Coral sea Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢧⡀⠀⠀⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠳⣄⠀⠀⢧⢸⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢹⠀⠀⢸⣾⣇⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡀⠀⠀⣿⢸⠀⠀⡸⠁⢉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢇⠀⠀⢸⡘⣦⠞⠁⡰⠁⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠳⢄⠀⢷⠈⠀⡰⠁⠀⠀⠘⠀⣧⠀⠀⠀⣠⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢳⣸⢀⡞⠀⠀⢀⡤⠞⠀⡟⢀⡀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠑⣄⠀⢸⠀⠀⠀⢾⠀⡴⣫⠵⠋⡿⠀⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣇⠀⠀⠀⢸⡆⠸⡄⠀⠀⠘⡆⠉⣁⡤⣞⣥⠔⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠘⣧⠘⢦⠀⠀⠀⢧⡀⠱⡀⠀⠀⢻⢸⢃⡞⠁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠴⠚⠀⠀⢧⠀⠀⠀⠳⣄⠘⡆⠀⡾⢸⡼⡇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣤⠴⠶⢦⡈⡇⠀⠀⠀⠘⡆⢡⡰⠁⠈⣧⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣇⣧⠀⣀⣤⣄⣿⠘⠃⠀⠜⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⣇⣀⡏⠈⠉⠁⠀⠀⠛⠀⠀⣀⣤⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡈⣁⣀⣤⠴⠋⠉⠳⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣩⣭⡥⠶⠶⠶⠶⢦⣧⣀⣨⣤⣤⣤⣤⡤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠐⠒⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⠤⠤

⠀⠀⠀⡀⡀⢖⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐
⠀⠀⠨⠷⢇⡦⠹⣛⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠙⣴⡾⣛⣂⣳⡜⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠀⠀⠀⠰⠁⠀⠀⠀⠀⣂⡄⣐⣤⠑⠄⢀⠠
⠀⠀⠉⠵⠦⠾⠼⠗⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠼⢿⣿⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢡⠃⠀⠀⠀⠀⠀⠀⠂⠁⠈⠐⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠸⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⢆⠀⡔
⠀⠀⠁⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡴⠀⠀⠀⠀⢠⣠⣤⡀⣠
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠀⠀⠀⠀⠀⠀⠀⠈⡄⣀⠇⠀⠀⠀⠀⠀⡟⠈⠁⢄
⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠐⠀⠀⠀⠀⠀⠀⢰⣄⣸⡞⠀⠀⠀⠀⠀⢠⡄⠀⢈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠉⠀⠀⠀⠀⠀⢨⡇⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠐
⠀⠀⠀⠀⡀⢰⠄⡠⠖⠀⡏⠀⢉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠐⠀⠁⠂
⠀⠀⠐⠀⠀⠁⣒⣃⢚⣷⡤⡤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢤⠂⠠⢀⣄⠆⣐⣆⢴⣶⢀⣤⣤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⡕⠁⠘⠉⠙⠠⢀⣝⡿⢧⣽⣿⣦⣜⣿⡷⠀⠁⠀⠀⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢔⠆⠊⠐⢅⠀⠀⢀⠈⠛⠛⢀⡡⠷⠌⠛⠇⠤⠀⠄⠀⠀⠀⢀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠐⠉⠂⠁⡀⠐⠀⠄⠸⠃⣀⣾⡁⠀⣾⠖⣻⣖⠃⠀⠀⠀⠲⠋⠀⠀⠀⠦
⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⢀⢾⣿⣿⣄⢓⣿⢿⣿⣿⡃⠁⠀⠀⠃⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⢄⣀⠀⠀⠒⠀⠀⠀⠀⡈⢡⡠⣄⠀⢀⠀⠂⠀⢃⣸⣉⣿⣦⣿⣿⣻⣽⡏⠃⠀⠀⠂⠐⠀⢁⠉⠁
⠀⠀⠀⠀⢀⠀⣀⠈⠀⠁⠀⠐⢀⣅⠹⠈⠔⠂⢉⣧⢀⡀⢀⣿⡀⢹⢴⣿⣏⣿⣿⡏⠀⢰⠀⠁⠀⠀⠀⠀⠡⠄
⠀⠀⠀⠀⣾⣿⣷⣯⠀⠀⠀⠀⠀⠉⠂⠠⠘⠀⠊⠀⠦⠁⠀⠀⠉⠉⠹⡇⡿⣶⣧⠁⠀⠋⠀⠰⠀⢠⠀⡁⠀⠀⠠
⠀⠀⠀⠀⠙⠋⠁⠁⠀⠀⠀⠀⠤⠆⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣇⡿⠇⠀⠀⠀⠀⠈⠀⢸⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⠀⠀⠁⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⡀⠀⠀⣜⠀⡠⠂⠄
⠀⠀⠀⠁⠀⡒⠒⠐⠀⠀⠀⠀⠈⠀⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡐⠀⠐⢂⠀⣀⠀⠀⠠⠀⢈⡜⢀⡔
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠛⠌⠀⠤⣄⣀⢆⡐⢤⡀⠀⠀⠉⠀⠊
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠠⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⠅⠂⠔⠒⡂⠠⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⠰⡞⠴⠦⠀⠾⢦⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⡆⡘⠑⡁⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⡔⠀⠀⠀⠀⠀⠀⠂⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⡠⠀⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣄⣢⠸⡎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠃⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⣤⠀⠀⠀⠀⠀⡀⠙⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠒⠠⢁⠄⠁
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⡄⠀⠄⠀⠀⡆⢳⡀⡄⠀⠀⢀⡿⠀⣇⠀⠀⢀⡄⠀⠀⠈⠅⠈⢀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠀⢀⡏⡀⠀⡀⢀⢰⣄⢃⣐⡜⡔⠡⣸⠘⠀⠑⡇⠀⣿⠀⢨⣏⠥⢂⣤⣁⡴⠀⠀⠀⢀⢸⡄
⠀⠠⠌⠡⢉⣱⠆⢰⠎⢰⡇⠀⢲⣸⠆⣿⣜⢱⣀⠀⠀⠉⠀⠀⠀⠑⠀⠾⡅⣸⣇⣳⡼⢻⣿⡇⠇⢀⠠⢺⡀⢹⡆⢰⡄
⠀⠁⠀⠀⣸⢻⡇⢾⡁⣿⢶⣤⣾⣽⢪⠁⠉⠈⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣿⣸⣷⣿⣿⢛⣿⠁⣴⣿⡴⢸⡇⣼⢇⡾⢃
⠀⠀⣶⠐⡇⣸⣹⣌⣵⣧⣾⣿⠟⠻⢷⣦⣤⣤⣾⣧⣀⣴⣄⣀⣱⣾⢿⢿⣿⣿⣿⣿⣿⠏⠙⠿⠟⢿⣦⣾⣿⣿⣾⣅⣄
⣶⣿⣿⣾⣿⡿⣿⣿⣿⡟⠓⡀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⠀⠃⡿⡽⢻⣯⣀⠀⠀⠀⢀⡈⠉⣻⣿⢻⣿⣿⣿
⣿⠟⡍⣯⡳⠾⣰⠻⣻⣿⣾⣿⣿⡏⡾⣫⢷⢿⡏⠿⣿⠋⠀⠈⣿⠏⠀⠇⢡⠞⢻⠿⠛⡃⣶⣇⣾⣿⣶⣿⠗⣿⣿⣿⣿
⡙⣶⣦⠙⡿⠀⠟⢋⣛⠟⣻⢉⡈⠉⠙⡋⣶⡟⠀⠀⡄⠀⠀⠀⠉⢀⠀⠀⠀⠠⣜⠎⢷⢻⠈⣿⣏⣾⣿⠟⣾⠉⡉⢻⣿
⡉⢿⠟⠑⠀⢰⠟⠁⢩⣼⠀⢠⢆⣬⠀⠀⠀⠐⡖⢠⠖⠀⠀⠀⠀⠈⠀⠀⢒⢁⠀⠁⠀⠤⣧⠜⣇⣛⢾⡰⣿⡏⢓⣪⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠰⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⢀⠄⢤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⢀⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠂⠠⠁⡤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢒⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠑⠂⠀⠀⠀⠀⠂⠀⠀⠺⠄⠀⡆⢀⠼⠓⠀⠘⠁⠈
⠀⠀⠀⠲⠆⠔⠂⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣠⠖
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠂⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠒⠈⡀⠂⠀⠄⢀⡀⠈⠀⠀⠀⠀⢀⠄⠀⡀⠀⢠⡤⠶⠢⢀⡀
⠀⠀⠀⠀⠀⠄⠒⠀⠂⠀⣸⠀⠀⠈⠀⠀⠀⠀⢤⠀⠀⠀⣀⠺⠈⡟⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠐⠠⠀⠐⡐⠁⡀⠀⠀⢀⠀⠀⡀⢀⠀⢀⠢⡩⠤⠐⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠂⠀⠊⢀⠀⠈⢠⠋⢤⠈⠠⠀⠀⠊⠀⠀⢄⣈⠁
⠀⠀⠀⠀⣡⠶⠌⠹⠂⠃⡑⠀⠀⣀⠀⠎⠀⠀⠐⠊⢙⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠉⠁⠢⠴⢡⣄⠀⠀⢀⡀⢼⡄⠈⠁⠈⠀⠀⠀⠐⣀⡍⠙⠚⢋⡀⠉
⠀⠀⠀⠀⠠⠄⠀⠀⠟⠢⠀⠃⣄⠀⠠⠀⠐⠀⣄⠈⠗⠘⠀⢀⡀⠰⠄⠀⠀⠀⠀⠀⠁⠐⢢⣤⣠⡤⠤⠖
⠈⠀⠀⠀⠀⠀⠀⠑⢰⠄⠶⠄⠊⢀⠀⢠⠀⢤⣄⡕⠀⠂⠑⢀⠠⠀⠁⢀⡀⠀⠀⠀⠈⣱⢦⡎⠁⠄
⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠠⠘⠀⢀⠀⠊⡄⠁⠀⠠⠋⣈⠁⠒⠂⡙⢋⣀⣄⠀⠁
⠊⠰⡠⣀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⡀⠀⠚⢀⡈⡁⠵⢠⡿⠙⠇⢀⡄⠀⠒
⠀⠀⠀⠠⠂⡝⠁⠀⠀⡀⠀⠀⠀⡀⠀⣀⠁⠀⠆⠀⠁⠲⠀⡁⡌⠀⠀⡀⠀⠐⠋⠘
⠀⠀⠀⠀⠀⠀⡴⠃⠈⠐⠀⢀⠀⠀⠀⡀⣶⠖⠒⣢⠜⣤⣤⣤⣴⠇⠌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠀⢀⢀⠲⠆⠈⣡⠀⣠⣯⣃⣀⠴⢧⣀⣼⢁⡈⢉⡖⢢⡏⡈⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠠⢠⠍⡀⢀⠈⠈⣵⣊⡀⣀⠡⡋⠀⠀⣍⠀⣬⡿⠂⠈⡃⠀⢹⠃⠀⢀⣠⡀⠀⠀⠲⠂⢠⠀⠀⠂⡠
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡂⠀⠈⣉⠄⠨⠀⠉⠀⠞⠙⣿⠟⠳⡤⠒⠻⡆⠐⣤⠈⠋⠁⠀⡄⢀⣅⠐⠀⢐⠆⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢠⣤⣦⡀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠶⠀⢩⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⡛⠃⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠐⢶⠄⢀⡄⠈⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⢀⣤⠀⢀⣷⠂⡄⣻⣧⠏⢰⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠛⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⣸⠇⣀⠀⠀⠀⠀⢰⣠⡈⣤⣜⠐⢄⣀⢠⡟⠀⣸⣿⡘⣿⡿⣻⠀⣾⠀⠌⣡⢁⡎⢤⣖⡐⠀⠀⠁⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢰⡆⠀⣾⠁⢀⡿⢤⢢⡀⠨⠆⣿⣷⡟⢹⣸⡇⡄⢘⣷⠠⣿⠋⠀⠀⠀⢈⠁⠛⢮⡶⣷⠎⣡⠘⣡⣿⡕⢄⠀⠀⠀⠠⣠⠀⠀⢧
⠀⠀⢸⣷⡠⣿⡅⢸⡇⠘⣬⡇⣤⠄⢻⣼⠛⣾⣿⠇⠁⠌⠙⣦⣧⠀⠀⠀⢀⠈⠀⠀⠘⡿⠛⠛⠋⠀⠹⣧⣟⣻⣄⠀⠀⠀⠀⠀⣧⢈⡆⢰
⠀⠀⢀⣜⣷⣬⣷⣾⣷⣄⡀⢣⢈⣾⡎⡽⢗⣿⡿⠀⠀⢿⣿⣿⣿⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣬⣿⣥⣤⣄⠈⠀⢀⣯⣸⢣⡟⠰⣄⢀⡅⠁
⣠⣾⡿⣿⣿⡟⢿⣿⣿⣿⡄⠈⡄⠻⠕⣱⣿⣿⡇⠀⠀⠹⠛⢹⣿⠟⠋⠁⠀⠀⠀⢀⠀⠀⠠⣤⣄⠀⠀⠀⣹⠟⠿⢿⣿⣿⣶⣾⣿⣿⣿⣿⠻⣿⣿⣿⣤
⣿⣿⣿⣿⣟⠁⢈⣿⠿⣿⡛⠀⠹⠀⢰⣧⢡⣿⣿⡦⠀⠀⠀⢸⠁⠀⣠⣶⡾⠀⠀⠈⠀⠀⣀⠉⡉⠀⠀⠐⣣⡤⡾⡀⢘⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿
⠟⠗⠈⠻⠋⠀⣼⡏⠀⠢⡁⠀⠀⠀⠀⢃⣥⣾⣿⣟⠀⠀⠀⢠⣆⡀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣾⠰⣆⠁⢸⠿⠋⠉⠛⣿⣿⠻⠿⠟⠀⢨⣿⡏⠘
⡞⠛⠀⠀⠀⠠⡏⠁⠀⡼⠤⡄⠀⠀⠴⣹⠟⣩⣿⣿⣄⡀⠀⣼⣿⣿⣯⠀⠀⡀⠰⡇⢀⣥⡀⠘⠃⠀⠈⢿⣿⡇⠀⢐⠊⢐⠂⢸⣦⡺⠺⠃⠀⢀⡎⠁
⠿⠚⠀⠀⠀⠐⠁⠠⡔⠁⠦⠁⠀⠀⠚⠡⠾⣿⠟⠋⠘⢁⣤⣿⣟⣿⣿⣦⡀⢳⠀⢀⠘⠿⢿⠷⠀⠀⠀⠼⠿⣷⠀⠀⢰⡿⠼⣜⢻⣧⠘⣧⠀⢠⠆⢠⣿
⠀⣿⣇⠀⠀⠀⠀⢼⣿⡄⠰⣦⠀⠀⣿⣄⠀⠀⠀⠀⠀⠘⠻⢿⣯⡛⠛⠋⢀⡜⢠⣿⣶⣶⣿⡄⠀⠀⠀⠀⠐⣿⠀⠀⣼⣿⠿⣶⣶⣌⡀⠉⠀⠘⠀⢼⡟
⠀⠉⠉⠁⠀⠙⠂⠘⠛⠃⠀⠋⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀⣈⣓⣿⣿⣿⡿⣿⣷⣜⣿⡿⠿⠷⠄⠀⠀⠀⠀⠞⠛⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠻⠆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠴⠆⠈⠀⠀⣄⠈⠋⠉⠉⠛⠋⠀⠙⢊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠁⠈⠉⠁⠀⠁⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⠶⡶⣶⣶⠶⢶⣶⠶⣶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠠⣃⠐⠉⡀⠀⠀⠁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠀⠀⣄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠁⠀⠹⢤⣤⠀⣤⡐⣠⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢏⡼⢿⡿⢷⣶⠆⡀
⠀⠀⠀⠀⠀⠈⡘⣁⣄⣻⣏⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣴⠦⠦⡌⠋⠀⠠⠄
⠀⠀⠀⡀⢀⡤⠿⠉⠉⠉⡽⠋⠁⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⠂⠂⠃⠀⠂⠀⠁
⠀⠀⠀⠀⠈⠘⡄⡀⠈⣿⠗⠉⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠸⢤⣾⣷⠘⠳⠲⢣⡄⠀⠄⠀⠀⠀⠄⢀⣤⡀⠀⢗⣀⠆⠈⠀⠀⠀⡀⠀⠀⠀⠠⠂⡄
⠀⠀⠀⠠⠀⠒⠀⠘⠻⠟⠲⡦⠼⠛⠀⠀⠀⠀⠀⠀⠀⢾⣿⡧⢠⠀⠨⠀⠀⠀⠀⠀⠀⠀⣾⡞⠁⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⣼⣀⠀⣤⣄⠀⠀⠀⠰⠯⠛⢿⡗⢫⡠
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢠⣦⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⡸⣿⠟⢀⣀⠀⠘⢦⠆⣐⠙⠋⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣍⣌⣻⣿⣿⡿⠒⡜⠀⠀⠀⠈⡀⠀⣀⣬⡀⠰⠖⡛⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡤⡖⢰⡿⠃⠀⠀⠀⠙⢲⠾⢇⡀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢐⠛⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢄⠳⠤⣍⡱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⢄⠈⠲⡀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠊⡔⠉⠀⡅⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⠎⠀⠀⠈⠢⠜⠁⠀⠀⠀⠎⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠘⠓⠒⠋⠀⠀⢸⠀⠀⠀⠀⢰⢲⠖⢫⠲⠀⠀⠈⠓⠤⠤⠤⢄⡀⠀⠀⠀⠀⡜⠀⠀⡘⠙⣝⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢰⠀⠀⠀⠀⠀⢆⠀⠀⠀⢸⠀⠉⠋⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢣⣀⠔⠀⠀⠈⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣕⢄⠀⠀⠀⠈⢢⡀⠀⠈⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⡠⢔⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢕⡢⣄⠀⠈⠒⠚⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠔⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⢀⡠⠃⠀⠀⠀⢪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⠁⠀⠀⢀⠔⡿⢖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠰⢢⠀⠁⠉⠁⢀⠔⢒⡀⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠎⠀⠱⢌⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠰⠴⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠐⠓⠶⠶⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠋⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠸⠤⠒⠁⠀⢀⠠⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠟⢦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⠀⠀⠳⢄⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢶⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣃⡠⠚⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠁⠈⠁⠒⠂⢤⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣍⠑⠤⠄⢤⠴⠊⠉⠙⠒⠠⠤⠤⠇⡀⠀⠀⠀⢸⡤⠒⠈⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠁⠒⣾⡀⠀⠀⠀⠀⣀⣀⣀⡀⣬⣦⠀⠀⢸⣤⣄⡀⠀⠀⢀⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠭⠉⣉⡉⠒⠦⠐⠈⢨⡉⠁⠒⠂⠁⢀⠤⠀⠀⠰⣟⣆⣈⠡⠔⢚⣟⣒⣂⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠒⠊⠁⠉⠀⠀⠐⠈⠁⠀⠀⠀⠀⠈⠑⠒⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠃⠀⠃⣰⡇⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⢲⠤⠖⠚⢋⠀⠎⠇⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠕⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣴⣇⠘⠁⠜⢀⠖⠒⠒⠉⠀⠀⠀⠄⢀⠀⠀⢀⠃⠀⠰⠆⠨
⠀⠀⠀⠀⠀⠀⠀⠂⠴⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠢⢄⠀⠀⡘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⠔⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢴⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⠴⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡘⠃⣡⠆⣰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⠼⠅⠀⠰⠋⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡀⠡⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⢫⢄⠀⣰⠒⢂⡀⠀⠀⠀⠀⠘⡄⡄⢀⠄
⠀⠀⠀⠀⠀⡆⠀⡠⠊⠀⠀⠀⠀⠀⠂⠌⠀⠠⠀⠀⠀⠀⠀⠀⠘⠉⠀⢅⠀⢛⢉⡀⢼⠀⠀⠀⠀⢌⡸⡀⡀⢀⡆
⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⢀⠀⠀⡏⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠠⠀⠓⠈⠈⠀⢠⠀⠀⠀⠀⢠⠢⢁⡅⡎⢀⢀⡂⠀⠀⠀⠀⠘⡠⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠣⣀⡀⠁⠀⣀⡀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀⠣⢀⣂⣓⠜⠀⠀⠀⠀⠀⠰⠀⠀⣿⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡇⣼⣧⢂⠰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⢰⠇⢀⠎⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠃⣧⠸⣇⠃⡎⢈
⠀⠀⠀⠀⠀⠀⢀⠄⠄⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢺⠁⡸⠀⡜⠀⡴⠁⠀⠀⠀⠠⠀⠒⠸⠄⠀⠡⢊⠀⠀⠀⠀⠀⠈⠳⠀⡆⠉⣅⡸⠎
⠀⠀⢀⢠⠂⠠⡹⠂⠈⠀⢨⠐⠀⡀⠈⢀⠰⠀⠀⠀⠀⡗⠄⣀⠀⣸⠊⠀⠀⠀⠀⠘⠀⠑⠀⠄⠀⡠⠀⠘⠁⡀⠀⠀⠀⠀⠀⠐⢃⡰⠀⠡
⠀⠀⠈⠈⠋⢁⠀⡧⠔⣀⠀⠒⠹⠀⠉⢠⠀⠀⠀⠀⠀⢣⡀⡟⢀⣿⠀⠀⠀⠀⠀⠈⢀⡄⠁⠸⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢄⣀⢃⢠⣠⣠⢊⡄⠤⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⡾⠃⠀⠀⠀⠀⠀⠀⠐⠀⠰⠃⡀⠀⠐⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦
⠀⠀⠀⠠⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⠶⣤⣀⣀⣀⣀⣤⠶⣤⣀⣀⣀⣀⣤⠆⠀⠀⠈⢷⡸⣷⣤⣄⣀⣠⣤⠞⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⢠⡞⢷⡀⠈⢷⡹⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠈⠛⠋⠀⠀⠈⢷⣹⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⡋⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⠇⠀⠀⠀⠀⣠⠟⠉⠀⠀⠉⠻⣦
⠀⠀⠀⢀⣤⡴⠞⠋⣡⡄⢈⣿⠞⢿⡀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣀⣤⣤⣤⣤⡏⠀⠀⢀⣤⣄⠀⢸⡇
⠀⠀⠀⠘⣧⣀⡴⠟⣩⡴⠋⠁⠀⠀⠻⣦⠀⠈⠻⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣤⠶⠛⠋⠉⣠⠶⠂⠀⠉⣀⣴⢿⣄⠙⣷⣼⠇
⠀⠀⠀⠀⠈⠛⠶⠞⠉⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⠓⠒⠒⠒⠚⠋⠁⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢿⡀⠀⢶⡴⢿⣅⢀⣩⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢳⣦⣤⣀⠙⢦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣃⠀⠉⠛⠻⠿⣭⣹⠟⠋⠉⠻⣦⣤⣄⣀⣀⣤⣤⠴⠶⠛⣿⠛⢻⡟⠛⢷⡄⠘⠷⠶⠶⠶⠶⠶⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢻⡏⠉⠛⠶⣤⣀⡀⠀⠁⠀⠀⣠⠾⠋⠀⠈⠉⠉⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡶⢸⠇⠀⠀⠀⠀⠈⠙⠳⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣸⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⣹⡟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠺⢧⣄⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠲⠶⣄⣠⡴⠶⠛⠛⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⢀⣀⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠋⠀⠀⠀⢰⠆⢀⡶⠈⠻⣦⠀⠀⠀⠀⠀⠀⢸⡇⣹⠟⠉⠀⠀⢨⡝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⣄⠰⠟⠀⠀⠀⠈⠷⢀⣴⠟⠀⠀⠀⠀⠀⠀⣸⣇⣼⢷⣄⣀⣀⣈⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠤⠶⠋⠙⠳⠶⣤⣤⣤⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠛⠁

⠀⠀⠀⠀⠠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠻⣿⡆⠀⢿⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⢀⢘
⣰⣿⣶⡄⠰⢯⡽⣿⣿⣷⣤⠀⡇⢀⡶⠂⠀⠀⠀⢀⣤⣤⣄⡄⣤⡐⠶⣷⣦⠘⡿⢀⠀⠀⠀⠀⡀⠀⠀⠐⣄⠀⡟⢠⠰⠾⣣
⢹⣧⣿⣴⣦⡀⠻⠛⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⡄⠀⠉⢙⢷⡇⡈⢿⣾⣷⠽⡿⣷⡾⢀⣾⣶⣦⣷⣤⡎⠙⢌⡆⢇⡏⢸⣷⡿
⣿⣿⡿⠋⣙⣟⢀⣺⣿⣿⣿⡿⣿⣷⣆⢲⣀⣽⠇⢀⠀⢈⣷⣷⣥⢺⣿⣿⣷⣰⢿⣅⣸⣿⣿⣿⣿⣿⢷⡇⣸⣽⣸⢤⣦⡿⣿
⣿⠟⢀⡘⣦⣽⡦⡿⢿⣿⣟⣾⣽⣿⣿⣿⣿⡗⡀⠀⠁⠙⣿⣿⣿⣮⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣧⣿⡿⣵⣽⣿⣿⣶⣿⣷⣿
⣿⣾⣿⢁⣄⣺⣿⣷⣦⣿⣿⡏⠛⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣽⢟⣡⢿⣿⣿⣿⣿⣿⣟⣿⣷⣽⣿⣿⣿⣞⣿⣿⣿
⠻⠓⠖⠩⠋⠽⣿⣿⣿⣿⣿⡅⠀⣾⣿⣿⣿⣿⠶⠛⠸⠿⡿⣿⣿⣿⣿⣿⣿⡅⢾⣿⣿⣿⢿⣿⣿⣿⡿⠿⠿⠿⠙⡿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠈⠛⠿⠛⠋⠃⠀⠀⠀⠀⠈⠛⠛⠛⠹⠃⠀⠸⠿⠿⠋⠀⠈⠉⠉

⣶⣶⣶⢶⠶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⢺⠅⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣾⣅⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠌⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡃⠀⠙⠷⣤⣄⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⡷⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⢉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠉⠒⠒⠒⠒⠊⠉⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣀⣀⣠⡤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⢠⠀⠀⣸⠁⠀⠀⠈⠐⠊⠀⠀⠀⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠀⠀⡔⠀⠀⢀⣰⠊⠀⠀⠀⢧⠄
⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢄⠀⠀⠛⡀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠘⠡⠇⠀⣆⣇⡇⠀⡜⠏⠀⠀⠀⢠⣹⠂
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠴⠃⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣿⡁⠀⡀⠀⠀⠀⠀⣼⠟
⠀⠀⠉⠀⠀⠀⠀⠐⠐⠛⠊⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠳⡄⠀⠲⠀⠀⠐⠁
⠀⢐⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠃⠀⠀⠀⠀⠐⠤
⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠂
⠀⣁⠈⠈⡀⠂⠀⠀⠀⠀⢀⣤⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆
⠀⠉⡀⠀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣾⡄⢠⠇
⠀⠀⠠⠀⢤⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠋⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂
⠀⠀⠠⠤⢤⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⢂⠀⠀⠀⠈⠁⠐⠀⠀⣼⣿⡖⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⣀⡠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣂⠉⠉⠑⢆⠀⠀⠙⢧⠈⢻⠑⢤⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠉⠁⠈⠀⠀⠀⠘⠀⢰⠀⠀⠀⠀⠀⠈⠃⠈⡶⡄⠀⠀⠀⠀⠀⢠⡏⠉⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⢄⢸⢀⠤⠀⣀⠤⠀⠀⠀⠆⠘⠞⠆⠀⠀⢀⡟⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⠄⠀⣠⠶⠒⠒⠓⠒⠚⠃⠀⠈⠉⠒⠚⠛⠛⠠⢤⡀⠀⣸⡀⠀⣼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⡜⠁⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⢱⠀⠉⣥⢠⠇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢸⣀⣠⣒⣉⣁⣀⣤⣤⣤⡤⠤⠤⠤⠤⣬⣭⣶⣤⣠⣀⠀⣽⣼⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣋⣭⣭⣭⣦⣤⣤⣤⣤⣤⣀⣀⣤⡴⠶⠶⠶⠶⠶⣦⣤⣭⣍⣛⢧⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣾⠟⠛⠉⣩⡯⠶⠶⠶⠤⣄⠀⢀⣄⠀⠀⣀⣠⡤⠤⣤⣘⡄⠀⠉⢻⠹⣷⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⡏⠀⡐⠀⡧⠒⣲⣶⣶⣤⣾⢷⣻⣉⡓⢯⡤⢒⣊⣉⡒⠺⣿⠀⠀⢸⡇⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣷⠀⡇⠀⡇⠘⠉⣯⣿⡿⡳⢋⡤⠤⡉⢦⣱⡹⣿⣿⠻⣤⠇⢀⡇⠀⡇⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢻⠀⠀⠠⡁⠀⠐⠀⣼⡟⣱⠏⠀⠀⠈⢦⡱⣷⡉⠩⠀⢸⡆⠀⠀⢀⡇⡎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⢌⡓⠦⠤⣵⣄⡤⣾⢏⠞⡉⠀⠂⠀⠀⠀⢿⣜⢿⡢⠤⠼⠷⣒⡿⠽⣊⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣯⡶⣶⣶⡾⠟⠋⠀⠇⠀⡀⠀⢰⠀⢸⠈⠳⠬⠭⣭⠭⢶⡖⠋⣽⠉⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠈⡆⠀⠑⢄⠀⠀⠀⠦⠴⣂⣂⣺⣦⠆⠐⠀⢀⡜⠁⢀⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⡀⠀⠈⠑⠂⠴⠴⢦⣄⡠⠶⡶⠦⠤⠖⣋⣤⠖⠋⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⡒⠒⠚⠛⠛⠛⠛⠚⠛⠉⠉⠁⠀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠐⠓⠶⠶⠶⠶⠶⠶⡶⠶⠒⠒⢚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠓⠒⠒⠛⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣱⢤⣀⣀⣀⣀⣀⣀⡴⠋⠀⠀⣀⡠⠤⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠒⢦⣴⣄⣀⣀⣀⣀⣠⣤⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣠⣴⡏⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢳⣟⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠦⠤⠤⠶⢒⣺⣟⡥⢺⡇⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣀⣀⣀⣸⣿⡇⣀⡀⣸⣷⠀⠀⢼⣿⣶⣶⣦⣴⢀⣀⣀⣠⣿⣀⡀⠀⡄⢰⣿⣿⣇⠀⢀⣀⣠⡄⣠⣄⡀⢸⣿⡇⣤
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠖⠒⠲⢜⡆
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⣤⣄⡀⠀⠹⡄
⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⢠⠊⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣶⣶⣾⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠈⠉⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣶⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⢠⡄⢠⠀⠀⠀⠀⠀⠠⠰⠁⠦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠞⢀⠶⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠬⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠈⣨⠂⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠈⠅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣀⠀⠀⠀⠘⡄⣵⠚⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⡅⠀⠋
⠀⠴⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡫⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⢀⡀⠀⢫⢹⣆⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⠰⠏⠀⠀⠀⣬⡃⠀⠀⠀⠀⠴⠀⡐⠆⠡⠀⢀⢯⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢄⡀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠠⣤⡄
⠀⠀⠠⠀⠀⠀⠙⠑⠀⠀⠔⣆⡢⠠⣇⣄⣠⡇⢐⣷⣿⢗⠀⠀⠀⠀⠀⣀⡀⠂⣀⠀⠀⠂⢀⢀⡀⢢⣷⡟⠀⠀⢸⡃⠀⠀⠀⠠⡶
⠀⠀⠀⠄⠀⠀⠀⣠⠀⠹⣠⠐⢿⡆⢿⣿⣿⣇⢸⣏⢃⠟⠀⠐⠂⡄⡾⣿⠇⠀⢺⠶⠦⠆⣾⠚⣁⠘⡿⠁⠄⠀⣺⠖
⢀⣠⣄⠀⠀⠀⠐⣿⠀⠀⣿⡇⢸⡇⢸⡛⠋⢻⣹⣿⣿⢸⣧⡀⠸⣯⣶⣿⠀⣶⣼⣿⣷⡀⢽⢠⠏⠀⠀⣄⢀⣶⣇⣤⣶⣦⣤⡀
⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠉⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠈⣧⠀⢸⡄
⠀⠀⠀⢠⡶⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠛⠓⠲⣆⠀⢹⡀⠀⣧
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠛⢉⣉⣀⣤⣤⠤⠶⠖⠚⠛⠻⡆⠘⡆⠘⣇⠀⢹
⠀⠀⠸⡇⠀⠀⠀⢀⣴⠟⠋⣉⣤⠤⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢷⠀⢿⠀⠸⡇
⠀⠀⠀⢷⠀⠀⠀⢸⡇⢰⡟⠉⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡄⢸⡆⠀⣧
⠀⠀⠀⠘⢧⡀⠀⠸⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠈⠻⣦⣀⣿⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⠾⠁⣸⠃⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢧⣀⠀⠀⠀⣀⣀⣤⠶⠋⠉⣉⣉⣉⣉⣉⣉⣁⡤⠞⠁⠀⣾⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠉⠛⠛⢋⣉⣁⣤⠴⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡼⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣠⡴⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠉⠉⠀⠈⣿⣁⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⣀⣠⡤⠴⠀⣀⣠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠶⠖⠚⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡤⡶⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠏⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣇⠀⡀⠢⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢦⣌⠢⣄⡐⠈⠀⢌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄⠴⠈⠀⠀⠀⠉⠓⠶⣭⣑⢮⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢫⠿⢹⠁⠀⡀⠀⠡⠀⠀⠀⠀⠀⠙⢾⣇⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣋⣠⠏⠀⠀⠀⠀⠱⡐⠀⠀⠀⣀⡴⠯⢭⠽⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡟⠀⡴⣫⠭⣕⣦⡀⠀⣠⣿⡻⠛⠷⣦⠀⢤⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠁⢸⢱⠃⠀⣀⢻⠹⡝⣧⠁⢠⣦⠈⢊⢷⠆⠂⣲⠹⡄
⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠦⠼⠾⠷⣏⡈⡏⠳⠛⠭⢳⣌⠉⠀⠀⢊⠇⠀⢻⠀⡷
⠀⠀⢏⠈⢉⣙⣒⣒⣋⡥⠴⣶⠿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠼⠧⢤⣤⣤⠴⠒⠉⠉⢳⢳⢳⡥⠀⠠⣹⡄⢿⠇⠈⢠⠁⠁⣰⠃
⠀⠀⡼⠀⡄⠀⠠⡏⠀⠀⣸⡄⠀⠈⠳⣄⠀⠀⠀⢀⣠⡞⢳⡚⠉⠁⠀⠀⢀⡨⠗⠻⣄⣳⣍⠓⢎⡹⣜⢀⡀⣰⣞⣠⠶⠃
⠀⠀⢇⣀⣁⠒⡄⢳⡶⠋⠀⠹⡄⠀⠀⠈⠲⠖⠋⠉⠀⢣⠀⢣⠠⠄⠒⠈⠁⢀⠒⢄⠀⡷⣬⠗⠢⠤⠜⠋⠙⠓⠙
⠀⠀⠀⠀⠈⡇⢷⠟⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢢⠀⠀⠀⠀⠀⣁⣥⣞⠁⠈⠳⣄⣀⣀⣠⡴⣻⣤⣤
⠀⠀⠀⠀⠀⠥⠋⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠤⢴⡤⠀⠀⢳⡀⠳⣤⠤⢖⡯⠟⠉⠈⠳⣄⠀⠀⠀⠀⠀⢹⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⡟⠉⠙⠒⠒⠒⠒⠉⠀⠀⠀⣠⠟⠙⠓⠚⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠉⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⡟⠀⣇⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⡤⢚⠥⠊⡼⠀⢀⡏⠉⠉⠙⠛⠒⠒⠚⠉
⠀⠀⠀⠀⠻⣄⠓⠒⡂⢇⣀⡜
⠀⠀⠀⠀⠀⢸⠀⣔⠥⠆⣽⠃
⠀⠀⠀⠀⠀⠀⠓⠛⠲⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣦⡀⠀⠀⠀⣰⢶⣶⣶⡄⠀⠀⣾⣷⣿⣿⣿⣿⡿⠇⠀⢀⣀⣀⣠⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣈⣻⣶⣾⣿⣿⠿⠿⣏⠀⠀⠀⠉⠙⢿⣿⣿⡿⡿⢿⠿⠿⠟⠛⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠤⠶⠛⠛⠃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⣿⣷⡄⠀⢀⣿⣿⣿⠁⠀⠀⢀⣠⡤⡖⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⢧⠀⠠⢾⣿⣿⢻⣿⡀⠸⣿⣿⡿⠀⠀⠈⠉⠉⠀⠀⣀⡀⠀⠀⢰⣧⡴⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠀⠈⢀⣠⣾⣿⠿⠋⠿⠃⠀⢻⣿⣇⠀⠀⠀⠀⠰⠾⠿⠋⢀⣠⣴⡾⠃⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣷⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⢠⣀⠀⢀⣠⣿⡟⠋⠀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣦⠀⠀⠀⢀⡞⠀⠀⣿⡀⠀⣸⢿⣿⣿⠿⢻⡀⠀⠚⠉⠩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⢀⣿⡄⠀⠀⠸⡇⠀⠀⣿⠃⠀⠘⢾⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠳⣄⡈⢷⡀⠀⠙⠛⠛⠁⠀⣢⠆⠀⠀⢸⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣷⣽⣤⠀⠀⠀⠀⠀⠀⠈⢧⡀⣷⣄⠀⠀⠀⠤⠴⣿⣶⡶⠆⠘⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⡌⠙⠳⠶⠦⣤⣤⣀⠀⠀⠈⠛⢻⣿⣿⣷⣦⡀⠀⠈⠉⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⣦⣄⡀⠈⠛⠿⡿⠀⠀⠀⠉⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠃

⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠂⠀⠒⠒⠐⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡞⠀⠀⠀⢠⡄⠀⠴⠆⠀⠀⠀⡇⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠐⢃⠀⠀⠀⢀⠚⠉⠑⠤⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠠⠤⠤⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠆⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡜⠁⠀⠀⢀⡀⠀⢀⣀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⢇⠀⠀⠀⠈⡡⠐⠬⡉⠀⠀⠀⢰⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢌⠂⠀⠈⠒⠤⠄⠊⠀⠀⠀⠙⠀⠤⠐⠁⠀⠀⡁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⡀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠂⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⡀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⠑⢀⠁⠄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠉⠒⠚⠀⠀⠈⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠈⠣⡤⠤⢤⠜⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠬⠤⠤⠤⠤⠤⠀⣀⡀⠀⠀⠡⠀⠁⠤⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡾⠁⠀⠀⢠⡀⠀⣠⡀⠀⠀⠈⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡄⠻⡀⠀⠀⢈⠔⠒⠪⡀⠀⠀⢀⠟⠠⠘⠀⠐⠀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠈⠁⠀⠀⠀⠁⠐⠒⠉⠀⠀⠀⠄⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠀⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀
⡀⡀⢀⢀⢀⡀⣀⣀⢀⠀⠀⣀⣀⢀⠀⣀⢀⣀⣀⣀⣀⣀⠀⣀⠀⣀⣁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⢀⡀⣀⡀⢀⣀⠀⣀⠀⠀⣀⣀⢀
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠄⣀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⣴⣿⣿⡦⠀⠀⠀⠀⠐⣌⣉⠆⢠⠁⣬⠂⠀⡥⠈⡠
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⡜⠁⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⢀⠲⡀⠀⠃⢶⠴⢃⠀⡰⠒⠉⡂⠠
⠀⠀⠀⣆⠀⠐⢄⠀⠠⠀⡀⠀⢀⠀⠀⠀⠀⠀⢠⠀⢁⠰⠀⠁⡃⠞⠀⠄⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠈⠘⠉⠉⠀⠻⣦⠀⣶⡵⠲⠤⠐
⠀⠀⠀⠨⠀⠀⠀⢷⡄⢡⢣⣦⠆⠀⠀⠀⠀⠀⠘⡤⠘⠐⢀⠀⡁⠀⢠⠆⠀⠀⢂⡠⠂⢠⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣹⣞⡁
⠀⠀⠀⠀⠀⠀⠂⠀⢙⣾⠞⠋⠁⠀⠀⠀⠀⠀⠀⠘⢦⣻⡀⣀⡰⠊⠀⠀⠀⠰⡆⠀⠘⠠⠀⠀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡸⢞⠃⠀⡂⡧⢌⠁
⠀⠀⣸⠇⢲⢠⢸⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢀⡆⢰⠖
⠀⠀⢹⡀⠾⠘⡈⢸⠃⠀⠀⠀⠀⠐⠀⡀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢽⡄⠇⡿⢂⣛
⠀⠀⠈⢇⠀⢸⢣⡎⠀⠀⠀⠀⠀⠀⠀⢈⢦⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠬⢧⡟⣼⠇⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠘⣦⣾⠏⠀⠀⠀⠈⠐⠂⢄⠐⠁⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠈⠆
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠇⠀⠀⠀⡀⠀⠀⡄⢀⠀⠀⠀⠠⠀⢠⡀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠼⠴⡙⡘⣐⡄⠔⠰⢸⡆⠀⠀⢠⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢂⠀⠀⠀⠸⡀⠀⡆⠀⠀⠀⠀⠘⢿⡸⡼⡱⠎⡙⣱⢋⣿⠟⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠉⠉⠠⡐⡍⡎⠐⢁⠀⠀⠀⠀⠀⠉⠙⢿⣴⠷⠑⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⣤⣀⡶⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⡇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣼⣯⣷⣷⠀⠀⠀⠀⠀⠂⠈⠀⠈⠀⠀⠀⢰⡗⢾⣤⡟⠛⣇⣹
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠨⡟⣻⣤⡟⠛⣧⣼⠂
⠀⠀⠀⠀⠀⠀⠀⢳⣱⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠀⠀⠀⠀⠀⢀⣀⢢⠔⠁⣾⠈⣷⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⣀⢤⡰⡆⣴⢢⡷⡶⣰⠄⠄⣀⠀⠀⠀⠀⠀⢺⠀⢀⠃⠂⠀⠀⠀⠰⣄⣌⣿⣌⠀⠀⢽⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠛⠷⣷⣷⣸⡼⢰⠓⣯⣯⠾⠚⠀⠀⠀⠀⠀⠸⣀⢂⠀⠀⠀⠀⠀⠀⠈⠨⡀⣸⠟⠶⣾⣧⣀⡼⢑⠀⠀⠀⠀⠀⠐⠀⡡⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠉⠻⣧⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠹⠐⠋⠀⠀⠻⣿⡄⠀⠁⠀⠀⠀⠂⠀⢀⢀⠀⣀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠙⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣯⣿⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣷⣾⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⢤⠀⢠⡶⠠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⣾⠇⡀⠀⠀⠀⡛⠲⢀⠶⠆⠀⠻⣧⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⠂⠀⠀⠀⠀⠇⠀⢻⣁⣶⣸⡇⠀⠀⠀⢠⢆⠃⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠃⠀⠀⠀⠀⠀⠀⢠⣄⠀⢈⡽⠿⢉⠣⠄⠀⡄⠉⣼⡦⢧⡀⡀⠀⠀⠀⠀⠐⠂⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣀⣤⠴⠶⠟⠉⢿⠿⣇⢂⠁⠀⠀⠀⠀⡰⢻⠑⢮⡷⠒⢦⣤⣀⡀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠛⠛⠉⣉⣀⠔⠀⠀⠀⠀⠀⠙⠻⠴⢀⣄⠀⢸⣿⠇⠀⠈⠁⢀⠀⠉⠉⠙⠛⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢶⡶⢤⢀⣤⡴⠿⠋⠀⠀⠀⣴⠃⠀⠀⠀⠀⠾⣷⣤⠈⠃⠀⠀⠀⣀⠈⠂⣤⣤⠀⣠⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⠀⠀⠀⠀⠀⠸⣿⣿⠒⠲⣤⣀⡀⠹⡏⠀⠀⣀⡴⠚⣥⠞⠀⠀⠀⢄⣁⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢋⣠⠀⠀⠀⠀⠀⠀⠉⠀⣤⡄⠁⠀⠈⠐⠀⠴⠾⠋⠐⡠⢿⡄⠀⠀⠠⣀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⢀⠀⠀⠀⠀⣠⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠈⠙⢶⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠈⠇⠀⠠⡞⠁⠈⠙⠂⢠⠀⠀⠀⠀⠀⠀⠀⢁⣴⢞⡋⢉⠀⠀⠀⠀⠂⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⣀⡀⠤⠄⡀⠀⠀⢀⢇⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⠀⢘⢥⠀⠘⢈⡄⠀⠀⠀⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠻⠶⣬⣷⠛⠁⠀⠀⠀⠀⠀⠀⠈⣇⣤⣴⠟⠛⢨⣶⣞⡋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⣀⣤⠤⠄⡀⠀⠈⠳⢿⡦⣀⠀⠀⠀⢀⡀⣠⣴⠟⠛⠁⠀⠀⠈⢻⡟⠳⠈⠇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠉⠉⡥⡄⠘⡧⠂⠒⠈⠸⠃⠈⠁⠂⠀⣸⠟⢹⡀⠴⠆⠐⠛⠶⠶⣤⣿⠟⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢁⣠⡄⢀⠃⢱⣀⣿⡃⠀⠀⠀⠀⠐⠦⠀⠀⢈⡴⠋⠀⠀⠀⠀⠀⠤⣄⣼⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡴⠋⠉⢃⡼⠃⡼⠁⠉⠃⠀⠐⡄⠀⠀⠀⠀⠀⠛⢀⡄⠀⠀⠀⠀⠠⠆⣸⣿⣿⢳⡈⠆
⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠃⠁⠀⣠⠏⠁⠈⠁⠀⢠⡄⠐⠀⠘⠒⠀⢀⠀⠀⣰⠏⢁⠤⠒⠊⠁⠀⡀⠙⠇⠈⠁⠙⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠄⠖⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠘⣄⣊⡤⣀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠈⣩⣴⠏⠀⠀⠀⠃⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⣤⣀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⠟⡯⠷⠠⠄⠀⠓⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠉⠉⠉⢀⠀⠀⠤⠀⠋⠀⢠⣲⠤⣀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡋⠉⠉⠀⠀⠀⠐⠒⠒⠂⢀⠈⠃⠀⣀⣸⡟⣀⠀⠀⠠⠀⢒⠀⠀⠀⠁⠋⢀⡂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⣄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⣸⣿⠯⠙⠉⠁⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠑⠂⠐⠂⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣬⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣽⣃⠽⣧⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢘⠇⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⡁⢻⡄⠀⠀⠀⣾⡁⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢀⠀⣸⠠⠄⠩⡅⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡆⢸⡇⠀⠀⣸⠏⠀⣽⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠀⢠⠀⡟⠀⠀⠑⡇⠀⠀⠀⠀⠀⣿⠝⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣹⡇⠀⣸⣟⠈⢸⡶⠀⠀⣴⠁⡄⢀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠃⠀⠰⠆⣻⠈⠀⠐⡇⢠⣦⠀⠀⠈⣿⡌⢭⣇⠀⠀⠀⣠⣄⠀⠀⠀⢹⣿⡷⡞⣇⣰⡿⠀⢰⣿⠁⠀⠀⢛⠀⠙⠻⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⣀⠀⠅⢹⠀⠒⠡⣧⣼⣿⡇⠀⠀⢻⣷⠂⢿⠀⠀⣼⢏⡹⣧⠀⠀⠸⣿⡷⠈⠸⠟⠂⢠⡾⠁⠀⠀⠀⣸⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⣆⠀⠐⠠⠚⢼⠁⠀⣠⠘⡿⠆⠔⡆⠰⢿⢎⢤⡏⠀⠀⠀⢿⣿⠍⠑⠀⢚⣿⠃⠀⠀⠀⢀⣇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⡀⠰⢼⣧⡄⠈⠐⢺⣆⠀⣿⡀⠙⠀⠠⠼⠃⠀⢠⠟⠀⠀⠀⠀⠸⣿⣤⠈⠄⠺⣿⠀⠀⠀⠀⡾⠁⢀⠀⠰⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢄⠈⠛⢂⠀⠀⠀⢹⣧⡈⢷⡀⠀⠀⢂⠀⢜⡏⠀⠀⠀⠀⠀⠀⣿⣿⣆⢠⣄⣿⠀⠀⠀⢰⣏⡀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠛⠷⣵⣬⠅⡀⠀⣨⡹⣿⣾⡏⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⢸⣿⣉⠂⠹⢟⡇⠀⢠⣿⠯⠁⡀⣌⡟
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢰⡅⠐⡎⠛⢷⣏⡀⠁⢀⣻⣷⣷⠀⠀⠀⠀⠲⠇⠀⠀⣯⠻⣆⠀⢸⣿⣝⠁⠐⣊⣧⣴⠏⠄⠒⠄⢁⡟
⠀⠀⢀⣀⣀⠀⣶⡀⠀⠱⠀⠀⠸⣷⠀⠙⡀⠀⠹⣾⡏⠈⠹⣻⠻⡁⠀⠂⠠⠠⢽⡄⠀⣿⡀⠽⠀⣸⣿⣯⠃⠀⠀⠙⠋⠁⠡⢌⣰⠟
⠀⠀⠈⢷⡟⡻⠿⡷⠀⠀⠘⠦⡀⠻⣟⠀⠑⣄⠀⠘⢶⣦⠀⠈⠆⠉⠀⠠⠐⣚⢿⣿⣆⢹⣇⠨⣷⣿⣿⠎⠐⡀⠀⠀⠠⠠⣌⡟⠉
⠀⠀⠀⠈⠛⠻⠿⢾⣷⣨⡀⠤⠛⢷⠾⠻⠀⠀⠙⠲⠌⠛⠳⠀⠀⠀⠐⠀⢄⠀⠘⢿⣿⣧⢿⢀⠸⢟⡈⢁⠀⠀⠀⠠⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣧⣴⣄⡀⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠡⠀⡠⠀⠐⣿⣿⣘⠇⠀⠄⡁⢠⠀⡄⢾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣷⣿⣾⣿⣿⣶⣤⡄⡈⠀⠀⠐⡠⣹⣟⣷⠘⠀⠀⠃⡁⢄⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣷⣴⣃⣀⣥⣹⣿⣟⢡⡄⢐⣴⠁⣭⢂⣿⠀⠀⣴⡛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠹⣿⣟⡐⡤⠠⡝⣳⠂⠄⢹⣶⡾⠛⠖⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣎⢘⢫⣿⣿⣿⣿⣿⣿⣿⡻⣿⡿⢇⢓⣳⣾⣧⡾⢅⣤⠉⠍⣠⣹⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠣⢛⣿⣿⣿⣿⣿⣿⣞⣩⣿⣿⡶⣟⡭⣿⡿⣆⡘⢫⠠⣀⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣶⣟⣿⣷⡿⣷⡦⠹⣈⢄⡄⣁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣷⢌⣟⣴⢤⢀⣈⣔⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠛⠛⠛⠋⠉⠉⠈⠉⠉⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠉⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢋⣡⣤⣴⣶⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣤⣶⣶⣤⣤⣉⠻⣶⡀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⣧⠘⣷⣠⣿⣀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢀⣾⠋⣠⣶⢶⣦⡉⢻⣆⠀⠀⠀⠀⠀⢀⣿⠀⣿⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⢿⣄⠀⠀⠀⢠⡿⢁⣾⣿⠇⠀⣿⣿⣆⢹⣇⠀⠀⠀⣀⣼⠇⣸⡏⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡙⠻⠷⠶⠟⠁⣼⢃⣿⠀⠀⢸⡇⢿⡄⠛⠷⠶⠿⢛⣡⣾⠟⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡶⠶⠶⠟⠋⢸⡇⠀⠀⠈⣿⠈⠛⠷⠶⠶⣾⡟⠉⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣿⠟⠛⠛⠻⢿⣇⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⢀⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣦⣀⣀⣰⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠛⠋⠀⣼⡇⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣽⡖

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐
⢀⣠⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⣀⣤⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈
⠘⠃⢴⡏⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣀⣀⣄⢄⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣾⣛⣷⣖⣠⣿⠉⣠
⠀⢨⣥⡀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠘⣿⣻⣶⣿⣶⣾⣿⣾⣃⣦⠦⢀⢤⣴⡆⢰⡀⠀⠀⠀⢀⠀⢤⣶⣾⣿⣿⣿⣿⣿⠭⢚⡋⠀⢀⡯
⣴⣼⣺⣏⣀⣾⣦⣾⣥⣿⣶⣷⡶⢄⠀⠀⠀⠐⠶⡉⣩⣿⣿⣯⣿⣶⣿⣷⣇⢰⠉⠀⠈⠙⠈⠀⠀⠀⣾⣿⡟⢚⢻⣿⣿⣿⡿⣿⣟⣿⣿⣷⣤⣬⠟
⣿⣾⣤⣿⣿⣿⣿⣿⣻⣾⣟⣼⣷⣶⣼⣲⣶⣾⣿⡟⣿⣿⣿⣿⣿⣿⣤⣍⣃⡉⣓⣼⡗⠒⢢⡄⡄⠻⣿⣶⣷⢾⣾⣿⡿⣿⣯⣿⣽⣵⣿⣩⣿⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣷⣿⣿⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣬⣵⣿⣿⣯⣤⣴⣿⡿⠀⠔⠛⣿⡟⡝⣴⠟⡷⣤⣦⣿⡿⣿⣿⣿⣟⣿⣿
⡿⠿⠛⠛⠻⠿⠿⢿⡿⠿⠿⠿⣿⡿⠋⠳⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⡿⠿⢿⠟⢿⠻⣿⣿⣿⠷⢀⣠⠿⠷⢾⣿⣶⠷⣿⣿⡹⠟⠻⢿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣤⣄
⠀⠀⠀⠀⣿⡿⣿⣿⣿⡛⠿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⠟⠋⠍⠘⠻⣿⡿⣿⡟
⠀⠀⠀⠀⠈⣿⣾⣿⡃⠀⠀⢀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⠈⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠂⠀⠀⠀⠨⣳⡄⠀⠀⣼⠁⠀⠀⠀⠊⠀⠀⠀⢀⣉⣿⡁
⠀⠀⠀⠀⠀⠀⠘⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⢏⠀⠐⠁⠀⠀⠀⠀⠀⢠⣼⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⢀⣀⣀⣀⢠⣾⣿⣿⣥⣤⣤⣤⣤⣤⣀⠀⣀⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡴⠚⠋⠉⠠⠀⠀⢰⣟⢹⣇⠀⠀⠀⢄⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠠⢸⣿⣾⣿⡀⠄⠀⠀⠠⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣷⡀⠀⠀⠀⠀⠀⠀⣾⣿⢻⣿⣇⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⡀⠀⠀⠀⠀⣰⣿⠏⠈⠻⣿⡄⠀⠀⢀⢠⣰⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣆⣀⣠⣴⡿⠁⠀⠀⠀⠙⠻⣶⣶⣰⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠛⠛⠛⠓⠒⠦⣄⢰⠋⣳⠀⢀⣀⡀⠀⠀⠀⠘⢦⣀⣀⣠⠞
⠀⠀⠀⠀⢠⡏⠁⠈⢳⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⡠⡀⠀⠀⠈⢻⡍⠁⢰⡋⠀⠙⡆⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠧⣄⣠⠞⠀⠀⠀⢸⡯⠴⢎⣀⣀⠄⡊⠀⠈⠱⡀⠀⣀⣷⡎⡢⠓⠒⠚⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠖⠒⢆⠀⠀⠀⠀⢀⣼⣷⣶⡶⠖⠚⣛⣻⢟⢿⣦⠗⠉⠁⣿⡉⣁⠀⠀⠀⠀⠀⠀⣾⠀⢸⠆
⠀⠀⠀⠘⠦⠤⠎⠀⠀⠀⠀⢸⣿⣿⠉⡔⠊⠀⠀⢐⣲⢱⢻⣇⠴⠚⣿⠟⠛⢿⣦⠀⠀⠀⠀⠈⣉⡉⠀⣠⢤
⠀⢀⡔⠒⡄⢀⣀⠀⠀⠀⠀⠀⢿⣿⣆⣱⣩⡿⢿⣦⣤⣾⡿⠁⠀⣰⣿⣶⣶⣾⣻⠶⢤⡀⠀⠘⠧⠞⠀⡈⠁
⠀⠀⠓⠖⠁⢯⣀⡇⠀⠀⠀⠀⠀⠙⠻⣟⢋⣠⣤⣍⠉⠁⢀⡠⠾⠗⠛⡖⠲⢤⡀⠀⠀⠙⢦⠀⠀⢰⠋⠉⢱
⠀⠀⠀⡠⢤⠀⢠⢄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠶⠞⠉⠀⠀⠀⢠⠁⠀⠀⢳⡄⠀⠀⢸⡆⠀⠈⠳⠤⠞
⠀⠀⠀⠈⢊⣀⣨⣥⣀⣀⠤⣄⡀⣼⣿⣿⡿⡿⠭⠭⠥⠵⠶⠶⡄⠀⢸⠀⠀⠀⠀⣷⠠⠤⢸⡇⠀⠀⠀⢠⠖⠲⡄
⠀⠀⣠⣾⣿⠿⠾⠷⣿⣋⡓⠦⣝⠳⢿⣿⠃⡄⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⣿⢠⣬⢼⡇⠀⠀⠀⠹⣄⣠⠎
⣀⠾⣷⣿⢶⠀⠀⠸⣟⠦⣭⣙⡂⠀⠀⠛⢄⢉⡉⠉⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⠀⣿⢚⣻⣻⡇⠀⢠⢤
⠣⠋⠛⡅⢸⡀⠀⠀⠈⣹⠖⠂⠤⢄⣀⠀⠸⠀⠈⡋⠐⠂⠠⠤⢀⣀⣘⠀⠀⠀⠀⣯⢭⡉⠉⡇⠀⠈⠊
⢚⡉⣈⣦⠀⠙⢛⡛⢯⡉⠀⠀⠀⢠⣿⣿⡿⢃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣱⠀⡇⠀⢠⠤⡀
⠀⠹⣿⣷⣤⣀⠼⠃⢀⡇⠀⠀⣰⠋⣿⣿⣇⠀⠀⠈⠐⠂⠤⢀⣀⠀⠀⠀⠀⠀⣠⣯⠔⠁⠀⡇⠀⠈⠚⠁
⠀⠀⠈⠙⠻⠿⠶⠶⠾⠓⠒⠋⠁⠀⢻⣿⣿⡂⠀⠄⠠⠠⣤⣤⢤⡾⢛⠷⣶⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣷⣶⣟⠥⣬⢽⠀⠀⠀⣿⠿⡩⢻⡉⠉⠁⣿⠀⠀⠀⠀⢀⣠⠞⠛⠨⡙⣆
⠀⠀⠀⠀⠀⠳⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠭⣉⠙⠒⠀⠚⠳⠶⠞⡣⠊⠀⠘⡇⠀⠀⣿⠀⠀⢀⡴⢏⠉⠑⡄⠀⢁⣽⡄
⠀⠀⠀⠀⠀⠠⡦⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠉⠒⠤⣀⠀⠀⠌⠀⠀⠀⠀⢷⠀⠀⣿⢀⡴⠋⠀⠀⢈⣿⣤⣤⣾⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣆⠀⠀⠀⠀⠉⢚⠀⠀⠀⠀⠀⢸⡦⣠⡾⠋⠀⠀⢀⡴⠉⡏⢸⢩⠁⢰⠈⣧
⠀⠀⠀⠀⣞⢹⠀⠉⢉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢿⠋⠀⠀⢀⡴⠋⠀⢠⡇⢸⠈⣦⠈⡀⠸
⠀⠀⠀⠀⠈⠁⠀⢈⣿⣧⡤⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠀⠀⣠⠏⠀⠀⠀⢸⡇⡘⠀⢿⠀⢃
⠀⠀⠀⠀⠀⣦⠀⠘⣿⢞⣃⠀⠀⢀⣀⣬⣾⣵⠆⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⠁⡃⠀⢸⡆⠸
⠀⠀⠀⠀⠀⠀⠚⣧⣾⣵⡮⠁⠀⢺⣯⡤⠛⠋⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠑⢤⡤⠴⠊⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢸⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠛⣧⣽⡇⠀⢰⣿⡿⠀⠀⣿⣶⡿⡆⠀⠀⠀⠀⠈⠷⣄⣀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣁⡀⢸⡇⠀⢃
⠀⠀⠀⠀⠀⣤⢤⠀⠉⠿⣷⣄⣿⢷⣳⢐⢾⠻⣞⠻⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠙⣾⡟⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢁⠐⢧⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣆⠀⠈⣿⣦⡎⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠉⠉⠳⠉⠙⣿⠀⠀⢸⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠥⡀⠀⠀⠘⠀⣴⡿⢀⣤⣾⣿⣄⣠⡇⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠹⣶⡷⠀⢀⡇⠀⢸⡅⠀⣿⣿⠋⠀⢀⣿⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠘⢻⣇⠀⠀⢹⠆⠀⣿⠀⠀⣀⣿⡇⠀⠈⠀⢀⣾⡿⠛⠁⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⢘⡇⠀⠈⢿⣦⡀⠀⠀⠀⢠⡀⡀⣤⣼⠇⠀⢶⣿⣿⠋⠀⠀⣀⣾⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠻⠀⠀⠈⠻⡿⠾⣄⣀⣰⡟⠉⠁⠀⣀⣰⡾⠛⢧⡄⠀⣰⣿⣿⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠋⠁⡀⠀⠀⠆⠀⣿⡏⠉⠁⠀⠀⠀⠉⣹⠃⠀⠃⢀⠐⢻⣍⢉⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠴⢷⠀⠀⠰⢷⣿⠋⠀⠀⠀⢀⠤⠂⢙⣆⠔⠀⡴⠓⣿⠟⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⠂⠄⠴⣿⣿⠃⣠⣄⠀⠀⣀⠞⢻⣿⣤⣶⢿⡞⢿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣤⡆⠀⣌⠉⠉⢳⠞⠉⢰⡛⠀⣽⣇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠖⢿⣿⡦⠶⠿⠷⠾⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡄⣤
⠀⠀⠀⠉⠻⢿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣿⣷⣿⣦⡀⢐⣤⣀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⢀⣨⣿⣙⠻⢿⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢀⡠⠤⠖⠛⠉⠉⠛⢿⣶⣿⣿⣿⣦⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣶⣦⡀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠛⠃⠀⠀⢸⣿⡿⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣼⡟⠹⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣬⡿⢿⣿⣿⣿⣿⣿⣷⣾⣿⠁⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠙⠻⢿⣿⣉⡉⠙⠉⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣤⣠⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⠂⠀⠀⠈⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠏⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⡿⠟⠙⣿⣿⣿⠛⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣴⣶⡿⠟⠛⠉⠉⠁⠀⠀⠀⢘⣿⣿⠆⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀
⠀⠀⣼⣿⠋⠀⠀⠀⠀⢀⣴⣿⣷⣾⣿⡿⠿⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣏⡀
⠀⣾⣿⠏⠀⠀⠀⠤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦
⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⡿⠉⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣿
⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡟⠿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⢸⣿⣿
⠳⣾⣷⣄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣤⣈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⢸⣿⡿
⠀⠀⠀⠙⠿⠏⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠋⠙⠛⠿⣿⣷⣤⣄⣠⣤⣾⠟⠁⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠏⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⢰⠁⠀⠀⠀⣠⡚⣟⠿⣶⠀⠀⠀⢬⠐⡲⣄⠊⡄
⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢠⠐⡆⠇⢸⠀⣆⠆⠀⠻⢯⣭⣿⡝⠀⠀⢄⠦⠅⣅⠛⢤⡁
⠀⠀⠀⠀⠀⢤⣟⣇⠄⠀⠀⠀⠀⠀⠀⠀⢣⠸⡸⠎⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠘⣯⠵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠠⠀⢀⢸⢉⢠⡤⡄⠀⠃⡀⡀⠀⠀⠀⠑⠦⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠢⠽⡈⢇⠀⢣⠁⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⡄⡤⠂⡀
⠀⠀⠀⠀⠀⠐⠬⣣⣼⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⢀⢁⣠⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡀⠀⠀⠀⠀⠰⣌⠀⠀⠀⠀⠀⠼⡀⠀⠀⠀⠀⣤⢹⠈⡷⠃
⠀⠀⠢⠀⠀⣰⠌⢁⠀⢴⠀⢀⡴⠥⠂⠀⠀⠀⡀⠀⠀⢐⡆⠀⡀⡺⣝⣄⠀⠤⠠⠀⠙⠄⢀⠀⠀⡀⡀⢁⠀⠀⠦⢬⣇⡌⢹⡋⠉
⠀⠀⠀⠀⠛⠀⠀⠈⢣⠃⣟⡼⠂⠀⣆⠄⠀⠠⠢⡈⠄⠀⠡⡠⠃⢐⣯⠁⢠⡄⠆⠀⠂⢠⠈⡆⠀⣅⢣⢘⡰⠀⠀⢒⢾⡀⣯⣤⠃
⠀⠀⠀⠀⠀⠀⡄⡴⡘⣱⣫⡠⠄⠤⠋⠀⠀⠀⢀⠙⣬⠀⠀⠉⣿⢻⣤⡔⢭⡤⠔⠀⠀⢀⢢⢣⢰⢫⢻⢸⠀⠀⠈⠺⢿⡟⠁⠈⠁
⠀⠀⠚⡀⠀⠀⣏⣼⠟⠉⠁⠈⠳⠤⠀⢀⡀⠀⠀⠀⠈⣀⣰⣀⣿⣿⣻⠄⠀⠀⠀⠀⠀⠀⣄⠙⡎⢾⢸⡇⢀⠄⠀⠀⠀⠁
⠀⢐⣿⡏⠀⠀⣸⣣⡞⣉⠈⠁⠀⠀⢠⡈⣇⢠⣄⡿⠀⠀⠙⠿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢠⠈⠄⣇⣨⠎⡀⠄
⠀⠈⠛⠃⠀⢸⡟⠁⠀⠀⠀⠀⠀⣿⡄⢧⣻⣾⣿⠟⠀⠀⢀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢆⣈⡟⢃⠰⠂
⠀⠀⠠⠄⠀⠸⠀⠀⠀⠰⠀⠀⠐⣾⣿⡜⣿⣿⠃⢀⡀⠀⠀⠑⢃⢤⠳⣸⠀⠊⠎⠀⠀⣰⠾⠁⠂⠁
⠀⠈⡁⡀⣀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣇⣿⣿⣿⣼⣃⠀⠽⣜⡈⠀⠆⣳⠈⠈⠃⠈⠀⠃⠀⢠⡄⣗⠖
⠀⠈⠃⠣⠈⠀⠀⢀⠆⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠁⠀⡤⠁⠴⠀⠁⠀⠀⠀⠀⠰⡴⢫⠦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠐⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡛⣽⢳⣴⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣗⡹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡿⠟⢯⣿⣿⣿⣿⣿⣿⣿⣧⠇⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣤⡴⣚⢻⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⢍⣜⢿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠇⣵⠀⢀⣿⠃⠈⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⠋⢀⣼⣿⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⡀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⢀⣴⡿⠋⠀⣰⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣴⠿⠋⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠈⠁⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⡀
⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄
⠙⢿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⣠⡀⢀
⠀⠀⠈⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢈⡁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣶⣦⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠙⠃

⠀⠀⠀⢠⡖⠋⠓⣺⣷⡄
⠀⠀⠀⢸⠀⠀⠬⠄⣿
⠀⠀⠀⢸⠀⠀⠤⠭⣿
⠀⠀⠀⢸⢀⠀⠶⡫⣿
⠀⠀⠀⠘⠀⠀⢑⠀⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⢸⠀⠀⢝⠄⡇⠀⠀⠀⢀⡴⠅⠒⠛⠉⠙⠛⠛⠷⠶⠶⢤⣤⢤⣤⣤⣤⣤⣴⣒⣂⠩⠄⠐⠒⢚⠛⠿⣦
⠀⠀⠀⢈⡀⣀⣵⣂⡅⢀⣀⣔⡿⣪⣭⣄⣄⣄⣴⣶⣦⣖⣒⣮⣤⣭⣭⡍⣍⣵⣶⢶⠶⠦⠶⠶⢶⣿⣦⡒⢣⣿⣇⡀
⠀⠀⠰⠏⠀⠀⠀⠁⠀⣠⠊⣻⣸⡽⣩⢁⡤⠠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⠙⣌⢢⢿⣻⡃⣰⡀
⠀⠀⢀⠀⡀⠀⠈⠄⠀⣷⣰⠈⢷⠃⡏⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢽⠈⠐⣿⡟⡐
⠀⠀⠀⠒⡏⠉⠉⢉⡞⠛⣧⢸⣻⠀⡇⣀⢸⡆⠀⠀⠀⠀⠀⡀⣿⠃⠀⢹⣟⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡄⠁
⠀⠀⠀⠀⡇⠀⢐⠄⡁⠀⠈⣿⣺⠀⢣⡀⠀⠀⠊⠀⠀⠀⡐⡸⠁⠀⠀⡂⢿⣾⣦⠀⠀⠁⠀⠀⠀⣀⠔⢽⢸⣶⡿⣦
⠀⠀⠀⠀⡁⠀⠘⠀⠀⠀⠀⢸⡿⡄⠀⣈⣙⣛⣛⣛⡡⢋⠔⠀⠀⠀⠀⢆⠘⣿⣎⠩⠉⡥⠀⠩⡡⠐⠐⢗⣿⠈⠳⡽⢡
⠀⠀⠀⠀⠀⠀⢐⠔⠀⠀⠀⠈⠻⠶⠦⢤⣤⣤⣤⣤⣴⠿⠒⠤⡀⡀⡀⢀⠖⢼⣮⣑⣒⡒⣐⣐⣒⣈⣡⣾⠇⠀⠐⣡⣿⠄
⠀⠀⠀⠀⠀⠀⢀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠙⠦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣁⣄⣴⡿⣺⠷⠋
⠀⠀⠀⠀⢐⠀⢐⠁⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣑⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⡯⠗⠊⠉
⠀⠀⠀⠀⢰⢀⣀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣤⣀⣉⠓⠢⠤⣀⣀⢄⡲⡞⣋⠗⠋
⠀⠀⠀⢠⠗⠈⡉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠻⠿⠻⠿⠯⠧⠛⠁
⠀⠀⠀⢸⠀⠀⡀⡀⣠⡀
⠀⠀⠀⢘⠐⣏⣋⣩⣽⠗⡀
⠀⠀⠀⠸⠀⠈⠉⠉⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢰⣤⠀⠀⠀⠀⡤⢤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠋⠛⠿⠶⠖⠶⣶⠚⠋⠂⠁⢹
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠒⠈⠐⠠⣀⠀⠀⠀⠀⠀⠀⠙⣷⠆⠀⠀⠤⠲⢀⡀⠐⠈⡫⠃
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠖⠀⠂⠁⠀⢀⠀⢤⠂⠼⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣈⠊⠀⠀⠌⠀⠄⠄⠀⢀⡠⠔⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠉⠀⡀⠀⠀⢈⠁⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠐⠀⠂⠀⠀⠂⠨⠔⠄⢊⠔⠔⠨⠂⠅⠀⢊⠀⠔⠨⠀⠄⠀⠨⠀⠔⠔⠠⠀⠀⠀⠠⠊⠂⠀⠐

⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠘⠛⠿⣶⣆⢀⣼⣿⣿⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡖⠁⣠⣶⣿⣿⣿⣏⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣄⣀⣿⣷⠞⠛⠿⠛⠋⠿⢋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠛⠻⠿⠿⠿⠟⠛⠻⠖⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⢰⣶⣀⠤⢀⣠⣤⣴⡆⠰⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣄⣾⣿⣿⢿⣌⠙⢬⣅⣨⣟⣶⣆⣿⣦⣿⣆⠀⢀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣏⣠⣤⣏⠀⠘⢻⣆⠐⢘⣻⣿⣿⣏⢻⠃⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣏⣈⠿⣄⡿⢷⢿⣄⡈⢳⡝⣏⣹⣿⣿⣏⣻⣉⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣬⣽⣍⣽⣅⣽⣟⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢻⣯⣤⣤⣿⣉⣹⣅⣽⣿⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢾⣿⣿⣿⣯⣯⣿⣭⣿⣿⣇⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣏⠻⢟⠻⣿⣿⣿⣷⣾⢻⣍⠈⣉⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣀⣤⣼⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣈⠻⣿⣿⣍⠻⣿⣿⡟⠛⠉⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⢿⣿⣿⣾⣿⣿⣷⣶⡶⠾⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡙⣿⣿⣿⣿⣿⣿⢻⡆⠈⣍⣹⣇⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⢬⢻⣿⣿⣿⣿⣤⢿⣏⠉⣠⣈⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⠋⠀⠀⠀⣀⣡⣿⣿⣿⣏⣤⠤⢻⣏⠉⣋⠀⠹⢿⣦⣄⡀⠀⠀⣷⠀⣀
⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⣀⠀⢀⣤⡤⣴⣤⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣯⣄⡠⢿⡞⠉⣱⠖⢠⡈⠛⠿⣿⣶⣇⣀⣿⣷⡀
⣤⣖⣺⣏⡥⠼⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠹⣉⣤⡄⠈⣿⡴⣶⣷⣴⠷⡄⠀⠈⠙⠻⠿⣿⣧⣄
⣽⣿⡿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⢿⣿⠟⠻⠷⠄⠀⡴⠟⠘⠉⠥⠀⠀⠀⠀⠀⠀⢫⣿⣿⠛⠙⣷⡿⣿⣿⣀⣵⣄⠀⠀⠀⠀⠈⠉⠻
⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣤⡾⢷⠿⣿⣧⣄⠹⡄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⠱⣚⣷⣿⡟⣻⣤⣿
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⢟⣙⣿⣯⣍⣻⣿⡗⣆⠀⠀⠀⢀
⣿⣿⣷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣿⣻⣿⣿⣛⣻⣷⠋⠀⠀⠰⣾
⣿⣿⣿⣿⣷⣷⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢿⡿⣿⣿⢿⣿⣋⣠⡤⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣠⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣴⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢄⠀⠈⠓⢿⡦⢔⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠠⠤⠤⠀⠐⠒⠐⠒⠒⠒⠒⠛⠚⠢⢄⡀⣂⠌⠀⠀⠘⢣⢋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢗⡀⡠⠀⠀⠀⠀⠀⠀⠀⠐⡤⠄⣀⠀⠀⠀⠀⠀⡰⠙⡁⠀⠀⠀⠰⡀⢉⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⡔⠉⠀⠀⡠⠊⠉⠒⠒⠉⠀⠀⠰⣠⠐⠉⠒⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⣄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⡩⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁
⠀⢀⣀⠠⠤⠤⠤⠤⠤⠀⠀⠠⠤⠀⠀⠠⡄⠠⠤⠀⠒⠂⠀⠉⠐⠒⠂⠩⠁⠀⠀⠀⡰⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠂
⡎⠁⡠⠤⠄⠐⠒⠒⠒⠂⠀⠐⠄⠀⠀⣈⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢠⠀⠀⡠⠊⠀⠀⠀⠀⠀⣱⠄⠒⠈⢁⠔⢁⡠⠊
⠱⡀⠢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⡠⠚⢡⡄⠀⠐⡁⠔⠁
⠀⠸⠀⠇⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⣀⠔⠉⠀⠀⣞⣷⡠⠜
⠀⠘⣀⣑⡠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⡁⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠔⠉⠉⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⡠⠊⠀⠀⠀⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠔⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠤⢀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⠡⣀⢌⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⣟⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠐⠾⣿⣵⣾⣽⣿⣟⣹⣿⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠡⠀⠀⠴⠃⠀⠀⠀⢀⣤⣶⣾⣿⣟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠴⠃⠀⠀⠀⠀⠀⣠⣾⣿⣟⣫⣴⡽⢪⣿⣷⣦⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠺⢿⡟⢆⠀⠀⢤⢠⠀⠀⠀⠀⢀⡔⢺⣿⡟⠟⣨⣽⣟⣥⣿⠟⣹⣿⡿⢿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠠⠸⠆⠀⠀⢀⣞⢿⢓⡘⠁⠀⠚⠉⠚⢹⣱⣾⣿⡿⠋⠁⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⡄⢯⣟⢿⣿⣇⠲⣶⣶⣾⣿⣿⣿⠟⠉⠀⠀⠀⣼⠏⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡷⠹⣿⢿⣬⣿⣯⣿⣮⣭⣭⡭⠉⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠃⣰⣿⣾⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠋⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠁⠚⠉⠉⠀⠀⠠⠤⠶⠖⠻⠿⠛⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⣈⣗⣄⢀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣤⢾⣿⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠿⣧⣉⠂⠀⠀⠀⠖⠈⢹⢟⣿⣿⡁
⠀⠀⠀⠀⣠⣴⣿⣿⣷⣿⡿⣯⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠓⢠⣾⠛⢿⡄
⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣾⣧⠤⠦⣤⡀⠀⠀⠘⠂⠙⠻⠃
⠀⠀⠀⠿⠿⠛⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡆⠀⠉⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃

⣿⣿⡿⠟⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠶⣦⣄⣀
⠀⠀⠀⠈⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠉⣻⣷⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣀⣠⡄
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦
⢀⣀⣤⣴⣾⣿⠟⠋⠉⠉⠉⠙⠿⢿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⠙⠛⠛⠻⠿⣿⢿⣿⠋⠉⠉⠛⠋⠉⠛⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠀⠀⠸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠗






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠀⠀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣉⠤⠐⠂⠁⠉⠉⠁⠁⠒⠢⢌⡁⠂⢄⡀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠉⡆⠀⠀⢹⠉⡚
⠀⠀⠀⠀⠀⠀⠘⡀⢨⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⠀⠀⠀⠀⠀⠀⡆⢀⠁⠀⠀⢨⣉⡅
⠀⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⠀⠀⡔⠀⣠⣄⠈⢆⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⣤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠳⣀⣀⠔⠁⡘⢰⠈⡄⠀⠓⠤⡠⠊⣠⠊⠀⠀⠀⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡤⠒⠒⠤⣑⠼⠤⣃⠴⠊⠉⠀⡖⡙⠀⠀⠀⠀⠀⡗⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠑⢄⠀⠀⠀⠈⠀⠀⠀⠀⡠⠎⢠⠃⠀⠀⠀⠀⠀⡏⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⡐⠂⠀⠀⠐⢒⡉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠧⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠍⣉⣉⠉⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠤⠤⠤⢰⠄⠀⢀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⢔⠁⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠑⠒⠒⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠠⠒⠁

⠀⣴⣶⣶⣶⣶⣶⣦⣶⣶⡤⢄⣤⣄
⠀⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣄⣹⣿⣷⡀
⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣏⢻⣿⣿⣿⣗⣀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣝⠺⣿⣷⣤⣶⣄
⠀⣌⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣌⣻⣿⣧⣀
⠐⠛⠿⣷⢹⣿⣿⣿⣗⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⡅
⢀⣄⣠⣿⣶⣤⣝⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡃
⠀⠙⠿⣿⣍⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠳⣀⡀⠀⣀⠀⠀⠀⠀⣶⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴
⠐⣾⡷⡎⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣶⣦⡰⣄⣿⣿⣿⣿⣶⠀⠀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠈⠠⢀⣬⣿⣿⣿⣿⣿⣿⣻⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣤⣬⣿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡼⢾⣿⣿⣤⣿⣿⣿⣿⣿⣟⣽⡾⣷⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢄⠂⠶⢦⡠⢐⢦⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡭⠭⡅⠓⠂⠀⠙⠂⠑⢮⢪⢣⠀⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠒⠀⢀⣠⢖⡀⢀⡀⢀⡠⠠⠀⣏⡃⠀⠀⠀⠀⠀⠔⠊⠉⠉⠳⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠦⠤⠴⠁⠘⠈⡔⠉⠉⢢⡠⠀⢯⠂⠙⠀⠀⢀⠄⠀⠀⢀⡀⠀⠀⠘⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⠀⢄⣲⡆⠀⢀⢸⠀⠀⠀⠰⠑⠀⢀⠃⠰⢰⠊⠉⡶⠊⠉⠉⡃⠀⠀⠀⠈⠅
⠀⢲⠀⠀⠀⠀⠀⣰⣀⠀⣸⠀⠼⡑⡠⠄⠐⢄⡘⠘⢄⣀⣠⢜⠕⢚⠧⠄⡦⡜⠒⠂⠧⠤⢠⠔⠁⠀⠀⠀⠀⠈⠄⠀⢀⠐⢁
⠀⠨⠤⠀⠐⠂⠚⠁⡾⠋⠉⠙⠷⠀⠮⠐⢀⠻⠓⠤⣉⠉⠡⡖⠡⢐⡯⠎⠀⠈⠫⠂⠄⠀⠀⠀⠀⠀⢰⠅⠀⠀⠈⢻⡏⢠⠌
⠀⠀⠀⠀⠀⡀⢀⣀⡄⣆⠀⠈⡄⠀⡠⠖⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⡱⢄⡀⠀⠀⠀⠺⣍⠀⢠⠠⠂⠙⠉⠈⡆
⣀⠄⠂⠁⠀⢀⠼⠏⠿⠮⣂⡀⠌⠚⠀⠑⠕⢢⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠁⠈⠒⠄⠠⠤⠚⠓⢾⠀⠀⠀⠀⠈⠁
⠉⠒⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⡀
⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠐⠀⠣⠀⠐⠀⠈⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⢀⠀⠀⠀⠱⣄⠀⠀⠈⠀⢁⠘⠁⢀⡄⠀⢀⠀⠰⣦⠀⢀⠵⠢
⠀⠀⠠⣈⡀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠈⠁⠸⠐⠊⡁
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⢠⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠊⢀⠄⢀⠀⢀⠀⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⢀⡀⠄⠠⠀⠁⡄⠀⠀⠛⠈⠁⠀⢀⡀⠀⠁⠀⣼⡀⢾⠋⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠠⡁⠀⠄⠰⠃⠀⠁⠀⠀⠀⠀⠉⠁⠀⠰⠛⡄⠥⢬⣄
⠀⠀⠠⠄⠠⠀⠀⠈⠂⡱⠂⡁⠀⡀⢁⠰⠋⠈⢡⠀⠓⠁
⠀⠀⠀⠀⢠⡤⡈⠲⠐⠙⠂⠁⠀⠁⠤⠂⠀⠈⠜⠛⡓⢄⠀⠀⠀⠀⠐
⠒⠂⢤⣴⣁⣀⠀⠀⢀⠈⣥⡀⡉⠁⠂⠀⠀⢀⠆⣹⠓⠖⠛⠁⠘
⠀⠀⠀⠀⠠⠀⠀⠸⠟⢄⠸⢀⡀⢁⠄⠀⠄⢢⡈⢻⠐⠂⢀⡁⢠⠤⢀⠀⠀⠀⠀⠂⠰⢄⣄⣠⡤⠤⠆
⠐⠀⠀⠀⠀⠀⠀⠃⢢⠀⠦⠄⠁⡀⠀⡈⠰⣥⣸⠂⠰⠐⠀⠀⠄⠀⢀⡀⠀⠐⠀⠁⠲⢤⠚⠉⠄
⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠃⠐⡀⠐⣡⠈⠀⠠⠛⣈⡁⠐⠒⡹⢛⣀⣄⠀⠁⠁⠀⠀⠀⠂
⠣⠴⢴⣀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠤⣰⠀⠒⢁⡀⣁⠽⢀⡾⠛⠇⢠⡄⠀⠒
⠀⠀⠀⠠⢊⠟⠁⠀⢀⡀⠀⠀⢠⠀⢀⡈⠀⠀⠀⠈⠙⠀⠥⡌⠀⠀⠀⠀⡐⠋⠘⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠘⠀⣄⠀⠀⢀⣰⡖⠃⢳⠦⢥⣶⢤⣴⠎⠈⡀⢉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠂⢀⣠⢀⠺⡂⢈⠄⣠⠴⣎⣠⡴⠚⣤⣼⢇⣠⠩⣏⡳⠯⣀⡀⡠⠄⠐⠀⡀⠄⢀⠀⠀⠀⢰⠀⠃
⠀⠀⠀⠀⠀⠀⣨⠠⠌⠌⠉⠱⣶⡥⢀⡈⢚⡀⠀⣸⡄⣦⣿⠃⠀⣵⠀⠸⠃⢀⣤⡤⠀⠀⠄⠚⠀⠆⢀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⡔⠂⠀⠈⠁⢜⠉⢹⡏⠙⡶⠈⠹⡆⠘⢶⣈⠁⠀⠤⠄⣤⡤⠀⠂⠸⠀⠀⡀

⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⣿⣿⠀⢳⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⢣⢸
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣤⣾⣧⣴⣦⣴⣿⣿⣿⡄⠘⣇⠀⠀⠀⠀⠀⡇⣿⠀⠀⢸⢸⡇
⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢹⡄⠀⠀⠀⠀⣿⣿⡄⠀⢸⢸⡇
⢸⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣷⠀⠰⡀⠀⢹⣿⣇⣰⣿⣿⣇
⢸⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠩⢟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢹⡇⠀⣇⠀⠘⣿⣿⣿⣿⣿⣿
⣼⣿⡎⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⣿⡄⣿⠀⠀⣿⣿⣿⣿⣿⢸⡄
⣿⣿⣿⣔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⡇⠀⢠⣿⣷⣸⡆⠀⣿⣿⣿⣿⣿⣾⡇
⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⡇
⣿⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡎⣿⣿⠏⣿⠃
⣿⡟⣿⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣇⣿⣿⢠⡿
⣿⣧⠁⠇⢰⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⣿⣿⣿⠃
⣿⡷⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣹⣏
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡀
⣿⣿⣶⣶⣶⣿⣿⣷⣶⣤⣴⣶⣶⣦⣄⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣧
⣬⣙⠋⠉⣹⡿⠿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣶⣤⣤⣤⣤⠤⠂⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣷⣌⠉⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⡇
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣿⣿⡤⠠⠦⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⡿⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠐⠹⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢹⠇⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠀⢠⣼⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠋⣠⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢣⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⢠⠀⠀⠁⠀⠀⠀⠀⠎⠄⡂⠘⡠⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠘⠺⡀⠀⠀⠐⡢⠀⠀⠀⠀⠷⡀⡅⠃⠈⠀⠀⠤⠀⠀⠀⢠⣒⠂⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡴⠀⡠⠂⢀⠀⠀⠀⠀⠌⠵⠄⡴
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠠⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡴⣀⠀⠀⠀⠀⠀⠐⠳⠀⠀⠁
⠀⠀⠀⠀⢠⠈⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠙⠋⠁⠀⠀⠀⠀⠀⠐⠂⠀⠃⡀⠀⢀⡀
⠀⠀⠀⠐⡀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡘⣰⠃⠀⠀⠆
⠀⠀⠀⠀⠠⡠⣄⡇⠀⠁⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢂⠠⠃⡇
⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠐⠐⠀⠢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠒⡂⠑⢫⠈⡤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠂⠀⡀⠀⠀⠀⠀⢀⠀⡅⢀⢁⡏⠈⣧⠀⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠉⠈⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠳⠶⢶⣦⣤⣤⣤⣤⣶⡶⠶⠞⠛⠛⢶⣄⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢠⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠉⠻⣿⣶⣿⠀⠀⣿
⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⣸⠃⠀⢠⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠈⢿⣿⣦⣀⠀⠀⠘⠁⢀⣴⣿⡿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣶⣾⣿⡿⠛⣁⣀⠀⠀⠉⠻⢿⣿⣷⣶⣿⡿⠟⠋⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠙⢷⡄⠀⠀⢠⡾⠋⢉⣿⠀⠀⠀⠀⣿⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⡛⠛⠟⠛⣁⣴⣞⣁⣀⣀⣠⣴⠟⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡛⠛⠉⠉⠉⠙⠉⠉⠁⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣤⣤⣤⡴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⢻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢁⣄⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠴⢿⣿⣿⣷⠟⠋⠉⢻⣿⡄
⠀⠀⠀⠀⢠⠃⠀⠈⣉⣉⠁⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠁⠀⠀⠀⢠⣿⠃⠀⠀⠰⠄
⠀⠀⠀⢰⡏⠀⠀⠀⠄⠀⠀⠀⠀⢠⣼⠏⠀⠀⠀⢲⡇
⠀⠀⠀⢸⠀⢀⡀⠐⠀⠀⠀⢀⠐⡜⠏⠀⠀⠀⢀⣾⣟
⠀⠀⠀⢸⠀⠠⠈⠀⠀⠀⠄⠁⣜⠀⠀⠀⠀⠀⠈⣿⡟
⠀⠀⠀⢈⡄⠔⢢⣁⠀⠀⠀⢨⡾⣶⣶⣖⣒⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣖⣦⡀
⠀⠀⠀⠠⢻⠡⡀⠉⣤⠀⢿⡞⠁⠀⢤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠰⢂⠀⠉⠀⠡
⠀⠀⠀⣿⣟⠀⢹⣄⠉⠀⠸⡴⠤⠄⢠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣴⠀⠈
⠀⠀⣰⡗⣱⣦⡔⠛⡁⠀⣥⢦⠀⠀⠀⠉⠉⠻⢟⣙⣻⠻⠏⠉⠁
⠀⢸⣿⡁⠁⠙⣧⠀⠰⢶⠂⠀⠢⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⢸⠟⣰⡄⠄⠉⣶⣄⠀⠰⣦⡔⠄⠀⠀⠀⠀⢀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠔⣻⡇⢿⣿⡀⠀⡀⠛⠙⠃⠀⠁⡄⠀⠀⠀⠀⢘⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠊⠁⢀⡜⢩⣷⠈⠀⡀⠈⠐⢤⠀⠙⢷⠆⡀⠀⢸⣟⣿⡁
⠀⠀⢬⡓⠀⠈⠀⠢⠄⣤⠊⠀⠸⣗⣀⡀⠀⢀⣬⣿⣷
⠀⠀⢘⠇⣠⠢⠀⠀⠀⢳⣤⡀⢰⠏⠛⢻⣾⣮⣿⣿⣿⡧
⢀⠀⡠⠆⢡⠁⠰⡆⣀⠀⠈⠻⣯⣯⡁⠀⢻⣿⣿⣿⣿⠃
⢦⡎⠘⡀⡅⠀⠀⠨⠻⡆⠀⠀⢈⠉⠙⣿⣿⢿⣹⣿⣿⠁
⠚⡀⡀⠢⢼⡇⠀⠐⠀⠀⠳⣶⡄⢄⠃⠘⣷⣶⡟⠛⠛⠒⢲⣦
⢠⡿⡍⠂⢺⡄⢠⠆⢦⠠⠁⠈⣿⡟⢷⣾⠟⠘⣿⠍⠙⢻⡟⠻⢧⡙⣡⣐⠴⠂⢀
⠊⢱⣧⠀⢦⣹⠂⠀⠀⣄⡀⠀⡿⡻⢶⣾⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡿⠋
⠋⢨⡟⠘⠋⡿⠀⢠⡗⠎⡻⣧⢡⡇⠊⠹⣿⡟⣿⢳⣊⣈⣁⣀⢀⡩⢠⠬⠍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣤⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣤⣀
⢀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣁⡿⢤⡙⢿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠑
⠀⠈⠉⠙⠳⢶⣤⣀⡀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣾⠃⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡳⢤⡀⠀⣸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣈⣻⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡴⠚⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣤⣶⣶⣶⡶⠾⠛⠛⠛⠛⠻⠿⠿⣿⣿⣛⠛⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣦⡀⡱

⢀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣷⡠⣀⠀⠀⠀⠀⣠⣦⣀
⠈⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠙⠳⠶⠶⠞⠛⠉⠙⠻⠶⠶⠶⠛⠉⠀⠀⠀⠀⠘⣷⡉⠛⠛⠛⠛⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣨⣥⣴⣤⣄⡀
⠀⠀⠀⢀⣠⣴⣶⣎⠿⠟⣭⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠠⣶⣿⡿⣛⣵⠿⠋⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⢶⣶⣄⣿⣿⡿⣣⣮⡻⢿⡇
⠀⠙⠵⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡟⣴⣿⡿⣿⠏⢫⣾⣮⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣷⡁⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣶⣤⣀⡀⠈⠛⠛⠛⠛⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠈⠛⠿⣿⣿⣿⣶⣤⣤⣾⣿⣿⡿⠂⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣶⣶⢴⠶
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣿⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⢀⣾⣿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠱⠷⠆
⠀⠀⠀⠀⠀⠉⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢀⣠⣦⣀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠈⠙⠛⠛⠛⠛⠉⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀⣠⣤⣶⣶⣶⣶⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣬⣑⣆
⠀⠀⠀⠀⠀⠀⢹⣿⡟⣼⣿⣿⢿⣿⣧⣿⡟⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣟⢼⣿⣿⣿⣿⢹⣷⠄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠜⢿⣯⣾⣿⣿⣿⣿⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠈⠛⠻⠿⢟⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠛⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠎⠁⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣣⠀⢀⣹⠇⠀⠀⠠⠶⠶⠂⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠾⠛⠀⠀⢀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣀⣴⣆⠾⣡⣼⢗⡀⠀⠈⠳⣶⣶⣾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋
⠀⠀⠀⠀⣤⠀⠰⡆⠘⠃⠀⠀⠀⠀⢛⢣⠬⣷⣼⠋⠈⢥⠀⠀⠀⠈⠙⢻⡟⠀⠠⠂⠀⣀⠀⠀⠀⠀⠀⣤⣾⣧⡿⣷⣿
⠀⠀⠀⢞⣩⡄⢀⡀⠀⠀⡀⠀⠀⠀⠘⢵⡦⢹⣿⢠⡄⠶⣤⣄⢀⠀⠀⢸⠁⠀⠀⠀⡴⣿⠀⠃⠀⠀⠀⠙⣱⣮⡿⣶⠅
⢸⣼⣿⡞⣿⣷⣿⣿⡄⠀⢹⠀⠀⠀⠐⢾⣿⣿⣧⣾⣿⣾⣿⣷⣾⡏⠀⢸⠀⡠⠆⠀⢡⡟⠈⡴⠀⠀⠀⢹⢧⣶⢿⣿⢳
⢸⣿⣿⣿⣿⣿⢿⣿⣿⣠⠘⠀⠀⠰⠀⢨⣿⣿⣿⣽⣿⠛⢻⡉⣿⣄⠀⢸⣬⣷⣶⣦⣿⣿⡖⠁⠀⡀⢀⠋⣯⣿⣿⣿⣄
⢸⣃⣿⢛⣿⣿⣿⣿⣿⣿⠀⡄⠀⠄⠀⣾⢩⡽⣿⣻⣿⣿⣾⣷⡷⣾⣦⣾⣿⣏⣿⣿⣿⣿⣿⡄⠀⠙⣿⣠⡜⣻⣿⣿⠋
⢸⠷⣾⣩⣿⣿⣿⣿⢿⣇⣶⡇⠀⠀⣸⣿⢎⡀⣿⢄⣿⣿⣿⣷⣾⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢰⠗⢹⢷⣿⠋⡘⠁
⢸⣇⠀⠿⢿⣿⢿⠁⠀⣿⣿⡇⠀⠀⣿⣿⡞⣿⣿⣸⣿⣿⣿⣿⣿⣳⡌⢻⣿⣟⣿⣿⣿⣿⣿⣿⡿⣾⣼⣧⣻⡟
⢸⠻⣷⡀⠀⠐⣟⣧⠀⣿⣿⠁⠀⣸⣏⣲⣽⣬⢸⡟⠹⢿⣟⢿⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⡷⣤⢦
⢸⢻⡞⢆⡀⠀⣿⣿⣼⠏⣿⡇⠘⣿⣿⣿⣿⣿⣿⠻⡆⣼⣿⡨⣿⣿⣿⡔⢩⣿⣿⣿⣿⣿⠋⢺⣿⣿⣿⣿⣿⢰⠇⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⢰⠀⠀⠀⠘
⠀⠀⠃⡀⠀⠀⡱⠇⠀⠀⠀⠢⢴⠀⠀⠀⢀⠀⠁⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⢰⣅⢠⠃⠀⠀⡎⡄⠀⠀⢠⡅⠀⠀⠀⢰⣀
⠀⠸⡀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢈⠀⠀⢀⠀⠸⡆⠀⠀⠀⠀⠀⡈⠀⢀⠐⠀⠀⢸⠟⡾⠀⢀⢸⠠⠂⠀⡘⡾⠀⠀⠀⠀⡀⣿
⠀⠠⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢈⡆⠀⣠⠐⠁⠀⠀⠀⠦⠁⠀⠘⠀⠀⠀⠀⣄⠃⠀⠘⢾⣾⠀⠀⠇⠁⠀⠀⠀⠀⣿⡿
⠀⠀⢹⠇⠀⠀⠀⠀⡀⠀⣠⣀⠄⠀⠀⠰⠀⠀⠀⠂⡏⠙⠃⠀⠀⢠⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠂⢃⠂⠀⠀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡀⢀⠀⠑⠆⠀⠈⠀⠀⠀⠁
⠀⢈⠀⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢐⠀⠈⠀⠀⠀⠀⠀⠈⠀⠂⠐
⠀⣠⠈⡁⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠐
⠀⡌⠘⠀⢁⠐⠀⠀⠀⠈⠀⢀⣀⠀⠀⠀⢗⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠀⠀⠄⠀⠀⠰⠀⡀
⠀⠁⡀⠀⠈⠀⠡⠀⠀⠀⠀⠘⠛⠁⠀⠀⡸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠁⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠄⠘⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠐⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠰⢤
⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠂⠀⠀⠐⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣶⣧⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡄⠀⡔⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠉⠛⠉⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠂
⠀⠀⠀⣁⣀⣀⡀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠅⠈⠀⠱⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⡠⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠀⠀⠀⠀⠀⠺⢿⣿⠀⠀⠀⠐⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠤⠄⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢤⠀⠓⠲⠤⠀⢈⡀⠠⠄
⠁⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠐⠀⠙⣴⡀⠀⢶⠼⣇⣀⣀⡀⠰⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⡀⠄⠞⡩⢷⡂⠘⡆⢨⣀⡀⠙⠟⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⠂⠠⠐⠀⠈⡲⡷⣴⠼⡉⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢂⢀⠀⢀⡤⠒⠉⠉⠝⠢⠀⠀⠀⠀⠸⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠉⠂⠀⠊⠀⠀⠀⠀⡶⡀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠆⠴⠀⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠠⠊⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠋
⠀⠀⠀⢀⠀⠄⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣧⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠻⠿⠷⠛⠋
⠀⠀⠀⠀⢰⡰⡜⣧⣧⢔⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠠⠦⠵⠦⢠⢀
⠀⠀⠀⢐⣢⠷⣜⣏⢳⣿⣦⢴⠂⠀⠄⡀⣂⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⠓⠒⠶⠶⠶⠷⠛⠋
⠀⠀⢀⠀⠋⠛⠒⢻⠿⣿⣻⡵⢤⡑⢴⡤⠠⣞⠑⠀⠴⣂⣠⣤⡠⠤⡄
⠀⢠⡌⢀⠀⠀⢰⣿⣙⣿⢿⣧⣴⣯⣿⣧⣶⢶⣴⡔⠶⣦⣔⣛⠯⠖⣂⠾⠰⠄
⠀⢨⢻⡀⣆⢰⠛⠿⢾⡚⢉⣽⣯⣐⢶⢯⡏⢿⣻⠃⢯⠉⢹⣿⠿⢥⣌⠉⡇⡖⢲⠀⡤⣀
⠀⢸⡌⣷⢸⡞⣄⠀⣠⣏⢺⣿⣿⣿⣿⢷⣿⣦⣧⣴⣾⡆⢰⣿⡀⢾⣿⣇⣿⢀⣿⣼⠁⡨⠂
⠀⢈⣧⣼⣿⣷⣿⠏⠉⠓⣶⣿⣿⣿⣟⣿⣾⣿⣿⠏⣾⡻⠾⢿⣧⡿⠁⠀⣿⡞⢉⣽⣮⣶⠃
⠰⠿⠿⠿⠿⠿⠿⠤⠤⠼⠯⠯⠿⠻⠛⠻⠿⠿⠿⠿⠭⠥⠤⠤⠿⠷⠤⠾⠛⠚⠛⠛⠛⠛⠓⠂

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢖⢷⡀⠀⠀⠀⢀⣀
⠈⠓⠲⠶⠒⠋⠙⠒⠶⠖⠚⠉⠓⠶⠶⠒⠋⠙⠲⠶⠖⠛⠙⠓⠶⠶⠚⢉⡤⣄⠘⣯⢿⠛⠒⠚⠉⠉⠙
⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠓⠋⠀⠘⣎⣧⣀⣀
⠀⠀⢀⣠⡤⠾⣏⣀⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⠇⠀⠀⠀⣰⠋⠁⠀⠈⠻⡄
⢶⠚⢉⣤⢖⣠⠟⠉⢳⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢒⣒⠒⠧⠀⣠⡞⢦⣀⣿
⠈⠷⢯⡴⠋⠀⠀⠀⠀⠙⢦⠀⠙⠦⠤⠤⠴⠖⠛⠛⠲⠴⠖⠛⠉⠁⠀⠀⣿⠁⢠⣠⣿⠉⢙⡶⠛⠃
⠀⠀⠀⠀⠀⠀⡴⠛⣶⢤⣈⡳⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⠈⠙⠉
⠀⠀⠀⠀⠀⢰⣇⣠⡯⣄⡈⠉⠛⠻⠿⠋⠉⣙⡷⠦⠤⠤⠶⠒⠛⢹⡏⢹⡏⠉⢧⠈⠓⠒⠒⠒⢲⣖⣶
⠀⠀⠀⠀⢠⡟⣀⢹⠀⠀⠉⠓⠶⢤⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⠳⢤⣈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⢀⡞⢠⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣈⢹⡶⣤
⠀⠀⠀⠺⠦⣼⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣀⣤⡴⠲⢤⣄⣠⡤⠖⠦⡄⣀⡀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣄
⠀⠀⠀⠀⢸⡛⠓⣦⠴⠚⠋⢙⠛⠳⢦⡀⠀⠀⠀⠀⠀⢤⠦⣄⡤⠿⠿⢦⣀
⠀⠀⠀⠀⢸⡇⠰⣇⠀⣤⠀⠋⠀⣏⠀⣹⠆⠀⠀⠀⠀⢸⠀⣯⡀⠀⠀⢇⣹⠇
⠀⠀⠀⠀⢸⣤⡴⠟⠳⢤⣄⣤⣤⡴⠚⠁⠀⠀⠀⠀⠀⠙⠋⠉⠉⠿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣤⣤⣄⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⣤⣭⣭⣿⣿⣧⣶⠾⠶⢷⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣾⡟⠁⠀⢀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⢻⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣾⠋⢀⣾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣏⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣹⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠟⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⠋
⠀⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣀⡈⠙⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⡆⣠⣤⣀
⠈⠻⢦⣄⣀⣀⣀⠹⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⠆⠀⠀⠐⢠⢤⡀⠘⣿⡿⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠦⢧⡈⠣⡈⠲⠈⠳⡀⠀⢾⠀⠘⢁⡞⠁
⠀⠀⠀⠀⠀⣴⢀⡤⣠⠀⠀⠀⠠⡀⣁⠈⠈⠀⠀⠙⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⢤⡹⣆⢻⡕⢀⠀⠈⢂⡜⢠⣀⠜⣤⣴⣠
⣺⡷⢲⠀⢀⡽⢎⡽⠁⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⢣⠳⡀⢹⣸⡇⢄⠑⢄⡌⢴⠋⠀⣠⠉⣸⣇
⡏⠀⢘⡶⠊⣴⠊⣀⢀⡴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡛⠧⣇⠀⢻⡗⣨⡃⠈⣧⠃⠀⣰⣮⠴⢻⡏
⠀⣠⡟⣿⡄⡬⠰⢣⠞⢟⣁⣄⠀⠀⠀⠀⢀⣠⠆⠀⠐⣍⢣⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡴⢫⡇⣄⢱⠘⡇⠈⠣⠘⣇⠀⣠⠟⢡⣶⣨⡷
⠀⠙⠀⢹⣼⣣⠤⣼⢖⡿⠚⠉⠀⡀⠀⠐⠌⢁⣀⠀⠆⠌⠙⢧⠀⡎⠀⠀⡄⢠⠀⠀⡔⠀⢲⢸⠄⡇⢸⡀⠘⣼⠀⡰⠘⡀⢿⠈⢾⣧⠀⢸⡇⢿
⢸⠁⣇⡴⢻⠁⣠⠸⡏⠀⠀⠢⠁⠀⣤⠀⡅⠀⠙⢷⡄⠠⡄⢈⣧⠀⣄⠉⠳⡐⠁⣌⣀⡄⠀⢻⡀⢿⡀⠙⠢⡀⣿⠰⠊⠁⢹⣠⡆⠻⣤⡾⠃⢈⡆
⠁⣠⠿⠒⣺⠏⠀⣸⠁⠀⠀⠀⢠⠀⠈⠳⢶⡀⠀⢄⠙⡦⣼⢸⡇⠀⠀⠱⣤⠀⠀⠀⠀⠀⠀⠈⡗⠀⣿⢶⡀⠸⣿⡄⠀⠀⢸⠃⣟⠁⣹⢄⡀⡄⣧
⠊⠁⠀⢀⡧⠔⠋⠀⠀⣠⣤⣐⣏⢢⠀⠀⠀⠛⣆⠛⡀⠘⢶⡖⣧⡶⠂⠠⣏⡤⠊⠉⢹⡆⠀⠐⣇⠀⢻⢠⠌⢶⡁⠙⣦⡀⣼⠀⡆⡜⣾⠀⠉⠱⣯
⠀⢀⣴⠋⠀⣠⠂⣠⠞⠀⠀⠉⠉⣱⠦⠀⠀⠀⠘⣦⣙⠠⠸⠇⡏⠀⣱⡦⠏⠁⠀⣀⡀⣘⣆⡀⠈⠑⢾⣠⠀⠸⠃⢸⣡⠎⢻⣜⢁⡏⣿⠀⠀⠀⡿
⣉⠉⣌⣡⠆⠠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢌⡉⠙⢳⡆⠀⢧⣷⣸⠆⠀⠀⠀⠀⡉⠀⠉⠀⠑⠲⢤⠈⢷⠃⠀⢰⠇⢠⡀⢻⡏⠀⣸⣦⠴⠾⠛
⣛⣭⠁⡀⠔⠃⢀⣀⣀⡀⠀⣀⣤⠀⠀⠀⠀⢠⡄⠈⠓⠦⢽⡟⢿⡟⢃⣠⠗⠛⠿⠟⠑⠒⠒⢶⣄⡀⠀⠙⠻⡄⠀⢾⠀⠀⠓⢤⣇⣠⣿⠁⠀⢀⣴
⠁⠀⢠⣃⡤⠴⠋⠀⠀⠉⠉⢉⠍⠀⠀⠀⠀⢐⠞⠉⠙⠺⢶⡇⢸⠟⣛⠀⠀⠀⠀⠀⠀⠲⠒⠦⠬⠿⢶⡒⢲⡛⠓⢼⣦⡀⠀⢠⣿⠏⠁⠀⡴⠛⠁
⠁⡼⠋⢀⡀⠔⣢⠤⠤⠔⠂⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠾⠲⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡄⠈⠛⠛⠲⢦⣿⡄⠀⣴⠃⢀⠔
⣾⣋⣒⣉⢀⡐⣁⡀⢀⣀⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠠⡄⠐⠒⢒⠆⣤⣀⠀⠀⠀⠀⠀⠀⠀⢙⣓⡆⠒⠋⠀⢙⣷⣰⠇⢀⣞⣀
⠧⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠋⠸⠌⠰⠁⠀⢀⡾⠀⡀⢉⠑⠢⢄⡀⢤⣀⠀⠀⠻⢇⡀⠀⢀⣼⣿⠟⢾⡭⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⡀⠠⢂⡔⠀⣰⠏⠀⢠⢁⠋⠄⠀⣞⠞⠂⡸⣵⡀⠀⠈⢳⣴⣿⡿⠤⠊⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠻⡅⠰⣆⡦⢼⣷⣳⠞⠂⢵⣯⠀⠀⠆⡌⡔⠀⣴⡏⠀⣰⢰⠁⡃⠀⠀⢾⣿⠷⠐⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⡑⢦⠀⣹⣭⡿⢽⢡⡀⣴⠋⡇⠀⡰⢐⡏⠀⣶⢹⣀⢜⡡⠃⠀⡓⠄⠀⠀⠁
⣄⠀⠀⢀⣸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⢷⡈⢧⠟⠅⣇⠈⡚⠱⠃⠀⡇⣰⠇⢸⣧⡞⢁⣞⡥⡏⠀⠀⢠⠖⠁⡈⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣇⠐⠿⣿⣿⣿⠀⣿⣶⡄⠀⠀⠀⢰⠙⠿⠶⣬⡷⣼⡢⣔⢸⡏⢂⢸⢰⡀⡼⠃⢠⡾⠋⢰⣷⠏⠀⣇⡤⠔⣣⠔⠚⠛⠈⡅⠀⠀⠀⠀⠀⠀⢀⣈
⡙⢿⣆⠀⠀⠹⣿⠀⣼⣿⣃⣴⡦⠀⠀⣦⡐⠊⢲⠀⢈⢟⡺⣿⣟⣹⣿⠛⠠⣧⡞⠉⠀⢈⣿⠋⠀⣰⠋⢀⠊⠁⠀⠁⣠⠞⠀⠀⠀⠀⠀⢻⣷⡙⠻
⣻⣌⠻⣷⡀⠀⣿⣷⣿⣿⣿⠟⠁⠀⠀⢜⢘⣓⣺⠋⢀⠠⢹⡏⢿⣏⡸⣆⣰⠃⠀⢀⡴⠛⠀⣠⠞⠁⣠⠎⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣀⠙⠻⠦
⣿⣿⣆⠉⢻⣿⣿⣿⡿⠋⠀⣀⠋⠀⠀⠁⢈⡀⠉⢷⡀⠀⢸⣇⣠⡿⠁⢹⡏⠀⣰⡏⠀⠀⣸⠃⣠⡾⠫⡰⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣙⠻⢶⣄
⣿⣿⣿⣇⠀⣿⣿⡟⠀⠀⡜⠁⠀⠈⠠⣄⠀⢔⡀⠀⠙⣤⣼⡏⠀⠀⢀⡿⢁⣴⡟⣀⣠⣴⣷⡟⣋⣠⣀⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢺⣿
⣿⡝⢿⣿⣷⣸⣿⠁⠀⠀⠱⠀⡨⢄⠀⠈⢢⠀⢘⢂⠁⠀⢹⡇⣤⡾⣋⣶⡿⠟⠛⠻⢭⣄⠀⠐⠀⠀⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠟⠋
⠻⣿⣄⣿⣿⣿⣿⡇⠀⠀⢠⠒⠐⠊⠛⢒⣾⣦⡀⢸⠑⠈⢸⣿⣷⡾⠟⠁⠀⠀⠀⢄⠀⢀⠈⣡⠴⠐⠋⠀⠀⠀⡄⡄⢲⠄⠀⠀⣆⠀⢠⣀⢀⡀
⠀⠀⠉⠻⣿⣿⣿⣷⡀⠀⠀⠁⠠⠂⠴⠋⡂⠀⠈⠻⣆⢠⣿⣟⠅⢈⢀⢸⠉⠒⠢⢤⣤⠶⠞⠁⠀⠀⢠⠀⢠⠅⢘⣇⣀⠆⠀⠀⣢⡔⠉⡄⢘⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠿⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢸⡠⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡄⠀⠀⠲⠶⠦⠤⠄⠀⢸⡇⠀⢿⠻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⢀⣴⠞⡀⠀⢸⡇⣠⡌⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠞⠱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⡀⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⢿⣿⠁⣾⡟⠀⠀⠀⠘⠠⠀⢄⢸⠙⠀⡀⠀⠀⠙⠤⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣿⣿⣷⡆⠉⠁⠙⠃⠀⠀⠠⡄⠀⢀⠉⡄⠘⠥⠛⠃⡀⡀⠂⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠁⢄⠁⠐⠈⠀⠀⠰⢇⠀⠀⠑⠁⠄⠀⠀⠀⠀⠀⠠⠌⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠁⠀⠔⠀⠂⢀⠀⠄⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡠⢊⣓⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠹⣀⡖⠠⠐⢀⠀⠀⠀⠠⠀⠀⠀⠂⠠⢤⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⢀⡀⠀⠀⠐⠀⠈⠈⠀⠀⠀⠀⠐⠄⡄⠀⢫⠐⡍⠀⠂⠊⢡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠌⠀⠈⠈⢀⡃⠄⢤⣔⠀⠀⠀⠠⡄⠀⠀⠀⠀⡠⢄⠌⢀⣈⠐
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣦⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠠⠚⠀⢈⠘⠊⠀⠨⠀⠄⠀⠁⠩⠀⠄⢛⠃⢀⠄⠁⡀⢂⠀⠀⠘⠁⢃⠚⢀
⠀⠀⠀⠀⠀⠰⡇⠛⢩⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠠⠀⡀⠀⠬⠒⠀⠆⠈⠆⠀⠐⠀⠌⠐⠊⠑⠄⠹⠈⣆⣀⣀⡂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠈⡀⢁⠀⠐⡀⠀⠈⢄⠀⢀⡠⠆⠀⠀⠀⠠⠂⠰⠀⢀⣠⡴⠟⢛⣉⣩⣄⣭⣬⣹⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡄⣄⡅⠚⠴⠀⠃⠠⠓⠂⠀⠀⠈⠈⠑⠠⠊⠛⢳⠶⣦⡋⠩⠟⢁⣀⣺⣿⣿⣿⣿⡙⢿⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠻⠙⠛⣧⣶⠀⠀⠄⠠⠄⠀⠐⠂⢠⠀⠀⠀⠀⠀⡀⢁⣤⣿⠷⣄⠲⢶⣭⣉⡙⠛⠛⠛⠛⠊⠉⠀⠀⠀⠁
⠀⠀⠀⠂⠈⢀⡀⠀⠀⢸⡗⠆⠀⠀⠀⣼⡏⠀⡀⠀⠂⠂⠀⠀⠐⠣⢤⠢⠒⠂⠄⠈⠉⠁⠀⠄⠀⠈⣞⠡⢸⡽⠟⠋⠙⠈⠢⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠻⣦⣀⡀⢠⠌⡇⠀⢀⠀⠁⠁⠀⠀⠀⠊⢦⠶⢤⡀⠀⠃⠀⠀⠀⠀⠠⠁⡈⠤⣨⠤⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠒⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠁⢢
⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⠄⡐⠂⢨⡥⠀⠚⠠
⠀⠀⠠⠁⠀⠀⠀⠉⠒⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⣁⣀⢠⠀⠀⠀⠤⠀⢰⠔⠦⡀
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠉⠐⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠁⠀⢄⢄⠀⠒⣠⠏⠀⠀⡨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡁⢀⠔⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠁⠑⢉⣡⢖⠀⠉
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠗⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢤⠀⢄⢘⠩⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⠢⢠⠞⠳⠂⠐⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢆⠀⠑⣄⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠊⡂⢠⠀⠀⠈⡄⠀⠀⠀⠀⠠⠡⠊⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠄⣀⠬⠃⡀⠀⠀⠀⠃⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠦⠀⠨⠐⠀⢣⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠑⠦⣀⠀⠀⠀⠀⠠⠃⠀⠣⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠀⡁⠀⠀⠀⢈⠵⠶⢤⣄⣈⣹⡈⠙⢄⠀⠀⠀⠀⠀⠀⠉⢓⡶⠶⠶⠒⠂⠁⠀⠠⠠⠂⠈⡂
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⠁⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⢉⠟⠉⠀⠀⠁⠐⠀⠀⠀⠲⢾⠉⠀⠀⠀⠀⠁⠀⢒⠁⠀⠚⠭⠁
⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠔⠛⡀⠈⠀⠄
⡠⠐⠉⠀⢀⠔⠀⠀⡠⠊⠀⠀⠀⠈⠉⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢁⠀⠀⠊⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠢⡀⠀⠀⠀⠠⠁

⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢀⣼⣿⣶⣿⣿⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠿⢿⣿⣿⣿⣿⣿⣿
⢸⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠘⢿⡽⣿⣾⣿⣿⣿⣿⡿⠟⠋
⢸⣷⣷⣾⣿⣿⣿⣿⣷⣿⣧⠀⠀⢀⣄⣤⣦⣰⡷⠀⠀⠀⠤⡄⣹⣿⣿⣾⣟⣷⣿⣿⣿⣿⣿⣿⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⢻⣿⣿⠟⠠⣻⠿⠋⠰⣿⣿⣿⡏
⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⠷⡆⠀⠀⠀⠻⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⢸⡟⣿⡿⠟⠉⠙⠛⠿⣿⣿⣿⠿⠿⣿⠿⠟⠠
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠾⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠈⠀⠀⠀⠀⠀⠹⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢶⡖⠟⠻⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⣠⣿⣷⣄⠀⠀⢹⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⢉⣻⢻⡖⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠒⡸⣷⢼⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⡈⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣦⡄⣳⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠀⠄⣷⢘⠄⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⡇⣿⣠⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⣸⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣤⣤⣤⣬⣿⣿⣟⠋⠁⠀⣷⠀⠀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣀⠀⠀⠀⠀⡇⠀⠉⠛⢿⣋⣉⡉⠉⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⡿⣿⣤⣤⣄⣹⡟⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⣶⣶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⢤⡤⢲⠋⠉⠁⠀⠸⠁⢙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠀⠀⠀⠀⢠⣍⠀⠨⠀⢀⠀⠀⠐⠇⠘⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢠⠈⣏⠙⠛⠛⠚⠲⢆⠘⠁⠀⠀⢀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢻⡟⠛⠛⠛⣿⠌⡀⣿⠀⣀⣀⣠⡤⠎⠸⠀⠀⠊⠀⠀⣤⢴⠶⠶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⠂⠂⠋⠛⠛⠛⠋⡹⠏⠂⡀⣿⠀⣯⣟⣀⡀⠀⠀⡆⣇⠀⠀⠀⡇⡸⣇⣀⣿⡭⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢢⡛⠛⠒⠳⠤⣀⣉⠉⣳⡆⢸⡗⢄⡀⣳⣧⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠑⢦⡀⠀⢀⣠⠧⠶⠶⠾⠧⣀⠀⠀⠀⠀⠀⢩⠃⢠⠘⣷⠀⠀⠈⠉⠙⠛⠒⠒⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠆⠤⣯⣇⣀⣀⣿⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡙⠓⠶⢦⣀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⣠⠴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠛⠛⠛⢹⡇⠀⡟⠣⠄⡠⠤⠐⠖⠋⠉⠉⠉⠉⣛⠀⠀⠛⡙⠓⠒⠲⠒⠒⠋⢸⠀⢠⠿⣠⡾⢛⣻⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢄⣀⠀⢀⠈⠉⠙⠓⢤⠈⠀⠀⠀⣠⡔⠂⠛⠋⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣾⡀⡞⠀⠹⠖⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠹⡄⠀⠀⢀⡤⠃⠀⠀⠰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⣼⡧⢝⢧⣀⠀⡰⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣀⣡⡌⠢⣄⢘⣨⠀⠀⠀⡀⣽⠓⠂⠤⠤⠤⠤⠤⠤⠀⠂⠣⠤⢦⡴⠒⠛⠛⠺⠶⣾⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠣⠁⠈⣻⠻⣤⡀⠀⡆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⣆⠂⠹⡄⠀⠉⢳⡇⢀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠹⡔⣀⢻⡀⢂⣀⡅⠀⠀⡜⣧⠀⠀⠀⠀⢸⠖⠒⠲⠖⠒⣸⠃⠀⠀⠀⢀⡴⠋⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡙⠛⠛⠛⣿⢡⠛⠉⠀⡇⠀⡀⠀⠈⢷⡀⠀⠀⢸⠀⠀⠀⢀⠞⠁⠀⢠⠄⣠⠞⡡⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢹⡷⣤⣀⣀⡷⠤⠦⠶⠤⡈⢧⠀⠀⣹⠀⢀⡴⠋⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⢻⣿⣆⠀⠀⢀⠠⠲⠟⠀⠸⡇⢀⡏⣴⠏⠀⠀⢀⣠⡶⠋⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠝⣿⣄⠀⠠⣄⣀⣀⡤⠤⠚⣾⣞⣡⠤⠖⠚⠙⠋⠁⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠌⢦⣄⣠⣀⢶⣿⡿⠷⠖⠒⠒⠒⠚⠊⠉