Nuts Emojis & Symbols

⠀⠀⢜⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠿⢀
⠘⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⣈⠁⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠠⠀⠀⠹⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢷⡀⠀⠀⠀⠐⡄⠀⠀⠀⠢⡄
⠂⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⣦⠀⠸⠀⠀⡧⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢅
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⢞⡡⠂⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠙⠷⣄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠛⠀⠀⠀⠁⠉⠀⠀⠀⠉⠒⢤⠤⠠⠀⠀⠀⠈⠉⠀⠠⠀⠀⠘⠃⠖
⢀⣤⠒⠀⠠⣤⣀⠀⠀⠀⠈⠋⢀⣀⡤⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠀⡀
⡛⠀⠀⠀⠀⢈⣿⡇⠀⢠⡴⠛⠉⠀⠀⠀⡽⢡⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠱⠀⠀⠀⠈⠁
⣧⣀⣀⣀⣀⡿⠋⠀⣰⠋⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠰
⠈⠙⠛⠋⠁⢈⣠⡴⠗⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠈⠉⠀⢀⣠⣤⣤⢤⣄⡀⢀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠤
⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⠀⢰⠋⠀⠀⠀⡀⠀⣄⠀⠈⠋⠀⠀⠀⠀⠈⢀⣄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠳
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⡹⠀⠀⢀⠀⠀⠈⠀⠐⣄⡀⠀⠁⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠳⠤⠖⠂⠁⠂⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⣫⠂⠀⠀⠀⠈⠐⠠⠤⠤⠊⠀⠀⠀⠀⠀⠁⠀⢀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠤⠤⠀⠀⠰⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣐⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠈⠊⠁⠢⢀⠀⠀⢄⣵⠀⠀⢰⠏⠀⠀⠀⣠⢀⠆⠀⠀⠀⠠⠀⠀⢀⡤⠂⠀⠀⠂⠀⠀⠀⢀⡀⠀⠂⠀⢰⠋⠉⠓⠀⠠⡀⠸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⠠⠀⡿⣡⠄⠀⠀⠠⠤⠶⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⢻⣄⠀⠀⠀⠐
⠄⠀⠀⠠⢀⠤⠀⠀⠀⠀⠀⠠⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⢀⠀⠈⠹⡆⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠘⢦⡀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠦⣄
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⣠⠀⢀⠓⠂⠀⠤⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠰⡄⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡠⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠍
⠀⠀⢱⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡆⠀⠐⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠠⠤⠤⠠
⠀⠀⠀⠘⢷⣛⠓⣂⠔⠀⠀⢀⡼⣿⠀⠀⢐⠀⠀⠔⠉⠛⠁⠀⠁⠀⡠⠀⠀⠀⢾⡀⠐⢀⢂⣀⡔⢰⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠟⠐⠁⠀⠀⠘⠦⠤⠂⠐⠢⠀⠀⠐⠊⠀⠀⠀⠀⠈⠉⠓⠊⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢢⡑⠂⠀⠀⠧⠥⠤⢤⠂
⠀⠀⠀⠹⠶⠄⠀⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣨⠇⠀⡄⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠧⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣨⣿⣀⠀⠀⠀⠈⠂⠄⢀⣈⠭⠋⠀⠀⠠⠤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠑⡀⡀⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⣄⣀
⠀⠀⠀⢦⣤⠤⠴⠆⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠁⠀⠈⠀⠀⢸⠀⠀⠂⠀⠐⡊⠀⠔⠀⠈⠻⢦⡀⣀⣠⠾⠃⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠰⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣴⠖⠁
⠀⠀⢠⠂⢠⣷⠤⣀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⢀⡤⠀⢤⠀⠁⡐⠒⠲⢦⠀⠀⠀⠀⠀⠙⠛⠀⠁
⠀⠀⠘⢶⣿⣁⣠⣻⠇⣄⢰⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⡀⠘⡀⠀⣀⡾⠀⠀⠤⣤⣴⣶⣶⣶⣶⣶⢀⣀
⠀⠀⠀⠀⠀⠙⠛⠋⠀⣈⡛⠋⠀⠀⠀⠈⠓⢄⣀⣀⠄⠀⠀⠀⠀⢙⠚⠋⠀⢀⠈⣈⠉⠁⠀⢶⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⣀⣀⣴⡇⠀⠒⠛⠃⠀⢧⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣅⠀⢐⠀⠀⠀⡌⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠊⠀⠐⠒⠛⠁⠀⠀⠋⠉⠉⠉⠉⠉⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠉⠉⠓⢲⠏⠀⠀⠀⠀⢀⡴⠷⠿⠦⣤⠴⠃⠀⠙⣆⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣏⠀⠀⠀⠀⠉⠀⠈⡇⠀⢀⡴⠀⠀⢀⡴⠓⠒⠒⠠⠤⠄
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⢀⠗⠂⠄⠀⣿⣆⢀⡆⠀⠀⠀⢀⣷⠞⠛⠉⢳⣖⡭⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⣧⡀⠀⢀⣠⡏⠀⠀⠀⢠⡼⠛⠛⢧⡀⠀⠀⠈⢷⣀⣀⣀⣼⣧⣤⣀⢀⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠊⠉⠉⢢⣀⣘⣿⡷⠞⡽⠁⠀⠀⠀⣾⠀⠀⠀⠀⠙⣆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⠷⠶⠶⠛⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣄⣀⡠⠤⠒⠒⠒⠒⠒⠲⢾⡀⠀⠀⡴⠋⠉⠑⠄
⠀⠤⠤⠤⠤⣄⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢠⠁⠀⠀⠀⡄
⢣⡄⠀⠀⠀⠈⠙⢦⡀⠸⡄⠀⠀⠀⢰⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⣸⡇⡆⠀⠀⠸⢧⣄⡀⠠⠄⣄
⠀⠉⠐⠢⣄⠀⠀⠀⠹⡄⠈⠢⣄⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠉⠀⠀⠀⠈⠙⠶⢤⣤⡴⠛⠀⠙⣄⡀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⣤⡴
⠀⢀⡎⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⠘⢦⣀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠈⠣⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠄⠀⠐⢀⠀⠀⡀⠄

⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢋⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣽⣽⡇⠂⠀⠀⠀⠀⠀⢠⡿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠤⠀⠀⠀⠠⣄⣀⠀⠀⡁⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⡀⠀⠀⠀⠄⠠⠀⠀⢠⠀⠀⠀⠀⠀⣀⠠⡶⠆⠀⢆⠿⡁⡅⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⠇⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⣀⠀⠀⠐⠒⠹⠁
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⡀⠀⠀⠀⣄⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠶⣭⠙⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⠀⠀⠴







⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠶⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈
⠀⠀⠀⡠⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣖⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠
⠐⠀⠐⣴⠔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣮⣯⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠤⠼⠂⠀⠀⠀⢤⣤⠂⠀⠀⣰⡿⠀⠠⠼
⠀⠀⠀⠈⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⣀⣄⠀⠀⣀⠀⡀⠀⠀⣀⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⡓⢀⣲⣀⣄⠀⠀⠀⠀⡀⠀⢀⣀
⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⣠⠴⡒⠈⢛⡋⢐⠒⠦⢄⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠙⢦⠀⠀⠘⠁⠶⠶⠤⢤⡉⠁⠢⠈⣢⠍⠢⡀⠀⠀⠀⠠⠤⠄⢄⣀
⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠠⠑⠦⣀⠒⠈⠲⣄⠠⠘⠀⠀⠁⠀⡠⠐⠈⢉⢓⡲⣤⣍⡢⡀
⠀⠀⠀⡼⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠸⡄⢤⢦⡀⠳⢤⡈⠀⠑⠂⠀⠀⠀⠀⣷⠒⠋⠉⠉⠉⠉⠉⠙⠛⠦⣄⡀
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠋⠉⠀⠀⠀⠀⠈⢄⠣⢜⠃⢤⠚⠒⢤⣀⠀⠀⠀⠂⢀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠒⠊⠉⠀⠀⢀⡀⠤⠤⠤⣄⡀⠀⠀⠀⠈⠣⡀⠳⢤⡉⠁⣠⠐⠀⠀⠀⣦⢌⠓⠶⠤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠊⠉⠁⠀⠀⠁⠀⠐⠙⠆⠀⠀⠀⠀⠈⠢⣄⣉⠒⠦⠤⠌⣍⠢⣉⠒⢭⠒⢤⠬⠉⠳⣄⣀⣀⣀⡀⠤⠖⡫⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠛⠋⠉⠓⢤⡈⠐⠤⠀⣀⡀⠀⠠⠀⠀⢀⠀⢒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠙⠁⠀⣩⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣤⡤⠤⠒⠋⣁⣤⠖⠒⠒⠒⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠄⡠⠤⠴⢋⢁⡠⠤⠐⠊⠉⠙⠁⠀⠆⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠖⠉⢁⣀⣀⠠⠀⠀⠀⠂⣀⣬⠵⠖⢒⠛⠿⠅⡈⠳⠤⠾⠀⠀⢳⡄⠀⠀⠀⢀⡔⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠋⠔⠚⢋⣁⡀⠤⠀⣤⠀⠀⢀⣀⡀⠠⣄⠀⣀⠆⠀⠥⠤⠀⢀⠀⠀⡜⠀⠀⠀⠀⡞⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⡏⠠⠖⢰⣊⣁⠩⠤⠴⠚⠊⣉⠃⠁⠐⠚⠁⠤⠠⠄⠀⠠⡐⠂⠣⢀⠞⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⢻⡉⠋⠈⣈⣀⣠⠴⠔⠊⠉⠀⠀⠀⠠⠄⠀⠀⠀⠃⠀⠐⠀⣣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⡀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠑⢄⠀⣀⣀⣀⠤⢀⠈⠀⣀⡤⠚⠁⠀⠁⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠼⠤⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡫⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⢀⡏⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠋⠀⠀⠀⠀⠀⡴⠚⠉⠓⠲⠶⠶⠛⠉⠀⠀⠉⢢⠀⣠⠞⠉⠙⣿⡇⠀⠀⠀⠈⠒⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⣿⠁⠀⠀⠀⢠⠖⠛⣇⣀⣀⣀⣀⠀⣠⠔⠒⠲⠦⣤⣴⠾⠋⠀⠀⠀⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⣿⡀⠀⠀⠀⢸⣴⢞⠋⠉⠈⠉⣩⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠙⢗⠢⣠⠖⠋⢳⡀⠞⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠁⠀⠈⠈⠙⠒⣤⠟⠑⠁⠀⠀⢀⡞⠑⠀⢻⣀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠐⡲⢤⣄⣠⠜⠁⠀⠀⢸⠃⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣯⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾⠰⠀⠀⠀⠈⡙⠛⠒⠒⠚⠻⣤⣰⡇⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠙⠻⠿⣿⣧⡀⠀⠀⢿⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢀⣠⣯⡴⠞⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⠉⠛⠒⠾⠷⣤⣄⣤⣾⣷⡀⠀⠀⠀⢈⣇⣀⣤⡀⠀⠀⠀⢈⡃⣉⣓⣶⡶⠶⠞⠛⠉⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠶⠾⠿⠷⠶⠚⠓⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣟⣛⡻⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠖⠚⠛






⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⢉⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡜⠁⠀⢀⡰⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣯⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣹⣦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢄⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠈⡆
⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠈⠳⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢱
⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣠⣤⠽⠶⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠈⠻⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢠⠞⠋⠀⠀⠀⠔⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠔⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠒⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠠⠊⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣄⣀⣀⣀⠀⠐⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⣀⣤⡴⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡉⠉⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠉⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣀⡀⠢⠤⢤⡄⠠⠄⠒⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡒⠚⠙⠶⡚⠛⠦⣄⠀⠀⠀⠀⠉⠓⠶⠤⠴⠶⠚⠋⠛⠋⠉⠀⠀⠐⠤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠠⣇⣴⠶⣄⠙⢦⡄⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⣀⣀⣀⠀⠀⠄⢠⠂
⠀⠀⠀⠀⠀⠀⢀⠴⢦⠙⢄⡤⢬⠁⠀⠉⡷⠀⠧⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠂⡎⠉⠀⠠⠎⢱⡟⠓⠚⢦⠣⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⢀⢤⡂⢠⠞⠁⠀⣈⠒⠦⣌⠳⡄⠀⠀⠀⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡴⡆⣸⣶⠇⡀⡀⢀⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠈⣦⠁⠀⠣⣠⠜⢀⣉⣀⡈⠲⢬⡁⠂⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣿⢻⠃⠀⠘⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠲⠤⠆⠰⡉⠀⠈⠙⣇⡀⠙⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠇⠈⠀⡠⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⡌⠀⠒⠒⠉⢻⡆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠐⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢀⡴⠚⠋⠉⢀⡼⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢳
⠀⢠⠏⠀⠀⢠⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡤⠖⠋⠁⠀⠐⢒⠀⠀⢠⡟
⠀⠁⣀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣧⣀⠈⠀⠠⠄⠂⣁⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⣈⣱⣄
⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠠⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⢹
⠀⠘⢌⠢⡀⠀⠀⠀⠀⠑⢄⡀⠀⠱⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠄⣀⣉⣶⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠀⠀⠉⠉⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⡀⠀⠀⠉⠉⠁⠀⠀⠀⠐⠄⠙⠷⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡌⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠶⠋⠁⠀⠀⡠⠤⠶⠄⠒⠒⠒⠦⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣁⣀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠖⠂⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠒⠶⢦⣤⣤⣌⣁⡀⠀⠀⠀⠀⠐⠛⢀⣁⡤⠴⠖⠛⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠀⠠⠄⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠉⠛⠲⠤⢤⣑⠒⠒⠶⠤⠔⢂⣉⣉⣠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣠⡔⠢⣍⠛⠉⠙⢛⡉⠉⠗⢦⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⠉⠉⠉⠉⠀⠀⠀⢀⡓⢦⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⣁⠁⠀⢿⣤⠟⢦⣄⠙⢶⠄⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡆⢀⣀⣀⠠⡄⠀⠀⠀⢠⠂⠁
⠀⠀⠀⢀⠖⢦⡈⢦⡤⠦⡄⠀⠀⢹⡇⠘⠆⢀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⡤⠘⠲⣄
⠀⠀⠀⠀⠀⢀⡽⠇⢴⠉⠁⠀⠴⠋⣼⠟⠓⠞⢤⠳⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠀⢸⣆
⠀⠀⠀⢀⣤⠆⠀⡴⠋⠀⢈⠓⠦⢄⡈⠳⡀⠀⠀⠀⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣦⡆⣸⣴⠏⡀⠀⠀⣾⠻⣆
⠀⠀⠀⠙⣎⠁⠀⠣⣀⣠⠋⢙⡂⠀⠱⢤⣑⠂⠠⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣷⢿⠋⠀⠑⣿⢸⣿⠀⠈⠁
⠀⠀⠀⠀⠫⡀⠤⣄⡀⢠⡒⠋⠈⠙⠳⡄⠈⠳⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡇⠉⠀⢀⠀⠘⢿
⠀⠀⠀⠀⠀⠈⠃⢀⢀⠀⢈⠂⠀⣤⡴⠻⣶⡄⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡀⠔⣉⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣈⣀⣠⣄⣀⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢤⣤⣤⠤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⢳⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣽⡟⠛⠳⣦⢹⣀⡧⢀⣀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢀⠀⠘⢄⠀⠚⠓⠦⠄⡠⢀⠀⠀⠀⠘⠷⠟⢸⡛⠢⢟⡀⠉⡠⠋⢉⡇⠀⠀⠁⢠⢂⠀⠀⠀⠀⠛⠀⠨⠀⠄⢀⠦⡄
⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⢳⡀⢀⣀⡀⠀⠑⠀⠀⠀⢠⠂⢈⣿⠶⠶⠃⠰⠥⠴⠟⠁⠀⠀⢠⡎⠀⠀⠀⠀⠘⠀⠋⡄⠀⡀⠀⠄⠦
⠀⠀⢣⡀⠀⠀⠈⢰⠳⠀⠀⡿⠉⠀⠀⠀⡰⠀⠀⠀⠈⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢤⣤⡘⢷⣦⡀⠀⠀⣀⣤⣢⠿⡀
⠀⠀⠀⠙⠲⠖⠚⢁⠀⢀⡼⠀⠁⠀⠐⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡬⣍⣙⢉⣉⣈⣵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⡄⠈⠐⠢⠀⠀⠠⠀⠀⠀⠀⠭⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⠀⠄⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⠐⠄⠀⢀
⠀⠀⠀⠀⠀⢀⠴⠞⠋⠓⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠞⠁⠀⠀⠀⣀⣀⣤⠤⠚⠀⠀⠀⠀⠈⢆⠀⢀⣀⣰⣄
⠀⠀⢀⡤⠚⠋⠁⣀⣤⡆⡈⠉⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠖⠛⠈⢀⠈⠁
⠀⠀⡃⣄⠀⢀⡞⠁⠉⠉⠛⢦⣤⣤⢄⠀⠀⠘⠀⠀⠰⢻⡇⡾⡀⣀⢰⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠂⢄⢰⡾⠿⠃
⠀⠀⠑⠦⠠⠶⢆⠰⡤⢤⣄⡀⠀⠈⢉⡷⠒⠁⠀⠀⠀⠿⠸⠗⠇⠏⠾⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⠶⢞⡉⠉⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⣠⢄⡤⣰⢆⣆⡤⣠⠄⡖⡌⣠⢄⡤⡄⠀⠀⠈⠓⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠓⠙⠚⠛⠃⠛⠚⠓⠓⠓⠙⠃⠓⠀⠀⠀⢤⠖⠀⡀
⠀⠀⠀⠀⣀⠄⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠦⡄⠀⢠⡇⡠⠊⢡⡀
⠀⠀⠀⢰⢇⠀⠀⠀⠀⢈⡶⠟⠛⠳⢤⡀⢀⡔⠃⠠⠞⠋⠐⠂⢸⠀⠀⠀⠀⠀⠀⢠⡾⠋⠈⠀⠘⠀⠀⡴⠋⠀⢠⠇
⠀⠀⠀⠘⠈⠓⠤⠶⢶⡏⠀⠀⠀⠀⢀⡏⠀⠳⠦⠀⠀⠀⠤⢖⠋⠀⠀⠀⠀⠀⠀⠈⠙⢀⣀⣀⣴⡀⡔⠀⢀⣤⠋⠀⠲⠖⢂⡁
⠀⠀⠀⠀⠐⢄⡀⠀⣠⡷⠄⠤⠐⠆⠻⢷⠀⠀⠀⠒⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⣾⡿⠇⢋⠁⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣩⣥⣬⣍⡒⢴⡿⠞⠀⠀⠈⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡟⠃⠉⠀⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⢆⠘⠀⠀⠀⠀⠀⢠⠀⣿⣶⠆⠀⠀⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠿⠉⠉⠉⠙⣄⡀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠘⡆⠑⢤⡀⠀⠀⠒⢁⡰⠁⠉⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣩⣖⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢲⠛⢶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢟⠟⢡⠂⡰⢹⢻⠟⣦⡀⠀⣠⢞⠏⠍⠀⠀⠀⠈⠀⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠏⡌⡎⢀⠏⢰⠃⡎⣼⢀⢇⢻⣶⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⢉⡟⡏⡼⢸⢀⠞⠀⠀⡸⡐⡏⠸⡌⢠⢻⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠰⡄⣼⢡⡇⠇⣜⠂⠀⡆⢀⡟⢰⠃⣴⠁⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢨⡇⠘⢰⢠⢿⠀⡸⠃⡘⢀⠏⡸⢃⣴⢃⡿⡀⠂⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠁⠀⡆⠌⡞⢠⢡⡶⠁⡞⠀⢀⠏⡈⣼⡇⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠚⠋⣿⡸⠀⣤⠰⢡⠇⡞⠀⠸⢃⡴⢁⡜⣼⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡇
⠀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠤⢀⡀⣿⡇⠀⠇⠀⡏⢰⠇⠠⢟⡽⡠⢊⡼⠃⠠⠀⠹⣆⠠⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠙⠳⢦⣀⠀⠀⠀⠀⠈⠦⠀⢀⡀⠙⣿⠇⡄⠀⡼⣡⠞⠀⡠⠂⣶⣡⢾⡀⠀⠀⠈⠦⢌⢧⡈⢦⡠⠀⠀⠀⠀⠆⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠐⠉⠀⠀⣿⠀⠇⠘⡰⠁⡠⠚⢁⣴⠿⠓⠒⠛⠶⣤⠤⠤⠤⠷⠽⣦⣙⠢⡀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⢹⣄⠀⡰⢁⠜⢁⣤⠞⠁⠀⠀⣤⠔⠊⠁⠀⠀⠀⠐⠚⠃⠈⠳⢤⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⡵⢾⣞⣋⣀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠒⠋⠉⠛⠲⠶⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠀⣧⠘⣿⡅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⣇⠀⠙⠀⣿⡇⠐⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢉⣉⣩⡉⠉⠛⠓⠮⣭⣓⠢
⠀⠀⠀⠀⢸⣿⣿⡹⣿⣿⣧⠀⢹⣆⠀⠀⠘⣿⡄⠘⠀⠀⠀⠀⠀⠀⣼⣿⡏⠸⣆⠀⠀⠀⠛⠲⠀⠀⠀⠈⠻⢿⣦⡀⡀
⠀⠀⠀⠀⠈⣿⣿⣇⠹⣿⣎⢷⣄⠙⠦⠀⠀⠈⠻⢦⣄⣀⣀⣰⣶⣾⣿⣿⡻⣄⣀⣉⠓⠀⠀⠀⠀⠀⠀⠀⠑⢦⠙⢿⣎⢦
⠀⠀⠀⠀⠀⢹⣿⣝⣦⠈⠪⡳⣮⣷⣦⣀⣀⣀⣀⣀⠀⠉⠉⣉⠉⢹⣿⣿⣿⣾⣿⣷⣭⣕⡂⠀⠀⠀⠀⠀⠀⠈⢳⡀⠻⣎⢷⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣮⣳⣤⣬⣿⣿⡿⠿⠟⢛⣛⠛⢿⣦⡀⠈⠁⠈⢿⣿⣿⣿⣿⣶⣾⣍⠛⢶⣄⠀⠀⠀⠀⠀⠀⢳⣰⠹⣎⢧
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⣩⡴⣺⠾⠋⠉⠀⢸⣿⣷⣶⣤⣄⣀⠙⢻⣿⣿⣿⣷⣾⣭⣝⣿⣧⡀⠀⠀⠀⠀⢆⠁⡇⢻⣎
⠀⠀⠀⠀⢀⣠⣶⡿⢟⣭⣀⣴⣾⣽⣺⠗⢀⡔⢠⢇⣾⣿⡇⢀⡉⠙⠻⣿⣿⣏⡏⠀⠀⠀⠀⠉⠻⣿⣿⡄⢤⠀⠀⠘⡆⠹⠸⣿⡀
⠀⠀⠀⣠⣾⠟⣩⡶⣫⣾⣿⣿⡽⠋⠡⠖⠉⠀⠟⣼⣿⣿⡇⠀⠉⠳⣦⡈⠻⣷⡀⠀⠀⠀⠰⡌⠀⠈⣿⣿⠈⡆⠀⠀⡛⠀⠀⣿⡇
⠀⢀⣼⣿⣷⠾⣫⢾⣿⠟⠋⣡⠆⠀⠀⠀⢀⠀⣰⣿⣿⣿⡇⢰⡀⠀⠈⠁⢀⠹⣷⡀⠀⠀⠀⠸⠀⠀⣿⣿⡄⢿⣶⡞⣼⠀⠀⣿⡇
⢀⣾⣿⡿⣿⣿⣿⡯⡠⣢⡾⠃⢀⡄⠀⣰⠋⢰⣿⣿⣿⡟⢷⡄⢳⡄⠀⣴⠘⠇⢹⣷⠀⠀⠀⠀⠀⠀⣿⣿⣟⢤⣉⣛⣁⡴⢎⣿⡇
⢸⣿⣟⣼⣿⡿⢫⢞⡼⠋⠀⣰⠋⢀⣼⠃⣰⣿⣿⣿⣿⣷⡈⠻⣆⠻⣄⠈⢇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠹⣷⣍⣛⣒⣚⣡⣤⣾⡿⠁
⠜⣿⣿⣿⡟⢱⡫⠋⣀⠀⠈⠁⣠⡿⠃⣴⣿⣿⣿⣿⢿⡿⣟⢦⡘⢷⡙⢧⡘⢧⡀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠙⠻⠟⣛⣛⠛⠉
⠘⣿⣿⣿⡇⠟⢡⠞⠁⣀⣤⡾⠋⣠⣾⡟⠈⢻⣿⣿⡷⣝⣌⠳⣿⣆⢻⣦⠀⠈⢿⣼⣿⣧
⠀⠘⠻⢿⣷⣄⡓⠶⣾⣿⣯⣴⡾⠻⠋⠀⠀⠀⠙⠿⣿⣮⡻⣷⡈⠊⠳⡙⣷⣔⣌⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⢶⣤⣄⣀
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣲⣤⣐⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣴⡾⣟⡯⣿⠚⠋⠉⢁⣀⣤⣭⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣄⠀⠀⠉⠛⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⣠⣾⢟⡽⡻⠵⠋⢀⣤⣶⢿⣿⣿⣟⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡽⠞⠋⠉⣿⡇⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡥⠊⢀⣤⡶⣿⡿⠞⠋⢉⣠⣤⡿⠿⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠋⠀⣀⣼⡿⢡⣿⣿⠟⢿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣫⢀⣴⣿⠟⢀⣿⣧⣶⠿⠛⣉⡠⢀⡀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠿⠿⠟⠉⠀⠘⣿⣿⣶⡈⣿⡐⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣣⣶⠿⢛⡩⣀⡴⢚⠅⠀⢀⡴⣣⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠹⣯⢳⣷⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢡⢖⣩⢞⡵⠊⠴⣞⡴⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣿⡆⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣷⢑⡵⣫⠖⢋⡤⠴⣞⣯⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠿⢼⣥⣤⣶⣶⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣌⡙⢠⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠉⠳⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠒⠲⣤⡀⠀⠀⠀⠰⣄⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠹⣄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⣀⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠸
⠀⠀⢠⠊⠀⡀⠈⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⡰⠁⠀⠈⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠊⠉⠁⠈⠙⠳⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠘⢦
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠂⠈⠆
⡇⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸
⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢸
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠳⡄⠀⠈⠒⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠈⠲⠤⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠛⠛⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠈⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣀⣤⠶⠛⠋⠛⢄⠀⠀⠀⢀⣰⠆⠀⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠑⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠄⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⢀⡀⠀⠧⢄⠸⡇⢹⢰⠧⠜⢨⢀⡆⢠⠀⠀⣷⠋⢣⢸⠀⣸⠀⢸⠀⣙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⠄⠱⠜⠑⠀⠐⠚⠀⠀⠈⠈⠙⠋⠈⠋⠙⠃⠀⠀⠙⠀⠈⠈⠙⠁⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

⣿⣿⠿⠿⡿⠛⠿⢿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣇⠈⡇⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⠚⢻⣿⣿⣿⠿⠶⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⢻⡜⡄⠀⢠⠀⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠚⣡⡾⠉⠉⡡⠄⢀⣈⢩⣶⣾⢣⡀⠀⠀⠀⠀⠀⠀⠀⣦⡆⢧⠈⢿⣜⠀⢐⡄⢀⠈⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⠹⣦⠟⣿⣿⣷⠀⠀⠀⠀⢠⣶⣼⣿⣧⠈⢇⠈⢿⡂⠀⠀⣀⣠⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠚⣡⣿⣿⣿⣿⠀⠀⡀⠀⠈⠿⢿⣿⣿⣿⣎⠢⣀⠛⠲⣶⣝⣿⣦⣿⠇
⠀⠀⠀⠀⢀⣎⡀⠠⠃⠀⠀⠀⠀⠠⠐⢁⣴⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⣀⣿⣯⣿⣿⣷⣬⠑⢄⡙⠿⣿⣿⡿
⠀⠀⠀⠀⢠⠟⡄⠁⠀⠀⠀⠐⢀⣴⣀⣨⣿⡿⠛⠃⠀⠀⠀⠾⡿⣿⣟⣻⡿⠛⠙⣿⡿⢹⣿⣿⣦⣬⣑⡢⣝⡗
⠀⠀⠀⠀⠀⣆⠀⢀⣀⢤⣔⠠⢚⣽⣿⡿⠋⠀⣠⠎⠀⠀⠁⣰⠟⠉⠉⠙⢿⣤⣴⡿⢁⣾⡿⠿⠿⠛⠛⠛⠺⠃
⠀⠀⠀⠀⠀⠘⠢⢽⣞⠯⣖⣤⣿⣿⣿⣷⢴⡶⠋⣀⣀⣤⣾⠏⠀⠀⣀⣤⡾⠃⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⣸⡀⠊⠀⠉⢙⣥⣄⡠⠴⠋⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣍⣙⣒⣒⢒⣁⣀⣠⣤⠖⠋⠁⢓⣿⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣻⡟⠁⠀⠉⠀⣰⣯⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣷⣍⣀⣠⠀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠠⠗⡾⠋⣥⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⢦⣀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡡⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠢⢨⡷⠈⠴⢻⣦⣸⠆⣒⣿⣀⣠⣆⣀⡀⠀⠀⣇⣀⣀⣀⣠⠜⠋⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⣈⣳⣦⡀⠀⠀⢈⢖⣀⡴⢻⡁
⠀⠀⠀⠀⠀⠘⣠⢡⡟⢑⣸⠖⣾⣽⠛⢠⠯⣍⠿⢷⣌⢻⣥⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⣀⠔⠀⠟⠈⣻⣿⣷⣤⣴⣿⡿⠝⠉⠁
⠀⠀⠀⠀⠀⢀⢃⡟⣰⣿⣿⣿⣿⠟⢳⡄⢻⢡⡶⠶⣧⣤⣿⣷⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠛⠃⠀⠀⠏⠀⠀⠀⠀⣷⡾⠃⠀⠈⠻⠷
⠀⠀⠀⠀⠀⢤⡿⠤⣼⡿⠿⠛⠉⢀⠺⣿⠾⠷⣶⣦⣿⣿⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡄⠀⠀⠀⠐⠀⠐⠋⠉⠀⠀⠀⢆⣀⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠛⢭⣯⠤⠿⠟⢃⣠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⡤⠀⠀⠀⠀⠓⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠁⠀⣆
⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⢻⣿⣿⣷⡄⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠒⠐⠒⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⣰⢟
⠀⠀⠀⠀⠀⠀⠨⠔⢉⣭⣔⠿⢻⠁⠂⠆⠀⠀⢻⣦⡇⣀⠤⡷⡀⠀⠀⠀⠀⢀⣽⡀⠀⠀⠀⠀⠐⣆⠀⠀⠐⠌⢉⣩⠭⠁⠀⠀⡔⠉⠐⠂⠀⠴
⠀⠀⠀⠀⢀⢁⣴⣶⣻⡟⠩⠄⠋⣠⠎⠀⠀⠀⠀⠙⠓⠒⠊⠉⡐⠠⠀⠀⠒⠀⠘⠓⠂⠀⢀⣠⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⠀⡶⣾
⠀⠀⠀⠀⠈⠙⠿⠿⣧⠠⢀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠲⠤⠥⠾⠾⠞⠁⠀⢀⣤⡶⠶⠆⠀⠀⠀⠀⠻⣿⣿⣷⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⢀⡈⠛⢃⣤⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⣒⣶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⢧⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣼⠷⠛⣍⠁⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡿⣽⣤⣴⣧⣼⣿⡁⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠄⣘⡻⠶⠋⠵⠿⠷⠐⠉⠀⠐⠀⠀⢀⡄⠀⠢⢴⡶⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠢⠴⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠴⣲⣤⣦⠒⢈⡠⠂⠀⠀⢀⡾⠀⠀⠲⣧⡘⠁⠈⠳⣄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠍⠒⣢⣄⣤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣇⢀⡤⠀⠀⢿⣦⣤⣀⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠷⢤⣬⣉⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⣀⣴⣄⣫⢋⣋⡁⢠⣜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠋⠀⠀⠄
⠀⠀⠀⢀⠈⠀⢀⣉⣺⣿⡭⣠⡝⠿⠟⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⣦⡀
⠀⠀⠀⣌⣀⢠⢾⣿⣿⣿⣷⣿⣽⣟⣉⢶⣶⡟⠀⠀⣀⠤⠀⠀⠀⠈⠁⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⡓
⠀⠀⠀⠙⠛⣱⣿⡿⠛⠁⣨⣼⣿⣿⡋⣷⡾⠃⠀⢰⣏⡄⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⣦⣷⣿⣿⡟
⠀⠀⠀⠀⠀⠛⣿⣵⣿⣿⣿⣽⠿⢊⠷⠞⠀⠀⠀⠘⢿⣇⣀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠀⠀⠱⣄⣤⣼⠆⠀⠀⠀⠀⠉⠛⠉⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠘⠻⠶⠿⠥⠟⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠰⣶⣆⠙⠶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⢷⣤⠛⡋⢰⣠⡀⠀⠀⠀⠀⠔⠀⠁⠀⡶⠾⣁⣀
⠀⠀⠀⠀⢣⣄⡤⠛⠷⠤⣌⡙⠿⠃⠀⠀⠀⣠⡖⢀⠀⠐⠛⠡⠒⠒⠚⢻⣧⠀⠀⣠⠀⢀⡔⢨⣉⣴⠋⠀⢠⡦
⠀⠀⠀⠀⠈⠋⠃⣀⠠⣦⣀⡉⢛⠁⠀⠀⠘⢍⡣⢤⣄⡀⢀⣴⠄⠶⢛⣣⡞⠀⠀⢁⠀⠈⣡⣤⠞⠁⣀⣏⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠺⠏⠉⠁⠀⠀⠀⠀⠀⠛⢄⣰⠠⣴⣶⣶⣿⠿⠋⠀⠀⠀⠀⠒⢛⢉⠁⣰⠶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠉⣉⣵⣤⡀⠀⠀⠀⠀⣀⢀⣴⠒⠄⣀⡄⠀⠀⠀⠀⠀⡀⢿⠀⣹⡀
⠀⠀⠀⠀⢠⠋⠀⠀⣀⣤⠶⠏⡍⠩⣿⣿⡄⠀⢀⠞⣧⣮⡀⢿⣧⠙⠤⡀⢷⢄⠀⠀⠱⠀⠁⠈⡍⠀⠀⢀
⠀⠀⠀⠀⠸⣼⡶⠋⠁⠀⠀⠀⣀⣸⣿⣿⠇⠀⠘⠾⣦⠀⡏⠈⠙⠀⠀⠀⣘⡷⠀⠀⠀⠀⠀⠒⠁⠀⠐⠈⡷
⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⡀⢠⣴⣿⣿⡿⠀⠀⠀⠲⣤⣉⣛⡶⠦⠦⠤⠔⢋⡼⠃⠀⠀⠀⠀⢀⡀⠈⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠳⣶⣤⣴⣶⣷⣾⡿⠟⠁⠀⠀⠀⠀⠈⠻⢧⣜⣥⣝⣩⡍⠀⠁⠀⠀⠀⠀⠀⠀⠁⢊⡹⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡿⠋⠁⠀⢀⠀⠂⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⡡⠊⠀⢀⠠⠂⠁⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⠔⠉⢀⠤⡚⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⢀⡠⠊⠁⡔⠀⠀⠀⡠⠂⢠⡟
⠀⠀⠀⠀⠀⢸⠇⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⡰⠋⠀⢀⠎⠀⢀⠔⠊⢀⣰⡟
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢹⣇⡜⠀⠀⡴⠁⠀⡴⠁⢀⢔⣿⠏
⠀⠀⠀⠀⠀⢻⠀⠀⠈⠀⠀⠀⠄⠙⢷⡀⠀⠀⠀⠈⢻⣦⡠⠊⠀⢠⠎⠀⣰⣷⠟⠁
⠀⠀⠀⠀⠀⢸⣇⠀⠀⡄⠀⠀⠈⠆⠈⢻⣆⠀⠀⠀⠀⠙⠻⢶⣶⣧⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠸⣇⠄⠀⢰⢀⠀⠀⠘⡄⠀⡽⣧
⠀⠀⠀⠀⠀⠀⣿⠘⡀⠘⡀⠡⡀⠀⠰⡀⠘⢿⣧⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣇⢡⠀⢣⠀⠘⢄⠀⠱⡄⠈⢿⡆⠀⠀⠀⢠⣾⠟⠙⠢⢄⠀⠉⢻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣌⡆⠈⢆⠀⠈⢆⠀⠘⢆⣼⡇⠀⠀⢠⣿⠁⠑⢄⡀⠀⠑⢄⠀⠱⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠈⢦⡀⠈⢆⢀⣼⠟⠀⠀⠀⢸⣟⠢⣄⠀⠙⠢⡀⠀⠱⡄⠈⢆⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣷⣶⠾⠟⠉⠀⠀⠀⠀⠈⢿⣄⠀⠑⢤⡀⠀⠑⠠⠈⢆⠀⠑⢝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡦⡀⠙⢆⠀⠀⠀⠈⢂⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣆⠀⠑⢄⠀⠀⠀⠡⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡁⠠⠀⠀⠀⠄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⣀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡔⠚⠉⡡⠋⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠂⠀⠀⠈⡇
⠀⠀⠀⠈⠀⠤⠊⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠸⣷⡋⠁⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢣⣹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⡀
⠀⠀⠀⢀⠀⠀⠀⠈⠢⡀⠀⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠑⠦⢄⣀⣀⣬⠵⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⣧⠀⠀⠀⠀⠑⠢⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡒⠲⠤⢤⣅⣀⣀⣀⣐⣂⣠⠄⠒⠋⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀⣀⠄⢀⣉⠁⠄⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡄⢤⠊⡙⢒⡉⠒⣄⠀⠀⠈⠙⠒⠒⠚⠉⠉⠉⠀⠀⣐⠶⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⡐⠀⣘⡚⠙⢲⠙⡇⠘⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠂⠀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⠹⠆⡆⠁⠠⠊⡖⠒⠣⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣱⡀
⠀⠀⠀⠀⠠⡲⠀⠋⠀⡴⠍⠒⣌⠂⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⣧⣿⠋⢠⢠⡏⠓
⠀⠀⠀⠀⠀⠃⡀⢄⠉⡔⠋⠒⢆⠙⠢⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠏⠃⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠒⠉⣻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⣀⣀⣀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⡰⠊⠉⠉⠑⠢⠤⠀⠄⠀⠒⠠⡀⠀⠀⠀⢀⢴⡶⠟⠛⠉⠁⠉⠉⠙⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣅⠠⠀⠀⠀⠀⠀⠀⡀⢡⠀⠀⠸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠂⠀⠀⠘⢶⡤⠭⠀⢀⣀⠀⢀⡤⠴⠶⠟⢠
⠀⠀⢀⠔⡈⠤⠀⠔⠒⠤⢍⡛⡶⡤⠤⣀⣒⣚⣛⡻⠀⠀⠘⢮⣝⡀⠂⠀⢋⣠⠄⢙⣲⢲⣤⣿⡁⠀⠀⠀⠀⠙⠛⠛⣻⠖⢀⠀⠀⠀⠀⠐⢫
⠀⠸⡍⡒⠒⠒⠠⠦⠤⠀⠰⢒⢃⡎⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠉⢉⣉⠭⣭⠴⠋⢊⠟⠁⠉⠹⡾⡂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠱⡀⠈⠉⠉⠉⠉⠉⠀⠀⡼⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠈⠀⠀⡠⢗⣒⡒⢢⠭⢒⡇⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠙⠢⢅⣠⡀⣀⡠⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⣀⣄⠒⠮⠔⠃⢠⡔⠴⠦⠞⠀⠀⠀⠀⠀⠀⠙⠶⠤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣁⡊⢀⢂⠸⠟⠁
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡤⢤⢄
⠀⠀⠀⠀⣀⡔⠁⠀⠑⣤⣀⠔⠛⠫⡉⠉⠉⠐⣄⠀⠀⠀⠀⠀⣠⠶⠒⠀⠀⠐⠂⠀⠀⠈⠙⠁⣀⠀⠀⠀⣠⠋⢠⡞⢠⠇⠈⠃
⠀⠀⠀⡼⠻⣿⣠⡖⠉⠉⠛⣆⠀⠀⠈⠆⠀⠀⠈⡡⠀⠀⠀⠀⣷⣀⠀⠀⠐⠀⢀⡀⠀⠠⠄⢴⡌⠀⠀⢸⠁⢠⡞⢀⡞⠀⢸⣂⡤⠔⢒⠢⢤⡀
⠀⠀⠀⣄⠀⠀⠁⠀⠀⠀⢠⣿⠃⠀⠀⡐⡀⠀⡰⠃⠀⠀⢠⢎⠁⠘⠉⠉⠁⠤⠒⠁⠀⠈⢉⣆⡃⠀⠀⠘⡄⢿⠀⡞⠁⡴⠋⣡⠔⣊⡴⠚⠉⣤
⠀⠀⠀⠹⣷⡀⠀⠀⢀⣠⡿⠧⡀⣀⣴⡋⠤⠚⠁⠀⠀⠀⠸⣦⣁⣄⠀⠀⠀⠠⠄⢀⣀⣀⣉⣴⠇⠀⠀⠀⠀⠀⠀⠀⡎⠠⢊⣴⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠛⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠉⠁⠉⠁⠀⠈⠁⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⢥⣚⢀⡤⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣖⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⣄⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⣠⣾⠤⠤⠤⣄⢠⡾⠁⠀⠀⠀⠀⢾⠀⠑⢒⣀⣠⡏⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⠀⠀⠀⠓⠂⣠⠄⠀⠠⠵⢀⡀
⠀⠀⠀⢸⡀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠈⠢⢊⠁⠀⣠⠈⠑⣔⠚⠊⠀⠠⠂⠀⠀⠡⠀⠀⡠⠐⠉⠉⠉⠉⠐⣀⠀⢸
⠀⠀⠀⠀⠉⠁⢛⠀⠀⠀⢀⠠⣒⣀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠁⠀⠀⠓⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⣀⡀⠠⠄⠀⠂⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣶⡤⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠒⠈

⠀⠀⠀⢤⣤⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢶⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠛⠓⠦⣄
⠀⠀⠀⠀⢀⡽⠟⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⠀⠙⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢠⡟⠳⢦⣤⣀⠈⢳⡄
⠀⠀⠀⢠⠏⢀⣠⢖⣥⠞⠁⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡉⣦⣎⡘⢯⣀⡙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠟⠀⠀⠀⠢⡙⢷⡀⣷
⠀⠀⠀⠸⣤⠽⠞⠋⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣌⣹⢦⡉⠛⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣯⠀⢰⡏⠀⠀⠀⠀⠀⣹⣼⠇⡟
⠀⠀⠀⠀⠘⢆⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠱⠦⣄⠹⣧⡀⣳⣞⠀⠁⣼⡇⠀⠀⠀⠀⠀⠀⢸⣆⠈⢷⣄⣀⣀⣀⣠⡾⠋⣼⠃
⠀⠀⠀⠀⠀⠈⠳⣍⡳⠦⣤⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⢊⢷⠘⢿⣤⣟⣷⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠶⢭⣉⣉⣭⡥⢔⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡤⠟⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠴⠖⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣠⠾⠧⡈⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⢼⡏⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣯⠴⠻⣄⠀⢀⡼⠓⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⠙⠻⣟⢿⣌⡈⣎⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣤⡀⠀⠀⣠⣿⠀⠀⠉⢸⣷
⠀⠀⠀⠀⠀⡜⠱⣄⣀⡬⠿⢯⣀⢀⡾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠈⠳⣌⠻⣾⡜⣷⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢻⣻⣿⢟⠜⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⣼⠖⠋⠳⣄⠀⢀⡼⠛⠓⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠳⡄⠀⠘⢧⡘⣷⣿⡆⠀⠀⠀⠀⠀⠀⠘⢷⣁⣾⠛⠉⠉⠁⠀⠀⠠⢋⣾⠇
⠀⠀⠀⠀⠀⢻⣧⣀⣀⠼⠛⠷⣤⣀⣸⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣜⢦⡀⠀⢳⡘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠣⣍⠳⢦⣄⣀⡴⢚⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡀⠀⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠹⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠏⡇⡿⠁⠀⢹⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⡒⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠙⢶⣄
⠀⠀⠀⠀⠀⢀⣾⠃⠀⡇⡇⢠⢁⡾⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡸⠈⠳⣝⢲⡄⠀⣀⠴⠊⠉⠀⢱⠀⠀⠀⠀⠀⢀⡴⡟⣹⣠⢦⡰⢄⢻⠙⢳⣄
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠇⣇⢀⡾⣱⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠊⢷⣙⡎⡹⢤⡀⠀⠀⠘⡇⠀⠀⠀⠀⡞⣰⠁⠟⠁⠘⠇⠀⠙⠆⠀⢹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⡟⡰⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡟⡼⠀⠀⠻⠦⢤⣼⠃⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠈⣹⢏⠜⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⡀⠀⠀⢨⡇⡇⠀⠀⠀⠀⣴⢻⠆⠀⠀⠀⠈⢷⡘⣀⠀⢀⣀⣀⣀⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠓⠦⣤⡤⢷⠳⣄⣀⣀⡼⢣⠏⠀⠀⠀⠀⠀⠈⠻⣶⣋⠉⠉⠉⠉⣉⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠘⠷⣶⣒⣒⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠒⠋⠙⠒⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣤⡤⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠠⠀⣛⡁⢄⣛⠂
⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⡚⣿⣷⠀⠀⢠⠀⠀⠀⠀⢀⣾⣃⣩⠿⠐⢊⠁⠭⠛⠐⢿⠀⠀⠀⣀⠴⠒⠒⠒⢦
⠀⠀⠀⢿⣿⣧⡀⣀⡈⠀⠀⠀⠀⠸⡞⣿⣷⡀⢐⡆⠀⠀⠀⠈⡿⢃⡤⠀⣀⡀⠀⠒⢠⡾⠂⠀⢀⠞⠁⠀⠀⢠
⠀⠀⠀⠈⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⣷⡿⠃⠀⠀⠀⠀⠘⢿⣇⡀⣀⠠⠔⠂⠁⠀⠀⠀⡎⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠎⠠⠆⠐⠒⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠑⢐⣄⣄⣠⣧⡿⠀⠀⠀⠀⠀⠀⠀⣠⣞⣛⡻⢷⣶⡀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⢠⡈⠭⠷⠿⣅⣠⣄⣤⢅⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⣮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⢻⡈⣁⣀⣈⣽⡉⢁⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⢀⣤⠤⠰⠖⠒⠐⠲⢤⡀
⠀⠀⣠⠒⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⣰⣍⠀⠀⠂⠀⠐⠒⠀⣺⣿⡀
⠀⢰⣿⡂⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡴⢶⣄⠀⠀⠀⠀⠀⣃⡒⡒⢬⣌⢡⠄⣤⣀⣤⣶⡇
⠀⠀⠹⣆⠀⠀⠀⢈⡇⠀⠀⡈⠀⠀⠀⠀⢀⣦⠀⠀⠀⢻⣺⡭⣟⡇⠀⠀⠀⠀⠸⢥⡴⣶⡀⠀⠈⣁⣂⡾⠟
⠀⠀⠀⢸⠀⠀⠀⣨⠀⠀⢰⣷⣄⣠⣤⣥⣾⣿⠀⠀⠀⠈⣿⠤⢹⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠂⠀⠀⡰⠃⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣡⠥⠆⢹⢧
⠀⠀⠲⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡦⢆⠘⣠⠾⡆⠀⠀⠀⠀⠀⢀⣤⢶⣫⣵⣿⣾⠄
⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⣛⣿⣺⡇⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠁⠀⠌
⠀⠀⠀⠀⠀⢠⣟⢯⣬⠓⠞⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠻⣯⣅⡀⡠
⠀⠀⠀⠀⠀⠈⠻⣯⣷⢜⡃⠼⠐⡷⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⢲⠲⣄⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⣴⡥⣼⢡⢻⡇⠀⠀⠀⢀⠼⠁⢊⠀⢀⣊⠷⢿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠠⠂⠋⠽⣷⣄⠀⠀⠈⠛⠿⠿⠟⠁⠀⠀⠀⠸⣆⣉⠓⣿⠋⢀⣤⡾⡲⡆⠀⠀⠀⠀⢰⡗⠾⠶⣍⣻⣷
⠀⠀⡐⠀⢀⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠩⢑⡋⠉⠉⣏⣁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⢰⣶⣿⠿⣻⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⠠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠾⠛⠁
⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⡀
⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠓⠄
⠀⠀⠀⠀⡀⠈⠓⠄⠀⠀⠀⠀⠀⠈⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⡲⠀⠀⠀⠀⠀⠀⠀⢁⡀⡀⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢠⡒⠊⢉⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⢀⡴⠉⢉⣣⠤⡊
⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⠁
⠀⠀⠠⡁⠉⠒⢄⠀⠀⠀⠀⠀⠊⠁⠐⡄⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⡇⠁⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠤⠤⡀
⠀⠀⡇⠀⠀⡤⠊⠈⠢⠀⠀⠀⠣⡀⠀⠓⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⠈⡰⢃⡗⠀⠀⠀⠀⠀⠀⠀⢰⢃⢄⠀⡇
⠀⠀⠈⠒⠾⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⠄⠀⡄⣬⠊⡐
⠀⠀⠀⠀⠘⠲⠤⠴⠔⠁⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀⠀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠄⠳⣅⢁⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠈⠀⠀⠘⠀⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠐⣂⣤⠀⢀⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠸⠈⠆⢀⡇⠀⠂
⠀⠀⠀⠘⠄⣠⢉⠃⠸⠂⠀⠀⠑⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⣆⠑⠄
⠀⠀⠀⢎⠂⠢⠠⠄⡍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠸⡄⡠⠒⠶⡄
⠀⠀⠀⠈⠀⠍⣐⣐⢠⠁⠀⠀⠀⢄⣀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠊⠀⠄⡠⠋⠀⢄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⣀⣀⠔⠁⠀⠀⠀⠀⠤⠂⢠⠒⢢⠀⠀⠀⠀⠀⠀⢏⠀⠐⠁⠡⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠃⠄
⠀⠀⠀⠀⠀⠰⠀⠋⠉⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡾⠋⠭⣙⢇⠀⠀⠀⠀⠀⢀⠄⠤⠤⠠⣄⡀⠀⠀⡐⠁⠀⠁
⠀⠀⠀⠈⠠⡁⠀⣀⢀⠄⣒⠞⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⢹⡄⢸
⠀⠀⠀⠀⠀⠊⠶⠶⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠜⠁⠘⠦⠴⠊

⣿⣿⠻⠿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠔⠉⠲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐⠉⠑⠦⡀⠀⠀⠐⠤⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⡄
⠀⠀⡠⠚⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠁
⠀⡔⠁⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢄
⣸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡀⠀⠀⠈⠀⠀⠱⡀
⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢡
⠃⠀⠀⠀⠀⠀⠑⠲⢤⡀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣠⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡘
⠈⢣⡀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠙⠒⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠖⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣤⠴⠚⠉⠁⠈⠢⡀⠀⠀⠞⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠠⠶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⢠⡄⠘⠒⡄⠇⠙⢺⣚⠡⣠⣇⠆⠀⢸⠀⡇⢇⡸⠀⠐⠠⢙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠄⠀⠗⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡈⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠒⠀⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⠌⠉⠁⠒⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠚⠉⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣁⠀⠠⡀⠀⠔⠀⠀⠀⠔⠁⣀⡼⠁⠀⠀⠀⠀⡀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣖⠀⠀⠀⠀⡀⠀⠀⣁⣠⠜⠉⠀⠀⠀⢀⠔⠺⠀⠛⠀⠉⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠲⠖⠒⠊⠉⠀⠀⠀⠀⠀⣰⠛⠀⠀⡔⢁⡀⠀⠴⢊⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠘⢀⠄⠀⠈⢰⣯⠴⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠑⠘⠅⠀⠀⠈⢀⠀⡀⠊⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡜⢠⡀⠀⠀⠀⠀⠀⠀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠒⢠⠐⠀⠰⠖⠂
⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠄⠤⠍⠉
⠀⠀⠀⠀⠘⠈⣧⣸⣇⡘⢰⢲⡄⣿⢰⡖⣦⢰⡄⡦⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠃⠛⠁⠻⠘⠃⠛⠘⠃⠏⠘⠓⠛⠘⠃


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⠶⢤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡿⠙⠛⠉⠁⢒⡀⠬⠅⠀⠤⠀⠉⠉⠛⠿⠟⠛⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢐⡩⠔⡠⠔⢊⣭⠅⠀⠀⠀⠀⠈⠐⠂⠀⠀⠥⢐⠒⢌⠠⡙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣁⠴⠟⣋⠉⠁⠤⠾⠛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⢀⠀⠑⠬⣒⠺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⠄⠊⢁⠔⠉⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠉⠒⠶⠄⠈⠐⠀⢌⠂⠀⠈⠳⠌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠋⢒⡴⠋⠀⠀⣠⡤⠖⠒⢂⡉⠁⠀⠀⠀⢀⣀⣀⣄⣀⣀⣀⠀⠀⠄⡀⠁⠂⠑⠀⠈⠘⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣫⠀⢡⠋⠐⢁⢔⡟⠡⠀⠀⠀⠀⣀⠀⠀⠈⠉⠑⡂⠀⠒⠀⠤⢀⠀⠤⢀⠀⠉⠂⠄⠢⢄⠀⢁⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠏⡆⠁⢈⠔⡁⠁⠠⠀⠀⠀⠉⠀⠀⠀⠐⠂⠨⠤⠤⠤⠤⠌⠀⠀⠈⠀⠂⠈⠁⠒⠐⠲⠀⠳⣄⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⡅⠀⠸⠈⠀⡀⠄⠐⠒⠀⠀⠀⠀⢀⠲⠟⠛⠒⠲⠀⠐⣀⡀⠀⠀⠀⢀⣤⣬⣤⡀⠀⠀⠀⠌⠑⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⣧⢀⠃⠀⣈⠠⠀⠀⠀⠀⠀⠉⠁⠀⠂⠠⠀⠀⠄⠠⠀⣀⠀⠒⠒⠈⠉⠐⠂⠈⠉⢉⣉⡐⣒⣚⣶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⡗⢬⣉⣛⡚⠒⠚⠀⠀⠉⠉⠉⢉⣐⣀⣀⡠⠄⢒⡀⠁⠀⠀⢀⣤⠤⠤⠒⠦⣤⣤⣬⣭⠴⠖⠚⠛⠉⣁⣄⡠⠨⢽⡦
⠀⠀⠀⠀⠀⠀⢸⡟⣶⣤⣤⣉⣛⠒⠲⠶⠶⠶⢶⣦⣤⣌⣉⣉⡛⠛⠓⠒⣀⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⠤⠤⠔⠒⠒⢉⣉⣤⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠘⣧⡁⡟⠓⢝⠫⡙⠻⢗⡒⠢⠤⢀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠤⠤⠀⢀⠰⠞⠛⠍⢉⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢡⠀⠀⠑⢌⡢⠄⠠⠁⢀⡀⠠⠀⠀⠀⠒⠒⠲⢚⡉⠉⠉⠉⠀⠀⠀⠁⠀⠀⠬⠁⠀⣀⠠⢐⡴⣫⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠠⡳⣷⡄⠀⢈⠒⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⣰⠟⢨⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⢌⡻⢦⡄⢉⠒⠄⠤⠤⠀⠉⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠒⠒⠀⠀⢉⠀⠀⣀⠼⢁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⣒⠤⣀⠠⠀⠀⠀⢒⠒⠲⠦⠤⠤⠤⠤⠀⠠⠤⠤⠄⠀⡂⠔⣨⠤⠒⠈⢁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⢅⠢⢤⣀⣀⣀⣉⡐⠒⣀⡂⠀⠀⠀⠀⣒⣈⡥⠖⠛⣉⣭⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣄⣀⣀⣀⠀⣀⣠⣤⡴⠞⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉