Sweet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠉⠄⠉⠑⢄
⠀⠀⠀⠀⢠⠖⠉⠀⣀⠠⠂⠁⠀⠄⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠇⠀⠈⠀⠈⠀⠀⠂⠀⡀⠀⠰⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣬⡀
⠀⠀⠀⠀⢇⠈⢁⠀⠉⠀⠋⡀⠀⠀⠀⠀⠀⡠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡎⠐⠾⠓⢹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⠀⠁⢠⠋⠉⢆⠀⠰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⠀⠀⡧⣀⣀⣀⠜⢦⡀
⠀⠀⠀⠀⠀⠸⡌⠀⣾⠉⠙⠒⠋⠀⠀⠈⠂⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⠀⡁⠐⠀⠬⠀⠈⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡠⡶⡻⠃⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⣩⠊⡴⠁⠀⣇⠑⠤⣆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠁⢰⠁⠀⠀⠈⢦⡀⠀⠉⠳⣽⢦⡔⢢⢀⣤⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⣠⡎⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣦⣹⠃⢸⠤⠻⢖⠚⠉⡦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠒⡏⠀⢸⣇⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⣠⠣⣈⠒⢛⣦⣀⠠⢵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⢄⣾⠀⠑⠒⠚⠢⠄⣈⠷⠤⠠⡤⠚⠉⠉⠉⠀⠏⠉⠣⡀⠀⠑⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠂⠉⢸⡁⠒⠪⠕⣤⠊⠉⠢⠔⠉⠑⠤⠊⠉⠲⠊⠙⢦⠖⠻⢶⣀⣉⠯⠽⠥⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⠀⡏⠒⢶⠐⠸⡆⠀⠐⡄⠀⠀⡆⠀⠀⡛⠀⠀⣇⡤⠚⡉⠀⠠⠀⠀⠂⠀⠠⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠰⠀⠘⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡼⠃⠀⠂⠀⠀⣠⢄⠴⠛⢤⣀⠀⢁⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⢱⣀⡈⡆⠀⢸⠀⠀⠁⠀⢰⠁⡜⠀⠈⡁⠉⢔⡲⠗⠂⠉⠉⠐⢦⠇⠄⠐⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣧⠄⠠⢔⠂⠘⠿⠁⠀⠈⢷⡀⠀⡆⠀⠀⠀⡸⢠⠅⠈⠀⠀⠂⡈⠣⢄⣀⣀⡀⠤⠊⡀⠀⢠⠲⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠘⡂⠀⠀⠀⠀⠀⢸⠥⠄⠁⠀⠀⠤⠅⠤⠵⡞⠦⠚⢢⠀⠀⠀⠁⠄⠐⢀⠁⢀⠤⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡸⣁⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠓⠒⠉⠑⠤⠔⠉⠁⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠖⠊⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⡀⠤⠔⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣧⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠄⢳⣴⣎⠑⢀⠉⢠⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣈⡛⣺⣿⣄⠷⡀⠈⠄⠀⠆⢩⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣉⣽⣿⣿⡥⣶⣷⣦⡴⢾⣿⣥⢍⢼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣹⡇⣊⣶⣦⢿⡿⢻⣟⣉⢁⣄⠀⠛⣿⡎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣻⡟⢸⣿⣍⡰⣶⠾⡻⠇⣻⣅⢿⡷⣠⠄⢻⣧⠈⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣾⣿⠻⣽⣇⠈⢯⣿⣿⣶⣾⣿⣋⡈⣧⡼⢾⠃⣀⣻⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠛⡟⣿⣆⠈⠛⠳⠄⣉⠛⣿⡿⢿⠿⠿⣻⣿⣿⠟⠛⠉⣁⡴⠀⠀⠀⠀⢘⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠁⠶⣿⣿⣄⠀⠀⠀⠀⠉⠛⠲⢤⡄⠒⠛⢋⡥⠖⠛⠉⠉⠀⢀⠜⠁⠀⣼⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡄⠀⠈⠻⣿⠳⠦⠤⣤⣀⣀⣀⣽⡷⠒⠉⠀⠀⠀⢀⣤⣎⣠⣤⣤⢾⠁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠠⣿⣿⣿⠀⡀⢰⣼⣦⣤⣤⣤⡾⠟⢋⡁⣀⣀⣀⣤⣤⠖⣻⠛⠉⡼⠋⠀⠸⠀⠈⣧⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠁⠙⢿⢷⣦⣤⣮⣿⣿⠿⠶⠛⠉⠉⠉⠉⠉⠁⠀⢀⡼⠁⠀⠠⠀⠀⠀⡆⠀⠀⡼⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠀⠤⣚⣿⣫⣽⡎⠁⠀⠀⠀⠀⠀⢀⣀⡠⠾⠋⠀⢀⡴⠀⠀⠀⠀⠀⢀⣼⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣼⣷⣋⣀⡤⠔⠊⠁⠀⠀⣀⣴⡦⠖⠋⠀⢀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣐⠛⠿⠿⠿⠶⢶⣦⡶⢾⢛⡋⠉⠉⠛⠛⠻⠿⠶⠶⠖⠛⠉⠁⠀⠀⣀⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⠟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠁⠀⡍⠙⠏⠁⠀⠲⢦⣶⠶⡖⠒⡲⠞⢻⠛⠉⠹⠏⠀⠂⢳⢠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢨⡇⠘⡀⢰⠄⢠⠀⢠⠀⠀⠧⠀⠀⠀⠘⠃⢸⠃⠇⢸⠁⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣧⣄⣇⢸⡄⠀⠀⠈⡄⠀⢰⠀⠀⠀⢸⠀⢾⠀⠀⡘⢠⡧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⣧⣿⣏⡿⢸⣧⠐⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⡕⠀⠀⣇⣘⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣦⣿⣿⣿⣅⣀⡻⠆⠈⠀⢷⣀⠘⠀⣀⢀⡾⠀⠃⣐⣀⣩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢿⡿⢽⣿⡿⣿⣿⣶⣶⣶⣷⣶⣶⣶⣿⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡚⢿⣿⢿⣿⣽⣟⣛⣻⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠍⠛⠷⠛⠛⠉⠉



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⢸⢻⣿⢿⣳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⢵⡞⢣⣾⠸⡏⢷⡏⠳⣌⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡱⢮⢀⢠⡖⠙⠁⢀⡿⢸⣧⠐⣿⠀⣿⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠛⠒⣻⣛⣩⡤⠿⠧⠺⠏⢠⣟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⡠⠴⠒⠛⠛⠉⠁⢛⣃⡀⠤⠐⠊⠉⣋⣴⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⢀⣠⣶⣶⣿⠿⠿⠛⠛⣛⣻⡿⢛⣽⠏⣿⣿⡝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣀⡴⠟⠋⠉⣉⢹⠭⠤⠒⢊⣉⣻⣅⠴⢛⡯⢃⣿⣿⣿⢸⣇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡞⠋⠀⣠⠖⠋⠁⢀⣤⠖⠂⠉⠁⠀⢀⣀⣨⡤⠞⣹⣿⠏⣸⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣧⣿⠀⣰⠋⠀⠀⣰⠞⠉⠀⣀⠤⠖⠊⠉⠀⣀⣀⡴⠞⣋⠤⠞⠟⢳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠘⢿⡄⣧⠀⠀⣴⠁⠀⣰⠞⠁⢀⣠⡴⠚⠋⠉⣠⡴⠋⠀⠀⣀⣤⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢤⡀⠀⠉⠚⠧⣄⣿⡀⣼⡏⢀⣴⣿⠁⢀⣀⣤⢾⣿⡏⢛⡿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢆⠉⠉⠊⠓⠰⠤⣍⣉⣙⣛⣻⣛⣻⣟⣿⣵⣾⣴⣾⢿⠿⡟⢻⠏⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⡍⢩⠉⣏⠉⡯⢹⠇⢹⡇⣾⣼⢸⡇⣿⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡗⢸⠀⣸⢁⡏⡇⣸⢧⡏⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⢸⡆⡿⢘⠀⡾⢸⢃⣉⡏⣿⢸⣿⣿⣿⣆⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⡄⢡⠰⢠⠀⡆⢀⠰⠈⡇⡻⣸⢰⡇⣼⣴⢼⢳⣿⣾⣿⣿⣿⣿⣿⣶⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡺⡎⣦⣇⠡⠀⡇⡆⣷⢾⣾⢸⣷⡟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⡿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⢿⣿⣄⣧⣓⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⡏⠻⢿⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⣒⠺⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣽⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡥⡦⡙⡦⡍⢆
⠀⠀⠀⠀⠀⢀⣐⡙⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡈⠈⠀⢇⢣⠀⠀⠀⠀⠀⠀⠀⠈⡄⣦⢧⡑⢧⡆⡌
⠀⠀⠀⠀⠀⠹⣀⣹⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠧⠤⠤⠼⠤⣆⠀⠀⠀⠀⠀⠀⠀⢎⡴⢋⣋⠷⣜⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⢲⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡀⠉⠢⡀
⠀⠀⠀⠀⠀⣼⡓⢓⣲⣒⠛⣲⡄⠀⠀⠀⠀⠀⠀⠀⢏⠉⠀⠀⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⣏⢈⡧⠤⡇
⠀⠀⠀⠀⠀⣿⢿⣻⠇⠿⣻⢿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢠⢖⠫⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢎⠢⡑⢌⡞⠀⠀⠀⠀⠀⠀⠀⠀⣸⡒⣊⣑⢒⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡭⡣
⠀⠀⠀⠀⠀⡠⠚⡵⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠚⠒⠒⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣨⠟
⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠈⠃⠍⠍⠩⠍⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⡏⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢀⡠⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡡⠐⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡠⠒⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠂⢁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⡧⢂⠡⢺⠁⠀⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠳⠥⠄⠐⠀⠀⠀⠀⠀⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠈⠏⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠔⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⠀⡏⠁⠒⠆⠀⠀⢤⠀⠄⣤⠠⠀⠖⠒⠈⢹⠀⠀⢠⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠰⠀⠀⢰⠀⠀⢰⠀⠀⢸⠀⠀⡇⠀⠀⡆⠀⠀⡆⠀⠀⠆⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠀⡄⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⢠⠀⠀⠸⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡀⠀⢠⠀⠀⡆⠀⢠⠀⠀⠀⠀⠰⠀⠀⡄⠀⢀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⡀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠂⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠧⠄⢠⡀⢰⠀⢠⠀⠀⠆⠀⡆⢀⣄⠀⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣤⢠⢀⡄⣀⢠⣤⡀⣤⡄⢠⡤⠀⣤⣄⠀⠀⢠⣤⢠⢤⡀⣤⠤⢀⡤⣤⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⡏⢸⢼⡇⣿⢸⣤⠇⣧⡿⢸⠶⠀⡇⢸⠀⠀⣿⠈⢸⣼⠃⣿⠆⢸⣧⣼⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠃⢸⠘⠇⠿⠸⡇⠀⠯⠀⠸⠤⠄⣧⠞⠀⠀⢻⡴⠸⠘⠆⠿⠤⠸⠇⠸⠸⠇⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠆⠀⡆⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠘⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⡻⠀⠀⠀⠁⠀⢰⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⢀⡔⠁⠀⢀⠌⠀⠀⠀⠀⠀⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠚⠁⠀⢀⠠⠋⠀⠀⠀⠠⠀⢀⠌⢠⠃⠌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⠔⠁⠀⠀⠄⡀⠔⠁⡠⠂⡴⠃⢠⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠑⠀⠀⠀⢀⠠⠔⠊⣀⠄⠊⣠⠀⠀⠀⢠⠀⢰⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⠂⠀⠈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠊⠀⢀⠠⠐⣈⣉⣀⡠⠤⠔⠊⠁⠀⠀⠀⡀⠔⠁⠀⡠⠀⢀⣼⡅⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡥⠚⠉⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠀⢀⡠⠊⡠⠞⠁⢸⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠉⠀⠀⠠⠒⠀⠒⠒⠒⠀⠉⠀⠀⠀⠠⠔⠊⡁⠀⠈⠀⠀⠀⡸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠄⠐⢒⡀⠀⡈⢉⣉⠥⠄⠒⠒⠒⠀⠁⠀⢀⠔⠀⢀⡴⠁⠀⠀⠀⣾⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠃⢀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠴⠋⠀⠀⠀⢀⡜⠁⢇⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠈⠀⠀⢀⠤⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠖⢹⠀⠀⡸⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠀⡀⠀⢠⠞⠉⠉⠓⠒⠢⠤⠤⠤⠔⠂⠁⠒⠁⠀⠀⢀⠀⠀⠁⠀⠀⠀⣠⠃⠀⣠⠃⢀⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⠈⢙⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠁⠀⠀⢀⠤⠊⠀⠀⠀⠀⣀⡤⠚⠁⢀⠔⠁⡐⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠁⢀⣠⠴⠒⠋⠉⠀⠀⣠⠆⠀⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⡠⠒⠉⠉⠉⠉⠁⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣠⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣔⣋⡠⠴⢾⡉⠙⠂⠀⠛⠉⠀⠀⠀⠀⣠⣴⣒⣋⣉⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠐⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⢦⣤⣤⣄⣤⣤⠶⠞⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠂⠀⠀⠀⠀⢀⣀⠀⠀⠐⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢷⣤⣀⣀⣀⠀⢀⣀⣀⣠⣠⡴⠗⠋⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠉⠉⠉⠉⡉⠉⠉⠀⢀⡀⠄⠂⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠓⠦⢦⣠⣠⣀⣀⣀⣀⣀⣀⣠⣠⣠⣤⠤⠖⡋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣀⣀⡀⠀⠈⡈⠉⠉⠉⠀⠀⢀⣂⣈⢀⣀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠉⢹⠉⠛⠋⡟⠛⠛⢹⡏⠛⠋⡟⠉⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⠀⠸⡟⠀⠀⣇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠀⠀⡧⠀⠀⢿⠀⠀⢸⠀⠀⢸⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⡇⠀⠀⢸⠀⠀⢸⠐⠀⢸⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⠀⠀⢸⠀⠀⢸⠀⠀⡞⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠦⠤⠼⠤⠤⠿⠤⠴⠓⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠋⠉⠉⠉⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠏⠀⠀⠘⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⢀⣠⠼⠃⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣻⠄⠀⠀⠀⡇
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⢧⡀
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡞⠀⢰⠛⢳⡄⠀⠀⠀⠀⠀⠀⢠⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⠀⠀⠀⠀⠀⢠
⢷⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⡞
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠙⢶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠶⠶⠶⠶⢤⣤⣤⣀⣀⠀⠀⢀⣀⣀⣀⣤⡤⠴⠒⢻⡇
⠀⠀⠀⢸⡄⠀⠀⠉⠉⢻⠉⠁⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠉⠉⠉⠉⢹⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣿⣄⣀⣀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣀⣀⣀⣼⡥⠴⠖⠛⠉

⠀⠀⠀⠄⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⢀
⠀⢐⢀⠀⠀⠤⡤⠀⠀⠀⣀⠀⠐⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⢨⡑⠳⠶⠄⠠⠤⠤⠤⠤⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠁⠀⠀⠭
⠀⠀⠙⢗⠤⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠔⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠠⣄⣀⠈⠙⠂
⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⡀⡀⠀⣠⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠛⠋⠉⢉⡅⠻⠉⠉⢐⢊⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠄⣀⠀⡄⠀⢀⣉⠠⢄⣀⠀⠀⠀⠀⠘⠻⠄⠁⠤⠤⣤⣤⠬⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⢸⢯⡉⢦⣀⠛⠦⠰⠀⠡⡀⢰⠀⠀⠀⠀⠀⢂⠒⢀⠀⠀⠈⠐⠀⠀⠐⡠⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠘⢾⣴⢲⡾⠳⣜⣃⠉⡗⠘⠓⠟⠧⢁⡀⠀⠀⠑⠅⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠈⢿⣉⣙⡊⢶⠉⠈⠙⠑⠒⠒⠠
⠀⠀⠀⠀⠀⠙⠿⡝⠈⠦⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠛⠢⠵⢠⣄⠄⢀⡀⠂⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠦⠈⠂⠈⠁⠈⠁⠀⠀⠀⠀⠙⠤⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣈⣀⠀⠒⠒⠲⢶⡶⡶⡄⠐⡄⠀⠐⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⣓⠬⠤⠔⠁⠉⠛⠁⠸⠴⠤⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠶⡶⠿⡴⢄⣀⣀⠀⡀
⠀⠀⠀⠀⠠⠉⠒⠂⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢮⠙⡈⢏⣰⣄⣠⢐⣄⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢐⠢⠤⠤⠈⡧⠬⠤⠀⠫⠄
⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡤⠀⠀⠀⠈⠁⠀⠀⢀
⡄⠈⠈⡍⣉⣙⣛⡓⠒⢓⠒⠶⠶⠂⠴⠾⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠂⠑⢄⠀⠀⠉⠭⢭⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠳⢤⣄⣀⣤⡴⠋⠀⠀⠀⢀⡴⠁⠀⢠⠀⠀⣹⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠖⠚⠁⠀⢀⡴⠁⠀⢀⣿⠓⢮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠾⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⢀⣾⡏⠀⠈⢷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣠⣴⡿⠋⣿⠀⠀⢸⣧⢸⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠞⣋⣭⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠁⣠⣾⠃⠀⠀⣸⡏⢸⡇⠈⢧
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⠿⠛⢁⡰⠁⣰⡿⠁⣼⠃⠀⢸
⠀⠀⠀⠀⠀⣿⡏⠀⣀⣤⣶⣶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⢀⣠⠔⠋⣠⣾⠟⠀⣴⠏⠀⢀⡿
⠀⠀⠀⠀⠀⢿⣧⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠖⠚⢉⣠⣴⡿⠛⠁⢀⡾⠃⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠛⠉⠉⣀⣀⣤⣴⣾⣿⠋⣁⣀⣤⣶⣯⣤⣶⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣿⠉⠛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠋⣹⡇⠀⢸⠇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠸⡇⠀⢸⡇⠀⠸⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⡿⠀⠀⣿⠀⠀⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢳⠀⠀⣷⠀⠀⣿⠀⠀⢿⠀⠀⢸⡇⠀⢸⡇⠀⢠⡇⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡆⠀⢸⠀⠀⢹⠀⠀⢸⠀⠀⢸⠁⠀⢸⠁⠀⠸⠀⢀⣦⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣦⣤⣤⣸⣀⣀⣸⣀⣀⣸⣀⣠⣼⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢕⣠⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣊⡤⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⠭⠉⠀⠀⠐⡷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣀⡠⠄⠀⠀⠀⢀⡗⢆
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠐⠒⠒⣊⠩⠀⠼⠓⡄⠀⠀⠀⠀⠀⠤⠐⠒⠂⠐⠒⠂⠀⣉⠥⠄⠤⠋⡆
⠀⠀⠀⠀⠀⠀⠤⠒⠒⠀⠀⠤⠔⠊⢁⠤⠄⠀⢠⣁⠀⠀⠀⠀⠀⠔⠒⠒⠂⠤⠤⠒⠉⢀⠤⠄⠀⢀⠇
⠀⠀⠀⠀⠀⠾⢦⡄⣀⣀⣤⣴⣂⣀⣀⡤⠤⡤⡸⠻⠀⠀⠀⠀⠀⠚⠒⠒⠀⠔⠒⠒⠊⠓⠉⢊⠉⡇
⠀⠀⠀⠀⠀⢘⢤⢨⠀⠙⠉⠉⢉⠁⢀⠉⡈⢀⠀⡆⠀⠀⠀⠀⠀⠈⠄⢆⢰⠀⡄⣄⢰⠀⡇⡘⡘
⠀⠀⠀⠀⠀⠈⡘⠘⠀⠰⠀⠀⢸⠀⠈⢀⠃⠘⢰⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘⠀⠇⠻⠈⠠⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠈⠢⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢓⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⣈⠂⠀⠀⠊⣢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠲⠀⠀⠁⠉⠉⠀⠥⡀
⠀⠀⠀⠀⠀⠀⡇⠸⡉⠒⡒⠤⢤⣉⠒⠒⢉⣀⣰⠀⠀⠀⠀⠀⠀⡄⢘⠦⣀⡀⠀⠐⠤⢀⠠⠔⠁⢄
⠀⠀⠀⠀⠀⢠⡯⣁⣈⣓⢌⣓⣦⣠⢕⡢⢤⡠⠠⡅⠀⠀⠀⠀⢀⠣⣈⠢⡀⠤⡉⠑⠢⢄⠀⠐⠐⠂⣀
⠀⠀⠀⠀⠀⠈⡄⢠⠀⡄⢁⠀⠀⠀⡄⢀⠀⡰⢀⠃⠀⠀⠀⠀⠟⠶⣤⣤⣬⣀⣈⢭⣤⣤⡬⣤⠶⠞⡙
⠀⠀⠀⠀⠀⠀⠘⡌⠇⢳⠈⡇⢸⠀⡇⣸⠀⠇⠎⠀⠀⠀⠀⠀⢨⢀⢨⠀⡉⢈⠀⢩⠀⠀⠀⡄⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠈⠘⠀⠇⠘⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡘⠘⠀⠡⠈⠀⠘⠀⠇⢰⠁⠎⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠠⠤⠤⠤⠤⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠉⠁⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⢠⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠰⠃⠀⠀⠀⠀⠉⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢰⡆⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠈⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠛⠂⢀⠁⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡃⠀⣠⠄⠁⠒⠒⣒⡒⠐⠂⠈⠉⠐⠒⠂⠒⠁⠚⡡⠃⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠄⡁⠀⠀⠀⠀⠈⠁⠀⠀⠐⠋⠀⠀⠀⡀⠄⠊⠠⠴⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣄⠀⠉⠐⢒⠀⠠⠤⠤⠄⠐⠒⠂⠉⣁⠀⠀⣀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠘⠓⠀⠀⠀⠋⠀⠀⠀⢀⣀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠒⠐⠀⠂⠉⠁⠀⠉⠉⠀⠒⠒⠒⠒⠂⠈⠉⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⣓⣶⣤⣀⠀⠀⠀⠀⣀⣤⣶⣚⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢤⡀⢀⡤⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡸

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢠⣿⣧⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⣿⣿⡿⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣶⠿⣸⣿⣿⣯⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢌⣱⡞⢿⠛⠟⢻⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠐⡚⠛⣋⠩⣴⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠛⢷⣶⣴⣾⠖⢠⣼⢹⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠐⢴⠃⢌⣭⡾⠷⢺⣛⣱⡿⠈⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡕⠊⠉⠀⠀⢘⣠⡞⢁⣀⣤⡾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠉⠉⠙⠲⠖⠒⠉⠙⠛⠿⠛⠉⢶⣶⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠐⠐⠄⢠⠀⢀⡀⠀⡀⠀⡠⣦⡔⢾⢙⣧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣠⠀⣆⢔⣀⣀⡆⠀⡇⣰⡆⠹⠳⡿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢇⢻⡀⣄⠙⣿⣀⡿⢁⡗⣾⢦⣷⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢼⡾⡏⣭⠓⢿⣀⣧⣾⡧⣼⣾⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⣷⢻⣧⣼⡍⣿⣸⣏⣿⣹⣿⣿⡗⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢼⣧⣹⣟⣿⣻⣿⣿⣿⣿⡿⠽⣋⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⡗⠻⢭⠄⠊⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⡶⠶⠓⠓⠷⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⣤⣴⣶⣶⣿⢿⠾⢶⣶⣦⣬⣋⠛⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⣾⠟⠋⠁⢉⡞⠁⠀⢀⡼⠟⠉⢻⡿⢿⣦⡐⠻⣷⣄
⠀⠀⠀⠀⠀⢠⡾⢋⣴⣿⠟⠉⠀⣀⡔⠻⠀⠀⠔⠙⠦⣀⠔⠀⠀⠠⡏⠘⢦⡘⢝⢦⡀
⠀⠀⠀⠀⢰⡟⢀⣾⠛⠻⣀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠉⠂⣀⠀⠀⠀⠂⡀⠑⡌⢻⣿⡆
⠀⠀⠀⢠⡟⠀⣾⢿⣆⡀⠉⠒⢄⠀⠈⠐⢦⡠⠊⠑⠤⣠⠆⠀⠑⠤⠀⠀⢀⠎⠠⠈⢿⣧
⠀⠀⠀⣼⠃⢸⣏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠠⠖⠀⠀⡠⠛⠄⠀⡆⠈⢿
⠀⠀⠀⣿⠄⢸⡟⠀⠀⢀⠔⠣⡀⢀⡴⣣⣄⠠⣴⣛⣷⣿⣄⠁⠠⡀⠾⡁⠀⠀⠘⣿⠀⣿
⠀⠀⠀⣿⡄⢸⡇⠀⠰⢇⠀⠀⢀⣿⡀⠈⠛⠛⠻⣿⣉⢉⡻⣦⣄⠈⠀⢌⡢⣄⠀⣼⠀⣿
⠀⠀⠀⢸⡇⠘⣿⡀⠀⠀⠰⢄⡀⠉⠹⠓⢦⡀⠀⠈⠙⢿⣷⠟⠉⠓⢦⡄⠠⡨⠿⣿⢢⡿
⠀⠀⠀⠈⣿⡄⠹⣯⢢⠄⠀⠀⢹⠖⠀⠀⠀⠙⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡁⣰⢃⣾⠃
⠀⠀⠀⠀⠈⢿⣄⠙⠇⠀⣠⠞⠁⠂⠀⣠⠎⠀⢀⡴⠛⠀⠀⢀⠴⠂⠀⢀⢘⡿⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠧⠀⠀⠠⣄⠀⠀⠘⠛⡀⠀⠀⠐⠷⣄⠀⢢⡽⠋⢀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠄⠈⢳⣤⠀⠀⠙⣦⡄⡀⠀⠠⠟⢋⣤⡼⠛⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡈⠈⠙⠛⠋⠋⣀⣁⣤⠴⠞⢋⣥⣤⣴⣶⣶⣶⢤⣄⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠛⠛⣿⠟⠛⠛⣩⡴⢞⣽⠛⠁⠀⠀⢠⠀⠙⠳⣬⣜⡳⢦⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⣹⠂⠀⢠⡞⠁⣤⢴⣾⣩⣷⣿⠃⠀⢀⠀⠀⠀⠀⠐⠀⢻⡟⠏⠶⣿⣷⡀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⡟⠀⢠⡟⠁⠀⣾⣷⣿⡋⡇⣿⠀⠀⠀⠀⢀⢁⣄⠀⠀⢸⣿⡆⠀⠈⡟⢻⣆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣾⠃⠀⣾⠁⠀⣼⣿⡿⣻⠧⣅⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠙⢣⠀⢀⠇⠸⢿⡆⠀⠘⣧
⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⢠⣿⣿⢹⡿⡴⢛⣣⣉⠟⠶⣤⣄⣠⣤⣾⠇⣀⣦⣰⣴⣤⠆⣳⠀⢿⠀⠀⣿⡀
⠀⠀⣴⠋⠀⣠⡤⠶⠤⣄⠀⠀⣿⠀⢸⡇⠀⠸⣿⠃⢀⡾⠛⠉⠉⠉⠛⠲⢾⡉⠀⢹⣷⠟⠉⠁⠉⠉⠙⠳⣟⠃⢸⠀⠀⢸⡇
⠀⣸⠃⢠⡞⠁⠀⠀⠀⠀⠳⠀⢸⡇⠘⣇⠀⠀⣿⢠⡟⠀⠀⣀⠀⠀⠀⠁⠀⢳⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⠀⠀⣸⡇
⠀⣏⠀⢾⠀⠀⠀⠀⠀⠀⠈⠆⢸⡇⠀⢻⡄⠀⠹⣿⠀⠀⠀⠀⣉⠀⠈⠀⠀⢸⣾⡇⠀⠀⠀⠤⢤⠬⠣⡀⢀⣿⠀⠀⢠⣿⠃
⠀⢻⡀⠘⢇⠀⠀⠀⠀⢀⠐⠀⣼⠃⠀⠘⣷⡀⠀⢻⠀⠈⠀⠉⠀⠀⠀⠀⠀⢸⡏⣷⡀⠀⠐⠀⠀⢀⠀⠁⣼⠇⠀⢠⣿⡟
⠀⠈⠻⣆⡀⠈⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠘⣷⡀⠀⠑⣤⣀⠀⠀⠀⠀⢀⣴⠃⠀⡏⠷⣤⣀⡀⠀⣀⣠⡾⠋⠀⣰⢿⡟
⠀⠀⠀⠈⠙⠻⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠈⠻⢿⡶⠖⠚⣿⠁⠀⠀⡇⠀⠈⣝⢙⡉⠉⠁⠀⣠⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠉⠁⠀⠛⠤⠀⠠⠴⠄⠀⠉⠀⠀⢀⣠⢾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⣤⣄⣀⣀⣀⠀⢀⣀⣀⢠⡴⣾⣻⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣔⠿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠷⠬⠝⠖⠃⠀⢀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠉⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⢀⣀⡀⡀⠀⠀⠀⠀⢰⡆⢰⡆⢲⡆⢺⡇⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⢹⡿⣷⣶⡿⢻⣿⡟⣿⠁⠀⠀⠀⠀⠀⠸⣷⢸⡇⢸⡇⣾⠁⣿⠀⠀⠀⠀⠘⠛⠿⠛⠻⡿⠟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⢸⡇⣿⢠⡿⠀⠀⠀⠀⢰⣦⣀⣠⣤⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣄⣇⣸⡇⣿⣸⠇⠀⠀⠀⠀⠀⠛⠻⠛⠻⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠁⣠⣬⣍⠀⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣹⡿⠿⣿⣯⣀⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⣿⣷⡿⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⣿⠉⣿⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠥⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⡧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠙⢆⠀⠀⠀⠀⠀⡄⠀⠀⠰⠀⠈⢀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈⠀⠀⠀⡐⠀⠀⠠⠄⠀⠀⠀⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⣀⠁⠀⠀⠀⠀⢀⡀⠄⢀⣀⠤⢀⣀⠤⣀⠀⠀⠀⠐⢄⠄⠐⠄⠠⡀⠲⠄⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡏⣹⣿⢻⣿⠀⠀⠀⠀⠀⠛⠃⠀⠘⠋⠀⠙⠛⠀⠛⡃⠀⠀⠀⠀⠐⣿⠀⢸⣿⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣷⣿⣧⣬⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⠀⠸⠿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀
⠀⠀⢰⡚⠛⠉⠁⡀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⡦
⠀⠀⠀⠉⠣⣄⠀⠀⠀⠁⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠖⠋⠉
⠀⠀⠀⠀⠀⣈⣙⣓⣚⡋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣺⠿⠗⠋⠉
⠀⠀⢰⡞⠛⠉⠀⠀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⣀⡠⢴⣲⡯⠗⠛⠉
⠀⠀⠀⠉⢧⠀⠁⠀⠀⢀⣠⡤⠏⢀⡠⢤⣒⡭⠗⠚⠉
⠀⠀⠀⠀⠈⠓⠒⠒⢚⣉⣤⣶⠿⠗⠋⠉
⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠻⠶⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠒⣒⣋⣽
⠀⠀⢀⣼⡿⠋⠀⠀⠄⠀⠊⣰⠋⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣯⠭⠿⠶⠒⠛⠛⠉⠉⠁
⠀⠀⠸⢤⡀⠀⠀⠀⣀⣠⣶⣥⣤⣶⣶⠶⠿⠭⠽⠒⠚⠋⠉⠉⠉
⠀⠀⠀⠀⠾⠿⠿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢛⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠅⡚⠟⢃⠇⠀⡆⡄⢣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢊⡔⠈⢀⠤⠊⢀⠔⢠⠁⣰⠛⢍⢣⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠭⢀⣒⠚⠙⠳⠴⠖⠷⠒⠓⢉⠔⡀⠊⠰⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠤⣒⣾⣮⠐⢈⠁⠠⠤⠀⠀⠀⠀⠐⠒⡈⠕⢊⣀⡔⣡⣪⠃⡜⢢
⠀⠀⠀⠀⠀⠀⢸⠭⠬⠉⢉⣙⠋⠥⠈⢛⣉⠨⠌⢚⡋⠭⠑⠋⣉⠠⠐⢉⠤⠊⡠⢊⡇
⠀⠀⠀⠀⠀⠀⠘⣈⢈⠡⠄⢀⣒⠀⠭⠀⠒⠈⣉⡀⠤⠐⢂⡉⠤⠒⣈⠤⠐⣈⣔⠅⠣⡀
⠀⠀⠀⠀⠀⢠⠊⠈⠂⠢⠭⠤⡄⠐⣒⣈⣩⡅⠀⣒⣈⢭⡀⠒⠬⠵⠒⠚⠉⠉⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠸⡖⢢⠄⢠⡀⢀⣀⠀⡀⡀⡀⠀⠀⠀⠀⢀⢀⣀⣀⡀⢀⡠⠠⡤⠀⠶⠈⣿
⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡇⠀⠉⠀⢸⠀⠸⠁⠘⠁⠈⠁⠈⠁⠈⠀⠀⠀⠀⠁⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠁⠀⢰⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠘⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡄⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⡃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣇⠀⡄⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⡀⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠁⠈⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⡿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠁⠑⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⢟⣴⣜⡿⠿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⣤⡀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠇⠾⠿⢿⣿⣿⣗⣘⠿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣬⣄⡀⠀⠀⠀⠀⠀⠀⠤⠼⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⠺⣿⣿⣿⣿⣿⣿⡿⢟⡂⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠋⢾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡐⢁⠉⠛⠛⠛⠋⣉⠑⠒⠒⠶⠶⠒⠊⠁⠙⡀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣵⢷⣤⣤⣤⣤⠶⣮⣭⣭⣉⣩⣭⣴⣷⡹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⣶⣤⣤⡦⣤⡤⢤⣤⣤⢦⣤⠞⣶⡶⢶⡞⠁⠀⠀⠀⠀⠀⣿⣿⣿⣷⡌⠉⠉⢉⡉⢙⣛⠛⢛⡙⠉⡌⠉⣉⠉⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⡇⢿⡇⢸⡇⠀⣿⡇⢰⣿⠀⣿⠃⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⡇⠘⡇⠈⣿⠀⣼⡇⢠⡇⢀⡇⢰⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⠸⣇⢸⡇⠀⣿⠀⢸⡟⢰⡟⢰⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⢹⠀⣷⠀⣿⠀⣿⡇⢸⠇⣸⠁⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⠀⣷⠀⢹⠀⢸⡇⢸⠇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠸⡆⢻⠀⣿⡄⣿⡇⣼⠀⡟⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠣⠼⢀⣿⣀⣸⣀⣸⡁⠼⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣥⣼⣥⣿⣥⣿⣥⣭⣬⣵⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠁⠀⠀⠹⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⣤⣄⣄⠀⢠⠀⣀⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣄⣀⡀⡀⢀⢠⢀⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠙⠛⠚⠛⠋⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠓⠶⠶⠴⠤⣤⣦⣦⡤⠼⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠷⢶⣴⣴⣴⣠⣀⣆⣄⣶⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⣸⣠⢀⢀⡃⣀⡰⠈⠉⠉⠩⠅⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠯⠍⠉⠉⠛⠛⠛⠳⠶⡖⣴⣴⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⣯⡝⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⠏
⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⢀⡀⠀⠀⠀⠀⠸⣅⣸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠍⠀⢀⣀⠀⠀⠀⠀⢸⣇⣿⠀⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣉⡽⢿⡚⠳⢿⡵⣦⣤⣄⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠛⠻⠿⠿⠿⣶⣶⣯⣁⣀⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢙⣄⡤⠷⡖⠛⠻⣅⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⢀⠤⠄⠀⠢⠈⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢉⣧⡤⠞⢾⠉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⢀⠀⠐⠔⠀⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⡉⢀⣳⣤⠴⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢀⡀⠀⢤⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠛⢯⠁⣘⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠒⠀⠁⠀⣐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡖⠚⠻⣅⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠢⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣦⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⠛⢿⣷⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣸⡟⠀⠀⢀⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⡇⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠻⣄⣈⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⠉⠛⢿⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣰⡿⠛⠛⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠛⠁⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢿⣄⣀⡀⠀⠀⢀⣀⣀⣀⣀⠠⠄⠀⢀⣀⣠⣤⡴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣭⣭⣭⣭⣭⣤⣤⡶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢉⣠⠾⠋⠉⠉⡙⠻⣷⣦
⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢒⣉⣤⡴⠞⠋⠁⠀⠀⠀⠀⠙⣦⠈⣿⣇
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿
⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⡿
⣸⡏⣼⠁⠀⠀⠀⠀⠀⣠⠖⢉⣠⡴⠶⠞⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⣧⣤
⣿⡇⢿⠀⠀⠀⠀⠀⣸⢃⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⠞⠋⠀⣨⢻
⢻⣷⡸⣆⠀⠀⠀⠀⠟⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⠛⠋⠉⠀⠀⠀⢀⠞⣸
⠈⢿⣷⣝⠦⠤⠄⠀⣀⣾⣿⣄⠀⠀⠀⠀⢀⣠⣤⣍⡉⠓⠦⣤⣀⣀⣀⣀⣀⣀⣀⠤⠔⠊⢁⣀⣤⡴⠶⠛⠉⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⠴⠞⠉
⠀⠀⠉⠛⢻⣿⡟⠛⠋⠀⠙⠻⠿⠶⠶⠛⠋⠁⠉⠙⠻⠷⣶⣤⣤⣭⣭⣥⣤⣤⣴⠶⠾⠛⠋⠙⠿⠷⠶⠶⠶⠶⠛⠛⠉⠉⠉⠉⠉⠀⢀⣠⡄
⠀⠀⠀⠀⠘⣿⣿⣷⣤⠶⠻⢿⣶⠾⠿⣷⣦⡴⠿⢿⣦⣤⡴⠿⣿⣬⣉⣥⣤⣄⣀⣠⠶⢶⣶⣄⣀⣤⠶⣶⣄⣀⡴⢾⣦⣴⠟⠿⠶⠾⣻⣿⠃
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣤⠀⠀⠀⣷⠀⠀⠀⣷⠀⠉⠁⢸⡆⠈⠉⠉⣴⠈⠛⠛⠁⢰⡇⠉⠛⠋⠁⡖⠈⠙⠉⣴⠈⠉⠁⢸⠇⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢹⡆⠀⠀⢿⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⡿⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣷⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢹⡆⠀⠘⣧⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⣼⠁⠀⢀⡿⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠈⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⢸⡇⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢻⡆⠀⢸⡇⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⢀⡿⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠘⣧⠀⠘⣧⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⢀⡟⠀⠀⠀⣼⠀⠀⢸⠇⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⡿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⣧⠀⢸⡇⠀⢹⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⢸⡇⠀⢸⠇⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠘⣧⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⢀⡟⠀⠀⠀⣾⠀⠀⡿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⣧⠀⣿⠀⢸⡇⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢀⡟⠀⢸⠇⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠛⠀⠸⠇⠀⡷⠀⠀⠸⠇⠀⠘⠃⠀⠀⠀⡿⠀⠀⠺⠀⠀⠀⠸⠇⠀⠿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢧⣀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢰⣿⣿⣿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⣀⠈⠿⣿⡿⠟⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣠⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠛⠛⠻⠷⠶⠦⠤⠴⠖⠀⣠⡀⠈⠉⠀⢀⡈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣷⣦⣄⣀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠐⠒⠒⠋⠉⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠦⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣿⣿⣿⣿⠿⠟⢻⣿⡗⠲⠦⣤⣤⣄⣀⣀⣀⣀⣤⣤⣴⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⡇⠀⠈⣿⡆⠀⢸⣿⡇⠀⠀⣿⣿⠉⠉⢹⣿⠉⠉⣿⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣾⡇⠀⢰⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⢻⣷⠀⢸⣿⣿⠀⢰⣿⣿⠀⠀⣿⡇⠀⣼⡏⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣷⠀⢸⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⠇⢠⣿⠇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣿⡆⢸⣿⡇⢸⣿⣿⡀⢸⣿⣿⠀⢸⣿⠀⣸⣿⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣷⠀⣿⣇⢸⣿⣿⡇⢸⣿⣿⠀⣿⡿⢀⣿⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠚⠛⠛⠓⠚⠛⠛⠒⠛⠛⠋⠉


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

⠶⢤⠴⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠤⠀⣀⡀
⠄⡘⢀⡇⠼⠒⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⣤⣤⣤⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣈⠉⠙⠎⠙⡓⠲
⣒⣛⣚⣓⣗⣓⣚⡳⢤⡀⠀⠀⠀⠀⠀⣠⣾⢿⣲⡶⠤⠾⠥⢤⣄⣸⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠢⢐⣤⠴⢯
⢀⠴⠒⠞⠛⠳⣦⠉⠓⣽⡄⠀⠀⠀⠀⢿⡞⣩⢂⡰⠶⢠⡢⢦⡰⠈⢗⣼⠇⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣴⠊⠀⠀⣈⡆
⣇⢀⡁⠊⠀⢔⣽⡧⠔⡿⠀⠀⠀⠀⠀⠘⢿⣾⣧⣼⣿⣷⣶⣷⣿⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡙⠻⠶⠶⠶⠿⠷
⡈⠉⠉⠉⠉⠉⢁⡤⠊⠀⠀⠀⡄⠀⠀⠀⠀⠙⣶⠬⠭⣭⡭⠯⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠦⠤⠤⠴
⠛⠷⣶⣶⣶⡾⠟⠀⣀⠀⡴⠒⠋⠀⠀⠀⠀⠈⢻⣦⣀⣀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⡎⢙⡏⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣞⠛⠛⢶
⣠⠶⠦⣄⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣥⠞⣫⣾⠋⣿⡁
⠃⢄⠀⠸⡆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡄⠐⠁⣪⢿⠾⠦⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣋⣡⠉⡀⠜⢙⠉⠃
⠀⠀⣱⢞⣁⣀⠀⠀⠀⠘⡄⠈⠁⠀⠀⠀⢀⠀⢠⠖⠛⠙⣤⣀⣽⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠞⠁⢏⠩⢚⠰
⠛⠚⡱⠋⠀⠈⠙⢦⠉⠉⠁⠀⠀⠀⠀⠠⢂⠀⢾⠐⠀⠀⡼⡇⠀⠹⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣤⣦⣤⣤⡴⠾
⠀⢸⠃⠈⢲⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⢠⡤⠊⠁⠛⡂⢰⡑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⣒⣂⣰⣤
⠀⠘⢆⡀⣸⣂⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟⢺⢂⠘⠀⠀⠀⠀⠹⠇⠷⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢈⠝⠂⠀⠀⠀⢚⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣀⣀⡀
⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣱⢳⢳⢃⡟⣹⢋⠟⡿
⠉⠁⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⠟⠀⠀⠀⠀⠀⠀⢰⣧⢏⢯⠇⡞⣴⢣⢏⠞⣰
⠖⣱⢶⡶⣤⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⣴⣟⡤⠤⢶⡷⠦⠀⠀⣿⡟⡘⡜⡘⣼⢡⢣⠊⣼⡿
⣾⠿⢷⣸⡉⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡤⠚⠉⠹⣿⣶⣾⠟⠁⠀⢠⡞⠀⠀⠀⢰⡏⠁⠙⠁⢰⢣⠣⠃⣼⡿⣱
⣌⣱⡴⣷⣦⣙⣧⠏⠀⠀⠀⣠⣿⠃⠀⠀⣠⠋⠀⠀⣠⣾⠿⠙⢿⣦⣀⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠌⠀⣼⠟⣱⠏
⠈⢹⣷⠥⢿⡶⠀⠀⣀⣤⣾⠟⠁⠀⠠⡾⠿⠤⠶⠞⡿⠃⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⢸⡏⣰⠏
⣶⣶⣶⣶⣶⣶⡾⠿⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣁⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣶⣶⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢰⣤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿⡏⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠉⢲⠇⣼⢸⠿⡂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡩⢷⡰⠀⠂⢐⣿⢸⡆⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣼⠁⠀⡹⠁⠀⢾⣿⠈⡆⠀⠠⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢐⢺⡇⠀⠀⡇⠀⠀⠘⣿⠀⢿⣄⠀⠊⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠄⠐⣄⠀⠳⣄⠀⠙⠹⣧⡈⢿⣼⣄⣀⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⢠⣶⠶⢈⡉⠒⠺⣟⣶⣶⠶⢷⣆⡈⠃⠒⠒⠺⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠿⣼⠁⠀⠀⢀⢀⡀⠈⠉⠛⠁⠠⠤⢀⡀⠀⠀⠒⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⢧⣄⠈⠢⠤⡔⠋⠀⠙⠲⢄⡀⠀⠀⠀⠀⠉⠲⣏⣿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠤⢤⣤⣀⣈⢙⡛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣀⣀⠙⠓⠾⣦⣠⡆⡀⠈⢉⠑⡒⠂⠢⠤⠈⠉⢉⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⣿⡦⠤⣤⣭⣭⣿⣷⣦⣤⣤⣤⡴⠶⠞⣮⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⡇⠀⡇⠀⣿⠀⣾⠉⢹⠇⠀⡿⠀⢸⡇⣼⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠀⢁⠀⣿⠀⣿⠀⢸⠀⢸⡇⢀⣿⢠⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡇⠘⠀⢹⠀⡿⠀⡼⠀⣼⡅⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⢧⠀⠀⢸⠀⣷⢠⣧⣰⣿⢡⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡆⠓⢺⣶⡿⢸⡟⣿⣿⣿⡿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠋⠓⠚⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠙⠳⢦⣤⣀⣀⡀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠞⠛⠛⠛⠛⠛⠉⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠳⢦⣄
⠀⠀⣀⣴⢿⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠉⠻⣦
⢀⣼⠋⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⣹⣷⡄⠀⠀⠀⠀⣴⣶⣄⠀⢀⣴⣦⡀⠀⢀⣴⣦⠀⠀⣠⣶⣄⠀⠀⣴⣶⡄⠀⢀⣴⣦⡀⠀⣠⣶⣦⠀⠀⣠⣶⣄⠀⠀⣠⣿⡅
⢸⡏⠀⠻⣦⡀⣠⡾⠃⠀⠹⣶⠟⠁⠈⠻⣶⠟⠁⠈⢷⡾⠋⠀⠙⢷⡾⠃⠈⠻⣶⠟⠁⠈⢻⡾⠋⠀⠙⢷⡾⠋⠀⠙⣷⠾⠋⠈⣿
⠀⢿⡄⠀⠈⠻⡏⠀⠀⠀⠀⠸⡆⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⢸⠁⠀⠀⠀⣼⠁⠀⠀⢠⡏⠀⠀⣼⠏
⠀⠈⣿⡀⠀⠀⢹⡄⠀⠀⠀⠀⢷⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⠀⢠⡇⠀⠀⠀⣼⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⢳⡀⠀⠀⠀⠸⡇⠀⠀⠀⢷⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⣸⠃⠀⠀⠀⡼⠀⠀⠀⢠⡇⠀⣰⡟
⠀⠀⠀⠘⣧⠀⠀⠈⣧⠀⠀⠀⠀⢻⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⡏⠀⠀⢀⡟⠀⠀⠀⢰⠇⠀⠀⠀⡾⠀⢰⡟
⠀⠀⠀⠀⠹⣇⠀⠀⠘⣇⠀⠀⠀⠈⣇⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⡾⠀⠀⠀⢰⠃⢠⡟
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠹⡄⠀⠀⠀⢹⡀⠀⠀⢿⠀⠀⡇⠀⠀⠀⢸⡇⠀⣾⠀⠀⠀⡟⠀⠀⠀⢸⠇⠀⠀⢀⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢹⡀⠀⠀⠀⣧⠀⠀⢸⡄⠀⡇⠀⠀⠀⢸⠇⢀⡇⠀⠀⢸⠃⠀⠀⠀⡟⠀⠀⠀⣸⢃⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⢷⠀⠀⠀⢸⡆⠀⠘⣇⠀⡇⠀⠀⠀⢸⠇⢸⠁⠀⠀⡟⠀⠀⠀⢸⠃⠀⠀⢠⣏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣬⣧⠀⠀⠀⢷⠀⠀⢿⠀⡇⠀⠀⠀⢸⠃⡿⠀⠀⢸⠃⠀⠀⢀⡟⢀⣠⡴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣼⣆⣀⣸⡆⡇⠀⠀⠀⢸⢠⡇⠀⠀⣟⣀⣤⣤⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⡐⣤⡤⠞⡁⠀⣀⡙⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠈⠀⠀⢸⣃⣿⡀⠀⢾⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠘⣆⡄⠙⠛⠛⠻⣷⡄⢀⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠈⣾⡖⠨⠶⠦⠴⣿⠶⢸⣿⠟⣿⠿⠿⣗⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠉⡮⠵⠻⡆⢸⡿⣆⡈⣷⢟⣩⠺⣷⣤⣀⢹⡷⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡵⣃⢀⣾⣥⡀⠀⡇⢚⢃⣪⣿⡇⣘⡏⣧⢻⠋⢙⣴⢋⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢠⣌⢧⣌⣛⢶⣥⣿⢈⠛⠿⣿⣽⣾⣿⣸⣃⢻⣣⢞⣵⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⢶⣶⠏⣉⣸⡿⡿⠧⠀⢠⡾⠋⣼⡯⣨⣿⡿⣛⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢑⡚⠿⢛⣿⣿⡓⠒⠓⠐⠿⢷⣶⣿⣿⣿⠿⠟⢋⣩⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠈⠐⠲⠶⢶⣯⣭⣤⣤⣬⣭⣥⣴⣶⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣄⠀⡇⠀⠀⢈⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣧⠀⢿⡄⡀⣿⣯⢩⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⢸⡇⢟⣿⣿⢹⣿⣿⣿⣿⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢾⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⠖⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⠙⣏⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠈⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣄⠈⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢂⡤⢈⣟⣿⡃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠰⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢁⡀⠑⠀⠲⢀⣀⡀⠀⣀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⣕⠈⠘⠃⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠈⣠⠀⠾⠂⠀⢴⠗⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠘⠃⣠⡀⠂⠀⣴⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠛⠃⣨⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⠙⠁⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⠕
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠻⠉⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠰⡿⠀⠀⠀⠈⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⢀⠀⠀⣶⣶⠄⠀⠀⠻⠿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⠋⠀⠈⠛⠀⠀⠙⠁
⠀⠀⠀⠈⠛⠛⠛⠶⠞⠳⡶⠟⠶⠖⠲⠞⠁⠀⠀⠀⠀⠔⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠄⠊⡁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⢀⣀⠤⠔⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠃⢉⡠⠄⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⣿⢿⠿⠿⢿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠃⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢻⠻⡐⠀⠀⠀⢠⡟⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠰⣟⣲⠿⣋⣩⡝
⠀⠀⠀⠀⠀⠀⠀⠉⣥⣀⣤⡀⣤⣤⣠⠁⠀⣠⡮⣭⡁⠀⠘⡆⠀⢸⣿⣿⣫⣭⣽⡿⣻⡆
⠀⠀⡠⠒⠚⠓⠶⣄⠉⣿⣏⠉⣉⣿⠟⢠⠞⠉⠀⣠⠼⠶⠴⢧⡀⠐⣿⣷⣶⣶⣶⣿⣉⠀⠀⣸⢷⣤⡀
⠀⢸⡁⠀⠀⠀⠀⣽⡆⢻⣿⠿⣿⣿⠀⣮⠁⠀⣴⠃⠀⠀⠀⠀⠨⡀⢻⣞⣽⣟⣩⣿⠇⠀⢸⡼⣊⡿⢽⣄
⠀⠀⠇⠀⠀⠀⠖⢾⡀⢸⣿⡟⣿⡟⠀⠀⡏⣶⠻⡄⠀⠀⠀⠀⢸⡇⠀⣿⣯⣭⣿⡏⠀⢲⡟⣓⢻⡆⣽⣷⡆
⠀⠀⢰⣠⢀⣶⣤⡞⠁⠈⣷⡟⣿⠇⠀⠈⠳⣿⣤⢈⣖⠒⢘⣿⡿⠀⠀⢸⣟⠟⣿⡇⠀⠙⣷⣷⣦⣭⣽⣶⠃
⠀⠀⠘⣭⢻⣽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠋⠀⠀⠀⠘⣯⡿⣿⠀⠀⠀⢻⣿⡿⣷⠺⡟
⠀⠀⠀⢆⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⢿⠿⣿⠀⠀⠀⠸⣾⡷⢿⢿⠇
⠀⠀⠀⢸⠷⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣶⢛⠃⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⢹⣿⢾⡟
⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⢖⡚⠩⠭⠭⣍⡛⣒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡀⢀
⠀⠀⠀⠀⣠⢞⢩⢾⡃⠠⠔⠥⠀⠀⠀⠉⠁⠨⡑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣙⠢⣑⢄⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⡀
⠀⠀⠀⣰⢣⡏⠀⠦⠾⠚⣆⢣⡀⠀⠀⠠⠀⠀⣸⣮⢳⡀⠀⠀⠀⠀⠀⠉⠑⠒⠚⢛⣾⣿⡿⠁⠀⠀⠀⠈⢿⠻⠣⠎⠈⠁⠈
⠀⠀⢠⠇⣿⠁⠀⠀⠀⣠⣿⡘⣿⠶⣤⣤⡤⠚⠿⠙⣇⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⡁⣀⠀⣀⡄⢀⡸⠟⠒⢄⠀⠀⡠⢰⢦
⠀⠀⢸⢰⡇⣀⠀⢰⣯⣨⡼⡈⣷⠠⣿⣿⠀⠀⠀⠀⠨⣹⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⠿⢿⣿⣿⣾⣿⣿⣟⠁⠀⠀⢸⣷⡾⢷⣫⡞
⠀⠀⠸⡄⣿⣿⣤⣾⣻⣟⠒⠽⣯⣼⣿⠇⠀⠀⠀⠀⡖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣭⣭⣭⣭⣤⣤⣶⣶⣾⣿⡿⠁
⠀⠀⠀⢳⡸⣿⣿⣿⢷⣽⣻⣟⣿⣿⣿⡤⡄⠀⢠⡔⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠙⢌⡻⣯⡺⣿⣿⣿⣿⣿⣿⣿⣧⠴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠢⢭⣛⣛⠛⠛⣛⣛⣫⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡀⡀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣷⣿⣯⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣠⡾⠏⠣⢄⣀⣀⡔⠁⠀⠈⢙
⠀⠀⠀⢀⣴⣶⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠞⠻⣶⣧⣄⠀⠀⠀⢠⡑⠒⠂⠈⣀⠀⠀⣀⡜⠏⠋⠀⠀⠀⢀⣾⡳⡄
⠀⠀⠐⢜⡿⣾⡏⠈⢽⣷⣿⣿⠉⠉⠋⠙⠉⠉⠆⠀⠀⠀⣼⡿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣋⡁⠀⢀⡠⠦⠴⡿⠟⣋⠴⠁
⠀⠀⠀⠀⠉⠒⠯⠤⣜⣛⣿⡿⠤⠤⠤⠤⠤⣄⣘⣢⡤⠭⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⠀⠉⠉⠀⠈⠛⠛⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠹⡄⠈⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠠⠷⠂⠀⠘⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣄⠀⠀⠀⠀⠀⠀⣠⠏⢱⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠈⢓⣦⣤⡤⠶⠋⢁⡴⠋⠀⢈⡷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠚⠉⣉⣀⣤⠤⠴⠒⠋⠀⠀⠀⡼⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠖⠁⣀⡤⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢰⠏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⢠⠎⠀⠀⣿⣤
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⡞⠁⢀⡤⠀⠀⠀⠀⢀⡀⠀⠐⠚⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠟⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⣠⠏⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⠞⣠⣿⣽⠁
⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣆⣇⡇⠀⢀⠞⠁⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢀⣴⣧⣾⠏⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⡿⠛⣷⢚⡥⡄⠀⣠⡀⠀⢀⣼⣁⣀⣀⣤⣤⡖⠲⣿⣿⠁⠀⡟⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⢸⡁⠀⢹⠋⠁⢹⡖⠋⠈⢻⠋⠁⠈⢻⠁⠀⠀⡇⠀⢰⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⠈⡇⠀⢸⡇⠀⠈⡇⠀⠀⢸⠀⠀⠀⣾⠀⠀⢸⡇⠀⡾⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢳⠀⢳⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡿⠀⠀⢸⠀⢰⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠇⢸⡄⠀⣇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣼⠀⡼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠃⠀⠻⠀⠀⣧⠀⠀⢸⠀⠀⠀⠇⠀⠀⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠉⠀⠀⠈⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⡏⡇⠈⠙⣒⠤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠑⠖⠋⠉⡷⠀⠀⠉⣉⡒⠲⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠣⣤⠴⠋⠀⠱⣀⡠⠔⠒⢦⠉⠉⠙⣒⣶⠦⠤⠤⣄⣑⣄
⠀⠀⠀⠀⠀⠀⢧⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⠒⠉⠀⠀⠙⠒⠶⠤⠖⠛⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⢾⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠋⢉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣎⠻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣟⠋⢍⢢⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⢶⣾⣿⣿⣿⣿⡿⠟⠣⡺⣝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠈⣇⢀⣉⣁⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⣿⣿⡿⣿⣿⣿⢟⣩⣀⠀⠀⣽⣝⢷⣝⠻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢳⣀⣀⣤⣶⣶⢳⣟⣿⣿⣿⠙⠿⠋⣿⣿⣯⣿⣿⣠⣾⣿⣿⣦⠻⣷⣮⡻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠈⠋⢻⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣻⣭⣽⣿⣿⣟⢿⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣜⢿⣿⣿⣿⣿⠿⣻⣿⠿⣛⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣶⣶⣶⣿⣿⡇⣾⣿⣿⣿⣿⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣶⣭⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⡀⠀⣐⣲⣶⡒⠠⢀⠀⠀⠀⢤⠤⠦⠴⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢄
⠀⠀⠀⠀⠀⠀⠈⠴⠀⠂⠈⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠡⠆⠐⠈⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣶⣍⣩⣥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖
⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠰⠂⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⣴⠋
⠀⠀⡴⠟⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣷⣶⡋⠀⠀⢠⡏⠀⠀⠀⠀⣠⠾⠁⠀⢀⣀⢀⠄
⢀⡾⠃⠀⢀⣔⡑⢂⣠⣴⠀⠀⠀⠀⠐⢤⣤⣤⣾⣧⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣀⡌⠐⣀⣴⡆⠀⠀⠀⠀⠦⣤
⠀⠁⠀⠀⠀⣿⣿⡏⢩⣿⠀⣀⠀⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠉⣽⠇⢀⡀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠈⣷
⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠶⢬⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠸⢦⣿⠀⠀⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠈⢷
⠀⢤⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⣠⠀⠀⢸⡗⢦⣬⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠘⠃
⢠⣶⡶⣃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠠⠀⠘⢧⣸⣿⣋⡔⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣞⡀⠀⠀⠀⠘⠃
⠸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠉⣷⢤⣇⣴⣴⠀⠀⠀⠀⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣻⣿⣿
⠀⠀⡀⠀⠠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢄⡃⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴
⠀⠒⢠⠶⠦⠶⡎⠀⠴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⠂⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠂⠴⠦⠰⢶⠁⠠⠄⢠
⠐⠻⠇⢀⣛⣁⣼⣞⣲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠌⠖⠀⠀⠀⠀⢰⣄⡈⣋⡀⠿⠚⠿⠀⣈⣁⣤⣷⣓⣾⡿
⢀⣉⣤⢾⣿⣷⡟⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣨⣿⢦⣀⣈⣡⡴⣿⣿⣾⠛⠛⠋⠁⠀⠀⠀⠀⠀⡀
⢸⣿⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢼⣿⣿⣿⡷⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⠉⠀⠀⠀⠀⠀⢰⣤⠄⡀⠀⠀⠀⡀⠈⠻⢿⠿⠟⠥⣀⠀⠀⠀⢤⠤⠤⠴⠠⣤⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠰⠁⠂⠈⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠆⠰⠈⠀⠀⠀⢾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣭⣉⣩⣭⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡧
⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡄⠰⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣤⠏
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣴⣶⣴⣶⣴⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠒⣈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠏⢸⠀⠀⢱⢄⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⠀⡟⠀⢸⠀⠀⠈⠚⠝⡲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣆⣇⣂⡇⠀⠸⠁⠀⠉⠑⠄⠘⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣇⣆⣲⣿⡿⠉⠀⠀⠀⠀⠀⡀⢠⠀⠀⡇⢸⣶⠀⢀⠀⢀⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⡶⠒⡟⣷⣿⡟⠀⠀⣀⠤⠀⠀⠀⡠⠋⠀⠜⠀⡿⣒⣾⠒⢀⣰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣿⣷⣶⣿⣿⡇⣠⠞⠁⣀⣠⠔⠊⠁⠐⠋⠐⠚⡇⢻⣿⣶⣸⠘⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠛⣿⣧⣄⣿⡉⠉⠉⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⡰⠁⢀⣿⣿⣿⣺⡛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡧⢄⣿⣟⣀⣀⣠⣤⡴⠖⣋⠠⠀⠀⣠⠞⠁⢠⢿⠹⣾⣾⠻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠟⢿⡁⠀⠀⠀⠉⠀⠀⠀⠀⢀⣠⠞⠁⢀⡴⠃⣸⠀⣹⠻⢿⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣥⣿⣃⠀⠀⠀⠀⢀⣀⠤⠖⠋⣀⣤⠖⠋⢀⡴⠋⢀⣿⣦⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡌⠉⠙⠛⠛⠻⠶⠶⠒⠚⠋⠉⣀⡤⠖⠋⠀⢀⡞⠀⡏⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢽⣇⠀⣀⠀⠀⢀⣀⣀⡤⠖⠋⠉⡁⠀⠀⢀⡠⠋⢀⡼⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⠻⢭⣝⣲⠶⠖⠒⠚⠈⣀⣠⣄⣒⡯⠶⠚⠁⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣓⠶⠤⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠁⡀⠒⠂⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠂⣀⠐⢀⡀⠐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣀⠐⢂⣀⠐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⢁⣀⠒⢂⣀⠉⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣁⠤⠒⢂⠤⡉⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣁⣉⣉⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⠿⢿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⢠⠚⠣⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢾⢀⡶⢊⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠢⣄⠘⠀⠀⢃⠀⠀⠀⠀⠀⠀⡔⠒⢚⣻⣙⣞⣋⠐⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⢉⠜⢁⠛⢄⠙⢆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠁⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠶⠊⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢈⠈⠢⣸⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠴⠂⠉⠉⠙⢢⡀
⠀⠀⠀⠀⠑⣤⣙⣤⡶⠘⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠔⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠛⠤⢤⡴⠿⡤⠞⠳⢆⡉⠀⠀⠀⠀⠀⠀⣀⠤⠀⠠⢤⣀⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣔⠁⣠⠞⠃⡍⠓⠤⠸⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠈⠉⠁⠀⣀⡇⠀⠀⠀⠀⠀⣀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠁⠀⠙⠒⢤⡀⠀⠀⣀⠴⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠉⠁⠢⡀⠀⠀⡆⠘⢳⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠉⠁
⠀⠀⠀⠀⡠⠄⣰⠁⠙⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⢤⠀⠈⠀⢀⠇⠀⠈⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠚⠁
⠀⠀⠀⠀⠀⠁⠒⠠⠊⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣀⠄⠤⣀⡀⠔⠠⣀⡠⠔⢤⣀⡠⠒⢄⣀⠔⠢⣄⣠⠔⠢⣀⡔⠢⢄⣀⠤⠾⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠠⠀⠀⢠⡄⠀⡄⠀⠀⢀⡀⡇⣡⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⠀⠀⠀⡇⠀⠀⢸⡆⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⡄⠀⠀⠘⠁⠀⠃⠀⠀⠳⡤⣿⡷⢯⡀⠤
⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⢶⠀⡆⠀⠀⠇⠀⠀⠸⠃⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠋⠐⢫⡿⢀⡅
⠀⠀⢀⠄⣨⡀⣵⢉⣁⣀⡀⠀⠀⢠⡄⢡⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠘
⠀⠀⠈⠑⢪⣵⣚⡯⢤⡒⠁⠀⠀⠀⠃⠘⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⠀⢀⠀⠀⢠⠀⠀⠀⠃⢀⡆
⠀⠀⠀⢮⠅⢾⠉⡗⠢⠘⠀⠀⠀⠀⠸⠀⡇⠀⠀⡆⠀⠀⣶⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠀⢠⠀⢈⠃
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⣀⡁⠀⠀⠛⠀⠀⠀⠂⠀⠀⠃⠀⠀⠚⠀⠀⢘⣀⡀⠠⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣼⣶⣾⣶⣶⣦⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢞⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠘⠁⠀⠀⡜⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⡠⠋⠀⠀⠀⡠⠀⠀⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠎⠀⠀⠀⠀⠔⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠁⠀⠀⢀⠔⠃⠀⠀⡠⠁⢠⠓⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢀⡦⠀⠒⠒⢂⢤⡎⠀⠀⢄⣤⠊⠀⠤⠋⡈⠐⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡐⠋⠢⣌⡠⠔⠊⠁⠀⣀⠤⠒⠂⠁⠀⠀⠀⠀⠀⠄⠀⠀⡄⠹⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣣⡈⠛⠤⢋⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠠⠁⢐⢦⠀⠱⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠈⠁⠒⠀⠤⢏⡀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⢀⣴⠡⡴⠊⠀⠆⠀⠃⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡒⠓⠤⠄⠤⠀⠀⠀⠀⠀⠈⠁⠲⠾⠤⠤⠀⠒⠂⢈⠉⠤⠐⠊⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⣑⡠⠤⠀⠀⠀⠂⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠀⠀⠀⢀⡀⠤⡴⠊⠀⠀⡰⠀⣰⠃
⠀⠀⠀⠀⠀⡀⠄⠖⠋⠙⡁⠀⠉⠐⠠⠄⠀⠀⠀⠀⠀⠠⠤⠄⠀⠒⠒⢀⡉⠁⠄⠂⠁⠀⠀⡠⢚⡠⢊⠆⢀⡀
⠀⠀⠀⠀⡊⡀⡌⠀⠀⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠐⠂⠉⠁⠀⠀⠀⠀⡀⠄⠒⡉⢔⡡⠐⠉⠢⠀⠈⠑⢂
⠀⠀⠀⠀⠑⡙⢳⣄⡀⡀⠀⠀⠀⠀⠀⠈⠁⠉⠄⠀⠀⠀⠀⠀⠠⡤⠀⠒⠂⢉⡁⠠⠐⠋⠁⠀⠀⠀⠀⢀⣂⢀⡔⠟
⠀⠀⠀⠀⠀⠘⢄⠡⡡⡘⡎⢶⠒⢤⠀⢄⠤⢄⡀⡀⢀⣀⠀⢀⠀⢈⣉⠉⢉⡀⠀⢄⡠⠢⡤⠂⡔⢰⢁⢃⢏⠨⠂
⠀⠀⠀⠀⠀⠀⠈⢂⠐⠜⠈⠄⢂⠀⠄⠘⡀⠈⠀⠈⠃⠀⢹⠀⠈⠁⠀⠸⠀⢨⠁⠰⠁⠀⠀⡜⠠⢡⢃⢂⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠌⠌⠄⢣⠘⠀⠁⠀⢃⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⡀⠀⠁⠠⠁⡘⢀⢃⢂⠆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⡌⠜⡀⠆⢁⠘⠀⠘⠀⠸⠀⠀⠀⢠⠀⠀⠀⢠⠁⡌⠀⠆⢰⠀⠀⠄⡌⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⡐⠐⠘⠈⡀⠃⠀⡁⠀⡄⠀⠀⢸⠀⢰⠀⠈⠰⠀⠰⠀⠆⠰⡘⠘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠠⠀⠃⠸⢀⠃⢁⡣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠬⣰⢠⠀⡀⢰⠀⢀⢀⠀⡂⠀⡇⢰⠀⡀⢀⠀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡈⠀⠉⠈⠈⠁⠀⠁⠈⠀⠉⠉
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⠂⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣀⡀
⠀⠀⠀⠀⣤⠊⠀⠉⠉⠐⢠⠀⠀⠀⠀⠀⡠⢄⡠⠤⣊⡣⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠀⠑⠒⡖⠀⠀⠀⠀⠀⠁⣀⠠⣿⣷⣿⡀
⠀⠀⠀⠈⢀⡀⠀⠚⠁⠘⠂⡄⠀⠀⢰⠀⠡⠒⢀⣚⠀⠀⠈⠉⠹⡀⠀⠀⠀⠠⠠⠃⠀⠀⠠⠀⠉⠿⡆⠀⠀⠔⠈⠀⠀⠀⠉⠀⠈⠢
⠀⠀⠀⠲⠬⢁⣀⣘⡃⠠⠔⠂⠀⠀⢎⠁⠀⢀⣀⣀⣀⣰⣖⣀⣀⡁⠀⠀⠔⠘⡶⠀⠁⠀⠀⠁⠀⢀⡱⠀⣌⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠒⡖⡄⠤⢤⢤⠤⢲⡃⠀⠀⠀⠹⡩⠈⠘⠀⠀⠘⠀⡀⡄⠀⠀⠀⠈⣯⣥⣤⣤⣤⣤⣤⣭⠾⠁⠀⠈⢾⠯⣍⣬⣩⣩⣭⢿⠋
⠀⠀⠀⢠⠥⣅⣀⣸⣸⠤⠼⡆⠀⠀⠀⠀⢁⢃⢂⢲⠀⠀⢀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣄⢠⡄⡄⢸⢸⣺
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢳⡈⣾⣴⢃⣂⡘⠀⠀⠀⠀⠀⠘⣠⠀⡄⢀⢀⢀⢠⣼⠀⠀⠀⠈⡆⡄⡆⣇⣸⣸⡏
⠀⠀⠀⠀⠣⢀⣀⠀⣀⡀⠤⠂⠀⠀⠀⠀⠀⠀⠉⣩⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠾⠧⢿⡾⠾⠿⠋⠀⠀⠀⠀⠳⠧⠽⠽⠽⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⢀⣏⡑⢺⠄⢄⠀⠀⠀⠀⠀⠀⣠⡾⣷⡹⣷⣌⡻⢷⣦⡀⠀⠀⠀⠐⠁⠀⠈⠉⠉⠛⢂⠀⠀⠀⠀⠀⢀⠄⡜⢒⣉⣆
⠀⠀⠀⡔⢣⠼⡼⢍⡽⣉⢆⡀⠀⠀⠀⢰⡙⣷⣝⡻⠦⣽⣿⣾⣟⠣⠀⠀⠀⡇⠀⠄⠀⠠⠀⠀⠈⠀⠀⠀⠀⡀⢎⡹⣉⠧⡼⢤⠓⡄
⠀⢀⠊⠉⠉⠈⠑⡚⠢⠂⠀⠈⠄⠀⠀⣿⣿⣮⣝⣛⠻⠷⣶⣌⣿⣣⠀⠀⠀⡇⠀⠠⣀⠐⠀⠀⠀⠀⠀⢀⠊⠀⠈⢢⠛⡖⠁⠈⠉⠉⢆
⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⣿⠻⢿⣿⣿⣿⣷⣬⣿⢟⣻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢨
⠀⠀⠒⠀⠤⠄⠄⠠⠤⠤⠐⢚⠇⠀⡋⢹⣿⣷⠂⡱⠛⠙⠛⠉⠉⠅⠀⠀⠀⣿⡓⠳⠷⡾⠊⢛⣿⠀⠀⠀⣇⠒⠠⠤⠤⠠⠤⠤⠀⠒⠃
⠀⠀⠻⠿⠶⠶⠶⠶⠶⠾⠿⢿⠀⠀⠉⡏⣙⡈⠏⠀⠀⠉⠀⠈⠀⠁⠀⠀⠀⢹⣿⣶⡆⠀⣶⣿⣿⠀⠀⠀⢹⠿⠷⠶⠶⠶⠶⠶⠿⠿
⠀⠀⢰⣶⣦⣤⣤⣤⣤⣶⡶⠟⠀⠀⢰⠀⣿⡇⢘⣤⣤⣤⣤⣤⣾⡄⠀⠀⠀⠘⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠸⠷⣶⣦⣤⣤⣤⣤⣶⡶
⠀⠀⠈⠒⠠⠄⠉⠁⠠⠄⠐⠁⠀⠀⠀⠙⠉⠛⠺⠿⠿⠽⠿⠿⠋⠁⠀⠀⠀⠀⢻⣿⣷⣴⣿⣿⠇⠀⠀⠀⠀⠒⠠⠤⠀⠉⠁⠤⠐⠂
⠀⠀⠀⠀⡀⠄⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣀
⠀⠀⠀⠀⠀⣀⠀⢿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠴⠞⠀⠁⠈⣇⣀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡔⢂⡀⠀⠀⠀⠀⠀⠀⡾⠃⠀⢀⡀⠀⣑⡄
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢔⠀⠂⠂⠀⠐⠀⠀⠻⡃⠀⠀⢀⠤⠊⡨⠁⠤⠈⠁⠘⠂⢂⠀⠀⠀⢰⠠⡤⠀⢈⣁⠀⠉⢐
⠀⠀⢨⢄⠀⣀⠀⠀⠀⠀⠀⣠⠆⠀⢎⠉⠗⠀⠈⠁⠉⠀⠀⢀⡜⠀⠀⡨⠂⠀⠀⠈⠉⠀⠄⡠⠀⠈⢡⠀⠀⢸⠐⠐⠂⠈⠑⠒⠀⣩
⠀⠀⠀⢱⠳⠤⠥⠤⢥⢤⢿⠃⠀⠀⠀⠷⠶⢤⣤⣤⣤⡴⠶⠾⠀⠀⠀⠈⠲⠰⠑⠛⢹⠙⢉⠹⠙⠙⠁⠀⠀⢨⠉⢹⢹⢙⠙⠋⠉⢀
⠀⠀⠀⢘⡇⠰⠔⡄⢸⢸⣸⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢁⢂⢂⢈⠀⠘⠀⠄⠃⠀⠀⠀⠈⡚⠒⠚⠐⠒⠒⠊⠙
⠀⠀⠀⠀⡟⡄⡆⡇⡎⡇⡏⠀⠀⠀⠀⠈⣤⢀⡄⣤⢠⢠⣠⡔⠀⠀⠀⠀⠀⠀⢢⠈⡞⡄⡆⡴⢠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⠳⠶⠿⠷⠓⠋⠀⠀⠀⠀⠀⠛⠛⠷⠿⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠓⠚⠓⠓⠓⠁⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠄⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢨⡿⠀⣰⡿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠃⢠⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣼⠇⢠⡿⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⢠⡿⠃⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡟⠀⣾⠗⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀⠠⠄⠒⠂⣈⣉⠉⠥⠀⢀⡿⢠⡿⠀⣼⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠰⠁⠀⠀⠞⠁⠀⠀⠀⠀⠀⣾⠃⣾⠁⣰⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢢⡀⠀⠀⠀⠈⠲⠄⣀⠙⠲⢄⠀⠀⠀⣸⠏⣼⠇⢠⡟⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⡙⠫⣝⢷⣦⣀⣀⣩⣭⣭⣴⣦⣤⣤⣦⣤⣶⣤⣤⣰⡟⣰⡏⢀⡿⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⢡⣤⡙⢿⣍⣉⣳⣈⠻⠿⣍⡠⠤⣄⠠⡤⣘⠀⠡⣄⠀⢈⣿⢡⡿⠻⣿⢁⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⡘⠓⢽⡿⢧⣌⠁⢞⠈⢷⠀⠈⠀⠀⠈⢄⡀⠀⠀⣸⠃⡼⠁⡼⢁⣾⠋⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⣹⡿⠿⠷⣶⣯⣉⡑⣭⡀⢸⡶⢄⠀⠨⠀⢀⠁⢰⣶⣧⣼⡧⣾⠷⢾⣷⣶⣤⣄⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣠⣾⠋⠁⠀⢒⡂⠀⠍⠉⠻⠿⠛⣷⣶⡏⡐⠀⠈⣀⠜⡋⠀⠌⠀⡤⠀⣤⣞⣉⣍⢙⠻⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣾⡯⠄⠀⢾⡶⣤⣥⣤⣤⣄⣘⠆⠈⠠⣼⣦⣑⣤⠞⡡⠀⡠⢀⠔⡠⠄⠀⢿⣻⡿⢻⣿⡷⠾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⡟⢻⠿⣯⣽⡇⢀⠀⠈⠉⠙⣯⡀⢢⡒⢡⣾⡿⡡⢊⡤⢊⣤⡪⢶⣤⣠⣴⣼⣿⠟⠻⣿⠀⣄⣞⡷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⢧⣎⢘⣷⠐⠚⢇⡀⠀⠈⢻⡅⣰⡿⢋⠜⡰⣡⢜⡠⢋⠔⢉⡿⡁⠠⠁⣬⠆⢘⣿⣷⣎⣁⣠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠷⢶⣾⣦⣿⣄⣐⣂⢻⣀⡐⣾⡷⣛⢖⡡⣚⢚⡵⣿⣷⣥⣶⣽⣇⣵⣾⣯⣷⣶⠿⠿⠟⠛⠋⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠳⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⠶⠶⠿⠛⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⢉⣉⣉⣉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣒⣚⣓⡒⠦⣤⡀
⠀⠀⠀⠀⣠⠞⢁⣤⣪⡬⠶⣶⠶⡦⢯⣷⣤⠈⠳⡀⠀⠀⠀⢀⡔⣩⡴⠿⠛⢣⠹⠇⠛⠛⠲⣍⠳⣄
⠀⠀⠀⣰⠃⣽⣿⡿⠹⡇⠀⡇⠀⠇⠀⡄⠙⢷⡄⠙⡄⠀⢠⢏⣾⠧⠤⠐⢀⠀⠀⠀⠂⠘⠀⠨⠷⠙⣆
⠀⠀⠀⡇⢰⣿⢿⡵⢜⡷⠔⣤⣴⡅⣠⢡⣠⢼⢻⠀⢹⢀⡏⣾⣁⣤⠀⢂⡠⠀⠠⣄⢲⡄⢠⡠⠔⠢⢸⡀
⠀⠀⠰⡇⢸⡇⢨⠀⠸⠀⠈⠁⢸⠋⠈⠋⢹⠈⠁⠀⢸⢸⡷⣿⡄⠘⠀⢸⠀⢠⣴⡟⠈⡅⠀⡀⠠⠀⠘⡇
⠀⠀⠀⢧⠈⢧⡲⢀⣶⢀⣾⣀⡼⣀⣼⣤⣜⢰⡘⠀⣾⠸⣇⠟⠂⠀⠁⠀⠀⠻⣏⣿⠀⢀⡠⠤⠀⢷⢰⠇
⠀⠀⠀⠘⢧⠈⠿⠑⡟⠑⡗⠉⡖⠋⡙⠋⣙⠝⢁⣼⠃⠀⠹⡌⢀⠀⢀⠠⠆⠀⢟⠉⠁⡀⡀⠀⡦⢃⡞
⠀⠀⠀⠀⠈⠳⣄⡉⠓⠀⠧⠀⠧⠀⠗⠂⢀⣴⡿⠃⠀⠀⠀⠻⢦⡄⢤⣄⠀⡃⠈⠀⢈⣅⣡⢀⡵⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣿⣓⣐⣛⣨⠭⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⣻⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⣴⣶⢾⣿⡄⣿⣲⡝⣛⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⠖⠒⠃⠀⢀⣠⠏⠉⠀⣼⣿⣦⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⣴⡖⠉⢀⣠⡴⠾⣟⣛⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣄⣠⣤⡴⠋⠀⡐⣦⣿⣿⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠖⠛⢿⣿⠗⠋⠀⣀⡀⢬⡿⢋⣵⠟⣿⣟⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢠⣶⣉⣿⡯⢾⠋⢁⡴⢫⣶⣿⠷⠚⢋⣹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣿⣿⠟⠁⠀⣰⠟⣴⠛⣻⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠌⢛⠻⣶⣶⡾⠓⢚⡛⣛⠻⣿⢿⢿⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⣿⣿⣴⣆⡙⠈⠣⣀⠠⣾⣿⣛⣻⣷⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠚⣿⣄⣿⣿⣇⡀⢤⣬⣼⣿⣿⢿⣿⣿⣿⡃⣾⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠸⣿⠋⣿⡇⢤⡾⣿⡿⣿⣿⡄⠻⣿⡟⢁⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣧⢸⣿⠀⠀⣿⡇⠀⣿⠇⢰⣿⡇⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣿⡘⣿⣿⢸⣿⠁⢸⣿⠀⣾⡿⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢻⠹⢸⣿⡀⢸⡿⢸⣿⣿⣿⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢼⣏⣸⣿⣃⣻⣿⣾⣿⣿⣿⣿⣿⣦⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⡿⠍⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠛⠓⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⡴⡚
⠀⠀⠀⡀⠻⠃⣤⠀⠀⠀⠀⠙⡀⢀⠀⠀⠀⠀⠀⠐⠀⢱⣙⡶⠆⣠⠃⠀⠂⠀⠀⠀⢀⠀⠙⠿⡆⡁⡧⡙⠂
⠀⠀⢔⡟⠀⢥⡃⢀⡀⠀⡒⡀⠀⠠⠀⠀⠀⠀⠀⢄⡣⠔⡻⠁⠐⣌⠁⠒⢄⡀⠀⠙⠿⠇⣠⡄⣧⠱⠱⣌⠁⠀⠀⠀⠈
⠀⢰⣎⣃⣀⡂⠀⠀⠉⡀⠀⠀⡒⢲⠀⠄⠀⠀⢀⡞⠀⢾⡁⠀⠀⠈⠑⠦⠀⠈⢆⠀⠀⠀⠿⣃⠘⣦⠱⢄⠙⠂⠀⠀⠀⠐⠂
⠄⢰⡆⠀⠄⠉⢁⠢⠄⠷⠀⠀⠀⠀⠰⠀⠀⢒⢚⡣⠄⠼⠷⠤⣀⠀⠀⠀⠷⠂⠚⠁⠀⢠⣆⡈⢧⡈⠳⢤⣁⠀⠀⠀⢠⠠⠴
⠀⠀⣛⣂⣠⣤⣬⣤⣰⣀⣀⣉⡤⠶⠂⠀⠀⡶⢬⣃⣀⠐⣤⡀⠀⠰⢤⣀⠀⠈⣒⡄⠀⠈⢧⣧⣭⡉⣠⢠⡈⠓⣒⠊⣄⢠
⠀⠀⢹⣽⠘⡇⠸⡇⢸⡇⠸⠁⠃⠀⠀⠀⠀⠈⢲⢰⠉⡍⢩⡉⠙⡋⠉⡍⢡⠀⠂⠀⠀⠀⠀⢩⠘⡇⠈⡇⢹⠁⢸⠁⠘⠸
⠀⠀⠀⠇⠇⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⡇⠀⠃⠀⠃⠈⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠃⠈⠀⠘
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⠙⠒⠓⠒⠒⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣈⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣠⠆
⠀⠀⠀⠀⠀⢀⠂⠀⡄⢠⡀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠐⢀
⠀⠀⠀⢀⠰⣇⠘⢦⡈⠀⢬⠙⠐⡶⠆⠀⠀⠀⠀⠀⠀⢈⣀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘
⠀⠀⣀⠈⠑⠒⠚⢈⠁⠀⢈⣀⣄⣀⣁⣠⠀⠀⠀⠀⡼⠋⢁⡀⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⣴⠂⠀⣠⠄⠀⡀
⠀⣄⣿⣙⣒⡂⠉⠀⠈⠉⠙⣦⣀⡀⣀⣀⠇⠀⢠⠸⡃⠀⠈⠒⠢⡀⠀⠙⡄⠀⠀⠀⠀⠹⢄⣹⣄⠀⠻⡀⠀⢱⣄
⠀⡀⠠⠀⠀⠉⠀⠀⠀⠘⠰⣌⣉⣉⣀⣀⠤⠂⠘⠓⠳⠤⣤⡤⠴⠶⠤⠔⠓⠒⠂⠀⣄⠱⠀⠠⢄⠈⠉⢍⡀⠁⠠⠄⠀⠉⡄
⠀⠀⠙⠲⣮⣕⠒⣒⣠⣤⢶⣤⢤⣴⢿⠒⠀⠀⠈⢷⣾⣄⣀⡤⢶⣆⠀⡖⣶⡄⠀⠀⠀⠳⠖⠆⠆⢠⠠⡄⢤⢠⢠⠴⠒⠛
⠀⠀⠀⠀⠇⠹⠈⠙⠀⢹⠀⠸⠀⠈⠀⠀⠀⠀⠀⠈⠙⢸⠀⡇⠈⣿⠀⠁⠙⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠢⢀⡇⠀⢠⣀⠆⠀⠀⠀⠄
⠀⠀⠀⠲⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠟⠀⠀⢀⠁⠀⠀⠀⠙⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡖⠀⠀⠀⠀⠁⠀⠈⠃⠐⡏⠀⢘⠆⠀⠁⢲⠀⠀⣀⠇⠀⢠⠞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠃⠀⡆⠰⢀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠘⢧⡀
⠀⣀⠀⠀⠠⠯⢸⠢⢠⢠⡈⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠐⠓⡀⠀⠈⠁
⠀⡁⣀⡀⠀⠀⠙⠱⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⢀
⠐⢻⠵⠂⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠄⠁⠀⠐⠀⠁⠀⠀⠀⠰⣁⠈⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⣀⣀
⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠦⣵⢿⡷⣯⣤
⠀⣏⠀⢳⣔⡀⠀⠀⠀⡀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⣂⡿⢿⣟⡶⡿⣗⠈
⠀⡏⠻⠾⠏⡦⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡽⠷⣴⠷⡍⡛⠒⠀⠆
⠀⡇⡂⠘⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣄⢠⣾⠧⢓⡀⠀⠀⡤
⠀⠁⠑⢀⠉⢀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣜⠹⣀
⠠⡆⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠔⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠊⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⣁⡠⠶⠖⠳⣄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠊⠉⠀⠀⠀⠀⠀⠣⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠄⠉⠀⠀⠈⠳⡖⠒⢦⣄⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠞⠋⠙⠳⣄⣧⣴⠤⢤⣀⠀⠀⠀⡇⠀⠀⣨⣅⡀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⠀⠀⣸⢁⣀⣤⠤⠤⠤⣄⠀⠀⠀⠈⠉⠛⠳⣇⡴⠛⠁⠀⠙⢦⣤⣬⣇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⣿⣤⡀⣠⠟⠋⠁⠀⠀⠀⠀⠈⠳⣤⣤⠴⠶⣏⢉⡽⠛⠋⠉⠉⠛⠳⢦⡀⠸⡇
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⣷⠒⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠇
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⡾⢧⣄⣀⣀⣀⣀⣀⣈⣹⣆⣀⣏⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘
⠀⣠⠞⠉⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣦⣤⣴⠚⢉⠉⢻⡄
⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⠀⠀⢰
⣠⠟⠀⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⣾⡁⢠⡄⠀⠀⢀⣤⠀⠀⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⢠⣿⠀⠀⠀⠀⣼
⣏⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⢷⢾⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣆⠀⠀⠀⢹
⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⡇⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⠀⠀⢸⡷⠈⢳⡄⠀⠘
⠀⠈⢹⡶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⢺⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⣠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⠀⠀⢠⡆⢹⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠳⣄⣠⠾⠁⠀⠹⣶⠶⠶⠓⢦⣀⣤⣄⠀⠀⣠⣤⡶⠋⣧⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡜⢸⠀⢠
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠢⡀⢀⡠⠌⠃⢾⠀⣾⠋⣼⠁⠀⣿⠘⣧⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡇⢸⣤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⢢⡀⠀⠒⠉⠃⠄⠀⢠⡟⢠⡇⣼⠃⠀⠀⢸⡆⢻⡀⠈⣷⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣼⠃⢸⠁⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⢂⣀⡀⠠⠈⠉⣹⠃⢸⣷⠏⠀⠀⠀⠈⣷⠘⣧⠀⢻⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⢀⡟⢠⡏⢸⡟
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠢⠀⠀⣰⠏⢀⣼⡏⠀⠀⠀⠀⠀⠸⣇⠸⣇⠈⢣⠀⠀⠸⡆⠀⠀⢸⠇⠀⠀⠀⡈⠁⠀⡘⢀⡾⢠⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠐⢤⡀⠀⠶⠈⠉⠙⠓⢛⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠈⢣⠀⠀⠙⡀⠀⠀⠀⠀⠀⠰⠁⠀⡜⢁⡾⢡⡿⠁
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠑⠠⡀⡀⠄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⢷⡄⠑⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠊⣠⠏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠘⠢⠀⠈⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢁⣴⠏
⠀⠀⠀⠀⠀⠀⢸⡆⠐⢀⠘⠓⠂⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣈⠉⠓⠒⠶⠖⠚⠛⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠑⠶⠆⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠦⠤⠀⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠢⢤⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢠⠀⠀⢀⡀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⣴⠋⠀⠀⠈⢧⠀⠀⠀⠀⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣀⣤⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣳⣦⣤⣶⣤⣤⣶⣶⣶⣚⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⣿⣦⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣠⣼⣿⡟⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢙⡽⢻⣿⣟⣵⡞⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠐⣺⠿⢗⣼⣿⣿⣿⣾⣹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠶⣀⣻⡛⠿⢫⢟⢛⣿⣿⢝⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠀⠀⠒⠚⠛⡋⡙⢡⣾⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠒⢻⠤⠶⣤⣼⡷⠉⣡⡞⣿⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢂⡶⢀⠛⢛⣵⣯⣬⠾⠿⣥⣿⠲⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢌⡣⠵⠞⠋⠉⢠⠄⣙⠷⠋⠁⢀⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠤⠶⠿⣀⣀⣀⣠⡤⢶⣾⣯⣤⡶⠞⣟⣫⡷⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠁⢻⣿⡿⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠂⠀⠆⠈⡆⠀⢠⠂⠀⡄⠀⡔⢻⣶⠈⡏⢸⢧⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⠀⣦⠴⠔⣆⣬⡀⠀⡇⣀⣷⠀⠏⢻⡟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡉⢿⠻⣅⢠⡀⠙⡷⠀⡿⠁⡌⢺⡿⣼⣧⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣸⣶⣿⢩⡟⠀⣿⢈⣧⣾⣷⢀⣧⣿⣽⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⣧⢸⡾⣿⡀⣿⠛⣿⢃⣿⢿⡟⣿⣿⣿⣯⡯⣄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⣇⣇⣿⡛⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣦⣝⣷⣢⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣻⣿⢟⡧⡭⠶⢢⣆⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠚⠁⠛⠁⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣝⣟⣽⣿⣦⣼⢿⠶⠛⠛⠉⠉⠛⠛⠛⢯⡉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣟⡛⠛⡓⠀⠀⣀⠀⠀⠀⠀⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠈⠁⠀⠈⡆⠀⠈⢻⣦⠀⠀⠰⠀⠉⠙⠳⣄
⠀⠀⠀⠀⢠⣄⡴⠋⠙⣝⠢⢈⠙⠛⠛⠛⠛⠉⠀⠀⡼⠀⢠⠆⠀⢸⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠌⠣⡀
⠀⠀⠀⠀⠀⡍⠀⢀⠀⠈⠑⠀⠀⠠⠄⠀⠀⣀⡴⠚⣀⡴⠋⠀⠀⡞⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡼⠂⠠⢄⣠⣤⣤⣤⣤⠶⠖⠛⠉⠀⠚⠉⠀⠀⢠⠎⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡄⢸⠀⠀⡀⠀⠠
⠀⠀⠀⠀⢨⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⡴⢋⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠘⢮⣁⠒⠒⢒⣒⣒⣋⣩⣤⣤⣶⣶⠿⠟⠉⠀⠀⣀⠴⠚⠉⠀⠉⣀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠇⠀⢰⡇
⠀⠀⠀⠀⠀⣠⠊⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⢀⡿⠀⠀⣤⡾⠀⢀⣾⠑⢄
⠀⠀⠀⢠⠞⠁⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠴⠒⠋⡁⠀⠀⠀⠀⢀⣴⡟⠁⠀⣰⡟⠁⠀⣼⣿⠃⠈⢣
⠀⠀⢠⠇⠀⠙⢿⣿⠋⢩⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⣠⡾⠋⠀⠀⣰⡿⠃⠀⠘⢀⡆
⠀⠀⢸⡀⢀⡆⠀⠙⣆⡀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠖⠛⠉⠉⢀⣠⠴⠞⠉⠀⢀⣠⡾⠟⠁⠐⠀⣠⣾⠁
⠀⠀⠈⣧⡘⣧⡀⠀⠈⠙⠛⠛⠛⠛⠋⠉⢦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⣤⣄⣀⣀⣀⣠⣤⠶⠏⠁⣀⣤⣴⣶⡿⠟⠁
⠀⠀⠀⠘⢿⣮⣁⠀⠘⠃⠀⠀⠂⠀⠀⠀⠀⠙⠛⠷⠶⠾⠿⠟⠛⠍⠀⡀⠆⠈⠉⡉⠉⠁⠀⢀⣠⠚⣿⡏⢰⡟
⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣶⣦⣤⣴⣷⣦⣄⡀⠀⢀⠀⠈⠀⠀⠀⣀⣤⣴⣶⣃⣀⣤⣤⣶⡾⣿⡟⢸⣿⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡄⢿⣿⡀⢸⣿⡟⠿⣿⣿⡿⠿⣿⣿⠿⢻⣿⠉⢹⣿⣿⠛⣿⡿⠀⣿⡇⣸⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣈⣿⡸⣇⢸⣿⡇⠘⣿⣇⠀⢸⣿⡇⠀⣿⣏⠀⢸⣿⠀⢈⣿⡏⠀⣿⡇⠀⣿⠀⣿⢇⣟
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣧⢻⡄⣿⣷⠀⢿⣿⠀⠘⣿⡇⠀⣽⣯⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇⢸⡿⢰⣿⣸⣿⣿⣶⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣧⢸⣿⡀⢸⣿⡀⠀⣿⡇⠀⢹⣯⠀⢸⣿⠀⢸⣿⡇⢀⣿⠁⣼⡇⣸⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⣿⡇⠀⣿⣧⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⢸⣿⠀⣿⡇⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣿⣿⣷⣴⣿⣇⣀⣽⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⣸⣿⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⠿⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠛⠛⠉⠉⠉⠉⠛⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠆⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠀⠀⠀⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡐⠐⠂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣤⣠⣀⣄⣀⡀⡄⣤⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡐⠀⠀⠈⠁
⢀⠄⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈
⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠀⠀⠀⠀⠈⠱⠶⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠳⣄⠀⢀⠠⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠰⠃⠉⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠈⠁⠰⠀⠀⠀⠀⠀⡀⠙⠓⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠏⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠂⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⡠⢀⣠⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣴⣧⣼⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠲⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣠⣶⡶⣿⣿⠿⠿⠛⣿⣶⣶⣯⣉⠻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⣿⠋⠁⢈⡴⠃⠀⣀⡜⠛⠁⠸⢟⠿⡷⢌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢠⡾⢁⣾⣿⠋⠀⠐⡴⠊⠑⢤⠐⠁⠉⠲⡎⠀⠀⠘⠃⠈⠳⡌⢮⢧⣄
⠀⠀⠀⠀⠀⢠⡟⢠⣿⡇⠈⠳⣄⠀⠠⡠⢀⠀⢁⢤⡀⠀⢈⠶⢄⠀⠀⠉⠦⡨⠆⢻⣿
⠀⠀⠀⠀⠀⣿⠀⣾⠋⢿⠂⠀⠈⠑⠀⠀⠀⠙⠁⠀⢈⠟⠁⠀⣀⠉⠀⢀⣔⠀⢈⠈⢿⡆
⠀⠀⠀⠀⢠⣯⢀⣿⠟⠁⠀⢠⡔⠀⠀⣠⢀⠀⢀⡴⢦⣤⣀⠜⠁⠀⣴⠃⠈⠁⢾⡆⢰⡇
⠀⠀⠀⠀⠸⣏⠈⡷⠀⢠⡜⠁⠈⡠⣾⠀⠻⠷⠿⣶⠾⠛⢿⣄⡀⠑⠈⡣⣀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣿⡄⠀⠈⢢⡀⠈⠻⣷⠦⣀⠀⠈⠻⢿⣷⡾⠋⠢⣄⡜⠉⢻⢶⡯⣸⠇
⠀⠀⠀⠀⠀⢹⣇⠘⣟⢤⡄⠁⠈⢳⠖⠁⠀⠈⠛⠀⠀⣠⠋⠀⠀⠀⠈⠀⠀⠃⡼⠡⡿
⠀⠀⠀⠀⠀⠀⠻⣧⠘⢏⡀⣠⠞⠁⠀⠀⣠⠃⠀⣠⠔⠁⠀⢀⣴⡂⠀⣀⢸⡟⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⠧⠀⠀⠠⡄⠀⠀⠛⢃⠀⠀⠈⠻⢄⡀⣺⡿⢋⣴⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠤⠈⣳⣄⠀⠈⢳⡤⣀⠀⠠⠟⣉⣤⠟⠋⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⣤⣀⣈⣉⣉⣉⣠⣤⡶⢞⡛⣭⣴⠶⠶⠶⣶⣖⠤⣄⡀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠉⠉⣹⠟⠋⠉⣥⣶⣋⡼⠋⠀⠀⠀⠢⠀⡉⢳⣶⣿⢷⣦⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣿⠀⢀⡾⠁⠘⣶⣿⡷⡿⢿⠁⠀⠀⠀⠀⡀⠀⠁⠈⣷⡝⠘⠻⣿⣆⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣸⠇⠀⣼⠁⠀⣼⣿⣿⣇⠇⣸⠀⠀⠀⠀⠀⠘⠢⠀⢀⡟⡇⠀⠀⡇⢸⣧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⣿⠀⢰⡇⠀⢸⣿⡿⣼⣏⡷⣌⠷⣤⡀⠀⠀⠀⢀⣴⠊⢁⢉⡃⡐⡃⢾⠹⣇⠀⠘⡇
⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⠀⠀⠀⣿⠀⢸⠁⠀⣾⣿⠃⢃⣮⠶⠾⠾⢥⣍⡿⠟⠛⣿⣩⠶⠟⠛⠳⠾⣥⡶⡄⢻⠀⠀⣿
⠀⠀⠀⣼⠃⣠⠞⠉⠁⠈⠉⢆⠀⢻⡀⢸⡅⠀⢸⡇⣰⠏⠀⡀⠀⠀⠀⠀⠙⣆⢠⡟⠁⠀⠀⠀⠁⠀⠀⠹⡄⠘⠀⠀⣿
⠀⠀⢰⡗⠀⡏⠀⠀⠀⠀⠀⠈⡄⢸⡇⠈⣇⠀⠘⣷⡏⠀⠀⠈⠐⡀⠀⠀⠀⣽⣾⠀⠀⠀⠀⠀⣀⠤⠀⠀⣿⠃⠀⢸⣿
⠀⠀⠈⣇⠀⠳⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⢹⣆⠀⠸⡇⠀⠈⠁⠉⠀⠀⠀⠀⣸⢻⣆⠀⠤⠤⠚⠁⠀⠁⣼⡏⠀⢠⣿⠇
⠀⠀⠀⠙⢦⡀⠈⠒⠀⠀⠈⣠⡾⠃⠀⠀⠀⢻⣆⠀⠙⢤⡀⠀⠀⠀⠀⢀⡴⠃⢸⡟⢦⣀⠀⠀⠀⣀⣼⠋⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⢿⣶⡖⠒⡟⠁⠀⢸⠅⠀⢉⡛⣏⠝⠉⠀⣀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠈⠁⠀⠓⠂⠀⠜⠒⠂⠈⠁⠀⢀⣠⢾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡋⠻⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⣻⣿⣷⠏⠁⢶⡷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣸⡂⢀⣤⣾⣷⢠⣤⢤⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⣿⣾⣿⣿⣿⡷⣌⣁⣉⣼⠟⠛⢩⢛⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠁⠈⠻⠏⠀⠀⠀⢠⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠟⠻⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⣄⡀⠀⠠⠀⠀⠀⣄⣠⣴⣾⠿⠟⠉⠉⠁⠀⠀⢤⣄⠀⢰⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠙⠛⠚⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⠆⠚⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠉⠁⠐⠒⠐⠦⠤⢦⡤⣤⣤⣤⢶⠶⠶⠞⠛⣋⠉⠳⣤⣧⢉⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⡀⢀⡀⠀⢀⠀⠀⢀⡀⠄⠉⣤⢸⣷⣦⣄⢇⡉⣰⣖⣼⣿⣶⠻⢿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡯⠵⠛⣯⣫⠾⠛⢦⣤⢶⠄⣰⠟⣿⢿⠋⠛⢾⣿⣿⡀⠙⠻⣿⠆⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠁⠀⡞⠚⠁⣼⠒⠁⠀⠈⠛⣶⠀⠀⠉⣿⡇⠀⣰⣿⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⠀⢰⡆⠀⠀⠀⠀⠀⣿⠀⣤⡀⠀⢰⣿⠐⠀⢸⣿⡧⠀⣿⡏⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠸⣷⠀⠀⣷⠀⠀⣿⣸⣷⣵⠀⢸⣿⣣⠀⣾⣿⠇⣀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⡆⢡⣼⣀⢠⣿⣿⣿⡿⠀⣿⣿⡏⢀⣿⣿⡇⢸⡿⣿⣿⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣾⣇⣸⣿⣿⡸⣿⢮⣿⣧⢈⣿⣿⡃⢰⣿⣿⡆⣿⣻⣿⣿⡧⣞⣶⣾⠭⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⢰⣿⣿⡆⢿⣿⣿⣿⣾⣿⣿⡇⢹⣿⣿⡁⣷⣿⣿⣿⣷⣶⣴⢶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠤⠿⣿⣅⣍⣽⣷⣏⣘⣿⣾⣧⣽⣿⠽⣿⣿⣿⡿⣿⣷⡿⣿⣷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⢿⠿⠿⢿⡿⠿⠷⠛⠒⠛⠛⠁⠤




⣿⣿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠞⠛⠙⠉⠉⠉⠉⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡠⣤⡴⠶⠒⠒⠶⠶⢤⣀⡀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⢀⣴⡾⣋⡠⣶⡶⣾⢸⠿⢷⡖⣶⣦⣝⣳⢤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠰⣿⣶⣯⢼⡿⢿⣷⠀⠀⢸⢸⠀⢈⠃⠀⠋⣽⢸⠿⣿⣦⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠀⢠⣿⣷⣿⢸⠀⢸⡟⠀⠁⡾⠀⠀⢸⠀⠀⠀⡟⠀⠀⢹⢹⣷⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢹⡆
⠀⠀⠀⠀⢠⡏⠀⢀⣿⣿⣋⡿⡲⣄⢶⢳⠄⢠⡟⣀⣠⣬⠖⠀⠀⢧⠆⠀⡞⣸⠹⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⢸⣿⡏⠿⣻⠋⠉⣦⡵⠋⠃⣈⡵⢍⣿⠟⣢⡺⡴⣗⡲⡞⢨⡂⢹⡆⠀⢸⡇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⢠⡇⠀⠀⣿⠀⠀⢸⠁⠀⠀⡟⠏⠀⢸⠹⠁⢻⡇⠊⠉⠀⡇⠀⢸⡇⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⡇⠀⠘⣯⠀⢸⡀⠀⢠⡏⠀⠀⣾⠀⠀⠀⣧⠀⠀⣸⠀⠀⢀⡇⠄⠀⡰⠀⠀⢸⡇⢠⡾⠁⢀⡤⠤⠤⢤⡀⠠⢸⡇
⠀⠀⠀⠀⠀⢻⡄⠀⠹⣤⡘⡃⢄⣸⣅⢄⣨⣽⡅⢀⣤⢱⣀⣐⡟⢧⡤⣨⡁⢞⠃⠇⠀⢠⣿⢣⡏⠀⡴⠋⠀⠀⠀⠀⢙⠄⠸⡇
⠀⠀⠀⠀⠀⠘⣷⡀⠀⢻⣧⡝⢪⡽⡽⠦⣰⣿⡷⠟⠛⠛⠛⠛⠿⠿⠿⢿⢶⣯⡞⠀⢠⣿⡟⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠙⣇⠀⣼⠾⠛⢋⣡⣴⣶⡾⢻⣿⡿⢿⣿⣶⣤⣉⡛⠿⡷⣿⡟⠀⠘⣇⠀⠳⡀⠀⠀⠀⠀⡠⠁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣨⠟⠁⣴⣾⢿⢟⡟⠀⠀⡼⠛⠀⡀⠛⠂⡾⠀⠙⠶⢌⠲⣿⣷⡀⠙⢷⣀⠈⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⣠⣾⠏⠀⠀⣾⠁⠀⡼⠉⠒⠴⢀⠀⠀⠀⠀⠓⠠⢌⠃⡌⢻⣷⡀⠀⠉⠛⠲⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣰⣿⠟⠂⢤⡞⠀⠉⠒⠄⢀⡀⠀⠀⠌⠑⠢⡄⠀⠀⣌⠀⠀⣄⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣸⡿⠿⣀⠀⠀⠈⠰⠠⢤⣀⠋⠉⠓⡞⠀⠀⣴⠀⠀⡼⠁⠉⠐⢿⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⣧⡀⠈⠁⠒⠴⠀⠀⠀⠁⠀⠀⣌⣠⣤⣠⠂⠠⣘⠓⠤⣀⡀⠀⢿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⣿⠉⠟⠀⠀⠀⠀⠀⢀⡆⣄⡠⣾⣭⣾⠟⠻⢦⣤⣀⠀⠈⠊⠉⣻⢿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⡞⠁⠀⠠⠋⠂⢀⣜⠈⠛⠛⠛⠛⢶⣶⣾⣷⡏⠈⠙⠻⠁⠀⠁⢰⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⡧⠀⠰⢧⡀⠀⠐⠻⠿⡶⠢⣤⣠⠀⠀⢈⡟⠀⠀⢀⠀⠀⠀⠾⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢻⣦⠀⠀⠈⠗⠠⢤⡤⠁⠀⠀⠉⠀⢀⣼⠀⠀⢀⠾⠁⢂⣾⡞⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠻⣗⡰⡖⠀⢀⡼⠁⠀⠀⡼⠀⢀⡾⠁⠀⠁⠛⠒⠤⣤⡟⣁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⢆⣀⡼⠁⠀⠀⣌⠀⠀⠈⠁⠲⢤⣀⢀⡀⠔⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣈⠙⠂⠀⠀⡀⠉⣲⣦⣀⣤⠾⠃⣉⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣹⢣⢎⣿⣝⢯⣝⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⡌⠀⢛⡠⡿⠋⢻⠘⣯⠈⣷⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⣧⣦⡿⣤⣤⠴⢋⣰⣟⣠⡿⠀⡿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠋⢛⣡⠤⡶⠖⠓⠺⠯⠉⣀⡀⠡⠚⠗⣠⣿⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠤⠊⠁⠀⣀⣤⣤⣶⣶⠿⠷⠶⢦⣶⠶⣾⠟⣿⣿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣤⠶⠛⠋⠉⣟⢡⠤⠤⠒⢻⣋⡡⠾⡟⢆⣿⣿⡇⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⡼⠋⠁⣠⠖⠋⠉⣀⡤⠖⠚⠉⠁⠀⣀⣘⣠⠾⣻⣿⢃⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢇⣿⠀⣰⠋⠀⢀⡴⠊⠁⢀⡠⠴⠒⠈⠉⣁⣠⡴⠞⣉⠴⠞⠛⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢿⡄⣧⠀⠀⡎⠀⢀⡖⠉⢀⣠⡴⠚⠋⢉⣠⡖⠃⠀⣀⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠦⣄⣀⠈⠚⠳⣤⣇⣀⣿⢁⣴⣿⣃⣀⣤⣴⠿⣿⣏⣻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠈⠉⠑⠒⠲⠬⣬⣭⣭⣯⣹⣯⣿⣷⣿⡶⣿⢿⢻⡏⡿⢹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠈⠄⠇⠸⠄⢸⠠⡇⢸⡇⣿⡞⢸⢡⣇⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⢸⠸⡇⢸⢠⡇⣇⣿⣾⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⡈⠂⠀⠀⠀⠀⠀⣧⢸⢠⠀⡟⢸⠰⢼⣇⡏⣿⣿⣟⣿⣷⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣦⣯⢪⢺⠈⠀⢢⠁⢸⢸⣸⢰⣇⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⢿⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⣏⣏⣿⣧⢱⣸⢸⣼⣿⣿⣼⣿⣷⣿⣟⣿⣿⣿⣿⣿⢿⡿⢯⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠹⠛⠛⠛⠉⠁

⡤⠀⡆⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠤⣀⣄⡉⠀⣁⣀⡴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠠⠇⠀⠀⠀⠀⠀⠀⠀⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠲⠆⢠⡄⠠⠄⠀⠙⠉⠀⠀⠀⠠⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⢴⡶⡀⠙⠀⠀⠀⢀⢀⣀⡠⠥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⠀⠊⠀⠀⠈⠂⣀⣠⣀⣀⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣀⣀⣀⣤⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⣤⣄⠀⠰⠶⠒⢀⠀⠀⠀⢀⠠⢴⠄⠀⠀⠀⠀⢈⠉⠀⢤⡴⠀⠀⠀⠀⠀⠛⠋⢀
⠀⠀⣀⡚⢃⠉⡄⠄⠀⠀⠀⠀⠀⠀⠀⠾⠃⠈⠉⠀⠀⢁⠔⠁⠀⠀⡠⢠⠀⠀⠘⠄⢁⡀⠆⠀⠀⣄⠈⠁⠀⠄⠀⠀⠄⡀⠀⠈⠓
⠠⠬⠛⠅⡭⠀⣰⡏⠀⠀⠀⠀⠀⢸⡇⠚⠂⠀⠀⠑⠿⢆⠀⠂⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠸⠠⠚⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⢤⠴⠃⠒⠒⠚⠉⠙⠂⣠⡔⠛⠀⠀⠀⠀⠀⠀⠀⡤⣄⠠⠤⠀⠀⠀⣀⣠⠤⠒⢠⠀⠀⠀⡰
⠈⠳⠦⣀⢀⣀⠤⠐⢳⡀⠀⠀⠀⠀⠢⣤⠄⠠⠈⡀⠀⠐⠀⢲⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠐⠀⠒⠒⠐⠐⠀⠀⠀⠀⠀⢡
⠲⠤⠤⣀⠠⣀⣠⣔⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠐⠂⠠⠆⠐⠒⠀⠉⠁⠀⠠⡀⠐⠂⢂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠃⠀⠀⠀⠀⠀⠀⠀⡎⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⢤⣰⣀⣤⠷⠜⠂⠀⠀⠀⠀⠀⠀⠀⠲⠷⡄⠈⠀⠀⠀⣀⣀⡠⠤⠖⠋
⠂⠤⣤⣤⡤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣀⠀⠠⠄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠲⠐
⠀⠀⠀⠀⢀⠠⡲⠂⠀⠀⠀⠀⢀⠁⠀⠤⠖⠀⠀⠀⠀⢀⠁⠁⠠⠀⠀⠀⠀⢀⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣀⡤⠤⡄⠀⢒⠟
⠔⢠⠀⠀⠈⠂⠠⠄⠃⠀⠀⢦⠀⠁⠐⠂⠀⠀⠂⠄⠀⠀⠁⠀⠀⠀⠀⢀⣠⡋⣁⠀⠄⣆⠀⠀⠀⠀⠀⠀⣠⢟⠁⠈⢁⡀⡊⠤⠂⠁
⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠋⡂⠔⢀⣰⠏⠀⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠈⠛⢅⡀⠉
⡞⠙⠀⠀⠀⠀⠀⠀⠀⣴⠤⠄⠒⠀⠀⠀⠠⠤⠖⠊⢠⠀⠀⠀⡰⣄⢀⡀⠀⠘⠐⠋⠀⠀⡀⠀⠀⠀⠀⢸⠂⠀⠤⠚⠉⠙⠛⠉⠁⠉⣁
⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣭⣥⣤⣭⣤⣭⣨⣥⣠⣤⣤⣤⣥⣤⣌⣿⣦⣤⣤⣤⣴⣤⣭⣤⣤⣤⣤⣄⣴⣶⣤⣤⣤⣤⣤⣴⣤⣯⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣤⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠉⠀⢏⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡞⠱⠁⠀⠀⠀⢸⠀⠈⡄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡔⠁⠀⡆⠀⠀⠀⠀⢸⠀⠀⠘⢆⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠋⠀⠀⡜⠀⠀⢰⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠑⠦⡀⠀⠀⠉⠒⠲⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠑⠂⠤⢀⡀⠀⠀⠀⠀⠣⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠐⠇⠀⠀⠀⠱⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⢃⠀⠀⢣
⠀⠀⠀⠀⢠⣀⡴⢉⡎⠀⠀⠀⡰⠢⡀⠀⢣⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡸⠀⣀⢠⢧
⠀⠀⠀⢠⠃⡃⠀⠈⠃⠀⠠⡄⠇⠀⠈⢆⡀⠹⡒⢄⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢑⡼⠁⠀⡞⢄
⠀⠀⠀⠇⠀⡇⠀⠰⠇⠀⠀⢲⡄⠀⠀⠀⠈⠢⣱⠀⠈⠑⠙⠲⠦⠤⣀⣀⠀⢀⡠⠂⠲⠀⠤⠬⠥⠖⠒⠀⠀⠈⠉⠀⠀⣰⠤⠀⠦⡀
⠀⠀⢸⠀⠀⡇⠀⠀⢃⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠶⣆⣀⡒⠒⠒⠒⠀⠐⠒⠒⠈⠁⠀⠀⠀⢀⡜⠁
⠀⠀⣸⠀⠀⠱⡀⠀⠈⢢⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠤⢀⣀⠀⠀⠀⠀⠀⠠⢻⣀⡀
⠰⣿⣿⡀⠀⠀⠱⡄⠀⠀⠙⠢⡀⠀⠈⠳⡄⠤⢀⡀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠰⠶⣾⣷⣆
⣴⣿⣿⣷⡄⠀⠀⠈⢦⡀⠀⠀⠈⠢⡀⠀⠈⠢⡀⠈⠉⠒⠠⠤⣀⠀⠀⠀⠉⠒⠠⠤⠤⠄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣿
⠨⡾⣿⣿⣿⣦⡀⠀⠀⠙⢄⠀⠀⠀⠈⠒⢄⡀⠈⠢⡀⠀⠀⠀⠀⠈⠙⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀⠀⢸⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣦⣀⣀⣀⣉⣦⣀⠀⠀⠀⠉⠐⠢⠌⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠒⡆⠀⠀⠀⠈⠑⠾⣿⣿⣿⣿⣯
⠀⠘⡀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣾⣿⣏⠉⣹
⠀⠀⢣⠀⢠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠛⢠⠃
⠀⠀⠈⢆⠀⡀⠀⠀⣿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣷⠈⠙⠋⠀⢀⠎
⠀⠀⠀⠈⡄⠸⡀⠀⢀⠀⠀⠘⠛⠋⠀⢻⣿⡿⠏⠉⢻⣿⣿⡿⠿⣿⣿⣿⠛⢿⣿⣿⡟⠙⢿⣿⡏⠀⠙⠛⠀⠀⠀⠁⠀⠰⠀⠀⡌
⠀⠀⠀⠀⢳⠀⢃⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠋⠀⠀⠈⠛⠁⠀⠀⠙⠋⠀⠀⢀⠉⠀⠀⡀⠀⠀⠀⡘⠀⢠⠃⠀⡘
⠀⠀⠀⠀⠘⡆⠈⡄⠀⠸⠀⠀⠸⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠀⠀⢰⡂⠀⠀⡎⠀⠀⢀⠃⠀⠀⢠⠁⠀⡎⠀⡜⠁
⠀⠀⠀⠀⠀⢃⠀⢣⠀⠀⡆⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⢠⠇⠀⠀⣸⠀⠀⠀⡌⠀⣸⠁⡜
⠀⠀⠀⠀⠀⠘⡄⠈⣇⠀⠰⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⠀⢸⠀⠀⢀⡇⠀⠀⢰⠀⢠⠃⡰
⠀⠀⠀⠀⠀⠀⠃⠀⢉⠀⠀⡆⠀⠀⢸⠀⠀⠸⠂⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⡈⠀⠀⡌⠀⠀⢸⠁⠀⢀⠂⠀⡎⢠⠇
⠀⠀⠀⠀⠀⠀⠰⡀⠸⠀⠀⢡⠀⠀⠀⠇⠀⠀⠇⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⡇⠀⢀⠃⠀⠀⠆⠀⠀⡌⠀⠰⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢆⠀⠈⡄⠀⠀⢰⠀⠀⠘⡀⠀⠀⢃⠀⠀⠀⠸⠀⠀⢰⠀⠀⢸⠀⠀⠸⠀⠀⢰⠁⢀⡧⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢧⡀⠀⠘⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⡄⠀⠀⡄⠀⠀⡘⠀⠀⠇⠀⢀⡧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⢄⣀⣸⠀⠀⠘⡀⠀⠀⡇⠀⠀⡇⢀⣀⠧⠤⠖⠓⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⡴⠶⠞⠉⣰⣶⣦⣄⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⠗⠀⠈⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣈⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣈⣁⣤⣤⡶⠶⠞⠛⠛⠋⠉⠉⠉⠀⠘⠛⢶⣄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠷⠾⠛⠛⠉⠉⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⣾⣾⣷⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⡾⡿⣃⣤⠶⠞⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠷⠶⠶⢦⣤⣤⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⠗⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣉⠈⣛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠶⠆⠀⠶⠶⠞⠛⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠛⡛⢋⣈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡾⢻⣦⡾⣷⣀⣾⣧⢠⣾⡆⣰⣷⠀⣾⡆⢠⣷⡀⢰⣷⡀⣼⣧⣠⣿⣆⣾⢷⣼⠿⣾⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠘⣯⠀⢸⡟⠀⢻⡟⠈⣿⠏⠸⣿⠏⢻⡿⠈⢷⡿⠘⣿⠏⠘⣿⠁⢹⡏⢈⡿⢀⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⠀⣿⠀⠸⣇⠀⢸⡇⠀⣿⡄⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⡆⢹⡆⠀⣿⠀⢘⡃⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⣸⡇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⡇⠀⢿⡀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⣾⠃⢼⠃⣿⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⠀⣿⠀⢸⡇⠈⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢰⡏⠀⣿⠀⣤⠀⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡄⢿⡀⢸⡇⠀⣿⠀⢸⡇⠀⢹⡆⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⣿⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢨⡄⠈⣿⠀⣿⠀⠸⣇⠀⢸⡇⠘⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⢸⡇⢸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠘⣧⠀⣿⠀⢿⡀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢰⡏⢸⡇⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄⣿⠀⢹⡆⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⠛⠀⢸⡇⢸⡇⣸⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡇⢻⡄⢸⡇⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⡇⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣸⡇⠘⣧⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⠇⣿⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⣿⣷⣦⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣫⡝⣰⢙⣷⣝⠳⢭⡙⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⡊⠀⠚⣃⣴⠟⠀⢻⠘⣿⠀⢹⡍⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣳⣄⣴⢏⣀⣠⡤⠞⢀⣿⠀⣼⠇⢸⡿⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠿⠋⣉⣉⣭⣭⠥⣶⣞⠛⠋⠈⠙⣠⢾⠄⢠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢀⡤⠖⠋⠉⠉⠁⣀⣠⣤⣵⣒⣐⣉⣁⣀⣨⣴⣿⣿⣿⣽⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⣤⣶⡿⠿⣿⠛⠛⠉⣉⣩⣭⠿⢋⣤⣟⠀⣿⣿⡜⣿⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣤⠞⠋⠁⣀⡀⠬⠖⠓⠊⢉⣤⠬⠥⠐⠋⡿⠊⣰⣿⣿⡇⢸⣇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣴⠋⠀⣀⠴⠋⠁⢀⣠⠴⠚⠉⠀⠀⢀⣀⡠⠤⠷⠞⣫⣾⠿⢁⣾⡟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠛⣼⣏⢀⡾⠁⠀⢀⡴⠋⠁⠀⣠⠴⠚⠉⠁⢀⣀⣤⡴⠾⣋⡤⠶⠛⠋⣸⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠙⢿⡸⣇⠀⠀⡼⠀⢀⣰⠋⠁⢀⣠⡴⠛⠉⠉⣠⣴⠟⠁⠀⣀⣠⣾⣿⣿⡿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠷⢤⡀⠀⠁⠛⠢⣄⣧⣀⣸⡏⢀⣶⣿⠁⢀⣠⣤⣾⡿⣿⠉⣹⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠁⠑⠈⠃⠦⠤⣍⣍⣉⣛⣛⣙⣻⣟⣿⣵⣾⣧⣾⡿⡿⢿⠟⣿⢩⣟⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢉⠉⣉⠉⠹⠉⡇⠁⣯⢸⡧⡇⣾⢢⡏⣼⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⠀⢸⠀⡅⢀⡇⣺⢹⠁⡿⣸⢡⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⠠⡀⠀⠀⠀⠀⠁⠘⡇⢸⠀⡇⢸⠁⡿⡈⢸⠃⡟⣸⣿⣽⣯⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠠⠈⠆⠡⢀⠀⡄⢀⠠⠀⣇⢸⢈⠀⣾⢀⣇⣏⡿⢸⣇⣿⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡜⠷⢱⡘⡜⡆⢃⠀⡇⡀⢻⢸⣼⡆⡷⣼⢻⣷⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣥⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠧⣧⣿⣷⡀⣦⠣⢡⢿⣼⣽⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⢿⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢥⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠏⠻⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⣟⠟⠀⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠐⠀⠀⠈⠁⠀⠀⣄⣀⠀⠂⠈⠉⠀⠈⠁⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢰⣆⣠⣀⢈⣉⣁⣤⣄⣈⢀⣺⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣛⣽⣿⡄⠀⠀⠀⠀⠘⠛⠻⢃⣬⠉⢙⡛⠛⠉⠜⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠋⠉⠛⠁⠀⠀⠀⠀⡆⠀⠀⣤⡾⠛⡾⣿⢿⣿⠿⣷⠀⠀⠈
⠀⠀⠀⠀⣄⣰⠐⡠⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⢦⣆⣾⣶⣾⣴⣦⣴⡄⠀⠠
⠀⠀⠀⠀⠈⠉⠉⠳⠮⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⡉⠉⠉⠛⠭⠯⣉⡙⠁⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣿⣷⡼⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠠⠀⠮⠽⠿⠄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠱⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠲⣦⣖⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢉⡞⣳⣛⣻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠫⢠⣥⣼⣷⢚⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⡁⠀⠀⠀⠀⠀⣰⣾⡯⣽⣿⣧⣴⡀
⠀⠀⠀⢀⣴⡀⠂⢀⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⣤⢀⣄⡀
⠀⠀⠀⠀⠙⠛⠃⠭⠀⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠩⠿⠿⠏⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠠⠀⠀⢀⣀⣠⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⢿⣿⢵⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠷⠶⠒⠛⠁⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦
⠀⢀⠀⠀⠠⣰⡏⠡⢄⡅⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡶⠶⠶⠆
⠀⠀⠁⠀⠀⠀⠁⠙⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣄⠤⣄⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⡦⠛⢉⣠⡴⠋⣀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠱⠟⠐⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⣹⠀⠴⠻⠯⠃⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠂⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣄⠀⠀⢀⡀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠁⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⡈⠀⠀⢸⢷⣔⣂⣐⢶⣉⡫⣥⣾
⠀⠀⠀⠄⠀⣀⣤⣨⣧⡤⠀⠀⠀⠀⠀⢀⠆⠐⢦⠀⠀⢀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠉⠒⠉⠉⠛⢋⡁⠁
⠀⠀⠀⠀⠒⠈⡞⠯⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠛⠡⠀⠀⡹⠖⠲⠾⢾⣧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⣂⠀⣀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢀⢀⠀⠀⠀⠀⠀⠀⡐⢈⠁⠶⠡⠠⡄⠂⠀⠀⠀⠀⠀⠀⠐⠓⠐⠀⠒⣲⠂
⠀⠀⠀⠀⢐⡄⠀⠂⠀⠈⢂⠀⠀⠀⣉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⡄⣀⣀⠉⠀⠀⠆⠉
⠀⠀⠀⠀⠀⡙⣄⣠⣰⣤⡤⠷⠒⠚⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠞⣈⣭⣷⠇⠁⡂⠀⠀⠀⢀⠄
⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢴⡀⠀⠀⠀⠀⠒⠾⠀⣠⣾⣯⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠐⠢⢄⡀⠀⠈⠉⠀⠠⠀⠀⠈
⠀⠀⠐⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠘⣢⠤⠠⠀⠐⠀⠀⡀⡀⢠⣆⠀⠀⠀⠀⠈⠑⠪⢄⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠒⠀⠒⠉⠀⠐⠀⠀⠉⠃⠀⠀⠀⠀⠘⠤⡀⠂⢀⣶⠈⠀⠀⠈⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⢀⣠⠤⠀⠒⠒⠒⠒⠂⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠃⠀⢨⡄
⠀⠀⡀⠋⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⡀⢳⡄⢀⠀⠨⠤⠴⠂⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠤⢸⠦⠄⠀⠀⠀⠀⡟
⠀⠀⡕⠀⣤⡶⣞⠿⢭⢵⣿⡆⠤⠤⢴⡚⡏⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠙⠲⢵⣛⢩⡙⢶⠾⠵⠞⣚⣤⠟⠉⠁⠀⠀⠀⠀⢀⠈⠀⠐⠘⡇⠐⠈⢉⠀⠠⠀⠀⠀⠀⠀⠀⠑⢄⣀
⠀⠀⠀⠀⠠⡀⠀⠉⠙⠋⠉⠉⣁⡄⠈⠀⠀⠀⠑⠀⠀⠉⠂⠀⡤⠚⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⢄⣀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠐

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠆
⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢪⠂⠀⠀⠀⠀⠀⢠⠔⣺⠃⠤⡀⠀⠀⠀⠀⠀⣀⣠⣷⠆⠀⠀⠀⠀⠀⠀⡤⢒⣒⠰⠤⠄
⣠⡖⠢⢿⡿⠖⢀⣄⠀⠀⠀⣤⣶⣿⣿⣿⣦⡀⠀⠀⠀⠠⠀⠉⠤⠀⠈⠂⡀⠀⠀⡸⢅⡁⠠⠴⠚⠉⢦⠀⠀⠠⡎⠉⠘⠛⠃⠙⢄⠀⠀⠀⡞⠉⠒⠙⠒⠂⣛
⠿⢿⣶⣶⣶⣶⡿⠿⠀⠀⢜⠉⢀⠀⠀⡀⠀⢸⡄⠀⠀⡁⠀⠀⠀⣁⣠⡤⡍⠀⠘⣆⢲⣄⣀⣀⣠⣤⢤⠃⠀⢸⡀⠀⣀⣀⣀⣤⢤⠇⠀⢾⣉⠉⠑⠒⠒⠊⠉
⢸⡼⡇⣿⢹⢰⣇⡇⠀⠀⠈⡟⣿⣿⢻⡏⡞⡿⠀⠀⠀⢸⢹⡿⡇⣿⢸⢳⡇⠀⠀⠘⡏⣇⣿⢸⣇⡇⡏⠀⠀⠀⣯⣿⢸⣿⡇⡿⣸⠀⠀⠀⢻⢳⢲⡖⣿⣿⢹
⠀⢇⣇⣿⣿⢸⣻⠃⠀⠀⠀⢻⣿⣸⢸⣷⣇⠇⠀⠀⠀⠘⣟⡇⡇⣿⣾⡸⠀⠀⠀⠀⢇⣿⣿⢸⣿⣷⠇⠀⠀⠀⠸⣹⢸⣿⡇⣇⡏⠀⠀⠀⠸⣸⣿⡇⣏⣿⡾
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣤⣷
⠀⢀⡀⣤⣧⣄⠀⠀⠀⠀⠀⠀⢘⣿⣿⣏⠀⠀⠀⠀⠀⠀⠰⡶⠀⠐⣠⡄⠀⠀⠀⢀⠴⣙⠛⠁⣓⢄⠀⠀⠀⠀⢀⡴⢿⣿⣷⣀⠀⠀⠀⠀⢀⣎⡛⠋⠛⠋⣢
⣴⣇⣈⠛⠛⣁⣨⣧⠀⠀⢀⠾⠟⠛⠒⠓⠽⢆⠀⠀⠀⡄⠀⠀⠀⠀⠙⠁⢄⠀⢀⠀⠒⠄⠀⠉⠁⠀⠱⡀⠀⢈⠇⠀⠀⠀⠀⠈⠱⡀⠀⢀⣯⣀⣈⣉⡁⣀⣬
⢹⢻⡿⣿⣿⠿⡟⡏⠀⠀⢲⣀⣠⣄⣠⣄⣀⣸⠃⠀⠀⢦⣀⣠⡤⣤⢲⡏⡇⠀⠈⢳⣬⡦⣤⢴⡖⡿⣿⠀⠀⠘⣦⣄⢴⣤⡴⣶⢹⠃⠀⠻⣶⣀⣀⣉⣉⣁⣠
⠘⡟⡇⣿⣸⢸⣧⡇⠀⠀⠀⣇⣷⣻⢸⡇⡏⡏⠀⠀⠀⢸⣼⡟⡇⣿⢸⢹⠃⠀⠀⠀⡇⣧⣿⢸⣷⡇⡇⠀⠀⠀⢷⣿⢸⣿⡇⡟⡾⠀⠀⠀⢹⢹⣹⡏⡿⣿⣸
⠀⠳⢧⣿⣽⡼⠞⠀⠀⠀⠀⠘⠿⣼⣼⡿⠷⠃⠀⠀⠀⠀⠣⢧⣧⣿⠿⠞⠀⠀⠀⠀⠱⠿⣿⣼⡧⠟⠃⠀⠀⠀⠘⠾⣼⣿⣧⠷⠃⠀⠀⠀⠈⠾⢿⣧⣯⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣔⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⢀⡀
⢀⡠⢀⣀⣀⡤⣀⡀⠀⠀⠀⢀⣿⣿⣿⡿⣅⠀⠀⠀⠀⢀⣀⠁⢠⡈⠤⣄⠀⠀⠀⢠⠚⠝⠛⣛⡭⠢⡀⠀⠀⠀⡀⠂⠀⠁⠀⠤⡀⠀⠀⠀⣠⠿⠅⣤⠈⢤⣵
⣾⣧⣤⣉⣉⣥⣴⣷⠀⠀⠠⠛⠋⠉⠉⠙⠛⢣⡀⠀⠀⠆⣠⠀⡄⠖⠀⣑⡦⠀⢠⡃⢉⠂⠀⠀⠀⣀⣘⠄⠀⢨⠃⠀⠀⠀⠀⠀⣘⡆⠀⣠⡷⠦⠤⠴⣀⡤⠶
⢸⣹⡏⣿⢿⢛⡏⡇⠀⠀⠹⡤⡴⣤⢴⡦⣤⣾⠁⠀⠀⢳⢤⣴⡖⣶⢹⢧⡇⠀⠀⠹⡖⡟⣶⢻⡏⡏⡿⠀⠀⠈⡷⣶⢺⣶⡞⣿⢹⠁⠀⠉⣿⢤⣤⣴⣦⢤⢴
⠈⡇⡇⣿⣼⢸⢷⠇⠀⠀⠀⢧⣿⣻⢸⡇⡇⡇⠀⠀⠀⠸⡾⡎⡇⣿⣸⢸⠁⠀⠀⠀⡇⣿⣿⢸⣧⣇⡇⠀⠀⠀⢻⢿⢸⣿⡇⡏⡿⠀⠀⠀⢸⢸⣼⡇⡿⣿⣼
⣀⣙⣳⣿⣿⣾⣋⣀⣀⣀⣀⣈⣻⣾⣼⣿⣋⣁⣀⣀⣀⣀⣙⣷⣷⣿⣟⣉⣀⣀⣀⣀⣈⣻⣿⣼⣿⣋⣁⣀⣀⣀⣈⣻⣾⣿⣷⣟⣁⣀⣀⣀⣀⣙⣿⣧⣷⣟⣁
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁⣤⡀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡇⠘⠒⢋⡷⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢾⣍⡀⠀⠀⠘⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢿⣠⠟⠓⠚⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢬⣥⡤⢴⡞⠁⠀⠀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡠⠖⠋⣩⠀⣀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⠀⠀⠀⠄⠐⠈⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⠤⠤⠤⠶⠶⠶⠶⠶⠶⠒⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⡀⠐⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣀⣠⠤⠴⠶⠖⠒⠒⠒⠛⠉⠁⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⡤⠒⠋⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⣀⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠛⠛⡞⠛⠛⠛⠛⡟⠛⠛⠛⢻⠛⠛⠛⠛⡟⠛⠛⠛⢛⡞⠛⠛⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢹⠀⠀⠀⠀⣧⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⡇⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⡟⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢷⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⡄⠀⠀⢸⡀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⡾⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣧⠀⠀⠸⡇⠀⠀⢸⠀⠀⠀⡟⠀⠀⢠⠇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣸⣄⣀⣠⣇⣀⣀⣸⣀⣀⣀⣇⣀⣀⣼⣀⡞