠤⠻⠁⠀⠀⠀⠀⠀⠀⣀⣸⣿⣻⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠙⠋⠁⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠋⠛⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠦⠀⠀⠶⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣏⠀⠀⠀⠀⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⠀⠀⠀⢀⣾⠂⠻⣄
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣰⡟⠁⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢹⡄⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⠏⠀⠀⠀⠀⠀⠀⠀⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣷⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⣶⣶⠀⢀⣤⣴⣶⣶⡄⢠⣤⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢗⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣩⣶⣿⣿⣿⣿⣿⣿⣎⠉⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣹⣏⣹⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢟⠻
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢩⣽⣾⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡐⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠄⠢⣈⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠉⠙⠘⠿⠿⠛⠉⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠂
⠀⠀⠀⠤⠴⠶⠦⢴⣦⠆⠀⠐⣄⠀⠀⠊⠀⠐⣶⡦⠴⠶⠦⠦⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀
⠀⠀⠀⣶⣶⣿⣿⣾⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣷⣿⣿⣶⣶⠀⠀⣠⣶⣿⣿⣿⠿⠟⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠻⢿⣷⣦⣄
⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⣰⣿⣿⣟⣒⠂⣠⣴⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣤⣄⠐⣓⣻⣧
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⢀⡀⣴⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠱⠷⢊⠀⢀⠄⠚⡱⠆⠄⠀⠀⣠⡟⠁⠙⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⣴⣊⠈⡄⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣉⡥⠋⢀⣤⣎⠀⠳⠤⠖⠹⣷⠖⢉⣯⡄⢀⠤⠒⠢⢄⠉⠛⠁⢱⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢃⠀⡀⠀⡀⠐
⠀⠐⣢⠤⣤⣀⣀⣀⣤⣤⡄⠒⠋⡏⠐⠀⡇⠀⠀⠀⠀⣿⡀⠈⠛⠀⡎⢀⣀⣀⣸⣧⠀⠀⠸⡆⠀⠀⢠⣎⣀⣀⣀⡀⣠⡠⣄⣀⣀⣀⣀⣈⣦
⠀⢰⠁⠀⢸⠀⠀⡌⠀⠀⣱⠀⠀⠈⠓⠊⠀⢀⡀⠀⠀⠸⣇⠀⠀⠀⢣⣿⣿⣿⣿⠏⢸⣷⠀⡇⠀⠀⠀⠀⢸⠆⢸⠆⠶⠂⢾⠀⠶⠀⡆
⠀⠀⠙⢒⠁⠀⠀⠘⠒⠚⠁⠀⠀⠀⠀⠀⢢⠋⣶⠀⠀⠀⢿⠀⠐⠿⣷⢉⣛⣛⣉⠀⠤⠔⠊⠀⢠⠂⠁⠉⠉⠁⠈⠐⠛⠓⠛⠒⠉⠈⠉⠉⠉⠁⢢
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠂⠓⠅⠀⠀⠀⢨⣇⡠⠒⠉⠁⠀⠀⠀⢀⣠⣞⠀⡴⢁⡠⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⡀⣀⣀⣀⣀⡀⠱⠄
⠀⠀⠀⠠⠔⡈⠇⠀⢠⠎⠈⠸⠀⣤⡀⢀⣄⠀⡀⠀⠀⠀⠀⢾⡅⠀⠀⠀⠀⡤⢘⡀⠎⠘⠀⠀⢀⡇⢺⠀⠶⠤⡧⠴⡇⢼⠤⡧⠤⡧⠼⠆⢷⠐⡆
⠀⠀⠀⠀⠁⡀⠐⠀⡈⠁⠢⠅⠀⢇⢣⠀⠈⠀⡝⠂⠰⠄⠀⠘⠷⠀⠀⢀⠃⠰⠎⠁⣠⠁⠀⢠⠞⡉⠉⠍⡙⠿⠿⠿⠷⠿⠿⠿⠾⠿⠋⠉⠉⠉⠜⢦
⠀⠀⠀⠀⠀⠈⠐⡀⣀⠘⠁⠀⠀⠘⡎⡆⢠⠀⠁⠠⠁⠀⡐⠆⠀⠀⠀⢘⠎⣁⣐⠖⠀⠀⠀⠉⠀⠙⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠛⠛⠓⠚⠛⠛⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⡹⡈⢀⡐⢁⠔⣉⠤⠔⣛⠷⠀⠈⢀⣠⠴⠒⠒⠋⠉⠐⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⡀⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⣾⠶⣛⡭⠶⠚⠉⠀⠀⢠⠖⠉⠀⠀⣀⡀⢀⣤⡐⢒⣦⠈⢣⠀⠀⡔⠀⠒⠎⠀⠁⢈⠠⣇⠀⢠⠐
⠀⠀⠀⠀⡄⢀⠀⠠⡄⠀⠀⠀⠤⠐⠈⠈⠚⠛⡉⠀⠀⠀⠀⠀⠀⡰⢁⠀⡼⢀⣄⣣⣟⢸⣞⣁⠳⠾⠃⣸⠀⢘⠀⢒⠌⣶⠆⢁⡠⠂⠀⠢⣵⡤
⠀⠀⠀⠘⠀⢧⠃⠀⢳⢠⠂⣠⠆⠁⠧⢀⡀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠈⢧⡧⡸⣄⡽⠯⠓⠈⠁⠀⠀⢰⣃⣀⠀⠑⠠⠐⠙⡄⠘⠃⠀⠛⠀⡼⠁
⠀⠀⠀⠠⠁⠀⢀⣀⢀⣀⠀⠁⠀⢈⡆⠀⠁⠈⠀⠃⠀⠀⠀⠀⠀⠹⢄⠈⠃⠘⠂⠀⠀⠀⠀⣀⠤⠤⠤⠔⠋⠀⠀⠀⠀⢀⣘⢤⡀⠀⣠⡔
⠀⠀⠔⠁⣴⠞⠉⠀⠀⠈⠉⠑⢄⠉⡄⢠⠀⠀⠀⠀⠀⢀⡀⠀⡠⢒⠆⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠈⡀⠆⢠⠁⠌⠈⠒⢄
⠠⠠⠈⡸⢇⠀⠀⢾⣶⠞⠀⠀⢺⡀⠡⠘⠀⠀⠀⡀⢌⠋⠹⠀⢛⣁⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⡈⠧⡜⠀⢀⠀⠈⠆
⠀⠀⠀⡟⢈⡙⠲⠦⠤⠤⠶⠚⣹⡄⠂⠀⠀⠀⢲⣺⣅⠦⠱⣄⠈⠛⠁⠀⠀⠀⠀⠀⢀⠀⠑⢀⠀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⢶⣾⡎⢻⠀⠀⠘
⠀⠀⠀⣴⢀⡀⠉⠀⠁⠈⢀⠁⣤⡇⠈⡀⠀⣠⢳⢻⣤⣛⣶⠇⠀⠐⠀⠀⠀⠀⠀⠀⣠⠂⣠⡀⠀⣍⠉⢠⡀⠀⠉⠐⠒⠤⠄⠄⠀⠙⠳⠜⠟⠒⠂⠉
⠀⠀⠀⠈⠑⠢⠽⠜⠧⠽⠼⠗⠋⠀⠀⠀⠠⢰⣏⢱⡄⣬⣿⠂⠀⣀⣁⠊⠐⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢲
⠀⠀⠀⡰⣄⢀⡀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠂⠆⠪⣉⣉⠝⡌⣾⠭⠥⠚⣧⠀⠀⠀⠀⠀⠠⣤⡄⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠹⣇⢹⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢰⠁⣿⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⣧⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⢸⡇⣾⠃⠀⡴⢤⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁⠀⠘⠷⠤⠔⠃⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣿⣸⣇⡿⠀⢠⠃⠀⠳⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠒⣄⡀⠀⠀⠰⠾⠟⢁⠀⠀⠀⠀⠀⠀⢀⢔⠆⠀⠀⡇⠀⠀⠀⢠⠂⠉⠁⢢
⠀⠀⠀⡾⠿⠿⠟⢿⠀⢸⠀⠀⠀⠘⢦⡂⠀⠀⠀⠀⠀⠀⠀⢴⠒⢧⡀⣀⣠⡧⠰⡄⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⢾⠂⠀⠆⠉⠉⠁⡄⠀⠸⠶⠶⠶⢾
⠀⠀⠀⡇⡄⢠⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⣍⠉⣣⡔⢼⠉⠉⢄⠀⠀⠠⠰⠶⢀⠃⠙⢾⠂⠈⠶⠶⠶⠶⠇⠀⢸⣤⣤⣤⣼
⠀⠀⠀⣇⡇⢸⢸⡟⠀⢸⡀⠀⠀⠀⡰⣧⢤⣤⣄⠀⣀⡄⠀⠘⢴⠟⠀⠙⣷⠁⣠⡃⣺⠉⠐⡀⠀⠀⢀⠏⠀⣰⠎⠀⠈⣦⣤⣤⣤⡇⠀⠀⠣⣉⡁⠃
⠀⠀⠀⢹⣿⣾⣾⡇⠀⠀⠱⠦⡤⠞⠁⠙⠈⠁⠛⠂⠉⠃⠀⠀⠈⠋⠧⠦⡜⠯⢄⢸⡇⢑⡞⠀⠠⠆⠁⠴⠛⠁⢀⠐⠠⠐⢄⣀⠜⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣰⠖⣿⠛⣿⢽⣷⢠⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣋⣿⣴⣿⣾⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠀⠀⠀⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠒⡠⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠉⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠴⠉⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡁⣁⡂⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⢰⣟⣭⣿⣶⠢⠰⡄⢠⢠⠀⠀⠀⠀⠀⠀⢀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢃⣲⠈⠻⠿⡟⠙⠀⠀⠠⠂⠘⠀⠴⠾⠤⠼⠀⢼⡃⠛⠟⣹⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⣢⠄⠅⠙⠱⠇⠀⠀⠀⠀⠀⠀⠒⠐⠃⠀⠉⠁⠀⠉⠁⠀⠀⠐⠀⠐⠀⠂⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠂⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⢄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⠀⠀⣠⡙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠤⢤⡶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠖⠀⣸⣯⣽⢧⠀⢸⣭⣳⣿⡆⠻⠿⠛⠟⠃⢀⡀⠀⠠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡠⠂⠔⠲⢺⠳⠆⠀⢲⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠐
⠀⠀⠀⢉⠉⠛⠓⠊⠒⠀⠀⠀⠐⠓⢉⡅⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢄⠈⠁⠀⢀⠀⠀⠀⠈⠁⡤⠀⠀⠀⠀⠐⢀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⢺⠛⢣⣑⠙⡏⣓⣦
⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢰⠛⢃⡠⠫⡼⢄⢾⡧
⠀⠀⠀⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠠⠀⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠈⠀⠙⠛⠯⡵⣶⠖⠒⠉⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡰⣤⣤⡔⢢⢄⠀⠀⠀⠘⠋⠀⠀⠀⣀⠔⢠⠒⡆⠀⠐⡄⡆⠀⠀⠰⠀⠰⡄⠀⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠞⠉⠀⡀⡛⢄⡛⠀⢧⠀⠀⠀⠀⠀⠀⠀⠛⢄⠸⣀⠇⡰⢆⠁⡇⠁⢠⠉⠃⠀⠈⣤⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠈⣂⣈⣻⣶⡟⠉⢿⡧⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠔⠳⠛⠃⢱⣤⡞⣩⠩⠋⢅⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠁⠀⠀⠀⡎⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⡠⠤⠀⡃⠀⠀⠀⣅⡀⢰⠁⠃⡌⠈⢸⠈⠣⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡢⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠒⠐⠂⠉⠁⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠇⠀⠘⠤⠂⠡⠰⠸⠤⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⠀⠀⠰⡀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠤⠤⠤⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⢀⢀⠀⠀⣄⢰⠂⠀⠤⠀⢀⢀⠀⠀⢀⢀⡀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢠⡄⠀⡄⠀⠀⡀⢀⡀⠀⠑⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠈⠐⠆⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢤⠀⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠐⠖⠀⠢⢀⠀⠀⢈⠉⠠⡁
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢈⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠈⠛⢿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⠄
⠀⠀⠀⢀⣜⣀⣠⣦⣠⣈⠉⠀⠀⠀⠀⠀⣼⡇⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣩⣭⣭⣭⣭⣀⡀
⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⢤⡴⠊⠙⠳⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠳⠀⠀⠈⠀⠀⠀⠀⡠⠀⠀⠀⡄⠀⠼⠃⣶⣆⡀
⠀⠀⠐⠈⢠⣐⡂⡠⠀⠙⠂⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⠀⣸⣿⢿
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠘⠉⠁⠁⠂
⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⡄⢀
⠀⠀⠀⠈⠋⠀⠀⣀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠁⠀⡠⣶⠶⣢⡄⠀⠁⠈⠀⠀⠜⢜⠊⠥⡀
⠀⠀⠀⠀⠋⠀⠀⠈⢄⡄⠀⠀⠀⠀⠀⠀⢠⣬⡫⠙⢏⣷⡇⠀⠀⠀⠰⣿⡾⣍⡰⢞⡕⠀⠀⠀⠀⠀⠀⢀⡠⣤⢀
⠀⠀⠀⡁⠁⠀⠂⢡⠊⡀⠀⠀⠀⠀⠄⠀⠀⠸⣄⠀⣸⠟⠀⠀⠀⠀⠘⠿⣿⣿⣷⠜⠁⠀⠀⠀⠐⠀⠀⠘⠻⠿⠋
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢐⡀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡆⠀⠉⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⣆⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠸⠦⠞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠈
⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠦⠶⠆
⠀⠀⠀⠀⠂⠠⠀⣠⠈⡇⠀⠀⠉⠁⠀⠀⠰⣄⡠⠤⠆⠃⠀⠒⠴⠃⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠀⢁⡼⠁⠀⡀⠀⠀⠈⡀⢀⡦⠀⠀⠈⡅⠠⠛⣦⣇⡔⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⡥⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⠀⢀⡄⠀⠈⠁⡀⠀⠀⠀⠤⠉⠡⡅⠠⠗⠡⠠⡄⡀⠀⠀⠀⠤⠐⢈⠀⠔⠋⠀⠀⠀⠤⠞
⠀⠀⠀⢠⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⢀⣀⠄⠀⠀⠀⢢⠀⠐⠣⠇⠀⠀⠀⠒⠒⠀⠀⠨⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⡡⠀⠃⠀⡠⠈⠇⢀⠆⠀⠀⠀⠀⠀⠀⠦⠂⠁⠁⢠⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅⠐⠠⠌⡁⣀⠴⠋⠀⠀⣘⡴⠖⠘⣠⠀⠳⠄⠊⠁⣠⢔⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣤⣄⠁⠀⣀⡐⠀⠉⠉⠁⠀⠠⢂⠆⠌⠇⠀⢀⣼⠀⠀⠐⡶⠚⠁
⠀⠀⠀⠀⠐⢀⠄⠀⠀⠀⠀⢡⠀⢤⡼⠈⠛⠛⠂⠸⣿⣿⠈⠀⠀⠇⠀⠀⠉⠀⠀⠙⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠄⣀⠊⠀⣂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⡀⢤⣾⣿⡆
⠀⠀⠀⠆⡈⠇⠐⠧⠀⢠⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢠⣿⠆⠉⠉
⠀⠀⠀⠀⠀⠁⠈⠁⠀⡞⠀⠀⢬⣾⡄⠀⠀⠀⠐⠓⠁⠹⠰⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠤⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⠶⠖⠒⠒⠒⠛⠋⠉⢉⠉⠉⠉⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠴⣄⠀⠀⠀⠀⠀⠀⡰⠋⠳⢤⡀⠀⠀⠀⢠⣋⠂⠉⠓⣄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢠⣏⣀⠈⠙⢢⠀⠀⠀⢠⠗⠲⢤⡀⠘⢆⠀⠀⣸⠈⠉⠳⣄⢈⢢⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠈⠙⢦⡀⠑⡄⠀⢸⠀⠀⠀⠙⣆⠀⡇⠀⡇⠀⠀⠀⠈⡆⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢣⠀⢇⠀⢸⠀⠀⠀⠀⢸⠤⢹⠀⢷⠀⠀⠀⠀⢹⠀⡿⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⢀⡇⠄⡿⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢀⡞⠀⡸⠀⠀⡇⠀⠀⡠⢋⠀⡜⠀⠸⣄⣀⡤⠊⠂⣰⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣇⣠⠴⠋⠀⣠⠇⠀⠀⢳⠒⠋⢀⡨⠔⠁⠀⠀⢻⡀⢀⡔⠋⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠹⣄⢀⡔⠉⠁⠀⠀⠀⠀⠳⠤⠋⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠉⢀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠴⠶⠖⠒⠒⠒⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠴⣶⠒⠒⠒⠒⠒⣚⣋⣉⣉⣭⠭⠭⠭⠭⠗⠒⠒⠒⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⠖⠚⠓⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⣤⣶⣶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠖⢒⣒⣛⣫⠭⠭⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⢲⠖⢛⣏⣉⡠⠤⠤⠒⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠉⠉

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠒⠾⣄⠀⠉⠱⣄⣀⣀⡤⠤⠶⠒⠒⠚⢋⣭⣭⡉⠉⠉⠉⠛⠒⠒⡶⣦⠤⢤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣦⡀⠀⠈⠛⠙⣄⣇⠈⢧⣀⠀⠀⠀⠀⣠⡟⣽⢿⡟⢿⣿⠶⣤⠀⢰⢃⡷⣴⢳⢠⠏⣼⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠸⣀⠀⠈⣇⠀⠀⢀⠘⢾⠂⠈⠈⢧⠀⠀⢰⡟⢸⣇⣾⣳⣤⣿⠶⣾⡇⡜⣸⢠⢃⣾⢋⡜⢉⠗⡹⠊⠑⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠉⠓⠪⣕⢮⡳⢄⣦⡘⢦⡀⢿⣃⡞⢹⣿⡋⠁⢻⣄⣼⣧⣇⢇⡎⣸⢣⢞⡴⡡⢊⣤⣖⣽⠧⢚⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣒⠶⣭⡳⣌⠳⡵⡄⠉⢙⠲⣍⢿⣿⣀⡸⢘⡏⠲⣤⠏⢠⣿⡸⡸⢱⣣⢫⢎⣾⣿⣿⢟⡫⠗⠊⢁⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢡⣖⡺⠟⢮⣧⡹⡿⣄⠀⠙⢮⣇⣟⠻⣤⣾⣟⣦⣾⣖⣻⣿⣷⣷⡿⡳⣳⢟⣽⣫⡟⢉⡴⢤⢴⠋⠈⢳⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣰⢫⢮⢻⡻⣦⣀⣳⡳⣜⠪⣗⣶⣪⠽⡷⢚⠽⠀⠀⠀⠀⠀⠉⠛⢿⠿⢵⣵⣟⠵⢫⡏⠈⡹⠧⡤⢦⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣯⢨⣧⣷⣿⡛⠻⣍⠛⡻⠛⠉⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠉⠲⣍⢰⠚⢁⡴⢦⡞⠀⢸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠺⣿⡏⠳⣉⢳⠈⣷⡁⠀⠀⠀⠀⠈⠙⠒⠒⠶⠶⠶⠒⠒⠋⠁⠀⠀⠀⠀⠀⢈⡏⠐⡅⢀⠞⢓⡶⠋⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠙⠢⣌⣹⢀⡟⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⢲⣋⠭⠛⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⣀⠀⠀⠀⠈⠙⠓⠾⠧⣝⣛⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣾⣽⡿⠭⠖⠚⠉⠀⠀⠀⢀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠙⠒⠶⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⠉⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠙⠲⠤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠒⠶⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠋⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⣉⠉⠙⠛⠒⠒⠓⠛⠋⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠃⠀⠀⢀⣀⠠⠘⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣠⣄⡠⡀⠙⢿⣦⣴⡦⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⢔⡼⠞⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⣿⣿⣿⠁⠠⠀⠀⠀⠦⡕⢾⣄⠀⠀⠀⠀⢀⣠⣖⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀
⠀⠀⠀⠀⡹⠋⠽⠏⡉⣠⣤⣤⣾⣧⣭⡥⣬⡉⠲⠦⠀⠈⠱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠁
⠀⠀⠀⠀⠈⠢⡀⠂⠰⠿⠿⠿⠟⠛⡩⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠆⢐⠰⢰⠀⠄⠘⠀⠇⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠂⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠅⡇⡆⠁⠄⠁⠀⠀⢠⣤⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⢄⣀⣀
⠀⠀⠀⠀⠀⢀⠊⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⢿⠭⢿⡇
⠀⠀⠀⠀⠀⢸⢶⡤⠿⠣⢤⠀⠶⠖⠛⠀⠀⠀⠀⠀⠀⠀⢀⡤⡰⠆⠰⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⠸⢿⠿⠇
⠀⠀⠀⠀⠀⠀⡂⠽⠓⠒⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⡋⣈⡕⣾⠿⠳⢒⠒⢣⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣖⡢⠼⠦⣦⠤⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⢰⠀⡴
⠀⠀⠀⠂⠀⠀⢠⡄⠂⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⣀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠙⠛⠀⠀⡇⢸⡀⠁
⠀⠀⠤⠂⠐⠚⠄⢣⠈⠀⠁⠀⠠⠀⠀⠀⠂⠀⠀⠀⠈⠈⠁⠀⠀⠀⣀⡀⠀⠀⠁⠁⠂⠈⠀⠀⢄⠀⠀⠠⠀⠀⠠⠀⠀⠁⢲⠀⠀⡀⠶⠿⠃⠂⢸⡏⠀⢀
⠠⡆⠈⠁⠀⠀⠀⡘⠀⠀⠀⢀⠀⠀⠀⠐⠒⠀⠐⠃⠀⠀⠀⢀⡀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⡀⢀⠐⠘⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⢸⡀⣼
⠀⠁⠀⠀⣉⡁⠀⠀⠀⠀⠀⠚⠀⢤⠈⠠⠀⣀⠀⠀⠐⠀⠆⠈⠁⠀⠀⠀⠘⠂⠐⠀⠚⠀⠀⠀⠀⠀⢉⡀⢤⠈⢠⠀⠁⠀⠀⢀⠀⠀⠀⢀⡘⣥⠾⡃⢀⡤⡤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⣀⠈⠑⠀⠐⠁⠀⠰⠨⠀⡀⠀⠀⠰⠾⠀⠀⠀⠏⠀⠀⡇⠀⠀⠀⠀⠀⠍⠳⢇⣨⠦⠰⣀⡀⠈⠐⠚⣡⠍⢀⣤⣞⠙⠛⠉
⠀⢐⡢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⡠⠘⠈⠁⠁⠂⠐⠀⣤⠺⠃⣉⠘⠇⢱⢀⠀⠈⠀⠀⠀⠀⠀⠋⠁⠀⣈⠉⠀⠐⠃⠛⠋⠀⠉⠉⡅⠀⢀
⠀⢀⠿⠹⠠⠜⠁⠀⠀⠀⠐⠐⠒⠒⠆⠒⠢⠔⠂⠀⠀⠀⠀⠀⡀⠀⠀⠴⠀⠀⠥⠀⠀⢸⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠼⡂⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠀⠈
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠤⠈⠸⡇⠀⠀⠀⠀⠐⠀⣁⠁⠀⠁⠀⠀⠀⠃⠀⠀⠸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠠⠀⠀⠀⠀⡀⠂⠐⣄
⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠊⠠⢊⣬⣤⠏⠀⠀⠀⢀⠀⣋⠀⡀⠀⣶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⢁⡴⣤⣄⣤⣶⣦
⠀⠈⠉⠀⠗⢀⠥⠚⣽⠇⠀⠠⠀⠄⠀⠁⠀⠀⠀⡁⡭⠹⡿⣫⠄⠀⠀⠀⠁⠀⡥⠀⠈⠀⡟⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⢀⡟⢓⢚⠂⢒⢻⡀
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⡤⠠⠠⡴⠇⠀⠈⠀⠀⢰⠎⣤⠀⠀⠈⠀⢀⣠⠀⠖⠀⣤⡀⠁⢒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢂⡀⠀⠀⢾⠪⠬⠬⢫⠌⠥⣣
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣴⠁⠀⠅⠀⠀⠀⠋⠨⠺⡄⢀⠀⠈⠀⠀⠀⠗⠀⠈⠁⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⡗⠓⠒⠺⢷⡿
⠀⡘⠣⣦⡉⡑⠐⣆⡂⠀⠀⠀⠹⠀⠀⠀⠈⠀⠁⠀⠀⣤⣀⣄⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⠀⠀⢀⡀⢄⢤⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡃⠉⠉⠉⠉
⠀⡀⠀⠁⠒⠁⠋⠉⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⠀⠀⠠⠄⠀⡧⠀⠠⠀⢀⠄⠀⠀⠀⠀⠀⠸⠛⢇⡀⠀⠀⠀⡀⠀⠐⠊⠀⠁⣀
⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡗⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠖⠀⠘⠀⠀⠀⠀⠡⡄⠀⣡⠘⠂
⠈⢣⡇⣐⠒⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠈⠀⢀⠰⠁⠀⠀⠀⠀⠀⣏⠀⠀⠂⠠⠀⣀⡀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠠⢀⠨⡇⠀⠈
⠀⠀⠘⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⡧⠄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠈⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠶⠆⠀⠷⠀⢰⠦⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣀⣀⡀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⡐⠀⠀⠀⠀⠀⢠⡀⠀⠠⠂⠀⢈⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠚⠀⠈⠀⠀⠈⠐⠐⠒⠂⡂⠐⠛⢿⣿⡀⢘⡿⠁⣃⢀⣀⠀⢀⡃
⠀⠀⢠⢧⠀⣏⡁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⠀⠀⠀⡁⠀⠋⢲⣉⠉⢹⢁⢚⣁⣀⣀⣀⣈⣱
⠀⠀⠀⢒⡠⠇⣴⣀⣐⣀⢠⢀⡨⡀⡀⣀⢒⢀⢀⢀⢈⠨⢀⢀⢂⠴⠠⡠⡤⣄⣷⠀⠀⠀⠤⡠⢠⠋⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠁⠀⠈⠄⠀⠇⠀⢈⠀⠘
⠀⠠⠄⠄⡁⠛⠛⠗⠓⠛⠒⠂⠆⠢⠤⠤⠼⠠⠤⠤⠀⠀⠀⠒⠚⠮⠉⠙⠉⠙⡃⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠁
⠀⠀⢂⣻⠁⠎⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⣀⣌⠀⠀⠀⠀⠀⠬
⠀⢠⣠⣄⡤⡀⠀⠀⠈⣀⣰⣎⢆⡁⢀⣐⣀⣆⣂⣁⢀⣰⣀⣆⡀⡍⠡⡤⠴⢖⣓⣆⡄⠰⠀⠀⠒⠘⠀⠚⠓⠂⠠⠐⠒⠞⠀⠶⠶⢋⠀⠀⠈⠀⠀⠅
⠠⣀⠈⣊⠁⠑⠐⠀⠠⠤⠠⠬⠠⠀⠀⠄⠄⠬⠤⠤⠤⠤⠤⠀⠀⠐⣒⠂⠁⢊⠜⠁⠀⠰⠀⠀⠤⠀⠀⠠⠄⠀⠤⠀⠀⠴⠀⠘⠁⠀⠦⠀⢠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡠⠈⠀⠀⠈⠁
⠀⠀⢀⡀⠀⠂⠀⠈⠁⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⢈⢩⠀⠁⠀⠈⠉⠉⠀⠠⡀⢀⣀⡀⠀⠀⣀⠀⠀⠀⣀⠀⠀⣀⣀⠖⠀⠈⢃⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠄⠈⠀⠂⠀⠀⠁
⣀⡀⢀⣁⣀⡀⠀⣠⣄⣀⢀⢀⠀⣠⣤⣀⡀⠀⠀⣸⣤⡀⣀⢀⢀⣠⣄⡀⢀⣀⢀⡁⣁⢀⡀⠀⠁⣀⣈⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠚⠉⠓⠚⠁⠈⠓⠚⠉⠙⢦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⢤⠀⠀⢀⡄⠀⠀⠀⠀⠀⢹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠈⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠲⠶⠖⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⣚⣛⣛⣓⡒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⢊⡡⠖⠊⠉⠁⠀⠀⠈⠉⠙⠲⢬⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣡⠄⣠⠀⣌⠓⢤⣀
⠀⠀⠀⠀⠀⢀⡞⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠊⠁⠠⠃⠀⠈⠃⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⡾⢠⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣧⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⡇⢸⡀⠀⣀⠀⠀⠈⢧⠀⠀⡰⠋⠀⢀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢳⠈⢧⠀⠀⠙⠢⣄⠈⡆⣸⢁⡴⠚⠁⠀⠀⡸⢁⡟⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⢳⡈⠳⣄⠀⠀⠈⢃⡀⣷⠋⠀⠀⠀⣠⠞⣡⠞⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠻⣷⢤⣙⠲⠤⠤⢷⣧⡤⠤⠖⣋⡥⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⣤⣀⣀⣬⣥⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠤⠤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣁⣄⣀⣀⣾⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⣍⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠺⠻⠛⠾⠳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣠⣀⣰⣦⣤⣤⣤⣤⣤⣤⣇⣀⣀⣤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠨⠈⠀⠀⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣿⣾⣿⣟⣽⣽⣭⣿⣿⣿⣧⣯⣽⣽⣯⣿⣿⡷⠚⡁⢺⡀⠘⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⣄⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣠⣀⣂⣸⣀⠊⠂⡨⠀⠀⠀⠀⡔⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣤⣤⣌⣨⣡⣀⣌⣩⣃⣭⣿⣀⣸⣠⣠⣤⣤⣅⣤⣤⣽⣿⠋⠀⢸⡀⢰⡄⠀⠳⠛⡿⠄
⠀⠀⠀⠀⠐⠂⠀⣶⣤⡠⡄⠀⣹⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢉⡀⡠⣾⣄⣼⠀⢐⡀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡸⠇⢹⡃⣠⣮⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⣿⢿⡦⠤⡃⣿⡸⡷⠀⢐⢢⡿⢿
⠀⠀⠀⢀⠀⠀⡇⠞⠛⠓⠀⠯⠽⠏⠈⠌⠋⠉⠉⠿⠄⠹⠯⠤⠼⠑⠉⠱⠀⠀⠈⠇⠸⠄⠀⠘⠋⠁⠛⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠘⠓

⠀⢀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠊⡼⣴⣻⠀⠀⠰⠬⠁⠞⠆⠀⠀⠐⠖⢳⠂⠀⠀⠀⣖⣅⠀⡄⠀⠀⣀⢡⠥⠄⠀⠀⢀⢨⢅⢠⠀⠀⠀⣀⡉⣟⠀⠀⠀⠀⠋
⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⢀⣀⣀⢀⠀⠀⠀⢠⣾⣷⠂⠀⠀⠠⠦⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⢀⡰⠄⠀⠀⠀⠀⠀⡔⡤⠀⠀⠀⡠⡶⢶⡄⠀⠀⠀⢀⡴⠒⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠊⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠘⠉⠑

⠀⠐⠒⠊⠃⠀⠀⠀⠄⠠⠠⠀⠀⠀⠰⣽⡉⢢⠀⠀⢠⣄⡀⣤⡄⠀⠀⣠⣤⣤⣄⠀⠀⠀⣠⡤⡠⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⡤⢄⡀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣀⠘⠀⠀⠀⠉⠈⠉⠀⠀⠀⠛⠛⠛⠉⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠄⡀⢀
⠀⠤⠤⠤⠤⠀⠀⠈⠁⠒⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠭⠉⠂⠀⠀⠣⠁⡁⠐⠀⠀⠀⠁⠀⠂⠀⠀⠀⠐⠂⠒⠂⠀⠀⠐⠀⠒⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠐⠈⠁⠀⠀⠀⠀⢐⡥⠀⠀⠀⠀⠀⠖⠒⠂⠀⠀⠀⠊⠁⠀⠄⠀⠀⠂⠈⠀⠀⠀⠀⠀⣐⠀⠅⠀⠀⠀⠆⠂⠚⠰⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠘⠉⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣛⣿⣷⣶⣶⡄⢆⡨⣠⣤⣤⣄⡀⢀⣾⣿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡟⠸⣆⡞⠐⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⣶⣶⣿⣿⡏⠛⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠀⠀⠠⠤⢤⣼⣏⣀⢀⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠛⠛⠋⠉⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⣩⠖⠋⠀⣵⣿⣽⡆⠀⠀⠈⠁⠈⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣾⣿⣆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⣿⡿⢿⠟⠻⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠈⢿⣿⠛⢻⠿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⢾⡿⠀⠀⠀⠀⠀⠀⠙⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⢀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢼⣶⣅⠀⠀⠀⢐⣾⣦⠄⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠾⣿⢷⠂⠀⠀⠀⠀⠀⠀⠚⠹⠃⠀⠀⠀⠈⠿⠛⠂
⠀⠀⠀⠀⠀⠁⢈⣠⣴⣶⣦⠀⠀⢀⠈⠀⢁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣄⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣤⣶⣿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠄⠠⠄⠀⠀⠄⠠⠀⠀⠁⠁⠀⠀⠀⠀⣰⡄⠀⠀⢿⣿⢧⠀⠀⠀⣠⣾⣏⠀⢀⣠⣾⡿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⣿⣿⣿⣏⣀⣀⣤⣤⣤⣶⡾⠁⠀⠂⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠈⠀⠀⢀⣼⡟⠛⠈⠐⠋⠉
⠀⠀⠀⠀⠀⠻⣿⠟⢻⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣥⣤⣴⡶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠔⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠦⠂⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢿⣋⠀⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⡀⠀⠀⢀⠀⢠
⠀⠀⠈⠀⠀⠀⠀⠀⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⢄⠀⠀⠀⠀⠀⣾⣴⣦⢡⣤⣤⣶⣦⣤⢠⣵⡶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⣾⡿⠂⠀⠀⠀⡀⠉⠀⢋⣾⣄⣠⣥⣄⣠⡅⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠐⣚⢁⢛⣛⢹⢛⡛⣃
⠀⠀⠀⠀⠒⠧⢴⣁⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠜⠯⠿⠿⣿⠿⡿⠿⠿⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣼⣁⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⢍⠈⣒⣶⣤⡁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡜⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢪⠹⣝⢺⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠻⠇⣽⣠⣷⡖⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠠⠀⠀⠀⠀⣴⣾⢭⣿⣿⣴⣆
⠀⠀⠀⢤⣂⡐⢀⡀⠶⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⣤⣶⣾⣴⣶⡄⣤⡀
⠀⠀⠀⠀⠉⠙⠐⠂⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣿⡿⣿⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠤⢲⣶⣿⣇⣀⣠⡦⠐⠀⠤⢤⠀⠀⠀⠀⠀⠀⠛⠋⠻⠋⠻⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣀⣀
⠀⠀⠀⠀⡀⢰⠞⢋⢳⠀⢀⠀⠀⠳⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠂⠀⠈⠙⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡘⠖⠂⣀⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢲⡏⠠⢇⠉⠀⠀⠀⠀⠀⠀⠀⠒⢿⡖⣺⠁⡴⢿⡛⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠐⠢⢍⠉⠓⠲⣤⠀⡀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠃⠁⠐⠢⠀⠀⠀⠠⠤⣀⠀⠀⠈⠑⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢌⡑⠂⠠⠄⢀⡐⠀⠀⠀⡀⠠⠂⠂⠀⠀⠀⠹⢖⠒⠬⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠄⠠⠀⠐⠒⠒⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠈⠒⠠⣄⣀⡀⠈⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠲⠶⠖⠒⠀⠒⠒⠄⠘⠀⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠄⣀⣤⣶⣿⣿⣿⣿⡧
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠁⢠⠀⠀⠉⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⡰⠋⡸⣿⣿⣿
⠀⠀⠀⢹⣿⣽⣿⣟⣿⣿⡶⣤⡀⠀⠀⠠⠤⠀⠘⠛⣿⣶⠀⠀⠀⠀⠀⠀⠀⠘⢁⠞⠁⢹⣿⠃
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢀⡠⡶⠟⠂⠀⣿⣽⣷⡄⠀⠀⠀⠀⠀⢀⠀⢀⠄⠼⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⠙⠣⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠳⡆⠀⠀⠀⠉⠀⠀⠀⣾⣯⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠻⣿⠯⠀⠀⠰⡀⠀⠀⠀⠀⠀⢸⣿⣿⠈⠉⠛⠛⠻⣿⣷⣦⣴⣶⡾⣿⣶⣶⣶⣴
⠀⠀⠀⠀⠀⠀⠠⠉⠀⣄⠀⠀⠙⠀⠀⠀⠀⠄⢈⡿⠃⠊⠀⠀⠀⣀⠈⠀⠙⠛⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠢⠀⠀⠀⡀⠄⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠂⠉⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠰⠟⠁
⠀⠀⠀⠂⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠

⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⣴⣶⡦⢢⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡞⠳⡄⢀⠴⣆⠀⢀⡔⠉⠁⠈⠉⠉⠉⢣⡀⠀⠀⠀⣔⣩⣭⣥⣬⣭⣭⣍⣉⡒⠦⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣧⠀⠻⢁⡾⠁⠀⠸⠀⠀⠭⠭⠭⠤⠤⠖⡷⠀⠀⠀⢿⠙⠛⠛⠻⠿⠿⠿⠿⠿⠖⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⡀⡴⠋⠀⠀⠀⠀⡀⠀⣀⠀⠀⡠⡀⠀⡆⠀⠀⠀⠈⠣⣀⠀⠀⠉⠤⠄⠒⢀⡽⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⡆⠼⣤⡟⠚⣷⢣⡀⠇⠀⠀⠀⠀⠀⠈⠳⣶⡶⢾⡿⠛⠋⢀⠖⢉⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢀⣼⣛⣾⣩⣿⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡘⠀⠈⢲
⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢟⠖⣤⠤⠚⠁
⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣆⠀⠀⠀⢠⠖⠲⣀⡤⡄⠀⠀⠀⠀⠀⢀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⡙⠁
⠀⠀⠀⠀⠀⣿⣯⣽⣿⣿⣿⡄⠀⠀⢸⡀⠀⠉⡰⠃⠀⠀⠀⠀⣀⣯⣤⣥⣞⣷⠀⠀⠀⠀⠀⠀⢀⡴⠉⣀⣠⣤⣄⡀⠀⢀⠃
⠀⠀⠀⠀⠀⢿⣿⢿⣇⣿⠿⠃⠀⠀⠀⠳⣄⡞⠁⠀⠀⠀⢰⣾⣿⣿⡫⠛⠙⢿⣿⡆⠀⠀⠀⠀⠎⠀⣾⣿⡱⣣⠿⣻⡄⢸
⠀⠀⠀⠀⠀⠈⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠀⠂⠙⠉⠀⠀⠀⠀⠘⠀⠘⣿⣿⢝⣻⣷⡿⠁⡈
⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⣉⠤⠃⠀⠀⠀⠀⠀⠀⠣⡀⠈⠙⠛⠛⠋⠀⡠⠁
⠀⠀⠀⠀⢀⣀⣀⠀⡰⠑⠢⡌⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠺⢋⡻⠟⣿⡆⡄⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠠⠐⠈⠀⠀⡠⠔⢈⠆
⠀⠀⠀⠰⢡⡤⡈⢿⣿⣴⢿⡇⣿⣿⠤⠠⣤⣀⠀⠀⠀⠀⡜⠀⠃⠘⢁⣼⡏⠸⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣊⣠⠤⢞
⠀⠀⠀⡇⡊⣽⣾⢸⣿⡏⠾⢱⣿⡏⠀⢱⢸⣿⣷⠀⠀⠀⡇⢸⠀⣠⣾⡟⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡥⠊⠁⢀⠔⠉⢉⡠⠃
⠀⠀⠀⡇⠢⠵⠃⣾⣿⣇⣤⣿⣿⢡⣟⣿⢸⣿⡿⠀⠀⠀⠦⢸⣾⣟⣉⣀⣀⣠⣗⡃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢀⠠⣊⡤⠚⠉
⠀⠀⠀⠙⠤⣤⣾⣿⠟⠀⠀⠀⢿⢸⣿⡟⣸⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⡀⣔⡪⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⣠⡿⠟⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⣠⠞⢉⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣿⣿⣿⠀⠀⠀⠠⣮⠵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⡀⣤⡴⠶⠊⠉⠁⠈⠈⠍⠀⡂⠤⡀
⠀⠀⠀⠀⠀⢠⢬⣾⡥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠀⡏⠉⡁⠀⠀⡠⢒⡝⠊⠁⠀⡀⠥⢖⠩⠤⠶⢤⢀⡠⠑⢌⢢
⠀⠀⠀⠀⠀⠹⡄⠉⣰⠋⠀⢠⠖⡲⣤⢀⡴⠋⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡎⢠⠔⢢⠁⠁⣀⣤⣤⡄⠀⣸⡁⠠⠤⡀⡆⡆
⠀⠀⠀⠀⠀⠀⠈⠞⠁⠀⠀⢿⢸⡀⠀⣏⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠱⡀⠀⠠⠆⢀⠙⠛⠋⠁⢀⣜⡠⠔⠊⣠⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣤⢫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣙⠦⣀⠀⠀⠀⠂⠀⢀⣈⣁⡤⠴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠨⠉⠉⠭⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢑⡀⠠⠀⠀⠠⠄⠁⠤⠒⠉⠁⠀⠀⠐⠀⠈⠁⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠊⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠈⡠⠚⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢂⠐⠂⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠐⠒⠂⠈⠑⠂⠀⠊⠁⠠
⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⡀⢠⡀⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠔⠈
⠀⠀⠀⠀⠀⠉⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⡤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⠁⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠋⠁⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠅⠒⠀⠈⠐⠐⠋⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠁⢀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠉⠉⠀⠀⠀⠠⠀⠤⠒⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⡀⠴⠂⠀⠀⠀⢀⡀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⠉⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠐⠃⠀⠀⢠⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⣀⡀⠩⠌⠁⠄⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⣀⠀⠀⡀⢄⣡⠈⠍⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⢀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠂⠀⠀⠤⠄⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⢀⡤⠖⣁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⡀⠀⠀⣀⠠⠀⠀⠀⠀⠀⢀⠔⠀⠈⠁⠀⠈⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢀⡀⠀⠀⣀⠀⠀⢀⣀⠀⣀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⢸⠀⢸⣧⠀⢀⣿⠀⢠⡟⠉⠁⣿⠀⢸⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠇⠀⢸⠀⢸⣿⡀⢸⣿⡄⢸⡇⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡆⠀⢸⡆⢸⡟⣇⣿⢸⡇⢸⡇⠀⠀⣿⠓⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⢸⡇⢸⡇⢿⡇⢸⡇⢸⡇⠀⠀⢹⡄⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠸⡇⢸⠇⢸⠇⠈⠀⠸⠇⠘⢷⣤⠄⠸⠇⠸⡇⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⣀⣀⠤⠤⠤⠤⠴⠒⠒⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠩⠤⠤⠤⠤⠤⠤⠲⠶⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡄⢾⣀⠀⠠⣄⠀⣣⡀⣂⣸⢋⡔⢲⠄⡘⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢫⣻⡁⢈⢁⠰⡀⡸⢀⠀⡑⠈⣻⣮⣵⢃⠀⠲⠚⣀⣼⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⠛⠛⠛⠲⠿⠾⠷⠶⠷⢿⣿⣿⣿⣿⣿⣿⡿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣟⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠬⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢴⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠈⠀⠈⠀⢹⣦⡀⠀⠀⠁
⠀⠀⠀⠁⠿⢷⡽⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠸⠋⠻⠄
⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠿⠀⠀⠀⠀⡤⠀⠄⠊⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠐⠒⠆⠀⠀⠀⠈⢿⡇⡐⠀⠀⠀⠀⠀⣠⣴⠇
⡀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠋⠂⠂⠀⠀⠀⠀⠈⠤⢦⠀⠀⠀⠲⠤⡿⠃
⠀⣀⢀⠠⡄⠂⠀⠀⠀⠁⠀⠀⠀⠀⠠⣀⠀⠀⠐⠃⠀⠀⠀⠄⠘⠠⢁⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠊⡀⢩⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠊⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣶⣿
⠐⠐⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠴⠒⠊⠋⠀⠀⠀⠀⠀⠀⠐⢂
⠀⠁⠀⠀⠀⠀⠀⠀⣤⠸⢝⡶⣤⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⠤⠤⠖⠒⠒⠆⠀⠀⠀⠉
⠀⡌⠀⠀⠀⠀⢨⡜⣧⡐⣚⣶⡭⢤⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠶⠒⠓⠓
⢠⢃⠀⠀⠀⠀⣻⣤⢟⡻⢩⢁⡜⠯⢽⢠⠀⠀⠀⢰⠄⢐⢱⢘⢥⢸⠁⣰⡀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠒⠊⠛⠀⠀⠀⠀⠀⠀⢂
⠂⣼⠀⠀⠀⠀⠈⠱⣿⣷⣗⠚⣿⣤⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠄
⠀⡇⠀⡀⠀⠀⠀⠀⠀⠘⠃⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⣽⡈⠁
⠀⠀⠀⠀⠀⠈⡉⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠
⠀⠀⠀⠀⠠⠼⠷⠦⡧⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⢀⠀⢠⠀⠀⠀⠲⣶⣷⣶⣚⣛⣒⣒⣒⣒⡒⣓⣒⣶⣶⣦⠀⠁⠀⢀⡀⠀⠀⢀⢁⠀⣀⣮⣁⣶⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⣿⣹⣶⣭⣯⣭⣍⣏⣭⣍⣿⣻⣇⣀⠘⠀⠀⠑⡏⡉⣹⣠⡴⠋⠈⢳⣴⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣚⣲⣒⣻⣻⣿⣟⢻⣻⣻⣻⣿⢿⢷⠂⠀⠀⠀⡘⢻⢥⣤⣤⣤⡶⣿⣿⣿⠷⠦⠀⠄
⠀⠀⠀⠀⠰⢀⡀⠈⢙⡿⠿⠝⠯⠟⠹⠋⠽⠋⠿⠩⠝⠹⠿⣷⣞⡄⠀⠀⠀⠄⣸⣼⠿⠟⠏⠹⠏⠹⣏⢰⡀⡈
⠀⠀⠀⠀⢰⣿⣿⠞⠉⠀⡔⠋⠆⠀⢠⠚⠓⡄⠀⡠⠒⢢⠀⠈⠉⢠⠓⠢⣿⠛⠻⣦⣤⣀⠀⡀⠀⠻⠿⠗
⠀⠀⠀⠀⠠⠉⢀⡀⠀⠀⠁⢀⠀⠀⡄⠀⢀⣀⡀⠁⠀⢀⠀⠀⠀⠀⠀⠻⣽⣿⣁⠘⠛⠋⣌⠁⡄⣤⢈⡐⠂⠠⠃
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠁⠀⠊⠀⡀⠙⠇⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠧⡟⠓⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⢿⠛⡟⢿⡟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠹⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣥⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣬⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⣡⣶⣶⡆⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣾⣿⣿⣿⣯⣍⣉⣀
⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠈⠁⢠⣶⣶⡜⠛⠛⠁⠈⠀⠀⠆⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⢀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡢⠀⠘⠗⠀⠠⠑⢦⠄⣄⡀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡰⢠⠀⢈⠀⠀⠀⠆⡻⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠉⠐⢦⡠⠀⠀⠀⣰⢺⡄⢀⡁⠂⠾⢶⣡⢤⣠⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠻⠹⣦⣀⠁⠀⠀⠀⠀⣈⠂⣆⣙⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠈⢢⣅⠀⠀⠠⠀⠄⠁⠀⠀⠀⣀⠈⠐⣖⣀⣼⣗⣩⣒⣼⠿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡂⠀⡏⠳⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠪⣽⣓⣤⡟⣁⣠⠿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠰⠶⣘⡢⡶⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠿⠛⢻⡞⢫⣵⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢈⡈⠳⣯⡿⠇⣘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠍⣳⡤⢽⡏⠉⠛⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⣻⣆⣧⠑⢆⡟⠀⡀⠈⢄⡀⠄⠤⠀⠁⠀⠀⢐⣎⠓⣬⣧⡴⢄⢂⣴⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡘⣿⠈⢳⠛⣇⠀⠸⡆⠀⠈⠁⠀⠀⠀⠀⠀⣼⢸⡇⠃⡟⠛⢶⠌⠙⠀⣘⡠⢔⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠛⠻⣁⣼⠙⠙⢧⡀⠈⠑⢀⢀⡤⣠⣀⡤⣤⡏⢹⣷⣀⠎⢀⡦⡐⠁⣰⢁⠘⠂⠁⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠦⠀⠙⡛⣶⡈⢻⡗⠞⢋⠁⠂⠸⠀⠠⠀⠳⠰⠮⡟⢲⢠⠆⢀⠜⠃⠀⠀⠈⣃⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠯⣿⡖⠠⡟⠟⠀⠀⢁⠒⠄⡄⠠⠱⡞⢮⠗⢀⣴⠁⠐⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⡄⠀⠃⢀⡀⡀⠠⠀⢀⡄⠜⠋⣠⢴⡋⠥⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣤⣀⣀⠀⠉⠈⠀⠑⢒⣈⡩⣤⣶⣽⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡾⣹⢿⠂⣿⢿⣿⣿⠛⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠉
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠏⣼⣼⣤⣦⣿⣶⣸⣍⣼⡝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠉⠀⠈⠐⠃⠉⠉⠙⠛⠿⣿⣿⣿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠒⠙⢻⣿⣶⡖⢀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡷⠉⠀⠀⠀⢰⠒⡂⠉⠀⠀⠀⠀⢐⠶⡆
⠀⠀⠀⠀⣠⣾⣷⡾⠗⠒⠋⠿⠟⠷⣝⠶⠄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣯⡷⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⢃⠀⠀⠐⠀⠀⣀⣀⡀
⠀⠀⢠⣿⣿⣿⣿⣅⠀⠓⠄⠀⣈⡟⢪⡻⢶⣧⣀⠀⠀⠀⣠⣶⣯⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠉⠁
⠀⠀⠀⣙⢃⡚⠏⡠⣽⣶⣴⣾⣿⣿⣷⣿⡶⢄⣀⠚⠂⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠁
⠀⠀⠀⠈⠳⣄⠁⠔⠛⠿⠛⠻⠟⢛⠷⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢰⠂⠐⠀⠆⠐⡆⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠈⠀⠀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠃⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣄⠂⠀⠀⠀⠀⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠰⠂⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⣠⠀⠶⢔⡶⠖⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⣿⣭⡷⣶⣶⡄⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⢠⡁⠄⢰⣯⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣟⢻⣿⣏⣿⠁⠀⠀⢸⡷⣾⣿
⠀⠀⠀⠀⠽⠻⣷⡛⠁⢛⣆⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⣍⠛⠞⣛⠛⢓⠦⡀⠀⠀⠀⠀⠀⠀⠀⢄⠘⢿⣿⡿⠛⠻⠟⠛⠁⠀⠀⠸⠿⠿⠿
⠀⠀⠀⠐⠈⠕⠺⣋⣹⠡⡤⠚⡀⠒⠁⠂⠀⠀⠀⠀⠀⠀⢼⣅⠤⡤⢿⠿⠛⠟⢉⠉⣣⠀⠀⠀⠀⠀⠀⠐⠂⠬⠶⠀⠀⠀⠀⠀⠀⠁⠀⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣹⣶⣦⡴⠷⢶⣤⠞⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠠⠝⠒⢐⢒⠒⠢⠍⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢿⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⢴⣮⣻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣽⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣾⢿⣿⣶⣛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⢀⣠⡤⠶⠒⠛⣛⢉⠉⠉⠻⢿⣯⡽⣿⣦⣝⠛⠛⠓⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢿⣿⣯⣙⠿⡷⣌⡉⠲⣦⣤⣈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆
⠀⣤⣤⣽⡷⣦⣄⡜⢷⣸⠂⠈⣀⡾⠲⠙⢿⣷⣄⢋⣿⣶⣤⡉⠻⢿⣶⣄⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾
⣤⣴⣾⣷⣿⣮⣿⣷⠀⢹⠞⠁⠉⠁⠁⠐⢼⣔⠛⠋⣨⡛⠿⣿⣦⣤⡈⠻⢷⣄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢋⡠⢒
⣿⣿⣿⣶⣮⣭⡿⠟⠃⠀⢠⡆⠀⠀⠀⠀⠄⠀⠈⠻⣦⣤⣷⣌⠳⣬⣽⣶⣄⠙⠦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⢉⡠⢒⣭⡾⠛
⣿⣿⣶⠾⣿⣿⣇⠀⠀⠀⠀⠛⠧⣶⣦⠔⠀⠀⠀⠀⢘⠛⠿⢿⣷⡄⠙⠻⣿⣷⣦⣌⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡛⢻⣤⠞⣩⣶⠛⢁⡴⠊
⡟⢿⡷⣟⣛⣿⣿⠟⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣴⣠⣴⣤⣤⣾⣦⣌⠛⠟⢻⡿⣦⣌⠑⢦⡀⠀⠀⠀⠀⠀⠰⡟⢛⣤⢟⣫⣴⡾⣋⣡⠞⠁
⠉⠲⣀⡿⣷⡞⠁⠀⠿⠁⠘⣷⣤⣀⣀⣀⣠⣴⣿⣿⣿⣽⣩⣍⣉⣁⣉⣀⢚⣶⣀⠈⠳⣄⠙⠻⣦⣌⣳⡄⠀⠀⠀⠀⠉⠉⣴⣿⡟⢳⡴⠋
⠴⣀⠛⠃⠿⠀⣹⡀⡷⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣽⡿⠳⣦⣈⠑⢦⡈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠹⠵⠞⠁
⡘⠻⢀⣰⣆⡒⠀⡙⠃⣴⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⠛⣩⢴⡿⠋⠀⠀⠀⠙⠿⣿⠟
⣝⠒⠠⠌⢉⠛⠒⠠⠾⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⣉⠡⠴⠚⣻⡵⠋⠁
⠉⠻⣦⡀⠀⠉⠘⠒⠲⠶⠤⠤⠤⠤⠤⠶⠶⠆⠚⠉⠈⠁⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⢶⡴⣤⡿⢷⣶⣶⣶⣦⡔⢦⡴⢶⣶⢒⣶⣶⠒⠒⠲⣶⡶⠟⢡⠖⠲⠶⠲⠆⠦⠶⡶⠶⠶⠶⠦⠖⠀⢢⡴⣦⠀⣿⣶⡟⣴⠀⣾⠟⢷⣦⢰⣾⣷⣦⠆⣾
⣄⠁⣬⣙⣓⠶⠛⠻⢿⣿⣿⣷⣮⣷⣿⣶⣿⠄⠘⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⣿⣿⣷⡜⢸⣿⢏⢸⣿⡼⣿⣿⢇⡇⣿
⣽⣿⣯⣭⣭⣾⣷⣯⣶⣬⣽⣭⣭⣭⡏⢩⡍⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣿⡄⣿⡏⣿⣇⡸⣿⡟⢸⣿⣸⣿⣿⡏⠇⣿

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠒⠉⠥⢿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠻⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣳⣿⡄
⠀⠀⠀⠀⠀⣴⢾⡶⣧⠸⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡾⠃
⠀⠀⠀⢠⡀⠁⠀⠺⢖⠑⠤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠉⢷⣄⣀⣤⡒⣷⠞⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠘⠗⠀⠈⠀⢹⠛⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⣀⡀
⠀⠐⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣴⡷⢂⠀⠀⠀⠂
⠀⠑⠉⠁⠀⠀⠀⡠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠢⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⡙⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⢸⡄⠀⠀⠀⡴⠇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠲⡄⢀⠀⣸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠠⠆⠀⠀⠈⠳⡀
⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆
⠀⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠠⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡶⠿
⡉⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢦⡠⠈⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⢀
⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣁⡀⠐⠋⣠
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⢉⠉⠛⠛⠉
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣦⣴⡶⠖⠂⠒⠒⠚⠾⣶⣦⣤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⠛⠉⠙⠁⢁⠀⠀⠀⠀⢠⣀⠀⠀⠈⠛⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠿⢿⣿⡿⠀⠀⠄⠈⠀⠂⡀⠀⠈⢻⣿⣶⣤⣄⡀⠀⠙⠻⣿⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣧⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⡜⠛⠿⣿⡟⠁⠀⠀⠀⠀⠀⠙⢿⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠛⠿⣿⣟⣦⣄⡀⠀⠀⠐⠀⠀⠀⠀⣰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠙⠻⢿⣷⣄⡀⠀⣠⣀⡠⠴⠿⣾⣿⣷⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠗⠀⠀⠀⠀⠉⠛⢷⡀⠀⡀⠀⠀⠀⠀⠀⢠⠼⢿⣿⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣇⡀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⡿⠀⡀⠀⠀⠀⠀⢀⡁⠀⠀⣤⣄⣀⠀⠀⠉⠙⠾⣿⣿⣳⣦⣼⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⠃⠀⡀⠀⠀⠈⠀⣠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⢨⠛⠻⠛⠋⠀⠀⠀⠄⡀⠉⠛⠿⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⣑⡦⢤⡴⠠⢴⣾⣷⣦⣄⡀⢤⣄⠀⠀⠀⢁⣠⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠨⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣶⣤⣀⠀⠈⠙⠻⢿⣿⣷⣿⣟⡓⠚⠋⠛⠿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢣⠀⠈⠙⠿⣿⣿⣿⡶⠄⠐⠈⠀⠉⠙⠙⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠰⠈⠁⠀⡍⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣄⡀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⢿⣿⣶⣆⠀⠀⢠⡜⠁⢁⠀⣠⣸⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⡄⠀⠀⠈⠀⡤⠀⠀⠀⠀⢨⡄⠀⠈⠙⠻⢷⣬⣟⣿⣀⡶⢚⢛⠟⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⢿⣿⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣷⣦⣀⠀⠀⠈⠙⠿⣯⡽⠟⡁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠳⢄⣄⠀⠀⠀⠀⢀⣠⣞⠁⠉⠛⢿⣿⣿⣶⣤⡤⠐⠉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⠲⠶⠾⡿⠿⠿⠷⠶⠶⠊⠛⠉⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠒
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⠒⠂
⠀⠀⠀⠚⠉⠁
⠀⠀⠘⠛⠛⠛⠉⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐

⠀⠀⠄⠐⠀⠀⠀⢠⣶⠂⣠⠆⠀⠀⣴⣾⡿⠿⠟⠒⢶⣾⡄⢀⣼⣿⡷⠶⡿⣿⡇⠀⠀⣼⣿⠛⠛⠿⢿⡟⠀⢀⣀⣼⣷⣷⡀⠀⠀⠀⠀⠀⠒⠂⠐
⠀⣄⠀⠀⠀⠀⠀⠸⣿⣾⣯⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣬⣿⣿⠁⠀⠀⠀⢾⡿⠿⠇⠀⠀⠀⠀⢻⣿⣯⡈⢿⣧⠀⠀⠀⠀⠀⠀⠀⣌
⣈⣿⣧⣄⠀⠀⠀⠀⢿⠁⢹⣧⠀⠀⢠⣿⣆⠀⠀⣀⣠⣿⡆⠀⠀⣿⠋⠉⠻⣦⡀⠀⠀⣼⣇⣀⣀⣀⣀⡀⠀⡼⠁⠙⠛⠿⢿⡄⠀⠀⠀⠀⣠⣾⡿
⠀⣭⣯⣻⣷⣦⣀⠀⠈⠀⠀⠛⠁⠀⠀⠘⠉⠉⠛⠛⠋⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠂⠀⠉⠙⠋⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⢀⣤⣼⣿⡿⣷
⠐⠛⠛⠀⠁⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣹⣶⣶⣤⡄⠀⢀⣀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣤⠀⠀⠀⠐⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡽⠛⠁⠀⠈⢻⣿⣿⣿⣿⡿⠂⠉⠈⣤⣤⣤⣭⡈⠉⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡅⠀⠀⠀⠀⠀⣴⡿⠟⠋⠉⠀⣀⣠⣼⣿⣧⣿⣿⣇⠀⠀⠀⠈⠛⠛⠛⠀⠀⠘⠀⠠⠜⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⡤⠴⠀⠠⠉⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⣍⣉⡍⠛⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠿⣿⡼⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢻⠋⡛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣽⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣥⡾⠋⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠍⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠂⠀⠀⠀⠀⠐⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣴⣄⠀⠀⡀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡟⠿⢷⡦⣝⣦⡀⢿⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡾⣶⡝⡻⠍⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣯⢭⢹⡤⢉⣂⡀⢀⠋⣀⣀⣀⡤⣴⣿⣿⣿⣷

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠀⠉⠁⠀⠤⠤⠤⠄⠈⠁⠐⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠈⠀⠀⠀⠀⡀⠠⠠⠄⠀⠐⠀⠀⠐⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠂⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠡⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠑⠠⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠤⠃⠀⠀⢠⠊⠁⠀⠀⠀⠰⢄⠁⠀⠠⠀⡰⠃⢀⢀⠀⡫⠀⠀⠀⠐⠄⡀⠀⠀⠈⠢⡑⢄
⠀⠀⠀⠀⠀⠀⡔⠀⠁⠀⠀⢀⠞⠁⠀⠀⠀⠀⠸⡀⠀⠀⠁⠀⠀⠀⠁⠀⠀⡰⠃⠀⠀⡸⠁⠁⢀⠀⠀⠀⠀⢈⠢⠀⠀⠀⠘⢆⠣⡀
⠀⠀⠀⠀⢀⠀⠈⠀⠀⡀⠔⠉⠉⠉⠓⠤⡀⠀⠀⠇⠀⠀⠀⠀⠐⠉⠀⠀⡰⠁⠀⠀⣠⢀⣠⡦⡀⠀⡀⠀⠀⠀⠁⠀⠢⠀⠀⠀⠣⠐⡄
⠀⠀⠀⠀⠀⠌⠀⢀⠌⠀⠂⠀⠀⠀⠁⢀⠈⢢⠀⢸⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⡸⠁⠀⠈⢘⠂⠀⠑⢄⠀⠀⠀⠀⠳⠀⠀⠀⠡⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⠊⠀⠀⠀⢀⠜⠀⠀⢀⠔⢃⠀⠀⠀⠀⠱⣄⠀⠀⠀⢈⠶⠀⠀⠡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠂⠀⠇⠀⠃⠀⠀⠀⠐⠁⠀⠀⠀⡠⠊⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠑⠀⠐⠁⠘⠀⠀⠀⠀⢁
⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠌⠀⢆⠀⠀⠱⠀⠀⠆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢠⠈⡄
⠀⠀⠀⠄⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡠⠂⢀⠀⡎⠉⠣⡀⠠⠃⠀⠀⡠⠃⠀⠀⠘⠀⠀⠀⠇⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠘⠄⠀⠀⠀⠀⠀⠀⠀⡜⡴⠁⠀⠐⠀⢣⠀⡀⠑⠀⠀⠀⠀⠀⠀⠈⢱⠀⢀⠀⠀⠎⠀⠘⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠊⠀⠀⡀⠋⠂⠀⢦⠀⠀⠰⡀⠀⠀⠐⠐⠒⠤⣀⠀⠀⠀⠤⡀⡀⠱⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠴⠀⠀⠀⠁⠈⢆⠀⠀⠙⢄⠀⠀⠀⠀⠀⠈⠱⢆⠀⠀⠀⠈⠁⢡⠀⠀⠀⢷
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠂⠀⠀⡀⢀⠀⠀⠈⢣⠀⠀⠌⢢⠀⠒⠄⠀⠀⠀⠀⠑⢄⣀⡀⡀⢨⠀⢀⣀⣘⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⡀⡄⠀⠀⠀⡀⠀⠀⠀⡀⡀⠒⠊⠀⠀⠀⡐⠀⠀⠈⠒⠄⡀⠱⣀⡰⢊⠇⠀⠀⢀⠆⡀⠀⠀⠀⠱⡄⠀⠀⠯⠡⠀⠈⠀⠀⠀⠀⡀⡘
⠀⠀⠀⠰⠘⡀⠀⠀⠀⠀⠀⠄⠀⠉⠑⢄⡀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠐⠠⢁⡁⠀⠸⡄⠀⠀⠈⠢⡀⠀⠀⠙⡆⠠⠤⠂⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢠⠘⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠢⢄⡀⠀⠀⠙⠲⠤⣀⡀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⡘⢄⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠉⠢⣄⠀⠀⡠⣀⡈⠉⠓⠒⠂⠀⣀⣀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠙⢌⠢⡀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠐⠉⠀⠀⡀⠤⠔⠒⠒⠈⠉⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠢⡀⠀⠀⠀⠀⡀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠞⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠶⠶⠒⠛⠛⠉⢉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠦⠀⠀⠢⠀⠀⠰
⠀⠀⠀⠀⣀⣄⣠⣄⣌⣠⣄⣄⣠⣄⣀⣀⣤⣌⣠⣄⣌⣀⣦⣀⣠⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠉⠿⣦⣄⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠃⠀⠀⣀⠀⠀⠀⠁⠀⣀⡀
⠀⠀⠀⣀⣴⣤⠆⠘⠿⠷⣾⡦⣄⠀⠀⠁⠀⠀⠀⣀⣤⣾⠟⠉⠁⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀
⠀⠀⣾⡿⣿⡧⡀⠒⠀⣨⣛⣿⡳⡧⣀⠀⠀⢴⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠉⠁
⠀⠀⠨⣄⠉⠐⣼⣿⣿⣿⣿⣿⠟⠐⠎⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠄⢠⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠐⠁⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠁
⠀⠀⠀⠀⡀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣤⣤⣄⠀⠀⠀⢀⡀
⠀⠀⠀⣠⡀⢰⣎⠀⠀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣟⣿⣿⡏⠀⠀⢲⢾⣿
⠀⠀⠀⠹⢛⣯⣅⠝⢀⠉⡀⢀⠀⠀⠀⠀⠀⡠⠏⢾⣩⣭⣍⠭⣦⠀⠀⠀⠀⠀⢐⢀⡛⠛⠋⠙⠉⠡⠀⠀⠛⠛⠛
⠀⠀⠀⠈⠁⠐⠂⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⣮⣍⣹⣥⣄⡰⠼⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡆⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠽⠃⠐⠒⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣗⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⢀⣀⠤⠤⠤⠝⢿⣿⡿⣮⣗⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠖⠋⠁⠀⠀⠀⠈⢀⠀⠘⢿⣾⣟⢿⣆⡐⠦⣬⣙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⠷
⠀⢤⣼⣷⣦⣼⠻⡝⣀⠠⢞⠋⢻⢷⣼⠽⣷⣮⡙⠻⢦⣌⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴
⣿⣿⣟⣿⣾⣿⠆⠘⣠⠀⠀⠈⠙⠋⢥⣔⢨⡙⢿⡓⣤⡙⠧⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢋⠥⣢
⣿⣯⡽⣿⣿⡀⠀⠀⠻⢦⣤⣤⠀⠀⠀⢸⠿⠿⣦⡍⠻⣿⣷⣌⡛⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣯⡥⣪⡴⢛⡡
⣟⠿⢾⣿⣿⠟⣳⠦⡀⠀⠀⠀⠀⠀⣠⣾⣤⣤⣶⡤⡷⢦⡙⠟⣿⠶⣌⡓⢄⡀⠀⠀⠀⠺⣛⡷⣛⣵⠾⣯⠔⠋
⢈⢳⡞⡿⠃⠀⣙⣀⣽⣷⣦⣤⣶⣿⣿⣿⣿⣶⣶⣶⣶⡬⢿⣦⣈⠲⢌⠙⠶⣿⠆⠀⠀⠀⠀⢾⢟⡽⠛⠁
⠹⢇⣀⡄⠌⠱⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣫⣴⠟⠁⠈⠳⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣟⠂⠌⢉⡓⠂⠾⠿⠿⠿⠿⠿⠿⠿⢛⠛⠉⠡⠒⣻⠟⠁
⡈⠙⢦⣀⣀⣉⠉⠑⠀⠀⢀⢚⣉⣀⢀⣀⣀⣴⢊⣁⠀⢀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⣴⣠⡖⠀⣠⣄⡀⢀⣠⣀
⡙⢍⡳⢉⡻⠿⣿⣷⣿⣬⣯⣾⣿⠀⠶⠉⠉⠀⠉⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⢸⠙⠁⣿⣿⡔⢽⣿⠨⣿⢸⣿⡿⠌
⣵⣾⣿⣽⣶⣿⣮⣭⣭⣽⢻⣏⣍⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣲⡄⣿⡿⣿⢸⣿⢃⣿⡸⣿⣷⠡

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⡟⠉⠉⠉⠉⠋⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡉⠛⢹⠛⠉⠙⠛⢻⣿⠟⣿⡟⠛⠉⠉⠉⠉⠉⠉⠙⠉⠙⠋⠉⣻⠀⠀⢸
⣿⡇⠀⠀⡟⠀⢉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⢻⣭⣭⣿⡷⣦⢄⣖⡁⠀⠀⠀⣀⣤⣈⣀⣀⠠⠤⠐⠀⣻⠀⠀⢸
⣿⡇⠀⠀⡧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠨⢽⡍⠩⣿⣿⢾⠛⣷⣯⡶⠶⠚⠋⠉⠉⢥⣤⠤⠶⠖⠀⠀⢿⠀⠀⢸
⣿⡇⠀⠀⡇⠀⠀⠀⣄⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠈⢤⣼⠧⠤⠏⠋⡟⣀⣼⣿⠁⢀⡞⠀⠀⠀⢸⡯⠀⠀⠄⠀⠀⢺⠀⠀⢸
⣿⡇⠀⠀⡇⠀⠬⠃⠭⠬⠷⢀⣀⡀⠀⣀⡀⠀⠀⠀⡰⠋⠉⠀⠀⣿⣸⣷⡆⠀⢸⠙⣿⠉⡀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣻⠀⠀⢸
⣿⡇⠀⠀⡟⠀⠠⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠞⠁⠁⢀⠠⣴⡿⢸⠉⡧⠀⢸⠚⠛⠂⠀⠸⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢽⠀⠀⢸
⣿⡇⠀⠀⣯⣠⠄⠀⠀⠀⠀⠀⡇⠀⠙⠁⠀⡠⠋⠀⠠⣺⡽⡶⣭⡙⠚⠋⠀⠀⢸⠀⣿⠀⠀⠰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⣿⡇⠀⠀⡏⠀⡄⠀⡰⠂⠂⢈⡁⠀⢈⡠⠖⠀⢀⠀⠛⢩⠿⠇⣓⡒⣸⠂⠁⠀⠘⢳⣿⠀⠐⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⣿⡇⠀⠀⡗⢰⠀⠀⣀⠀⣐⣦⢩⡦⠟⠷⡴⠟⠅⢃⠼⣡⠞⠉⠴⢦⣾⣥⡌⡁⢀⣬⡓⠀⡇⠀⠀⡂⠘⠀⠀⠠⠀⠀⠀⠀⠀⢺⠀⠀⢸
⣿⡇⠀⠀⡇⠀⠀⢹⡇⠀⠁⢸⡏⠀⠐⠂⢤⣀⣆⣷⣺⡟⠒⠀⣸⣾⣿⠿⠄⠀⠸⠹⠇⠊⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸
⣿⡇⠀⠀⣿⡁⠀⡙⠁⢹⣦⠀⠱⠒⡼⣥⣏⣴⠉⡿⢃⣿⠠⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢽⠀⠀⢸
⣿⡇⠀⠀⡟⡇⢨⣿⠀⢳⡼⣧⡀⠙⣂⠟⣁⣰⡼⠔⠋⠁⠀⠀⠀⠠⢀⠠⢀⡤⢄⣀⣂⣀⣤⣽⣦⣤⣐⠀⡀⠀⠀⠑⠀⠀⠀⣻⠀⠀⢸
⣿⡇⠀⠀⣇⡅⢸⡿⢖⣸⣶⣿⣷⣤⡈⣤⣄⠭⠠⣦⣐⣶⣢⠤⢖⣛⣿⣿⣯⠃⣿⢭⣧⠟⢿⡿⠤⢰⣾⣿⣯⣤⣧⣌⣿⣿⣿⣿⠀⠀⢸
⣿⡇⠀⠀⣿⠀⠸⡇⠀⢻⣿⢿⣿⣹⠛⠫⣿⡀⠈⡽⠿⠛⠛⠻⠟⢯⢩⣿⣿⠀⠁⠈⣹⡏⢸⡿⢿⣿⣿⣿⣿⣽⣿⡽⠟⣉⡀⢸⠀⠀⢸
⣿⡇⠀⠀⣿⡀⢸⡇⢀⠸⡧⢺⣿⢾⣮⡇⠻⣱⣦⠤⠤⣶⣶⣶⣿⣿⣜⣿⢹⣸⠆⠠⡾⠡⡞⠻⢿⣿⡅⢬⣿⣿⣟⡁⣿⠟⢫⣽⠀⠀⢸
⣿⠃⠀⠀⣟⠃⠘⠇⢰⣠⠇⢸⠎⠀⠀⡀⣿⣿⣻⣿⣷⣼⡿⠿⣿⣷⢸⣿⠿⠞⠀⠀⠄⠀⠀⡶⠀⠀⠘⠻⣿⠿⣠⠟⠁⠒⠈⣿⠀⠀⢸
⣿⡄⠀⠀⣿⡄⠠⠃⠐⠆⠀⠀⠀⠀⠀⡤⢸⣿⣿⠃⣿⣿⠀⠆⠃⠛⠾⢻⣤⡤⡆⠀⢰⠀⠰⠀⠀⠀⠐⢀⠰⠄⣿⠀⠀⠀⠈⣿⠀⠀⢸
⣿⡇⠀⠀⡿⠣⢄⡆⢰⣤⠀⠀⠐⠀⠀⠁⣼⣿⣿⢠⣿⣿⡏⠀⠀⠠⠆⢺⣿⣝⡇⠀⠀⢸⡃⠀⠀⠀⠀⢈⠆⠠⠀⡀⠀⠀⢰⣼⠀⠀⢸
⣿⡇⠀⠀⡇⠀⡂⠀⢘⣿⡇⠀⠆⠠⠀⠘⢿⡿⡛⠿⠿⠉⣳⠄⠔⣰⡟⣬⡟⠊⠁⠀⠀⢦⠇⠀⠀⠀⢀⢬⠴⠇⠂⠓⠂⠤⣼⣿⠀⠀⢸
⣿⡇⠀⠀⡇⠀⠀⠀⡼⠁⠀⢠⠆⠀⡆⠀⢿⠁⡅⠀⠂⠀⠀⠀⢀⡈⠃⣼⠁⠀⠠⣥⠞⠁⢘⣟⢀⠛⡿⣤⡤⠀⠀⠂⠀⠀⣞⣿⠀⠀⢸
⣿⡇⠀⠀⣿⠟⠂⠀⠉⠦⠲⠉⢀⡀⠁⠀⣿⠀⡟⠀⣠⣤⡄⠀⠈⠀⢸⣹⢶⣖⣺⡛⢀⡀⠠⣟⣅⠀⢧⠀⡰⣴⡔⠃⣤⡄⠐⣿⠀⠀⢸
⣿⡇⠀⠀⣷⣤⣀⣀⣀⣄⣀⣀⣉⣀⣈⣉⣛⣹⣇⣸⣥⣼⣷⣦⣤⣤⣾⣧⣤⣼⣭⣥⣠⣧⣶⣿⣽⣤⣤⣤⣬⣬⣠⣼⣿⣦⣀⣽⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣿⣧⡶⠟⢋⣁⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡶⢶⣄⠘⢿⣛⣥⣤⣾⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣯⡿⢟⣽⣷⡄⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⣤⠖⣊⡤⢚⣩⡶⢟⣫⣵⣾⣿⢿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢪⣤⡾⢋⢔⣷⡿
⠀⠀⠀⠀⣀⡘⣷⠚⣛⢉⡥⢞⣵⠶⠋⣡⣶⣿⣿⢿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣊⣾⣿⢿⡿⣯⡾⠋
⠀⠀⠀⠀⢿⠉⢿⣽⠻⡧⠞⠋⣁⣴⣿⡿⢿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣾⡿⢏⡴⢫⣾⠟
⠀⠀⠀⠀⢀⣄⣀⠻⡆⣻⣶⣿⣿⠟⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣾⡿⢛⣷⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠛⠻⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⣀⠠⣄⣾⠟⠋⣸⡿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠘⠏⢿⠿⢿⣶⣾⡿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠰⡆⠀⠌⣩⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠤⠌⠳⡀⣿⢀⣴⠟⠋⠀⢒⣶⡶⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠈⠱⣶⣶⣶⣽⡉⢻⡿⠷⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢿⣯⢿⢯⣀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⠛
⠀⠀⠀⠘⠃⠈⠀⠀⠀⠤⠶⠟⠛⠉⠐⢁⡏⢿⡀⠙⠙⠛⠷⠞⠓⠀⠒⠀⠀⠀⠀⠀⠘⠾⢿⠿⠿⢿⠿⠟⠟⢿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠃⠘⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠚⠒⠈⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠓⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠊⠀⠈⠁⠀⠈⠁⠀⠑⠒⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⢀⠀⠐⠀⠀⠁⠀⠈⠀⠀⠂⠀⡀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠤⠤⠤⠤⠤⠤⠔⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⡛⠛⣓⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠢⣀
⠀⠀⠀⠀⢀⢞⡥⠊⠁⠀⠀⠀⠀⠀⠉⠒⢝⢦⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⡡⠂⡰⠐⢮⠑⠦⣄
⠀⠀⠀⠀⡏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢇⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢸⡅⡇⠀⣀⠀⠘⡆⠀⡴⠃⣀⠀⠀⡅⢸⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢧⠹⣄⠀⠉⢢⡘⢼⡴⠊⠁⠀⡠⢃⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠳⣬⣓⠤⣀⣰⣜⣀⡠⢔⣪⣴⠃⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠁
⠀⠀⠀⠀⠀⠀⠉⠚⠤⠤⠤⠬⠥⠤⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠥⠤⠔⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠾⠚⠛⠉⠁⠉⠙⠻⢷⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⡤⠀⠀⠀⠀⠀⠀⠘⣶⣤⣀⠈⠙⠻⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣧⡀⠉⠃⠀⠀⠀⠀⠀⠀⢀⣿⠿⡿⠋⠀⠀⠀⠉⠙⣷⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠉⠛⢿⣷⣦⡄⠀⠀⠀⠀⢀⣼⣯⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠙⠿⢷⣶⣷⠞⠛⠉⠻⢿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠁⠀⠀⠐⠀⠀⠉⠀⠀⠀⣀⣀⣠⣟⠁⠉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣤⡤⠤⠀⠀⢉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠉⠉⠛⠿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣘⣇⣀⢀⡀⢀⣠⣾⡁⠀⡀⠀⠀⠀⠀⣀⣼⠏⠁⠀⠀⠀⠁⠢⣄⠙⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣯⣉⠉⠙⠻⢿⣶⣽⣶⡦⢴⠾⢿⠁⠀⠀⠀⠀⠠⠀⠀⢈⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠙⠻⣿⣿⡆⠀⠀⠀⠉⠉⠻⣶⣤⣀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣀⡉⠀⠀⠀⠀⠀⠀⠀⢹⡟⠻⣿⣦⡠⣴⣅⢀⣀⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣇⠀⠀⠀⠉⠀⠀⠀⢸⣦⣄⡀⠉⠛⠿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⠤⣄⠀⠀⠀⣠⣴⡟⠙⠿⣿⣷⣤⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⠛⡛⠓⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⢀⢔⡶⠞⠳⢄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠈⢃⠀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢦⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⣀⣁⣤⡼⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠿⠶⠶⠩
⠀⠀⠀⠀⠀⣠⠎⠳⡄⠘⣧⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠅⢢⡀⢈⠢⡘⣧⠀⠀⠢⡀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠃⠀⠠⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⢆⠁⠀⠱⣌⢾⣷⡄⠀⠈⠓⢦⡈⠻⣦⡀⠀⡼⡉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⢒⠚⠓⠊⠀⠀⠤⡀⠀⢀⠔⠈⠳⣄⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⢧⡙⢿⣆⠀⠀⠀⠙⠷⣌⡻⢦⡀⠑⠄⠀⠠⡀⠀⢀⠀⠀⠇⠀⠀⠀⢀⠔⠁⢀⠀⠘⢦⠀⠀⠐⠂⠀⠳⡄⠀⡼⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠀⠀⠙⢦⡻⣧⡀⠀⠀⠀⠀⠙⢮⣷⣤⠀⠀⠀⠑⠀⠈⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢁⣰⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡾⠉⠉⠙⠳⣤⣀⠀⠙⢌⠻⣤⡀⠀⠀⠀⠀⠈⠻⢷⣄⡐⠆⠀⢀⡀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢷⠤⡤⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄⡀⠀⠉⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠢⡉⠻⣦⢤⣨⣤⠟⢻⡄⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠘⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠙⣆⠀⠀⠻⣆⠀⠀⠀⠈⡳⢦⡀⠀⠀⠀⠈⠀⠈⠳⢦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠦⣦⣄
⠀⠀⠀⠀⡜⠀⢄⣳⡄⠀⠀⠉⠳⣄⠀⢻⣧⡀⠀⠀⠙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⠖⢲⡶⠓⠛⠉⠀⠐⠒⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠐⡇⠀⠀⠱⣿⣄⡀⠀⠀⠘⣧⡾⠦⠿⣦⡀⠀⠀⠈⠳⢽⣷⣄⠐⢦⠀⠀⠀⠀⠈⠳⢦⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡉⠓⠒⠚⡇⠙⢦⡀⠀⠉⠓⠲⢤⡀⠀⠉⠻⢿⣦⣑⠀⠀⠀⠀⠀⠀⠙⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠶⡶⠚⠉
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠙⠲⢄⠠⡇⠀⠀⠻⣦⡀⠀⠀⠀⠳⣤⡀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑
⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⢷⠀⠀⠀⠀⠙⠪⣽⣦⡀⠀⠀⠀⠀⠀⠙⢦⡑⠢⠀⠀⠀⠀⠀⣠⡿⠀⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣭⡿⠶⠖⠋⡎⣷⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠉⠳⣄⠀⠀⠀⠀⠀⠙⠳⢶⣤⠤⠶⠛⠁
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⣀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡀⠀⠀⠀⠈⢦
⠀⠀⡏⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⠙⢷⣄⠈⠙⠳⢶⣤⣠⣤⣴⠾⢿⣆⣰⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠘⡆
⢀⣠⣤⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⡆⠈⠳⣤⣀⠀⠀⢀⣀⡼⢧⣤⡼⠋⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣴⡏
⠛⠛⠉⠠⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢀⡤⠤⠤⠭⠭⠭⠭⠴⠖⠋⠁⣠⠾⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⠋⠁⢀⣰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠙⢦⣀⣠⣤⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠛⠛⠷⠶⠶⢶⣶⣶⣿⠭⠥⠤⠤⠤⠤⠶⠶⠖⠛⢉⣠⣞⣀⣀⣰⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣄⣠⣤⣤⣴⡋⠁⠀⢀⣠⣤⣤⣤⣄⠀⢀⣀⣤⠶⠋⠁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠳⠶⠤⠤⠶⠶⠶⠶⠖⠛⠉⠁