Leafs Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡟⠄⣠⡄⠀⠀⠀⠀⣄⠀⢀⣠⡶⠔⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠁⠀⠀⣇⣴⡇⠀⢰⣿⠋⠉⠘⠁⠀⠀⠘⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢇⠀⠀⠀⠀⠀⠈⡇⣰⠏⡇⠀⠀⡇⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢜⠀⠀⠀⠀⢱⡏⠀⠃⠀⠀⠃⠈⠀⢀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⠘⠀⠀⠀⠀⠘⠁⠀⣸⠂⠀⠀⠀⠠⢶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠶⠞⠀⠀⠀⠈⡇⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣀⠔⢋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⢄⠀⠀⠀⠐⢦⣀⠀⢰⢁⡔⠄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠹⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠢⣄⡀⡀⠙⣄⡷⠋⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠚⠋⣻⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣈⣉⣙⣷⣿⣷⠶⠶⠒⠐⢦⡀⠀⠚⠒⠄⠀⠀⠀⠀⢈⠍⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡎⠢⣄⡀⠀⠀⠉⠓⠒⠂⠀⠀⡠⠀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢿⣀⠀⠉⢢⣄⠀⢸⡉⠉⠒⠒⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠙⠲⢦⣪⢿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣲⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠠⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣅⡀⢤⣀⠠⠦⠤⠘⠙⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⢶⠀⠀⠘⠁⠐⠀⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃
⠀⠀⠀⠆⡠⠈⡄⢀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠖⠋
⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠚⠋⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠔⠀⠉
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠱⢀⡀⠀⠀⠀⠀⠀⠀⠄⠸⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠘
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠀⡀⠈⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡍⠄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠼⡥⠥⠀⠀⠀⠀⠔⠈⠀⡀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠄⢠⠂⠀⠆⣀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢀⠆⣤⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⡀⠀⢠⡀⠰⠦⠐⠛⠪⡉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠊⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠆⠈⠑⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣄⠰⠛⠠⢀⠁⠀⠠⠀⠁⠀⠀⠀⠀⢀⠀⢀⠀⠄⣤⡀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠐⠆
⠀⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⣠⠷⠟⠁⡁⠘⠁⠲⠀⠈⠁⡄⠀⠀⠀⠀⡀⠀⠈⢲⠈⣄⣛⠓⠂⢠⠆⠀⠀⢰⢂⠀⡇⠀⠀⠀⠅⠠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠁⠈⠁⠀⠀⠀⠉⢌⠀⠀⠀⠈⣢⠁⠀⠀⠀⠀⢀⠀⠀⢀⠒⠂⠈⠉⠀⠈⠌⠹⡀⠀⠇⠀⠀⠘⠀⠀⠠⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⡀⠓⠀⠀⢀⠂⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢀⠐⠀⠁⠀⠀⠐⠆⠁⡀⠀⠀⠀⡀⠠⠀⠆⠀⠀⠀⠐⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢄⠐⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⠃⠀⠀⠀⠁
⠀⠀⠠⡄⠀⠀⠀⠠⠤⠠⠤⢈⠔⠉⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠐⠀⠀⠀⠀⡀⠒⠂⠀⠀⠐⢀⠢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢦⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⠂⠀⠃⠈⠂⠀⠁⠀⠀⡀⡀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠉⠉⠉⠙⠉⠉⠁⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠂⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⠗
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠰⠅⠐⠃⠀⠀⠀⢀⠠⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠈⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠆⠀⠀⡀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠀⠀⡀⠈⠁⠀⡈⠀⠀⠀⠀⢠⡌⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠄⠀⠐⠀⠀⠀⠀⡠⠁⠀⠀⠀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⢠⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠀⠀⢀⡿⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⠇⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣿⠏⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⠀⠀⠀⠈⠀⣄⠀⠀⠀⢠⠀⠀⠀⢠⣤⣼⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⢿⣖⠄⠀⠀⠃⠰⡄⠀⢸⡄⠀⣠⣿⣿⡿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠐⠀⠀⢹⣧⡀⠀⠀⠀⠷⠀⢨⠀⣴⣿⣿⣿⠒⠀⠀⠠⠂⠀⠀⠀⡀⢠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡇⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠙⣷⣄⠀⠀⠀⡤⠀⢶⣿⣿⢛⣠⣠⡶⠩⠄⠐⠀⠉⣈⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⡆⠈⠃⣄⠀⠀⠀⡁⠀⠀⠾⣿⣿⡄⠀⠀⠇⢀⡾⢉⡅⠸⠋⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣷⡄⠀⠀⠑⠤⣀⠁⣄⠀⠀⢼⣿⣷⡇⠠⢀⣾⡇⠈⠀⡀⣠⣤⣾⣿⡿⠟⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢿⣧⡀⠀⠀⠀⠀⠰⠀⠤⠀⠈⠻⣿⣿⢁⣾⣟⣴⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⢹⣿⣾⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠸⣿⣶⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠏⠉⠉⠘⠓⠒⣈⠳⠆⠿⠈⠛⠰⠓⠰⠂⠐⢂⣼⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠠⠆⠀⠀⣰⡟⠀⠀⠀⡴⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢩⣿⣷⣤⡄⠀⠀⡀⠀⢠⡿⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⡀⠀⠀⠀⠉⠤⠀⠀⠈⢿⣿⣿⡄⠀⠛⠀⢸⠃⠀⠈⠀⠀⠀⠀⠀⠀⡀⣴⣾⣿⣿⠏⠁⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡉⠢⠀⠀⠀⠀⠈⠐⠦⠀⠉⢿⣷⣄⡀⢀⡁⠀⠀⠀⠀⠀⣰⣶⣤⡾⠿⠛⠉⠁⣀⢀⣤⣤⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⣧⡀⠈⠓⠀⠤⢀⠀⠀⠀⠀⠈⠙⠛⢷⣿⣵⣶⣶⣶⠶⠟⠛⠋⣁⡀⠤⠄⠛⠘⠋⣤⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⣿⣧⡀⠀⠀⠀⠘⠁⣄⠀⠀⠀⠀⢸⡏⠉⠉⠉⠀⠀⡐⠖⠀⠉⠀⠀⠀⠀⣠⣾⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠀⠀⠐⢛⣿⣿⣶⣄⠀⡀⠀⠀⡀⠀⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⣦⣾⣜⡋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⠀⠈⠙⠛⢿⣿⣿⣧⣀⠀⠰⠀⣿⠀⠀⠄⠀⠀⠀⣀⢠⣴⣿⣿⡯⠄⠀⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⠙⠿⢿⣦⡀⠀⢿⠀⡘⠀⠀⠀⣶⣿⣿⣿⠟⠁⠀⠀⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⢰⣶⢀⡀⣀⠀⡀⠙⠃⠀⠀⡀⠀⠀⠙⢿⣷⣾⣸⣆⠀⣸⣷⣾⠟⡋⠁⠀⠀⠀⠀⣀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢽⠳⣤⣄⠀⠀⠙⠀⠂⣄⠀⠀⠈⠁⠂⠙⠛⣿⠿⠿⢿⠟⠉⠁⢠⠄⠶⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠻⣿⣦⣄⡀⠀⠀⠑⠄⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠒⠀⠒⠐⠂⠐⠂⣰⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠉⠋⠟⣿⣿⣶⣤⡀⢃⠀⠀⢀⣾⠃⠀⠐⠀⠀⠀⠀⢀⣀⣀⣤⣶⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠉⠻⠿⡿⣦⣄⠀⣼⣿⣆⣀⣠⣦⣴⣶⣾⣿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠶⠂⠀⠛⠻⣿⣿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠉⠀⠐⠐⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠐⠀⠀⠀⠀⡀⢠⠂⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠼⠀⠄⠀⠀⠠⡀⢸⡅⠷⠒⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⣠⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠁⢀⡸⠀⠀⠀⠀⣠⠐⡇⡸⠤⠤⠀⡠⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠈⢛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⢸⣄⠸⣅⡠⠤⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢠⡤⠀⠀⠀⠀⠙⠉⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠦⠀⠀⠀⠀⠀⠂
⠐⠒⠦⢀⡀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢣⠀⡀⡠⠊⠀⠀⠀⠀⠰⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⣄⢌⢇⠝⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⠆⠀⡆⠶⠁⠀⠀⠀⠀⢀⣴⣿⡁⠐⠀⠀⠀⠀⠘⣦⡌⣀⡤⠀⠀⠀⠐⠀⢤
⠀⠀⠀⠀⢀⡀⠛⢚⠁⠀⠀⢂⡆⠹⠃⠀⠀⠀⠀⠐⢿⡿⠟⠁⠀⠀⠀⠀⠰⡌⣸⠛⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢾⡄⢠⡀⠐⠊⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠇⢻⡇⢸⠆⠀⡌⠀⣀⡀⠀⢀⣠⠄⢀⠂⠀⠠⢾⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣟⠴⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣀⡄⠀⠂⠀⢀⡴⠊
⠐⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠉⠲⢠⣆⢋⠀⠄
⠀⠀⠺⠿⠅⣁⠐⢤⡀⠀⠀⠘⠀⣠⡶⣤⠀⠀⠀⠀⠀⢻⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠀⠐⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠲⢝⣆⠀⢦⠀⠸⢷⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢂⠾⠶⠒⠶⠲⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠸⠀⠄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠛⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⣇⠀⠀⢀⡠⠤⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣹⠀⡰⠋⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⠢⡀⠀⠀⠀⠀⠀⠠⣤⣤⡘⢆⢀⡇⢰⡅⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⣠⠤⠖⡆⠘⠦⣽⣦⣿⡵⠋⣉⣭⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⢨⠃⡞⠀⠀⠀⡇⠀⠀⢀⡴⠿⣶⠋⠀⠀⠀⠀⠈⠑⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠉⢿⡀⡅⠀⢀⡼⠁⢀⡴⠋⠀⠀⠀⠙⠢⢄⣀⡠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡁⠀⠀⠈⠱⡄⢹⡷⠖⠉⢀⣴⡫⠤⢤⡖⠋⠉⠉⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠐⠛⢮⡇⢀⡴⠋⡟⠋⠐⢦⡙⠢⠤⠤⠤⠤⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠟⡄⠀⠀⣷⠋⠀⠀⢧⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠉⠓⢄⠀⠀⠀⠀⢡⡀⢸⢀⣞⡡⠔⠲⢶⡌⠓⠦⠤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⡆⠀⢀⣴⡀⠙⣿⣾⡏⠀⠀⣠⠞⠀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠲⣄⡇⢰⠋⠀⡇⠀⡟⠉⠙⣯⡉⠁⡴⠋⠁⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠁⠀⠉⠶⣌⢣⣸⠀⠀⡇⡸⠀⠀⡘⣇⢻⣸⡁⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠴⣶⣯⣍⢳⣧⢠⠇⡇⠀⡼⠻⡌⠻⡏⠉⡩⠗⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣌⣻⣿⠃⠀⡇⠀⡇⠀⢹⢠⡥⢾⡀⠀⠀⣀⠬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠉⠙⠿⡷⢤⡇⠀⢧⠀⢸⣼⠁⢀⣈⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⣠⠞⠁⠀⢱⠀⠈⢦⣿⢇⡴⠋⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⠤⠒⠦⢤⡀⢧⠀⣸⣿⡏⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⢀⣠⠟⠛⢷⡁⠀⠈⠉⠉⣩⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⠜⢧⠀⠳⣄⠀⠀⡼⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⠀⠈⢢⡀⢧⡀⢈⣠⠖⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠛⠢⣑⢤⡾⢰⡯⣭⠟⠓⢽⣾⠿⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⢄⣤⠤⠔⠋⢓⡷⠚⠋⠉⠉⠉⢉⠉⠑⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠢⠴⡤⠚⢩⠧⣄⠀⠀⡔⠉⠉⠉⠛⡻⠁⠀⠈⠉⠙⠒⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⡜⠀⢀⠏⠀⠈⣆⠀⣇⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠔⠋⠀⠀⠀⠣⡀⠀⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢶⠇

⣶⣶⣶⣶⣶⡾⢶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢿⡾⠷⠶⡿⣶⣶⡾⠶⠾⢿

⠀⠀⢀⣬⠀⠀⠶⡀⠀⠀⠀⢰⠇⠐⠒⠒⠒⠮⠁⢀⢄⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠤⡄⢹⡆⠤⠀⠹⢦⣀⠀⡝⠀⠀⠀⠀⢠⠁⣐⡾⠋⠀⠀⠀⠀⠀⠀⢰⡖⠠⡀⠀⠀⠀⠀⠀⠈⢷⠶⠖⠋⠉⠉⠉⠁⠁⠀⢀⣦⠀⠀⠀⠀⠀⡾⠀⠠
⠀⣰⠀⠀⠙⠆⠑⠀⠀⠉⣻⠁⠀⠀⠀⠀⠈⣸⡟⠃⠀⠀⠀⠀⠀⠀⠀⢀⢹⡆⠀⠈⠐⠄⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢈⡀⠀⠈⢷⣄⠀⠀⣸⠇
⠀⡂⠀⠀⠀⢷⠀⠀⠀⢀⡿⠀⠀⠀⣠⠎⢐⢏⠀⠀⠀⠀⠀⠀⠲⣴⠎⠀⠈⠧⡀⠀⠀⠀⠁⠰⣄⠀⠘⢤⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠓⢶⠇
⣰⠃⠀⠀⠀⠸⡇⠀⠘⡛⢛⣈⠉⡤⢤⣀⣆⠇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠄⠈⠳⡖⠚⠛⠉⠁⢽⡢⡀⠀⠀⠀⣾⠂
⠀⠆⠀⠀⠀⠀⢿⠀⠀⢣⠐⠉⢷⣄⠀⢠⠏⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠘⡃⠈⢠⢶⠲⣿⠠⠤⠖⠐
⠠⠀⠀⠀⠀⠀⢞⡆⠀⠀⡀⠠⠀⠘⣷⠆⠀⠀⠀⠀⠈⠂⠀⢀⡜⠀⠀⠀⠀⠀⡀⠀⠹⡦⡄⠀⠀⠀⠀⣠⠂⠈⢆⠈⠉⠈⠀⡇⠀⠀⠸⡇⠈⠄
⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠸⠀⠀⠈⠳⣗⡀⠀⠀⠀⠀⠀⢋⠠⠀⠀⠀⠀⠀⠱⠀⠀⠘⢉⢦⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠒⢄⡃
⢀⡀⠤⣤⣤⣄⡈⣧⡀⠀⠘⠀⠀⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠩⣧⡼⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠀⢸⡃⡀⣀⣄
⠸⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⢠⡏⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⠉⠁⠉
⠀⡀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠸⠀⠀⠐⡀⠀⠀⠀⠘⢷⣄⠞⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⢣⠀⠀⠀⠙⣦⠀⠀⠀⠀⢈⠁⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠈⠄⠄⠐⠤⢄⠱⠀⠀⠀⠈⢳⣄⠀⢀⠞⠀⠀⠀⠀⣨⠆
⠀⠀⠳⡄⠀⠀⠀⠀⣻⠄⠀⠀⠇⠀⠀⠀⠗⠉⢉⡽⢓⠀⠙⣦⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠙⣟⢄⠀⠀⠀⠙⢿⡽⢄⣀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠘
⠀⠈⠀⢸⡶⠲⠦⠀⢿⡅⠀⠀⡀⢤⡂⠀⠀⣠⢋⠀⢈⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⣧⣄⣰⠒⠀⠈⠣⡉⠀⠀⠀⢀⠇⠀⠈⠑⠄⢸⠁
⠀⠀⣠⠏⢥⣀⠀⠀⢸⡇⡠⠊⠀⠈⠑⢄⡴⠁⠀⠁⠃⠀⠀⣀⡨⢿⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢦⡀⠀⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠠⠇⣮
⠂⣼⠃⠀⠀⠀⠄⠙⠚⡗⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⡌⠫⠉⠁⠀⠀⢷⡀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⢳⢀⡆⠀⠀⠀⠀⡜⠁⠀⠀⠀⢀⡐⠁
⣾⠋⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢈⣷⡼⠛⠉⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣴⠛⠛⠛⠛⠉⠉⠃
⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠎⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⠄⠙⣆⠀⠀⠀⠀⠀⠀⠘⣿⢀⣾⠏⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠄⠀⠀⠀⣀⡼⠋⠁⠓⠒⠃⠀⠀⠶⠁⠀⠀⠸⢦⠀⠀⠀⠀⠀⠀⠘⢷⠌⠑⠂⢒⠒⠂⠉⠀⠀⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⠶⡟⣋⣽⣾⡿⠟⠁
⠀⠀⢸⣟⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢛⡍⠁⠀⠀⠀⠀⢀⣉⠝⠛⠛⠛⠛⢛⠋⠉⢀⣮⠞⢁⣾⠃
⠀⠀⠀⠉⠛⠿⣷⣄⠀⠀⠀⢀⣠⣴⠟⣡⠔⠁⠀⠀⠀⢀⡴⠊⠁⠀⠀⠈⢀⡠⠖⠁⢀⡤⠞⠁⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⢛⣉⠔⠊⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡠⠊⠁⢀⣠⠖⠛⠁⠂⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠉⠙⠳⡶⢤⣤⣤⣒⣁⣀⣀⣠⣤⠴⠯⠴⠶⠾⣉⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠘⢄⠀⠀⠉⠉⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠠⠀⠑⠤⡀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠑⠦⠄⢀⣠⣤⠶⠶⠾⠷⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⠶⠶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⣀⡀⠀⠈⠈⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢰⠀⢂⠀⠀⠈⠀⠀⢀⠂⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠐⠀⠑⠀⡀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠂⠀⢀⠀⠀⡀⠐⠁⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠡⡀⠠⠁⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⢨⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠌⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠄⡀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠁⠀⠀⡀⠄⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠐⡀⠀⠀⠄⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠠⠈⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⠀⠉⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠉⠀⠀⠀⠁⠀⠠⢀
⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠖
⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢈⠒⠒⠀⠀⠀⠀⠤⠤⢨⠶⢮⠀⠄⠠⠀⠀⠀⠀⠲⢊⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⢾⠆⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⠊⠀⢸⠀⠈⠢⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠁⠘⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣷⠀⠀⣿⠉⠀⠀⠀⣿⣧⠄⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⣾⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣷⣄⡆⠀⢸⣿
⠀⢸⡇⠀⠀⣿⣆⠀⠀⠀⣿⣿⡆⡀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⣋⠃⠀⢸⣇
⠀⢸⣿⠀⠀⣿⣍⠀⠀⠀⣿⣿⡟⠁⠀⣼⣿⠀⢠⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠇⠀⢀⣿⢀⣿⠀⠀⠀⠀⢸⣏⢹⠀⠀⢸⣧
⠀⢸⣧⠀⠀⣿⡉⠀⠀⠀⣿⡿⡇⠀⠀⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⣿⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⣹⣿⣻⠀⠀⢼⣿
⠀⢸⡗⠀⠀⢿⣧⠀⠀⠀⣿⡿⡇⠀⠀⣿⣷⠀⢸⠃⠀⠀⠀⠀⠀⢾⡇⠀⠀⡿⣿⠀⠀⢸⣿⠀⠻⠀⠀⠀⠀⣹⣿⣿⠀⠀⢸⣯
⠀⠈⠓⠀⠀⠙⠋⠀⠀⠀⠛⡂⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢼⣿⣽⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡇⠀⠀⣿⣻⠂⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡋⡉
⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⣿⣯⣄⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢺⡏⣿
⣾⣿⣿⣿⣿⣯⣍⣑⣚⣣⣴⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢾⠆
⣠⣤⣶⣶⢉⣉⡉⠩⡉⠍⠉⠙⠛⠀⢶⠀⠀⡶⣖⡒⠂⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢸⡇⠀⠂⠀⠄
⣙⡛⠛⠿⠿⠿⠿⣿⣿⣿⣶⣦⠀⠀⠘⠂⣤⡀⢸⣧⣠⠄⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⡁⠀⠀⠀⠀⢀
⠛⡛⠿⠷⢦⣤⣭⣅⣠⣄⣀⣀⠁⠀⠁⠀⠸⠿⡁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⡄⠀⠀⠈⠘⠋
⠻⢾⠶⢶⣶⣴⣤⣶⡖⠉⢹⣿⡀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠃
⠈⠀⠂⠀⠒⠈⠉⠉⠁⢠⣀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠁
⣄⣀⣤⣄⣤⡄⠀⠀⠀⠸⠿⠄
⠈⠉⠉⠛⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠇⠀⡀⢹⠀⠀⠀⠀⡼⢷⣶⣧⣾⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣾⣯⠻⠀⠠⣽⣸⠼⣿⣿⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⢇⡄⣼⣿⣧⣿⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣤⠀⣀⣰⣤⣿⣿⣿⣿⣿⣿⣦⣼⣿⠛⣿⣿⡷⠧⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣶⣿⣷⣿⣧⣽⣿⣿⣿⣍⣿⣿⣿⣽⣿⣅⣿⡏⠀⠀⠀⢀⠀⠀⢅⣠
⠀⠀⠀⠀⠀⠀⡄⡂⠀⠀⣴⠯⠻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣦⣴⣤⡜⣤⣿⠟
⠀⠀⠀⠀⠀⠀⢠⣿⠶⢏⣁⡄⢻⣾⣿⣿⣿⣿⣿⣿⣯⠛⢿⣿⡿⣿⣟⢻⣏⣼⣎⣿⣿⣿⣤⠾⠀⣀⠀⢀
⠀⠀⠀⠚⣄⢂⢿⣿⣮⣉⡛⣿⣿⣿⣿⣶⣿⣿⣿⣝⢻⡗⠸⣏⢳⣸⠋⠙⢛⢿⣿⡿⡛⣹⡋⣀⢀⠡
⠀⠀⠀⠺⣽⣧⣸⣿⣿⣽⣯⣽⡿⢿⣿⣿⣿⣿⣿⣮⣿⣏⣠⢋⣼⣇⠀⠖⣹⣯⣎⡠⣞⣙⣓⠍⣍⠁
⠀⠀⠀⠠⠍⠙⠿⢿⣿⣿⣿⣿⡾⠯⠶⣿⢿⣿⢿⣿⣿⣯⡟⠁⢿⡿⠳⢤⠁⢸⣣⡞⠛⠈⠛⠛⠂⡤
⠀⠀⠀⠀⠀⠈⠀⢦⢼⣎⣙⣳⢬⣷⣺⣶⡘⠙⣦⡽⣿⣿⠀⠀⠀⣇⠀⢸⠷⣾⣹⠛⣇⠀⣜⡀⠀⠀⠀⠀⠀⠀⡠⣤⣴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣎⡛⠙⢹⣛⣿⣿⣟⠻⣿⣿⠀⠀⠀⢿⡰⠋⠀⢸⣏⠠⠀⠀⠘⢹⠛⡁⠀⠀⠀⣼⢿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠈⣿⣦⡤⠞⠛⠳⣿⡛⢿⣿⡆⠀⠀⣼⡁⠄⠀⢸⢧⠀⠖⠙⣳⡯⢾⣇⣻⠶⢛⣿⣏⣉⣮⣻⢧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⣧⡼⠀⠈⠳⡄⣿⡇⠀⠀⣿⠁⠄⠀⡞⢸⣧⣴⣿⣿⡟⠻⣯⣉⣴⣿⣿⡟⠛⠚⠉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠿⣦⠉⢔⠿⣿⣿⣂⣼⣿⡀⣹⣿⣷⣾⣿⠵⠀⢉⡁⣠⣾⣿⠿⣷⡦⠶⣤⣶⡛⠑⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢻⣖⢨⣿⣿⠴⣿⣿⣟⣽⢋⣘⣿⡒⢀⣶⠋⢠⣂⣀⣴⢻⠞⣪⣽⡇⠉⠊⠕⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣇⣼⣿⣧⣀⡽⣿⣿⣆⣿⣿⡿⠟⠋⢙⣯⣵⠏⣁⠠⡶⠛⠉⠚⢯⢉⠉⠃⠪⢯⠐⠆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣛⠻⠟⠛⠿⣿⣀⠁⣦⣹⣿⣿⣿⣿⣷⣴⠂⣲⣿⣷⣞⣡⣾⣡⣴⣾⢦⣾⣬⠭⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠁⣀⡀⠸⢢⡌⢿⣏⣹⠿⣻⣿⣿⣿⣅⣤⣹⣿⣿⣿⣿⣿⣿⣿⣾⣷⡿⣋⣨⠀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠁⠀⠀⠘⡩⠄⣿⡇⠀⢸⣿⠎⠛⣯⣠⣿⣻⡿⠿⠻⠟⠻⠟⠻⠻⠛⠿⡿⠿⢶⣍⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⣶⠁⠂⠸⣧⠀⠺⣿⡄⣴⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠱⡑⠤⠽⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⣿⣿⣿⡟⠀⠀⡠⢶⠚⠛⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⡀⠰⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⣿⣿⣁⣠⣀⡤⠼⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣴⣿⠤⠿⠿⠷⠶⡿⠿⣿⣿⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠿⠾⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠶⠖⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢶⣶⣼⣆⠀⠀⠀⢘⣧⣤⡶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣠⠶⠛⠉⣩⡽⠛⠋⠉⠉⠛⠻⣭⡉⠙⠳⢦⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟⠁⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⢷⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠹⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⣧⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡤⠶⠿⢦⡦⡼⠗⢦⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠛⣲⣦⣀⣟⠀⣠⢼⠷⠲⣄
⠀⠀⠀⠀⢰⣋⣀⣀⣾⠻⣣⠖⠻⣼⣁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⡝⢦⣰⠃⠧⠟⠹⠿⢻⡀⠀⠀⢿⡀
⠀⠀⠀⣾⠉⠁⣸⡽⠿⣤⡇⠀⠀⠸⣏⣠⣴⡒⠻⢦⣀⣀⣀⣀⣀⠀⢀⠀⢰⡓⠟⠀⠉⠀⠘⣿⣀⣀⣀⡀⠀⣠⣙⣦⢴⡞⠓⠲⢤
⠀⠀⣀⣼⣦⣞⣡⡤⠤⠤⣧⠀⡶⢶⠇⠉⠀⢹⠆⡴⠃⠀⢰⡏⠀⠙⢹⣷⣏⠀⣀⣀⢸⡳⣤⢻⣞⠁⠈⠉⠳⣿⠈⠀⠀⣿⠀⠀⣀
⢤⣬⡿⠉⠸⡅⠀⠀⠀⠀⢾⠳⠟⠀⠀⠀⢀⣼⡿⣥⣀⣀⣾⣅⡀⠀⠀⠁⣿⡶⠿⠈⠉⠁⠘⣿⡿⣄⡀⠀⠀⢸⠀⠀⣠⡾⠷⠯⣅
⠀⠈⢉⣙⣿⡳⣄⡀⠀⠀⠈⣳⣄⠀⢀⡤⠬⠗⠀⣸⠋⠉⠉⠛⢦⡀⠀⢠⡟⠀⠀⠀⠀⢀⣀⢸⡀⠀⠉⠿⣖⠚⠶⡏⠁⠀⠀⠀⢈
⠀⠀⠈⠙⠻⠶⢶⠭⠭⠿⠿⠏⠈⠓⢮⣽⣄⣠⠾⣅⠀⠀⣀⡤⣾⣥⠴⠾⠳⠶⣄⡴⣆⡞⠙⠞⠓⠒⠚⠏⠻⠛⠲⠿⠶⠤⠤⠖⠋

⠀⠀⠀⢰⡀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠆⠀⠀⠀⠀⠄⢠⠀⡀⠀⡄⢸⢀⢏⣾⢇⢻⣼⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⢠⣼⣧⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⢂⠀⠘⠸⢹⠇⡀⠚⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣄⠀⠸⣿⣯⢆⠙⠹⣄⠀⢀⠀⢀⠀⠀⠀⠀⢰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢀⠀⠏⠃⠁⠀⠀⠀⠁⠀⠀⢰⣿⠿⠶⠄⠴⠖⣶⠀⠀⢀⠃⠀⠀⣴
⣿⠐⠆⡹⣿⣾⣇⢣⠸⣂⣄⡿⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣦⠀⠀⠀⠀⠀⢤⣶⣦⣄⣧⠀⣀⡀⣀⠞⠁⠀⠀⠈⢧⡠⣼⣿
⣿⡆⠣⡄⠙⣿⣿⡞⣧⡘⣌⠴⢖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠀⠀⠀⠀⠀⠀⣿⠄⠀⣹⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢳⣸⣿
⣿⣿⣦⡈⢦⡈⢿⣿⣦⡄⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣏⠀⢀⣱⣿⡴⢀⡴⣊⠀⠀⠀⡌⠀⢀⡿⠀⠀⠀⠀⣄⠀⠀⢀⡆⠀⠀⠙⣿
⣿⣿⣿⣷⣎⢿⣷⣿⡷⢾⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠆⠈⠁⠃⠀⠀⠀⢸⣥⠞⠋⠀⠀⠈⠁⠶⠟⠉⠀⠘⠛⠏⠁⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⣤⡶⠤⢼⣆⠖⠀⠾⡍
⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⡅⣾⣣⠂⣀⢠⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠒⠻⢆⠠⠙⠛
⠸⣯⡻⣿⣿⣿⣿⡻⢿⣿⣟⡁⢳⡝⠂⠽⢿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣦⣤⣤⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠛⠀⢀⠀⠀⠀⠀⢀⡀
⠜⠘⢿⣮⣻⣿⣽⡿⣴⠊⢿⣷⢿⡏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠹⡿⠉⣿⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⢙⣿⣿⣿⣁⡈⠆⠘⡿⢘⣷⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⡰⢇⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠠⠿
⠂⠀⠐⠉⠀⠘⢿⣧⡙⣿⢿⢆⣼⣿⠇⢠⡟⠁⠀⠀⠀⠀⠠⠄⢸⣟⣿⡋⠒⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣷⠀⠀⠠
⠀⠀⠀⠴⣣⠀⠀⠙⢻⣦⢳⡚⣶⣿⣿⣁⡴⢞⠉⠀⠀⠀⠀⢠⢋⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⠻⣿⣿⣯⠞⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣀⠶⡀⡀⣄⣀⠀⠙⢷⡝⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⡴⠀⠀⣿⣦⡀⠀⠀⠠⠖⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣄⡠⠄
⠀⠀⠀⠈⣿⣷⡄⠺⠋⠉⠀⠀⠀⠻⠉⠀⠈⠇⣴⣄⡆⣠⣶⠞⠀⠀⢸⠿⠟⢁⠠⠆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡏⠀⣀⠀⢠
⠀⠀⠀⠀⢻⣷⡘⢿⣆⠀⠀⠈⢀⣀⠀⢠⠴⢗⣿⣾⡿⢡⣿⣤⡀⢀⣼⡤⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢨⣿⣡⡠⢟⣀⡤⠤⠤⠆
⠀⢠⣤⠀⠘⠿⠆⠀⠘⠳⠀⠰⣯⣿⣿⣿⣿⣯⣷⡜⠃⣀⣄⣼⡟⠚⠁⣡⠤⣄⡙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠘⢿⣿⠯⡽⡆⠀⡆
⢀⡘⠙⠀⠀⠀⠀⠀⣀⣴⣦⣼⣿⣿⣿⡏⣹⡏⢸⣧⣸⡿⣷⣤⡽⠶⢾⡱⠷⣄⡁⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⠀⢈⣶⣤⣷⡄
⢺⣿⠗⠀⠀⠀⡀⢀⡹⣿⣿⢿⣾⣿⣧⠠⣾⣷⣯⣽⣿⣳⣿⣿⣧⣾⣿⣷⡶⡟⠇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠸⣆⡞⠛⠏⠰⣷
⠀⠈⠀⠀⠀⠀⠉⢰⡾⠛⠳⠿⣏⣿⣥⡔⠛⣿⣦⣾⡛⣷⠂⣿⣿⣿⣿⠯⣷⡀⢠⡃⠀⠸⣶⠴⠂⠀⠰⠷⠐⠃⠁⠐⠃⠆⠀⠀⠁⠀⠀⢣⡅⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣘⢿⣯⠳⣾⣍⣭⣤⣿⣿⣷⢬⣙⠟⢻⣽⣿⣁⠀⡿⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠀⣴⣿
⠀⢀⠀⠄⠀⠀⠰⠤⣤⣀⣀⠀⠉⠀⠻⣄⢉⣹⣿⡟⣻⣛⣋⣤⣙⣦⡀⠙⠋⠈⠀⠀⠀⠀⠀⠀⣠⣴⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣯⡀⠙⠋⠁
⠀⠀⠀⠀⠀⠄⠀⢀⡀⠉⠍⠻⡓⠈⣠⠼⣟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀⢀⣤⣤⣦⠘⠙⠻⡾⠋⠀⠀⠀⠀⠘⠶⣦⣶⣾⣶⣤⡀⣿⠀⠀⣂⡖
⡠⡇⠀⠠⢀⡄⠀⠀⠀⢀⣰⡿⠋⠀⣡⠞⠉⠀⡴⢿⠟⠉⠉⠉⠉⠉⠈⠂⠀⢀⡐⣿⣿⣿⣿⣇⠀⠀⠀⣦⣤⡤⠄⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⡀⠀⡇
⠀⠀⠀⠀⠚⠐⠀⠀⣠⣿⠟⠀⠀⠐⠁⠀⠀⠞⠁⠉⠀⣔⠀⠀⠀⠀⠀⠠⠀⠀⣁⣸⣿⡟⣿⡟⠀⠀⣼⣿⣭⣤⣄⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⢦⠁
⠀⠨⠀⠂⠀⠀⢀⣰⠟⣱⡇⠀⠀⠀⠀⡀⠀⢄⣀⡀⡰⠏⠀⠀⣁⠀⠀⠀⠀⠀⠉⠻⠁⢸⡏⠁⠀⡿⡀⠀⠉⠉⠉⠉⠉⠉⠒⠀⠀⠀⠘⢏⠁⠱⣼
⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢍⡹⠁⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡌⠀⠀⠀⢷⣌⡱⠀⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⢂⠀⢹⣄
⠀⠀⠀⠀⠀⣤⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠀⢠⣾⡔⢠⣾⢻⡌⢷⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⢸⣣⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠡⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆
⠀⠀⡴⠀⠀⠀⠀⠠⢻⠐
⠀⠀⠂⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⠀⢀
⢸⡀⠃⠀⠀⣀⠀⠀⠀⢰⢆⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀⠠⢀⣀⠀⠀⠀⠀⠀⣇⢠⠀⠀⠀⣠⣀⠀⢐⣦⡀⠐⠀⠀⠀⡀⢸⠄
⢠⡅⠀⢀⢟⣞⡼⠀⢀⡋⢎⢫⡽⢀⠀⠀⠀⠀⠠⢀⠆⠀⢨⣿⣶⣻⠏⢀⠀⠀⠀⢀⣼⡲⡇⠀⡄⡟⠿⢧⣸⣽⡄⡄⠀⠀⢸⣷⣟⣖⡆
⠰⣿⡟⠀⡘⢩⠋⢤⣼⡅⠃⢶⣧⠈⠀⠀⠀⠠⢓⣶⡀⣴⣶⣿⠿⣯⣤⣸⠈⠄⠦⡜⢻⡿⣾⡜⠁⣰⣏⣸⣿⣾⣿⠙⠰⢸⡇⣽⣿⣿⣧
⠀⣿⡇⢸⠃⢼⡖⢉⢻⡇⣃⢸⡇⡾⢣⠀⠀⠀⣼⡿⡟⠀⣽⢏⡖⡿⣟⡀⣦⡀⣾⠧⢺⡇⣿⣸⣒⢿⣟⢻⣷⢻⢱⡀⢰⡟⠘⣿⣿⣈⣿
⣴⣿⣈⡟⠀⣸⠘⠈⢸⡄⠙⢾⡇⢸⠏⠐⠀⠀⡼⠀⡇⠀⣿⠻⢀⡇⠛⢇⢸⣇⡇⣀⣸⣻⣿⣋⣣⣼⣦⣹⣣⣿⣟⣆⣸⠀⠀⣿⣿⠼⠾
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣾⣷⣾⣶⣶⣶⣶⣷⣶⣾⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⣤⣶⢰⡤⢈⠎⡆⠀⠓⣴⠶⢆⣰⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠏⠙⢻⣿⢹⣧⡾⠛⣿⡟⠉⣄⡗⣿⡷⣂⡔⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⢀⠄
⣼⠀⢻⡏⣷⡟⣿⡴⣿⡟⣧⢿⣿⣿⡷⣾⣷⣮⠄⣟⠡⠒⣒⡒⣠⣶⡤⠤⠤⠴⠤⠬⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⢠⠀⢰⠿⠀⣼⠋
⣿⣧⢸⡗⡏⢳⣻⣷⣏⣷⣻⡏⣼⣿⠞⣱⠞⣩⢞⣡⠤⡤⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⣠⠎⠘⠃
⣿⣬⡼⣿⣷⠎⣿⣿⢟⡴⢿⡟⣱⢛⣼⡻⢾⡟⠁⠀⢠⣴⣿⣿⣿⣿⣽⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠂⠈⢷⣌⣇⠀⠀⠀⠀⠀⠠⠄
⢿⡎⣧⣿⣿⣀⣿⣿⠟⡵⣿⢿⣿⡿⣫⣾⣫⢠⢀⣼⣿⣿⣿⣯⣿⣿⣿⣟⣿⣿⣶⠀⠀⠾⠷⣂⡄⣠⣤⣄⠀⠀⠀⠀⠙⣦⡀⢀⠀⠀⠡⣾⣺
⢷⣿⣯⡷⣿⣿⣿⢃⣾⡼⣡⣿⣿⡚⠽⠟⣻⣿⣿⣾⣿⣿⢹⢻⣿⣿⡿⣿⣿⣿⣿⣷⣄⢠⣽⣿⣿⣿⣿⣿⣶⣆⠉⠀⠀⠘⣿⣎⠾⣭⣿⣿⣷
⣼⠹⣜⢧⣹⣿⣯⣾⣽⡿⣻⣟⣵⣠⢾⢟⣷⣢⣿⣿⡟⡇⣏⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣥⣄⣼⢙⣿⣷⣜⣿⣿⣿
⡙⠶⣼⣆⣿⣿⣿⢋⣿⣾⢟⡭⠿⣵⣷⣿⣿⣿⣿⠟⠷⣷⡇⣿⣿⣿⣿⣿⣿⢸⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⢳⣄⡈⣿⣿⣻⣧⡞⣴⣿⠿⠃⠩⠴⠿⣿⠋⠀⢹⠀⢰⣷⠇⣧⣿⡞⣿⣿⡿⣿⢻⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⢿⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⣤⣼⢹⣸⣽⢻⠁⣿⢹⡇⣽⢸⢷⣿⢻⣾⡏⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⢃⠠⡔⢄⣠⣶⣶⣠⣼⣷⡾⠟⠛⠿⠿⠿⠟⠿⠷⠿⠿⢿⣿⣾⣿⣿⣼⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⡂⣿⣿⣿⣿⡎⢁⣿⢦⣿⡟⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⠟⣿⣿⡇
⢴⢖⣿⣿⣿⣿⣿⣍⣉⢀⠀⠾⠷⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡯⢕⣋⣿⣿⡇
⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⠀⠀⠀⣀⣀⣴⣚⣱⣞⡩⢔⡵⠒⣿⣿⡇
⠚⠖⢛⣽⠋⠉⠹⡏⠻⠟⠋⠑⠂⠀⠀⠀⣴⣿⡧⠀⠀⣶⡿⠆⠀⠀⠀⠀⢀⠀⠀⣄⣚⡥⣿⣿⣟⣷⣼⠿⠿⠿⠿⠿⠗⠚⢹⣾⣷⣿⣿⣷⣴
⠙⡿⠉⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⣦⠀⠀⠰⣾⣿⣿⣿⡿⠒⣿⣿⡏⠀⠠⡴⣶⢶⠒⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠉⢀⠠⠊⢀⣿⣿⣷⣦⠀⠙⠋⠈⠁⠀⠠⠶⠶⠷⢿⡿⡿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃

⠀⠀⠀⣀⡠⠄⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠤⢍⣩⠩⣽⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣣⡄⠀⠀⠀⠀⣾⣷⣾⣂⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠨⠿⠞⠛⣟⣻⣿⣿⣧⡤⣀⡀⠀⠀⠒⣻⣿⡿⠅⠀⠀⣰⣾⣿⣿⣿⣿⣶⣦⠀⠀⠼⣿⣿⣟⣻⡿⣿⣿⡉⠃
⠀⠀⠀⢀⣀⣤⣴⣿⣿⣟⢿⣿⣿⣟⡿⢷⣤⣀⠈⠇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⢸⡏⠁⠉
⠀⠀⠐⠋⠉⠉⡬⣭⣿⠿⣟⡯⢿⣿⣷⣾⠛⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⢃⣀⡀⣐⣦⠤
⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⢠⡄⢀⣀⠀⠉⠛⠉⠉⢹⠏⠉⠙⠋⠁⠀⠀⠀⠀⢠⣿⣿⣿⣧⣿⣯⣵⡆⡻⢶⡀
⠀⠰⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⣠⣤⣶⣿⢐⣬⠶⢉⡇⠀⠀⠀⠀⠀⠸⠇⠀⠀⣀⣴⣶⣦⡄⠀⠀⠋⠛⠛⢿⡻⡿⠿⠿⠃
⠀⠘⡿⣽⣿⣿⡿⠄⠀⠀⠀⢠⣿⣾⣿⣿⣏⣿⣿⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣜⢻⣿⣿⡟⠛⡃⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠘⠉⣉⣉⠁⠀⠀⠀⠀⠾⠘⠋⠿⢿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢯⣈⣻⣿⣿⣭⣤⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠠⣽⠦⠀⠀⠀⣠⣤⣤⣤⣤⣠⣀⡀⠈⠉⠱⡿⠉⠀⠑⠀⠠⣤⣶⣦⣤
⠀⣠⣴⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣏⣻⣇⠤⠄⠀⠀⠀⠀⠀⣾⡿⢿⣿⣿⣿⣷⣦⡄
⠀⣿⣯⠽⠿⠿⠾⣿⣿⣿⣿⡟⠿⣿⣿⣿⣀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣄⣀⠀⣴⢶⡾⣿⣧⣾⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠈⠀⠀⠀⠀⠿⠿⠯⠟⣿⠧⢴⣿⣿⣿⣿⣦⠀⠀⠉⠈⠉⠻⣻⣧⡿⠋⠉⠈⠉⠉⠁⠀⠀⠀⠈⠁⠈⢻⡿⢩⠋⠻⠟⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⢹⠆⠀⠀⢀⣤⣠⡏⠉⠃⠀⠈⡗⠒⠀⠐
⠀⠀⠀⠒⠶⡶⢼⡶⣶⣦⡀⠀⠀⠀⠂⠀⠀⠀⠂⢤⠤⣘⣤⡟⠲⡁⠠⠒⠱⠋⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⢅
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡌⢿⠄⠈⠀⠀⠀⠀⠀⠀⡸⢐⠛⠀⠀⢀⣄⠀⠀⣤⠐⠉⠁⠀⢠⣾⢻⣻⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣣⠀⡇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠏⠈⠲⠒⠊⠉⠙⠋⠁⠀⠀⠀⠈
⠈⠺⡄⠀⠀⠀⠜⡿⠾⡟⠦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠄⠀⠀⠉
⠀⠀⠈⢩⠖⠀⠀⡅⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠀⠀⠀⠋⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠤⢰⡤⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠶⠀⠃⠆⠀⠇⠶⠘⠰⠆⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⢠⡴⠶⣶⠉⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄
⢀⠔⠚⠂⠀⠈⠀⠀⠜⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣤⣾⡛⠛⠯⣃⢄
⢸⠄⠀⠀⠀⢀⣤⣤⡄⠀⠐⠋⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣀⣴⡜⠛⠦⠀⠙⠦⡈⢳⣃
⢀⠀⠀⢀⣨⣿⣭⣷⠁⠀⠀⠠⢄⠀⠀⠂⠐⢀⡀⠉⠀⠀⠀⠀⠆⠠⢤⣿⣤⣔⠉⠀⠇⠀⠀⠑⠄⠀⠱⠄⣿
⠈⠟⠉⠁⠀⠈⠉⠀⠀⠀⢀⣀⠈⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢡⠈⢇⠀⠀⠀⠀⠀⠈⠆⠀⣧⡟
⠀⠀⡀⢀⠄⠀⠀⢠⠀⠀⠀⠁⣠⠎⠀⠀⠀⠠⠀⠀⠀⠀⠢⣀⡀⢈⠀⠀⡰⢀⣿⠄⠀⠐⠀⠀⠀⢸⡴⠋
⣤⣤⣥⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣤⣽⣶⣶⣿⣬⣥⣤⣵⣤⣤⣵⣦⣥⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠠⢲⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣯⣷⡄⢠⡩⠻⠃⠀⠀⠀⣠⠔⠚⠉⠀⠀⠙⠬⠱⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠿⢥⣆⡀⠀⠀⢀⢴⣞⠉⢠⣐⡀⠀⣿⠉⢺⣤⠏⣀⠀⢀⡠⠋
⠀⠀⠀⠀⠈⡳⠉⠀⣢⡄⠀⠀⠸⡀⠀⡈⠀⡇⢷⠳⡄⣰⠿⠟⠅⢀⣄⡙⠙⣶⣿⡠⣾⠏⠘⠁⠀⠀⠁⠀⠤⠀⠲⠲⡽⠈
⠀⠀⠀⠀⠀⠙⠁⠀⡉⢉⢢⠀⠀⢣⠀⣧⠀⡇⢸⠀⢸⣿⡀⣀⠤⢴⡛⢿⣷⣿⣿⣿⣿⠴⢃⣠⠊⠀⠀⠀⠀⢰⠢⠦⡶⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⣹⡃⠀⡈⣧⣼⣀⠧⣾⠄⣯⡟⠓⠋⠹⠭⣭⣭⣨⣿⣿⣿⣇⡀⠈⠀⠀⠀⠀⠀⢈⠼⠷⣿⣻⣿⡿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⣨⣍⢶⣬⣾⣯⠟⠲⢿⡏⠋⠀⡄⠐⣀⠀⠲⣶⢾⠿⣿⣿⢻⣓⣋⠩⠂⠀⠀⠘⠋⢍⡿⠋⠉⠀⠀⠈⠂⣶⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⣽⣽⠋⠙⢳⡀⢸⣷⢸⡆⢣⠀⠘⠁⠐⢹⡯⢶⡟⠋⠙⢉⠉⣠⠀⠀⠀⠀⡆⡸⡇⠁⢀⣤⢊⠠⠎⡍⡽⢀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣘⠿⠶⡒⠻⣿⣿⣽⣿⡔⢻⣦⡀⣀⠀⠀⠱⣸⢷⣄⣶⡏⠐⣁⠀⠃⠌⢀⣼⣰⣿⣤⠞⠛⣍⡠⠞⣼⠃⠈⢾⡇
⠀⠀⠀⠀⠀⠀⡶⡦⢀⣠⣄⣾⡃⢀⠶⠶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠌⣭⠎⣹⣼⢿⣷⣿⣎⢚⡡⠂⠀⠀⠀⠀⠙⢯⣠⣤⣼⣯⢶⡿⠃⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⣤⠴⠻⠛⠻⠉⠀⠀⡱⢒⣫⠿⣿⣿⢧⣀⡀⠀⠠⠦⣄⣠⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⢀⣠⣾⠿⣡⠭⠄⠚⠟⠀⠀⢀⣀⠀⠀⠀⣌⠃
⠀⠀⠀⠀⠀⢀⡟⠱⠂⠀⠀⠰⢤⣰⡛⠙⠋⠁⠚⠫⢨⠜⠁⠀⠀⠀⠀⠒⠭⣙⡿⣻⡿⠿⠃⠤⣤⣶⣶⢻⢿⡆⠀⠠⠖⠀⠀⠀⠂⠀⠸⠋⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠐⠀⢀⡅⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠁⠀⠁⣀⡘⠁⠁⠙⠀⠀⠀⠀⠙⢷⠀⢤⢳⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣁⠀⠦⣀⣀⠀⠦⠀⠀⡀⠀⠀⠀⠀⡔⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠈⠀⠐⠀⠀⠂⠀⠀⠦⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠉⠡⠀⣀⠨⢧⣜⣿⣄⣀⠀⠀⠀⠤⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠲⠄⠘⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢉⠓⢂⣈⣉⣼⣿⣿⣿⣿⢵⡤⠠⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⣑⠦⣀⠀⠀⠀⠘⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢄⠿⣏⠈⠙⢛⡿⣿⣿⡿⣿⣆⡅⠈⠁⠀⠀⠀⠐⠀⠀⠂⢤⣄⣤⢴⣾⣧⣤⡴⠾⠥⠈⣆⣀⠑⠢⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡱⠀⠀⠀⠈⠰⣾⣷⡯⠏⣝⢀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠘⠰⠈⠉⠺⡿⣿⡿⠙⠋⠁⠀⠀⠙⣌⠑⠲⠤⣬⠭⢄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⠌⠀⢈⡍⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠙⠚⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡀⠈⣷⣀⡀⠀⡈⠐⢲⠖⠒⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡀⡼⠛⢏⣿⣾⡇⠈⡿⠈⠀⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡮⢞⠵⠋⠀⠀⠈⢻⣿⡇⢠⠇⠀⡴⠛⢀⠠⡀⠀⠀⠀⠀⢀⠔⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⢹⠀⣾⣀⡼⣣⣤⡤⠰⠆⠀⠂⠠⠐⠉⠀⠦⢶⠑⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡅⣫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁
⠀⠁

⠀⠀⠈⢻⡀⠀⢀⠀⣻⣇⣸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠈⡇⢸⠈⣷⣿⣧⠏⠀⢸⡅
⠀⠀⡀⢨⠉⠒⢦⢰⢿⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢧⠸⠄⠘⣿⡇⠆⠀⣸
⠀⠀⠀⠰⡇⠀⢎⣻⣾⠁⢧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⢘⠀⠀⢸⡐⠀⠆⡻⣿⠀⠀⣿
⠀⠀⠀⣁⡇⠀⠀⣿⡻⠀⢸⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⢨⠄⠀⢸⡇⠀⠀⣿⣿⠀⠀⢹⡀
⠀⠀⠀⠸⡎⠀⣠⣿⡻⠂⣼⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⢰⡇⠀⠀⢹⣿⠀⠀⢸⡇
⠀⠀⠀⡀⣿⠀⢨⣿⠟⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⡇⠀⠀⠀⣿⡆⠀⢸⡇
⠀⠀⠀⠨⣻⠀⣴⠿⣦⠀⢰⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢘⡄⠀⠀⣇⠀⢠⢸⣿⡅⠀⢸⡇
⠀⠀⠀⠂⢹⠀⢹⢢⡄⠀⠈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠁⣿⠀⢸⢸⣿⡇⠀⢸⡇
⠀⠀⠀⡇⢸⡇⢰⣼⡇⠀⠀⣿⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⢸⢀⢹⡀⡌⣸⢸⣷⠀⢸⡇
⠀⠀⠀⡆⢸⡷⢸⡟⡇⠀⠀⣿⠀⢸⡄⠀⠀⠀⢣⠀⡆⠀⠀⠀⢸⠀⠀⢸⡇⢸⢸⢸⣷⢣⣿⢸⣿⡀⢸⡇
⠀⠀⡇⡇⢸⡇⢸⣭⣿⠀⠀⣿⡆⠀⣇⠀⠀⠀⠈⡇⠇⠀⠀⠀⢸⠀⠀⠘⠃⠀⠈⠈⣧⠈⠁⢸⣿⣇⠘⠋
⠀⠀⠀⠇⢸⡇⢼⢻⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣦⡄⠸⠂⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠘⠁⠉⢹⣧⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

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

⠓⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⣿⠒⠋⠉⣯⣉⣹⣷⠀⢀⠒⠈⠈⠁⠀⡀⡀⢠⡅⠄⣿⣿⣿⣿⣿
⠉⣉⣓⣟⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠛⠁⠈⣁⡀⠻⠙⠗⣾⡟⠁⠀⠀⣀⡀⠀⢁⠀⠀⠉⠻⠛⠿⠛⠋
⠀⠈⠻⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣅⣾⣟⠀⠀⠀⠁⣰⣾⣿⢤⡀⠀⠀⠉⠱⠴⠈⠓⠦⠀⢀⡀⠋⡋⠴
⠀⠀⠀⣯⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠄⢸⣿⡌⠀⢤⣖⠉⣛⣻⡧⡤⠀⠐⠎⣢⣶⣦⡸⢀⡀⠁⠀⠀⠁
⠀⠀⠀⣿⢤⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢻⣿⣯⡀⢀⣉⣭⠀⠙⢿⡆⠀⠄⢀⠀⠁⠛⠛
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⢸⣿⠋⠹⣮⠽⡇⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢸⡿⠀⠠⢿⣴⣦⠀⠀⠉
⠀⠀⠀⡇⢐⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⡇⠀⠀⠈⢸⠈
⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢸⡇
⠀⠀⢈⣇⡆⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄
⣧⣠⣾⣿⡇⠀⠀⡴⢀⠂⢘⣗⣠⡄⢀⣤⣿⣿⣿⡧⣄⢠⣶⡆⠀⠀⣀⡇
⣋⣤⣹⣿⣧⣀⡂⣾⢾⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⡿⣣⣾⠴⣿⡅⠠⣦⣤⣤⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⡀⠀⣀
⡿⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣯⣹⣃⣿⣷⣾⣿⣿⣿⡆⢴⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣰
⣙⣺⣿⣿⣿⣽⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠸⠿⢿⡿⠟⢹⢿⠁⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣥⣤⣤⣀⡀⣸⣿⢣⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡎⠀⠰⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠇⢠⠁⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠒⠀⠀⠀⡄⠀⠀⠀⡠⡋⠀⢠⣁⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣠⠋⠀⠀⠀⡀⠀⠀⠀⢠⣮⡄⠛⣀⠀⢠⣷⠞⠁⠈⠪⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣦⣄⣈⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⣀⠀⣀⠠⠚⠟⠁⠀⠋⠉⠛⠉⠛⠿⠦⠌⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡐⠁⢸⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⣥⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠀⠀⣼⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢿⣻⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⢰⡏⠀⢠⡇⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡀⠀⢸⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠇⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠈⣦⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠙⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠠⣸⠃⠀⠀⢀⢀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⡄⠀⣿⢦⠀⠀⠀⠀⠀⠀⠀⠈⢇⠜⠁⠀⠀⠀⢀⡌⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢹⡜⠳⣀⡀⢀⡠⠀⠀⠘⠁⠀⠀⠀⠀⠀⢿⡿⠫⢔⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡴⡸⣼⠃⠀⣇⣴⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⢆⠗⣎⢀⣄⣿⡉⡁⠈⠧⠜⣀⠀⠀⢀⣤⣠⡶⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢮⠔⢹⣟⣟⢁⠈⠈⢋⣑⠟⣁⠽⠭⠩⠤⠿⠾⠻⠙⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇⡄⠞⢻⠀⠃⠀⠀⠈⠁⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠁⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠴⠂⠀⠀⠀⠀⠉⠋⠁⡄⠀⡀⠀⠀⠀⠀⢠⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⣧⠞⠛⢫⠄⠀⣄⠀⡠⠀⠓⠀⠙⠖⠦⠀⡀⠀⡷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢨⠀⠀⢀⠀⠀⠹⣧⣣⡀⠀⠀⠠⡄⢀⠀⠻⡦⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠇⢀⣨⣻⡀⠘⡞⢠⡀⣰⠋⠉⠉⠀⠙⠶⡿⠋⠀⡰⠋⠀⣀⠀⠀⢸⡇⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠺⡄⣠⠀⠀⠀⣑⣄⠀⠳⣄⡀⠈⢻⡇⠀⠀⠠⠀⠀⠀⡇⣠⠞⢠⠆⠀⣹⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⢴⠶⢼⡟⠀⠀⠀⠀⠈⠑⣤⣙⣷⣄⢸⠀⠠⣄⠀⢷⡀⣠⣿⡧⠶⠚⠋⡙⠉⠀⠈⠓⠀⠀⠈⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠱⣄⠀⢀⡄⠀⠛⠁⠀⠀⡉⢻⣇⢠⠁⠀⢨⣿⠟⡁⠀⠀⠘⢦⡷⢚⡀⠀⢰⡇⠔⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⣈⣳⣼⣟⢠⣄⡀⣹⠙⠁⢀⠹⣷⡀⣰⣿⢁⠠⠇⠒⠀⢀⡜⠀⢈⡇⠔⠊⠀⢤⡌⣒⣀
⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⠋⠀⠠⠾⠛⠦⣄⡈⢏⠉⠀⠘⠢⣹⣷⣿⠋⠀⠀⣿⣀⣤⠾⠖⠚⠉⠛⠒⢰⣄⠀⢘⠋⠁
⠀⠀⠀⠀⠀⠚⠲⠛⠀⣰⠄⠀⠀⠘⠆⣀⠀⠭⠿⠷⣦⡀⠀⠘⣿⣿⠀⣠⡴⠟⠡⠤⢀⠠⠋⠀⡄⢀⠜⠁⢲⠌⢀⡀
⠀⠀⠀⠀⠀⠀⡘⠣⡐⠚⠣⡀⠀⠀⠐⠃⢀⠀⠀⢠⡬⠿⣦⡀⣿⣿⡾⠋⠀⠀⡤⠀⠈⠃⠀⣀⣿⣫⡤⠶⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣩⡷⠶⢬⣶⣤⣤⣤⣬⣧⣤⣄⣀⡀⠹⣿⣿⣿⢁⣤⣴⡾⠿⠿⠿⣛⠋⠉⠉⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠊⠀⠀⢀⠴⣎⣉⣠⠖⠛⠛⢿⣿⣿⣿⠟⠉⠉⠉⠻⡶⠞⠋⠑⢄⣀⠀⠀⢡⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡦⢠⡀⠀⠒⡿⠁⠀⠀⢱⠁⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠘⡄⠀⣤⠀⠹⣟⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣷⣀⠈⠀⠀⠚⠁⠠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠂⠀⠉⠀⠀⡀⡰⠋⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠈⠣⡴⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣧⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣀⡀⠀⠀⠀⠀⡠⣢⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠉⢰⡄⠀⡠⡪⢊⣀⣙⠲⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠈⠀⡌⡡⣪⠊⢗⡾⣭⠻⣓⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⢫⠞⠀⠀⠘⠙⠚⠛⠋⠀⠀⠈⠙⢦⡀⣄⣀⣾⣍⣇⡀⠀⠀⠀⠐⠃⠀⢠⣴⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢴⠗⠒⠂⠀⠀⠒⠒⠒⠒⢒⣐⡒⠒⠒⣿⡶⣿⣭⣭⣭⣥⣥⣤⣤⣤⣿⠤⣍⣜⣟⠉⠃⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠇⠀⢀⣈⣰⠂⠀⠀⠀⢚⣙⡇⠂⠀⣿⠃⠁⠀⠀⠀⠈⠀⠀⠉⠉⢳⠝⠣⣏⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡠⢰⡇⢀⠫⡂⠀⢠⣹⡥⠤⠀⠀⠠⠌⠃⡧⠀⠀⣿⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠠⠤⡭⣤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠂⡐⣾⡶⣞⣥⣃⢘⡃⢾⢦⡧⠀⣠⣶⣴⡤⣤⣥⣤⣤⣤⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣰⣤⢐⡗⠇
⠀⠀⠀⠐⣶⡾⠶⠿⡟⣩⢫⡄⠀⢈⡀⠚⠔⠀⠏⠋⠉⠀⠀⠉⠉⠁⠀⠍⠁⠀⠁⠀⠀⠒⠶⠶⡶⠶⣶⣟⢿⡛⠮
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠠⠀⠄⠀⠐⠈⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁


⣿⣟⢻⡿⢿⣿⠿⢿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⠂⣄⠀⠀⠰⠀⠀⠀⡄⢀⠀⢠⡀⠀⠀⠀⠄⢠⠄⠀⢀
⠀⡮⠷⠀⣠⠈⠀⠀⢀⡀⠀⠙⢆⠀⠈⠁⠀⡛⢌⡀⠀⠤⠀⠀⢻⡁⢲⠀⠈⠱⠀⢁⡁⠀⠺⠛⠁⢀⠖⠀⠘⠀⠀⠫⢠⣫⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⠺⠀⠠⠀⠀⣴⠼⠧⢹⠀⣁⠁⡀⠐⠆⠀⠂⠀⠀⠉⠐⠀⠀⠀⡀⡂
⠀⡐⢖⠩⢀⠀⠀⢀⠴⠒⠈⠉⠉⠓⠂⠀⠆⠀⣄⣀⣠⡄⠀⣈⠉⠉⠁⠀⣤⠀⠃⡀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣠⣀⠈⢉⡆
⠀⣚⣅⠤⠑⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢾⣿⠄⠀⠀⠄⠀⠀⠘⠀⠀⠇⠸⠀⡀⠉⠀⠄⠀⠠⡀⢉⠁⠀⠁
⠀⠠⡈⠁⡐⠀⡉⠀⠉⠉⠁⢻⠂⠉⠉⢁⣍⡁⠘⠒⠊⠀⢀⠁⠀⠤⠄⠀⡐⠂⣂⠀⠂⠁⠀⠀⠈⡀⡋⠁⠈⠏⣈⣁⠄⢶⢀
⠀⠠⣈⡁⠀⠀⢹⠃⠉⠀⠀⢸⠀⢤⠀⠨⢱⠀⠀⢰⢈⣄⠊⠀⠀⠀⠀⠀⠂⠀⠉⣉⠰⢢⡄⠀⢀⠁⠁⠀⠈⠱⠛⠓⠀⢠
⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡇⠀⠀⠀⠀⢈⠀⠀⢀⠀⢀⠄⣴⡀⠀⡀⡀⠀⡀⠘⠛⠃⠀⠀⡀⠠⣀⠂⠄
⠀⠠⠁⠀⡄⠂⠁⠀⢀⡀⢴⡸⠀⣀⠀⠠⠈⡇⠀⠁⠀⠀⠘⠀⠤⠚⠃⢀⣸⠁⡱⠀⢠⣴⠀⠹⢄⠀⠀⢀⠀⠀⠠⠐⠐⡀
⠀⢐⡂⠀⠈⠈⠀⠀⡉⠀⠀⡀⠘⠀⠄⠀⠠⠐⠄⠄⡀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣤⣌⡄⠀⠒⠋⠀⢀⣄⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠁⠐⠀⠺⠗⢀⢀⠁⠀⢀⠀⠠⠂⠀⢈⠂⠡⠀⠀⠀⠀⢠⠄⠀⢶⣦⣤⡄⠀⠀⠁⠀⢀⣶⡤⠐⢀⣉⢓⠄⠀⢀⠄
⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⠈⠂⠀⠁⠐⠀⠤⠐⠂⠀⠠⠀⠢⠄⠀⡈⠀⠀⠉⠀⢰⡇⠀⣄⢻⣺⣟⣃⣞⣿⣯⡄⢀⡀
⠀⠀⠀⠀⢂⡁⡀⠀⢦⠀⠀⠢⠘⠀⠀⡅⠀⠀⠂⠀⢈⠁⠀⢀⠢⠀⢐⡀⠂⠀⠀⠀⠀⠈⠁⠘⠉⠃⠈⡏⡍⠋⠈⠁⠑⠀⠁
⠀⢌⠤⠀⠈⣄⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢜⠀⠈⠀⠀⠀⠑⠀⡀⠂⠀⠀⡀⠀⣤⣄⡄⠀⠀⠃⠀⠀⠠⠀⠀⠦
⠀⠠⠎⡄⠀⠘⠀⠀⠒⠋⢀⠀⠃⠉⠘⠀⠃⠉⠐⠁⡀⠈⠁⠀⠀⠀⠀⡀⠈⢴⡥⠀⠀⠃⠀⠁⢛⠃⠀⠀⠀⠀⠂⡀⢠
⠀⢁⢚⡠⢡⠀⠀⠀⢀⠀⠉⢀⡁⠀⠁⠉⠁⢈⡁⠈⠁⣠⠘⠠⣀⣀⠶⠃⡀⣈⠈⠁⠀⠀⠀⡀⠘⠶⡄⠓⠃⠠⠀⠉⠠⠠⠆
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣀⠀⠀⠀⢠⠅⡊⠁⠀⠀⠀⠀⢉⡁⢁⠁⠀⠂⠀⠄⠠⣌⡀⠂
⠀⡎⠀⠀⠀⠆⠀⠰⣶⡴⣧⡄⠩⠤⠀⠀⠐⠋⢱⠀⠀⠈⢐⠃⠀⣀⠀⠐⠒⠁⠀⠒⠂⢠⠀⠀⢂⡊⠒⠀⠀⠀⡐⠀⠉⣀⡀
⠀⠀⠘⠈⠣⠀⠀⠀⠋⡏⠉⠇⠀⠀⠁⠄⠀⠀⢊⢄⠀⠁⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠇⠐⡁⠀⢠⠀⠀⠀⠩⠐
⠀⠀⠦⠀⠄⠀⠲⣒⠚⢁⣐⡇⠀⠀⠤⠀⠀⠄⠀⠽⠇⠀⠠⠄⠁⢀⠀⢀⡂⠈⡆⠙⠂⠁⢰⠘⠀⢩⢨⠅⠀⠒⠀⠀⠀⠀⠅
⠀⠀⣀⢠⠀⠀⢠⡌⠉⠉⠉⠁⠀⠄⣷⠲⠀⣠⢶⣖⠤⣄⠀⠲⠆⠀⠀⠶⢄⠀⠀⠀⠀⢤⠖⣆⠀⠒⠰⠂⠀⠀⠀⠐⠔⠁
⠀⠀⢘⠬⠆⠀⢈⠉⠢⠀⢀⠈⠀⠀⠀⠀⢨⣶⠋⠉⠙⢶⠆⠀⠄⢀⠘⠈⠁⠀⠀⠀⠀⢊⡗⢤⠀⠀⠂⠀⠤⣥⢀⢤⠀⠀⢄
⠀⠀⠈⠓⡯⠂⠈⠠⢀⠀⠀⠉⠀⠗⠀⠀⠈⢭⣷⣠⣶⡿⠂⠀⠂⢁⠀⢀⠀⠘⠉⠀⠀⠼⠧⣐⠀⠂⠀⢤⠀⠁⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠆⠀⠀⠀⠉⠛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠄⠀⢀⡀⢀⠀⢀⠐⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣙⣿⣧⣼⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⣤⡴⠂⣠⡾⠟⠁⠴⢾⣯⡴⠓⠂⠀⣰⠾⣿⣿⣿⣿⣿⡷⠲⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⣿⣏⣉⡀⠀⠀⠀⠰⣾⡋⠀⠀⠀⠀⠀⠠⢾⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠠⣬⣽⠿⠶⠖⠂⠤⣤⣼⡧⠀⢀⠀⠀⣀⠤⣾⣿⣿⡗⠊⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣐⣏⣙⢓⣶⠀⠒⠾⣿⣥⡤⣤⡟⠁⠀⠀⠀⠀⠋⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠁⠀⣉⣵⡶⠤⠜⣇⠈⠻⣾⠁⢀⡀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠨⠟⢿⣯⣁⠀⢀⣴⡿⣦⡀⢹⣴⡏⢀⣠⠷⣀⠀⠀⠀⠠⠄⠀⠀⡤⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣒⢆⠀⠈⢷⠀⠀⢼⡀⠈⠻⣾⠯⠀⢸⣧⣀⣈⡄⠤⠀⠐⠂⡴⠞⠁⠀⠖⠀⠗⠀⠂⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⣿⢶⣾⡅⠀⢸⣷⡶⠤⠘⣣⡤⢻⠋⠙⠃⠀⠀⠀⢹⣿⣿⣿⣟⣐⡁⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠉⠣⣴⠟⠉⠀⣀⣼⠏⠀⣼⣄⣨⠄⠂⠘⠛⣿⣿⣿⣿⣿⣿⡥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢤⣽⠅⠾⣛⣉⡩⠧⠀⣿⣝⡇⠀⠀⠀⠈⠉⠀⣾⠿⠛⠛⠿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠾⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀

⠀⠀⠀⠂⠀⠀⠀⠀⢠⣄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣤⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣴⣾⠋⠇⠳⢠⠏⢭⢿⣄⠄⠒⣀⠀⠦⠀⠀⢀⠀⠀⡀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⠜⠛⠻⢒⡖⠲⠻⢷⣀⠒
⠀⠀⠀⢠⡐⢄⣶⠉⠙⠷⣼⣜⡅⠀⠈⠙⡦⣌⡠⠖⢫⡡⠀⠁⠔⠀⣀⠀⢸⢴⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠛⠶⣼⣜⠄⠀⠀⢠⣉⠅
⠀⠀⠀⡀⢹⣷⣈⢆⠀⠀⠈⣙⣣⣀⠄⢘⡱⠉⠀⢰⣾⣁⠠⡀⠁⡀⣥⡀⢨⢰⣿⠁⠠⠀⠀⠁⠄⠀⡘⢷⣞⡙⣄⠀⠀⠀⣩⣶⣤⣒⢨⢎⡄
⠀⠀⠀⠠⠀⢿⣿⣿⣓⡁⣞⠭⠼⢛⣳⠎⠁⠙⠲⣜⣝⣦⣶⢷⠀⠰⣿⡇⠈⣼⣿⠀⠀⠀⠀⠀⣀⡤⢓⠈⣿⣷⣮⢓⣃⣾⠫⠔⢛⣽⠃
⠀⠀⠀⢢⡄⠘⡼⠔⠋⢻⣷⣄⡠⣪⠃⠀⠀⠀⠀⡘⠩⢒⣲⣼⣧⠀⢻⠀⠀⣿⠋⣰⣶⣶⠂⠘⡁⠐⢤⡂⠸⡉⠀⠝⢻⣷⣤⡐⠹⠁
⠀⠀⠀⢴⣿⣄⠸⢌⣠⣔⡽⣿⣿⣷⣄⡀⠀⠀⢀⣁⢉⣀⠉⣼⣿⡆⠀⠀⠀⠁⠐⢋⡩⠽⠗⠿⠿⣤⣬⣿⣄⡡⣔⣀⣄⡙⣿⣿⡷⣤⡄
⠀⠀⠀⢠⡟⢷⣀⡨⠍⢁⡈⠬⢿⢀⠈⠃⠀⡍⢈⢉⣯⣭⣛⣍⠻⣷⠀⠈⠁⠹⢆⡞⠛⢦⣄⠀⠀⠀⢈⡿⢷⣀⣈⠏⢀⠀⠬⢿⢅⢀⣂
⠀⠀⠀⠘⠀⠂⠁⠀⠈⠀⢀⠀⢰⠀⠁⡀⠀⠃⠘⠙⣻⣿⣿⣿⡷⠈⠁⠀⢢⠠⢀⣬⣀⣀⣬⠟⣠⢀⠼⠁⠘⠉⠀⠈⠀⢀⠀⠠⠀⠁⡀⠀⡇
⠀⠀⠀⢀⠀⡐⢀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢠⠀⠟⠛⠛⠛⠻⠛⠁⠀⠀⠓⢈⡴⡯⠼⡏⠉⠀⢁⡈⣵⡄⠂⠀⠂⠀⠀⠀⠁⠀⠀⠃⠀⢠⠠
⠀⠀⠀⠘⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠤⠤⠄⠀⠠⠀⡀⠀⠔⠧⠄⠠⠀⢈⣦⣊⣥⠞⢋⠞⠑⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠰⢰⠀⠁⡠⠁⠀⡠⠡⠊⣀⠀⠂⠀⠐⢦⡰⠿⠿⢿⡧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⢈⠀⢀⠠⠀⢀⠔⣤⢇⣔⠠⣄⣀⢠⢬⢏⠒⠦⣄⡊⠀⠈⢃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠂⠀⠀⢻
⠀⠀⠀⠐⣄⡤⢀⠀⠀⠐⢀⠀⠀⠈⢆⢻⠸⠈⠰⠄⢁⠄⡈⠸⣿⡆⠀⠙⡆⠀⠀⢀⡀⠀⠁⠀⠀⠀⠑⢄⡤⠀⠀⠀⠀⢀⠀⠀⠈⢄⢸⠸
⠀⠀⠀⢸⡟⠘⢦⡀⠀⠐⠁⠀⠐⠀⢘⢻⡇⠀⣶⢀⠂⢰⣶⣦⣝⡧⠤⠚⠋⠲⣴⡶⢶⣤⣀⠐⠀⣠⣶⡿⠰⢧⡀⠔⠀⠀⠀⠀⠄⠸⢻⣷
⠀⠀⠀⢘⠁⠀⠀⡈⠒⠄⣀⠀⠐⠀⢸⡌⣇⠀⣿⠇⢀⣶⣮⠍⠉⢁⠀⠀⠀⠀⠘⡏⠀⠙⣤⣷⠞⣿⢟⠃⠀⠀⣈⠒⠄⣀⠀⠐⠀⢰⡄⣿
⠀⠀⠀⠀⣠⣠⡞⠀⢻⣶⣏⠩⠙⠛⠠⢄⣿⠀⠏⠀⣼⣧⣈⠋⠁⠚⠀⠀⠀⠀⢀⣸⣴⣾⠟⠈⠁⢀⠃⣠⣠⡞⠁⢺⣶⣞⠋⠉⠛⠀⢤⣿
⠀⠀⠀⢰⣿⣿⣿⡟⢻⣒⣫⣧⡢⢎⢠⠖⠈⠀⠀⢰⣿⣏⣛⣭⡭⠉⠃⢃⠀⠈⠉⠉⡿⠑⠲⠶⡤⠃⢰⣿⣿⣿⡿⢻⣄⣫⣧⡂⢞⣀⠞
⠀⠀⠀⣾⡿⠛⠀⢷⢈⢂⠀⠐⠚⣠⡑⢄⣠⠀⠓⣾⠏⣴⣿⣟⣛⠛⠓⠀⠀⠀⠀⠁⠙⠒⠀⠠⠒⠦⣾⣿⠿⠁⢻⠰⣂⠀⠒⠚⣢⡁⢤⠠⠄
⠀⠀⠀⠟⠀⠅⠀⡈⢈⢽⡋⠓⡭⣉⣹⣦⡑⠴⠃⠀⠘⠻⠿⠿⠷⠶⢾⠈⡄⠐⠁⢀⠀⠀⠄⠀⠀⣼⠟⠁⠄⠀⠈⢃⠽⡏⠓⡭⢍⣍⡦⡙⠔
⠀⠀⠀⢀⠀⠐⠀⣜⠷⣔⠺⣄⠀⢀⢀⣀⣩⣄⠐⡀⠀⠄⠈⢀⣉⡀⢀⠀⠗⠃⠀⠀⢀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣔⢿⣗⡻⢦⠀⠀⣀⣠⣬⠦
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⣤⠔⢠⠀⢀⡄⣀
⠀⠀⠀⣦⠅⠀⡀⡖⣞⡘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⣊⠠⢆⠐⢶⠹⣠⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠄
⠀⠀⠘⢄⡢⣦⢠⡾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢆⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠓
⠀⠀⠀⠀⠑⣤⣤⣻⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠉⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠠⡄⠀⢀⣤⢄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣌⠘⣈⠳
⠀⠀⢲⡉⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠸⠦⠶⢢⡝⠘⢐⡀⠀⠀⠀⠀⠀⡄⡀
⠀⣅⡙⠡⡿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⢢⣱⡁⣢⣌⣛⢎⡀⠀⠀⠀⠀⢼⡏⢦
⠀⠼⢛⡏⣓⣍⠀⠀⠀⠀⠀⠀⢠⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢅⠨⠃⣓⠍⡸⡄⡀⠀⠀⠀⠀⣿⡇⡿⠆
⠀⢃⣻⡇⡇⢸⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡕⠀⠐⠂⠈⠀⠀⠀⠀⢈⡿⠏⣽⣱
⠀⠈⢾⡇⣟⠛⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢌⢾⠣⣉⢵
⠀⠁⣸⡶⡇⠚⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⢞⠺⠡⠘⢏
⠀⠀⠙⡆⠉⠀⠀⠀⠀⠀⠀⣽⣯⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢲
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⡯⢿⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣈⣙⣛⣛⣚⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣘⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢰⣶⣶⣶⣶⣶⣶⡖⠒⠒⠒⠒⠒⠲⠒⠖⠒⠶⠶⠶⢶⡆⢰⡖⠲⠖⠲⠶⠶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡟⣿
⢸⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣰⣿⣿⡿⣿⡟⣿⣿⣿⢛⢿⢸⠡⠘⣽
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⣾⣿⠳⣟⣿⡛⠆⣽⣿⢿⣬⡸⣾⠀⢠⣿
⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⣿⡧⣿⣿⣼⣽⣦⡸⢿⠈⣿⠇⡿⠀⡟
⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⡿⣾⣇⣙⡶⣜⢾⡀⡇⢀⡇⣸
⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠘⠿⣿⣟⡛⠙⢿⣿⣷⣿⣿⣷⣳⢸⢰⡉
⢸⣿⣿⣿⣿⣿⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠓⢮⠀⢸⣿⣿⣿⡇⣿⢸⣼⠃⢱
⢸⣿⣿⣿⣿⣿⣾⡈⢳⡴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⣾⣿⣷⣿⣾⣿⠴⠞
⢸⣿⣿⢻⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡿⣿⣿⠛⠙⡱⢀
⢸⣿⣿⣿⣿⣿⡟⣾⢙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣄⢘⡶⢫
⢸⣿⣿⣿⣹⣿⡟⣿⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣏⣸⣧⣿
⢸⣿⣿⣿⣹⣟⣷⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⣿⣿⠛⠟⠩
⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣋⣾⣿⠏⡀⢠⢂
⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠈⡴⠁⠀⡼
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠂⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠶⠷⠷⠶⠷

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠀⠀⢠⣀⠠⣿⣿⠀⠀⢨⣶⣦⣀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢶⡿⠀⠀⢘⢿⣷⣿⣯⣶⣶⠀⠛⢿⣯⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠘⣾⡷⠂⠀⠛⣻⡿⣿⣿⣯⡀⠰⢶⣿⠿⣇⣴⣤⡦⠹⣿⠇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⠚
⠀⠀⠀⡀⠀⠀⣠⣾⠀⠈⠀⠘⠃⢩⣤⣤⣴⡄⠀⠉⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠃⠀⢢⠇⠀⢀⠄⠀⢀
⠀⠀⠀⣿⣧⣰⣿⠃⠀⠀⠀⣤⣾⣿⣿⣿⠟⢀⣴⣾⣯⡀⢰⣿⣧⠀⠀⠀⠠⡀⢰⠁⠈⠣⣀⡼⠒⠋⠁⡠⠏⠁
⠀⠠⣤⣼⣿⣿⣷⣶⡷⠂⠀⠛⠛⠟⠛⠉⢠⣿⣿⣿⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠘⠢⣀⡀⢸⡇⣀⠤⠯⣤⠤⠤⠄
⠀⠀⠀⠀⠉⠻⣯⡀⠀⠀⢼⣿⣦⣶⣿⠀⠀⠉⠙⠻⠿⠛⣀⣧⣀⠄⠀⠀⠀⠀⠉⠙⠉⠙⣾⡿⠁
⠀⠀⠀⠀⣠⣤⣄⡁⠀⢀⣼⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⠀⣺⣷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣆⠈⠛⣿⣿⠟⠉⠀⠀⠀⠀⢿⡿⠀⢺⣿⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⡉⠉⠉⠉⠀⠀⠙⠁⢰⣤⣄⠀⠀⣤⣬⣶⣆⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠾⠟⠣⣦⡿⢿⣠⣤⡤⠀⣾⣿⣿⡇⢸⣿⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠛⠋⠀⠀⠁

⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡴⢶⣶⡄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠾⠿⠷⡄⠀⠀⠀⠠⠀⠀⡀⠀⠀⢰⣷⣶
⠀⡄⢀⡄⠀⠀⠀⠀⠀⠠⣶⣎⡉⡇⡓⢒⠷⣄⠐⢀⢤⣆⠐⠱⠀⡀⠀⣠⢀⡴⠀⠀⠀⠀⠀⠀⠰⣿⣭⡄⣫⡍⠻⠻⢦⡀⡡⢴⣣⠀⢀⠂⣠⢸⣿⣿
⢈⢱⡏⠀⠀⠀⠀⠀⣄⡠⠇⠨⠛⠿⠃⠀⢁⢄⠙⠁⣼⠃⢀⠐⠈⣅⠀⢣⣿⠀⠀⠀⠀⠀⠰⣤⠼⡁⠀⠙⠛⢃⢀⠀⡢⠋⠀⣼⠃⢠⠀⠀⣬⢸⣿⣿
⠈⣾⡇⠀⠀⠀⠀⡰⠘⣷⣌⡤⠀⡴⢚⡷⡤⠃⠲⢄⣫⣢⣼⡄⢰⣿⠀⢸⣧⠀⠀⠀⠀⣠⠇⢸⣷⣴⠤⢠⠞⠫⠗⠜⠁⠒⠤⣽⣶⡾⣇⠀⣿⢸⣿⣿
⠀⡿⢁⣦⡆⠐⠉⢄⡀⠩⠛⠱⣷⣅⠀⡼⠃⠀⠀⠌⢉⠨⡱⣷⠀⠿⠀⣿⠃⣴⣶⠒⠉⠠⣄⠀⢝⠭⠺⣷⣅⡀⡞⠁⠀⠀⢠⡍⢒⣞⣿⡄⠹⠸⣿⣿
⠀⡠⠚⡻⠷⠶⢧⣤⣷⡀⢠⠀⡈⢿⣷⣦⡀⠀⠀⢘⡁⣋⢢⣿⡇⠀⠀⡀⠘⡉⠽⠲⠿⢦⣬⣧⠀⠄⣀⡜⢿⣿⣦⡀⠀⢀⢀⣉⣩⡀⣿⣧⠀⢰⣿⣿
⠀⠣⣘⠛⢦⡀⠆⠈⡿⢧⣀⠛⢁⠀⢿⠅⠉⠀⠄⢈⣙⣙⣭⡙⢷⠀⠀⠘⢦⠋⠳⣄⢈⠀⢨⠿⣄⡈⠋⠀⠈⢿⠀⠁⡀⠅⣈⣽⣯⣍⣍⠻⡀⢸⣿⣿
⢀⠀⣰⣀⣤⡞⢑⠤⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⠀⢉⣉⣿⣿⣿⠈⢁⠀⠔⡠⣇⣤⠴⠃⡢⠘⠀⠉⠀⠈⢀⠀⠀⠈⢀⠀⠁⠏⣉⣽⣿⣿⠂⢉⣸⣿⣿
⠀⠚⠓⢇⠀⠀⢈⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠀⠉⠉⠉⠉⠁⠀⠈⠁⠼⠳⠺⡀⢀⡤⣼⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠀⠋⠉⠉⠉⠁⠀⠀⢹⣿⣿
⠐⠂⠀⣠⣦⡴⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠀⢀⣶⣤⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢺⣿⣿
⠀⢨⣞⡛⠛⠗⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠁⠀⠄⠃⠀⠀⠀⠀⣶⡛⠛⠛⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠅⢸⣿⣿
⠐⠚⠀⠉⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⡀⠠⠀⠚⢾⡉⠲⡤⠒⢁⠉⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢠⠂⠞⢶⡅⠒⣼⣿⣿
⠤⡄⣀⣂⠀⠀⠀⢀⣴⢪⠀⠀⠀⢂⠀⠀⢦⣇⠀⡃⠐⢀⣀⡺⡇⢀⡴⢤⢀⡂⠀⠀⠀⠀⣀⡶⢁⠀⠀⠀⠀⠀⠀⢤⣇⠀⡋⠠⢀⢀⠘⢇⠀⣸⣿⣿
⠀⠘⡷⠉⠟⣤⣤⣿⠏⠀⠑⠄⠀⠀⠀⠀⡀⣿⢸⣷⠁⣸⠻⠛⠎⠁⠀⠈⢿⠌⢻⢂⣄⣴⣿⠁⠈⠂⢁⠀⠀⠀⠀⡈⣿⢸⣷⠁⣘⣛⠿⠶⠉⢸⣿⣿
⠀⠀⢨⣠⣾⠋⠒⠱⢀⢀⡞⢠⣤⡲⠶⠦⠉⢸⠸⠏⢰⣏⠿⠆⠤⠀⠀⠀⠈⣄⣴⡿⠣⠊⠇⠀⣠⠖⢤⣐⢦⠤⢄⠃⣹⠘⡏⢠⡟⠷⠤⠠⠀⢸⣿⣿
⠀⠘⠋⣿⠣⢤⡴⠀⣼⣿⣷⠾⣛⣳⡂⡄⢠⠋⠀⠀⣾⡟⢂⠰⠲⠀⠀⠠⠞⢻⡟⠠⣄⠈⢠⣿⣿⣶⢿⢛⣦⢀⠄⣨⠛⠀⠀⣼⡿⢶⡴⠶⠂⢸⣿⣿
⠀⠀⠋⠐⠀⠀⠐⢴⣿⠿⠹⡐⡉⠀⠥⣈⠡⡀⠀⢰⡟⣹⣿⣷⠶⠆⠀⠀⠐⠉⠂⠀⠈⢤⣼⣿⡏⢷⠘⠉⠨⠥⠈⢋⠀⠀⢤⡿⢫⣿⣶⡶⠦⢸⣿⣿
⡀⠂⠀⠂⠀⠀⢀⡾⠁⠀⠀⢁⠽⠘⠪⠉⡵⡈⠰⠂⠈⠻⠿⠿⠶⠆⠀⠀⠀⠀⠀⠄⠀⢰⡟⠁⠀⠈⢊⢗⠒⢙⣛⣦⠁⠴⠊⠀⠿⡿⠷⠶⡄⢸⣿⣿
⢉⠁⠀⠀⠀⢀⠞⠀⠀⠀⢰⡻⢤⠳⠀⠀⠠⠮⢄⠀⠀⠀⠀⢬⠄⠀⢈⠅⠀⠀⠀⠀⣠⠏⠀⠀⠀⢔⢷⡂⢦⠀⠉⣊⣅⡄⠂⠀⠀⠀⢀⡁⠐⢘⣿⣿
⠘⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠻⠌⠳⠾⠆⠔⠂⠀⠄⠀⠐⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠈⢧⠙⢦⣶⡄⠤⠄⠌⠄⠀⠰⠀⠀⢀⠀⠸⣿⠿

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⣿⡧⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⣶⡄⢠⣿⣿⣤⣿⣿⣶⣶⣿⣿
⠀⣀⡆⢠⣾⣆⠀⠸⣿⣧⣼⣿⣿⣷⢆⣴⣧⡀⠀⣼⠀⠀⢀⣿⡀⠀⣸⣿⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣷⣼⣿⡟⢺⣿⣿⣿⣸⣿⣯⡷⢲⣿⣷⣀⣴⣿⣿⣀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣅⣼⣿⣿⣅⣽⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣁⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⡋⠀⠈⠑⠓⠄⠀⠀⠀⠀⠰
⠈⠋⠉⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡔⠀⡄⠀⠀⠀⠣⠄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠳⠀⠀⠐⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠐⣆⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁⠠⠤⠄⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣵⣤⢄⠐⠂
⠀⠀⠁⠀⠀⢐⣀⣠⡀⠐⠲⠶⣶⡶⠀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⠆⠀⠀⠀⢘⠀⠀⠀⢠⣤⣴
⠀⠐⠁⠀⠀⠀⠉⠁⣀⠀⠀⡄⠁⢐⡆⠀⠀⠀⠀⠀⠐⠈⠆⠶⣄⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⠑⠦⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⣴⢀⠀⢰⠁
⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠧⠠⠀⠃⠀⠀⠠⢄⡂⠐⢦⠘⠱⡀⢧⠇⢀⡠⠤
⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡓⠦⢙⣦⣁⣆⢀⡡⠀⡨
⠀⠀⠈⢀⠀⠠⡄⠁⠈⠀⠀⠀⠀⠀⡘⠖⠉⣠⡼⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠛⠙⠻⢿⣿⣿⡶⠒⠛⠁
⠀⠀⠀⠈⠷⠢⣤⠀⡀⠀⠀⠀⢀⠐⢁⣦⠟⡉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⢰⣥⠴⡺⠋⢁⠞⡿⢹⢟⢣⣀⠀⠁⠁⠀⠐
⠀⠀⠀⠀⠤⠒⠄⠁⠀⠀⠀⠀⠀⣴⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠤⠂⠁⠐⠀⣰⠈⣥⠜⢆⠉⠁
⢄⠀⡄⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⢠⡄
⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⠀⠀⠴⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠃⠀⠈⠸⠀⣴⡃⡀⠄⡠⠀⠀⠀⠀⠐⣡⠾⠀⠀⠀⠀⠐⠀⠂⡨⠿⢧⡀
⠠⠄⠀⠀⡀⠀⡐⠀⠀⠃⠀⠈⠁⠀⠊⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢸⠀⠀⠁⠈⠁⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⢀
⠅⠊⡀⠌⠀⠀⠠⠄⢀⠠⣈⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠁⣀⣒⠒⠂⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣈⠄⡤⠈⠓⠒⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠊⠉⠄⠘⠉⠉⠐⡄⠀⠀⠀⠤⢀⡐⠠⠀⠠⣄⠉⣠
⠀⠀⠒⠀⠂⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⢄⡙⣳⣄⡀⠁⠘⠛⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠱⣤⠉⠛⠶⣶⣸⠀⠋⠃⡀
⣉⣯⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⢒⡀⠙⢛⢃⣀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣾⣿⡿⣿⣦⠀⣠⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣛⣿⣿⣟⣿⣶⣿⡟⣯⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣻⣿⣿⣽⣿⣿⣿⣧⣴⡟⠈⠛⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⠍⡻⢿⣿⣿⡿⣿⣿⡆⣵⢿⣿⣏⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣟⣩⣾⣿⣿⣿⣿⣿⣿⣧⣜⣟⠿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣥⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣿⣿⡿⢻⣟⣛⣻⣟⢻⣿⢿⣿⣾⣿⣿⣽⣿⣯⣅⣤⢌⣋⣠⣄
⠀⠀⠀⠀⠀⠀⢠⣤⣖⣛⣉⣭⣽⠟⢻⡽⠿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣝⡒⠛⠛⠁
⠀⠀⠀⠀⠀⠠⠚⠿⠿⠿⢲⣾⡭⢩⣿⣷⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣉⢙⡁⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⢿⣾⡿⠿⠿⠷⣿⣙⣻⣿⣿⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢶⡾⠿⠛⣫⣭⣴⠞⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠨⠒⠓⠚⠛⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⣿⣿⣿⣷⣶⣬⣑⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⠉⠋⠛⢻⣿⢿⡉⠛⠙⠻⠿⠿⠟⠂⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣚⠛⠛⠻⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠉⠄⠉⡍⠙⠛⠛⠉⠉⠋⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠰⠀⡀⡀⠀⢆⡀⠉⠐⠈⡄⠓⠂⠄⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠔⠀⠀⢧⠀⠊⠀⠀⠤⠀⠀⠠⠠⡀⠀⢘⡄⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⢁⠗⠐⠃⠀⠙⠦⡤⢤⡈⠀⠀⠀⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠉⠀⢎⠀⠀⠈⠃⠑⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢫⠉⠢⠤⣄⡠⣄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠠⢀⡀⠌⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠢⠈⡀⢈⡕⡆⠏⢑⣃⡄⠀⠀⠀⡀⣀⡇⠘⠊⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⡇⠀⠀⠀⠁⢘⢠⠇⠳⠙⠊⠉⢙⣒⣲⠁⠧⠀⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠈⠂⡐⠀⠀⠀⠀⠀⠤⢄⠀⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠲⣀⢀⠤⡇⠉⠀⠁⠀⠀⠀⠉⢇⠀⣹
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠃⠀⠈⠨⠀⠀⢠⣀⢌⡠⠃⠀⠂⠠⡀
⠀⠀⠀⠀⠀⠈⠂⠐⠆⣨⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⡀⠀⠀⠀⠀⠀⠠⢀⠀⠁⠀⠀⠀⠀⠀⠂⠆⠀⠀⢀⡀⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠄⠠⠀⠄⠀⠉⡑⠀⠀⠀⠀⠠⠀⠀⠠⠀⠝⠐⡃⡀⠀⠁⠀⢢⠈
⠀⠀⠀⠀⠀⠀⠤⠚⠀⠁⢄⠀⢀⡁⠠⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⠉⠉⠶⠚⢛⠄⡔⠠⡆⠀⠀⠀⠀⠀⠉⠁⠀⠈⡦⢀
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠸⠀⠀⠀⡈⠀⠀⠀⣤⡰⠄⠎⠉⠉⠇⠀⠈⠉⠙⠐⠘⡔⠉⠀⢧⡀⠰⠄⡖⠦⠤⠄⠀⠠⠦⠈⠔⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⡀⢀⠀⠀⠀⠈⠙⠆⠶⡑⡄⠴⠒⠂⠀⠀⠀⠀⠀⠀⠈⠂⠑⠚⠤⢰⠇⠄⠐⠣⠄⡀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⠙⠁⠘⣀⣤⠀⠄⠦⠐⠁⠀⠈⠢⣀⠰⡄⣄⣀⣄⡞⣄⢠⣰⣂⣂⠔⠉⠋⠈⠀⠠⢌⠑⠒⠒⠘⢆
⠀⠀⠀⠀⠀⠈⠀⢂⡀⢀⠤⠀⢄⡨⠅⠀⠀⠀⠀⠀⠀⠀⡄⣁⣀⡀⠀⢁⡊⢀⡅⠬⠂⣉⠅⢠⣠⢄⡠⡠⢀⠘⡢⠀⠐⠀⢀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠐⠓⠊⠒⡈⢒⠆⠠⡀⠎⠈⠁⠋⣠⠒⠩⡀⣄⣠⠀⢄⢠⡄⠛⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠀⠁⠀⠀⠀⠢⠈⠀⡘⠀⠑⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠘⠂⠇⠐⠐⠲⠦⠋⢂⠧⠘⠛⠃⠿⠤⢴⣠⡄⣰⢶⡏⠦⠸⡔⢴⡶⡰⡧⠠⠼⠶⡼⠆⢲⠶⠶⢤⠤⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡵⠀⠀⠀⠀⢀⣼⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⠞⠀⠀⠀⠀⠀⣾⡏⢸⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⢸⣿⢠⠃⣰⡟⡸⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢠⠜⣿⡇⡠⣾⡧⠀⠀⠀⢸⣿⠏⢠⣿⣳⠃⠀⠀⡤⣤⡠⠊⠀⣠⠔⠊⢉⡴⠋⡾
⠰⡿⡢⠖⣄⡀⠀⠀⢿⠟⣰⣿⢃⣴⢦⠀⢸⣿⠀⢸⣿⠁⠀⢸⠃⢩⣿⠃⠀⢰⠃⢀⡴⠋⠀⢐⡇
⠰⣉⡘⠢⣁⢾⠖⢦⠀⠀⣿⡏⢸⣯⠜⢠⠏⠘⠛⢹⣿⠀⣠⠋⠑⠚⠋⠀⢀⡤⠛⢯⣀⣀⡤⠎
⠀⠺⠄⡤⠈⠷⣄⣚⠆⠀⠻⠧⠜⠷⠔⠁⠀⠀⠀⠘⠿⠚⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠴⠂⢤
⠀⠀⠘⠦⡤⠛⠃⠉⠲⠄⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⠠⠀⢀⣀⠤⣤⡤⢲⣦⠀⠘⢄⣀⡤⣿⡆
⠀⠀⣠⡤⡀⠀⠀⠀⡠⠒⠒⠛⠒⠶⢶⣿⡷⠴⠴⠶⠚⠋⠁⠀⠀⣿⡏⠀⣿⠃⣼⡟
⢀⣾⠋⣠⣿⠀⠀⣀⡀⠀⢀⣀⠀⠀⢸⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⠁⠀⠛⠀⣿⡇⠀⣸⣷⠴⠲⣦
⢸⣯⠔⣿⡏⠀⣰⣿⠃⢀⣾⣯⠀⢀⣾⣿⠀⣰⣿⠀⢠⣿⡇⠀⡸⠁⠀⠀⠀⠀⣿⡇⠀⣿⡏⠀⢀⣿
⠀⠀⠀⣿⣇⡴⢻⣏⡠⢛⣿⡇⢀⠞⠀⠙⠋⠘⣿⣀⢼⣿⠀⣰⠃⠀⠀⠀⠀⠀⢽⡇⢠⣿⠇⠀⣾⡟
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠘⣿⣧⠏⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⢘⣀⡠⠤⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠊⠀⢀⢤⡤⠆⢁⠠⢄⣰⡭⡄⣤⡤⣌⢑⡄⠀⢠⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣸⠉⠈⣖⠁⢹⢊⠇⢸⢪⡀⠀⣇⠀⢰⡏⠀⠘⠁⠘⠆⠉⡶⠂⢻⠤⢖⢃⠠
⠀⠀⠀⠀⠀⠀⠘⡤⠶⠀⢿⣧⠀⣽⠀⣜⢸⠀⡏⠁⠇⢠⠇⡇⢸⢹⠀⡴⠀⢀⡆⠀⡟⡄⢠⡄⠸⠂
⠀⠀⠀⠀⠀⠉⢨⠸⠸⠀⢸⡏⠀⣿⠀⣇⣾⠀⢧⠀⡇⢸⠀⡇⢸⢸⠀⣧⠃⠸⡟⠀⢷⠃⢸⠃⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠊⠓⠤⠣⡀⢀⡀⠈⣿⠀⠈⠲⡇⠀⠉⠀⠈⡎⠀⢹⡀⢀⡷⠤⠺⢤⠎⢉⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠉⠙⠈⠢⠤⠔⢉⠒⠊⠒⠊⠑⠒⠁⠍⠉⠂⠀⠀⠀⡐
⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠰⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠂⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠠⠔⠒
⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⠶⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⡴⠤⣀⣰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡤⠿⠷⡖⠛⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠀⡀⠀⢸⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠁⠀⠊
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣨
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀⠠⢂⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣀⠄⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠀⣸⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣡⡀⠀⠀⠀⠀⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣁⠉⠉⠋⠐⠒⠒⠴⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⠉⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠢⣀⠀⠀⠀⠀⠀⠉⠲⢌⡈⠸⣶⡀⠀⠄⠠⠞⢧⣀⣠
⠀⠀⠀⠀⣀⡼⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⠀⠀⠀⠈⡙⠿⣧⡀⠀⠀⠀⠀⠈⣿⠆
⠀⠀⣤⡾⠋⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⣀⡏⠱⢦⡀⠀⠀⢸⣿
⣴⠿⡃⠀⠀⠀⠀⠘⣷⣴⣖⣼⣛⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠤⢤⠤⠶⠛⠳⠶⢿⣷⣤⣾⣏⠆
⡏⠈⠀⠀⠀⠀⠀⠀⠘⢦⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢉⠟⢿⣿⣿
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠹⣿
⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠹⣄⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⢳⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡘⠀⠀⢀⣄⠀⣠⡴
⣖⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠈⡄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⡿⠛⠁
⣿⣆⢆⠀⠀⢠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⣤⣧⡀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⢀⣀⡤⠼⠒⠛⠉⠉⠉
⠙⣿⣦⣄⠀⣼⠏⠀⠀⠀⢀⡀⠀⠀⠑⢀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢿⣶⣄⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠈⠉⠁⠀⠀⠀⣀⣠⣤⣴⣶⣷⣶⣤⣄
⠀⠘⣿⣿⣿⡿⠦⢶⠏⠩⢩⣷⣈⠤⠒⠈⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣤⠀⠀⠀⠀⠀⠀⣀⣤⣠⣤⣴⣤⣶⣶⣾⣿⣿⠿⠿⠟⠛⠛⠛⠿⣿⣿
⠀⠀⢸⣿⠏⠙⠒⢶⣤⣤⣶⣿⡷⠤⣔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠿⠶⣾⠿⠿⠛⣿⠛⠛⠛⡟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⡟⠀⣀⣤⡾⠟⠛⡏⠀⠀⠀⠀⠹⢶⠤⠀⠠⠤⠄⣀⢀⣀⣠⡴⠞⠋⠁⠀⠀⢰⠇⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣼⣿⣷⣾⠿⠋⠀⠀⡼⠁⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⣤⠞⠉⠉⡀⠀⠐⠀⠀⠀⠀⠈⡆⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⣾⣿⡿⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⢇
⡿⠋⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠀⢀⠔⠁⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⢦
⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⢦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠚⠁⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢿⣿⠟⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⣿⣿⣿⣭⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣗⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢤⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣉⣤⡄
⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣬⡛⢶⣿⣿⣿⣿⣿⡟⢋⣀
⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⡯⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣻⣟⡍⠻⣾⣿⣿⣿⣿⣿⢿⣛⣩⡀
⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣶⡶⢊⣀⢀⡀⠀⠀⠀⠀⣀⡠⠀⠀⠀⡐⢿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠈⠈⠉⠉⠉⠄⠄⠴⠤⢯⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣼⣿⡗
⠀⠀⠀⠀⣤⣈⣿⣿⣿⣿⣿⣿⢚⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡥
⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣛⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀
⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣟⠟⠀⠀⢀⣿⠀⡇⠀⡆⢠⡆⣹⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣹⡆⢰⣤⣿⣞⣧⣴⣧⣸⣷⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠓⢄⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠉⣐⠀⠈⠘⡄⡴⠊⠗⡙⢉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠂⢄⠉⠰⠃⡰⢧⢇⡁⢸⠆⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡕⠒⠒⠪⢕⠤⡀⠀⢿⡟⡇⠀⠀⠀⠈⠫⣍⠉⡴⠊⢨⠄⠀⡵⠂⠸⠥⢲⡒⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡎⠙⠻⣶⡀⠀⠉⠪⡳⢌⢯⣿⠀⠀⣀⡤⠴⠞⡗⢳⡒⠛⠚⠳⠠⠆⣀⣤⣊⠀⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡇⡁⠀⠀⠘⣵⠀⠀⠀⠈⠳⣽⣝⣷⠋⠁⠀⡠⠊⠁⠘⡀⠁⣬⣀⠃⠠⠀⡶⢭⣀⣐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠱⡳⣄⣀⢴⡝⠀⠀⠀⠀⠀⠈⣯⠞⣆⠀⠀⣅⠄⠈⠐⢙⠀⢧⢸⡀⢒⠀⠈⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣝⣛⡟⣆⠀⠈⢆⣰⡀⠚⢢⣈⠎⢦⠮⣡⣹⠁
⡰⠋⠑⠂⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠫⡏⣀⠹⠊⢧⡀⠀⠁⠙⠢⠇
⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣤⣴⠾⣾⣷⢦⣤⠿⠛⠷⠻⠿⣦⣤⣤⣤⣤⣀
⠘⢦⣀⣀⡤⠞⠁⠀⠀⠀⢀⡴⣛⡉⢢⡀⠄⢡⢬⡸⣌⣛⡿⠀⠁⠔⡠⣒⡪⡔⠘⡆⢉⢰⠋⢨⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡏⣿⣷⠄⡇⣰⠿⢀⠅⣂⢀⢀⡈⢿⡜⣇⠳⠟⢣⣴⠣⠘⣾⡀⠻⡿⢃⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢄⠑⠬⠵⠚⣰⠯⡡⢀⡈⠄⠀⠃⠀⢸⡇⡈⠙⠋⠉⡲⠓⠓⢾⡝⠲⠒⠋⠂⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠂⡬⠀⡀⣾⡟⢢⠐⠀⡠⠚⠉⢉⢉⢺⡇⢀⢄⠰⠶⢇⠿⣿⠀⣷⡠⠖⢛⠓⣅⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠋⢅⣁⡤⢴⡀⣿⠿⠠⠀⠀⡇⢴⣫⢯⢣⢸⡇⠁⠣⡠⠄⡀⢝⠩⡀⣿⠡⢸⣟⡿⢸⢆⢻
⠀⠀⠀⠀⠀⠀⠀⢻⠇⡔⠁⣴⠲⡌⣿⠦⠴⣥⠤⡱⣤⣉⣩⢼⢸⣇⠔⠋⡉⠑⣔⣘⠀⢈⣿⠀⠘⠲⡖⠁⠜⢻⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧⠀⡳⢭⠖⣿⣤⣦⡄⢱⠈⠂⢠⣴⡅⣿⡇⠀⡎⣟⡇⣸⣀⣪⣦⣿⡢⠂⡻⠋⢋⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢙⠲⠤⠤⢿⣜⣚⣃⠜⢀⠄⢀⢠⠡⣺⠇⡁⡑⣢⢒⡏⣡⣤⣨⡏⣴⣕⠐⢈⠚⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠖⡡⢌⡘⡇⢩⠝⡋⠉⠑⢦⡌⡄⣿⢀⠂⠐⠙⠉⢣⣙⣛⣼⠏⣤⣌⠑⣬⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣴⣶⣁⣹⢏⡀⡔⡭⣷⢈⡗⡈⠃⡸⣋⡙⢦⡕⣠⠀⡸⠁⡧⣝⣝⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢤⣧⣉⣡⣞⣀⣤⡾⢧⣿⣿⣀⣏⣥⡶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠁⠀⠀⢀⣀⣹⠀⠜⠀⠀⠀⠀⠠
⠀⠠⠀⠐⠦⢤⡀⠀⠃⣼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠆
⠀⠀⠀⠐⠓⠒⢿⣦⢰⡇⠀⠀⠀⠀⡀⠀⢐⣀⣤⠀⣠⡑
⠀⠀⠀⠀⠀⠀⠀⠈⡌⠃⠀⠀⠀⣀⣁⣀⣀⣀⣀⣀⠀⡌⠷⢶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠯⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣠⠞⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣀⣀⣄⣠⣤⣠⣤⣤⡌⠁⣠⠟⠁⠈⠐⠀⠀⣈⣁⣀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⠿⠗⠋⢩⠻⠀⠇⠸⠁⠿⠿⣿⠿⣿⡀⢀⣀⣀⡀⠐⠧⠀⣠⡀
⠀⠀⠀⠀⠀⠒⠚⠒⠀⠀⠐⠋⠛⠁⠀⠀⠀⠐⠃⠀⠘⠀⠘⠀⠰⠀⠐⠂⠐⠀⠊⠃⠠⠄⠉⠃⠘⠅⠀⠀⠀⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⢴⢀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡰⢺⣷⡆⠀⠸⢄⡀⠈⢤⣄⠀⠀⡄⠀⣤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣰⡆⠀⣀⠀⣴⠾⠃⠀⠻⠲⠿⠛⠓⠓⠒⣾⣟⠋⠠⡘⠃⠇⠃⠀⠛⠀⠚
⠀⠀⠀⠀⠒⠊⠉⠉⠉⠋⠀⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠚⠉⡀⠀⠄

⠀⠀⠀⠀⠀⣠⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⡠⠞⢉⣤⣴⣶⣾⣿⣶⣬⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢀⡀
⠀⣼⣯⣾⣯⣹⡿⡿⣿⣿⣿⣿⣿⣝⡆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠟⠸⡣⠔⠀⠀⠀⠀⠤⠉⢷⡀
⠀⢸⣿⣿⣿⣾⣶⣿⣾⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⢴⡿⠷⠶⠀⠘⠀⠀⠀⠀⠀⣰⠀⡀⣴⣧
⠀⢸⣿⣿⣿⡿⢿⣿⣿⢫⢾⣿⣿⣿⡟⠀⠀⢀⡴⢩⡞⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣦⡀
⠀⠀⠹⣯⡻⢿⣿⣿⣿⣾⣿⡿⠟⠿⠃⠀⣴⠃⠈⣸⠧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠶⠖⠀⠉⠀⠉⢇⡀⠔
⠀⠀⠀⠈⠛⠖⢒⠛⣻⣭⠥⠐⠁⠀⢀⠚⢁⣷⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣅⣀⣴⠃⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⠿⠏⠛⠛⠋⠀⡉⠉⢩⣀⡀⠀⢀⡀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁⠀⠰⠂⠀⠒⠀⠙⠓⠀⠉⠉⠀⠠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⢶⣿⡇
⠠⣠⡄⢀⠀⠸⠟⠁⠀⠀⠀⠀⠀⢀⣠⣦⣾⠋⠀⠀⠀⠀⠀⠀⠙⢢⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠸⡿⣥
⠀⡵⣕⠘⠄⠀⠀⠀⠀⠀⠀⢀⠸⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⠃⣿⡆
⠀⠉⡄⠁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣿⡛⠿⣧⠀⠰⢻⢸
⠀⠢⣑⠀⠀⠀⠀⠀⠀⠀⡇⣠⠜⠂⠀⠀⣀⣀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣧⡀⠀⠀⡠⠋⢷⡀⠈⠇⠀⠨⠀⠄
⠀⠐⡄⠀⢀⡀⠀⠀⠁⠀⣷⠇⠠⠁⠀⠀⡏⡯⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠉⠀⠀⠀⠀⠈⠻⡄⢀⠀⠀⠣⣸⡄
⠀⠀⠉⣖⣒⡀⠁⠀⠀⠴⠁⠀⢀⠈⣄⠀⠐⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠙⠋⢁⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠠⠀⠠⢄⡈⣷⣤⣀⣀⣀⣿⡏
⠀⠀⠀⠒⢒⡿⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣿⡟⠛⠛⣿⣛⣋⡀⠂⡀
⠀⠀⠀⠀⠀⠃⠤⠄⠀⠶⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠿⠻⠛⠉⠃⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⡀⠀⠀⠘⢳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠓⠒⠒⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠄
⣆⡅⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣤⣶
⣿⣿⣿⣧⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣻⡄⣿⣿
⣿⣿⣿⣿⣿⣧⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢀⠀⣀⣸⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣧⣾⣇⣠⣸⣀⣆⢀⠀⣴⣆⣠⡄⠀⣄⢀⣴⣤⣶⡆⣀⠀⡧⣾⣦⣤⣿⣇⣼⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣷⣾⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡄⢲⡾⣧⡠⢀⣀⠐⣀
⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠢⢤⣁⡀⢂⣴⣂⣄⣇⢦⣯⣷⣿⡗⣣⡍⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢤⡄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⢿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣿⣾⣶⡿⣶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠡⠀⠀⠀⠀⠀⠀⠂⠀⡒⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢠⡒⠶⣮⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠡
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⣄⡀⠀⠀⠈⠀⠀⡾⠻⠝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⢰⡟⠉⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢾⡯⣿⣿⣿⣿⣿⢿⠿⣿⠋⣽⣾⣿⣿⢿⣿⣿⣿⣿⠻⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠷⢿⠿⣟⡿⠿⣿⣿⣿⣿⣿⣍⡬⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠄⠱⠏⠉⠀⠂⠀⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⡤⢤⣴⣶⣷⣿⣿⣶⣶⣿⣶⣖⣶⣶⣶⣾⣶⣶⣶⣤⣦⣤⣦⣄⣀⡀⠀⠀⠀⡀⣿⣿⡇
⠀⠀⠀⠀⢤⣠⣦⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣟⣋⣇
⢀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀
⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢃

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠋⠉⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠟⠁⠀⠀⡔⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⡾⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠛⠿⠃⠀⠀⠀⠀⠀⡇⠀⢠⡿⠁⠀⡀⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣡⠴⠊⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⣰⠟⠛⠷⣤⣤⡀⠀⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⣸⠟⠀⠀⠀⠀⠘⢷⣤⡄⣸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⡀
⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣰⡿⠁⠀⣀⣠⠴⠒⠉⠀⠀⠀⠀⠀⢀⣽⠃
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣥⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁
⣾⠋⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣄⣀⣀
⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠹⢷⣤⣄
⢠⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⡿⠁⠀⠀⠀⣀⣀⣀⣤⣤⡤⠶⠶⠒⠒⠀⠉⠀⠀⠀⠀⠠⣾⠋
⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠷⠾⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋
⠀⠘⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⢹⣟⣀⣀⣤⣴⢶⣿⢿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠉⠉⠉⠁⣰⡟⢡⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣾⠁⠀⠀⠀⠘⢷⣀⣶⣄⡀⠀⢀⣀⣀⣴⠶⠛⠁
⠀⠀⠀⡀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠈⠉⠁⡈⠛⠻⠟⠋⠉⠉
⠀⢊⠀⠇⣰⠐⡢⣿⡵⢻⣇⡰⢀⡰⠎⠺⢰⢌⠀⠅⠂⣇⠢⣐⡆⡇⢙⠀⢐⡀⢆⡰⠊⠗⢰⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣶⣠⡆⡆⢀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⢶⣶⡆⣲⣀⣿⣿⣿⠿⠿⠳⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣥⡀⡓⢻⣭⠀⠘⣷⣿⣿⠓⠹⡿⠿⠋⠀⠑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣻⣿⣷⣏⣿⣿⣏⠹⣉⡝⣿⣶⠿⠷⢶⡞⠉⠻⠿⣮⣶⡀⢍⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⡿⣿⣿⣿⣶⣚⢻⣿⣧⣦⣴⣿⠇⢀⡀⠀⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠀⢏⣉⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣾⣷⣾⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢻⣿⣿⣍⠻⠻⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢉⣨⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣺⢦⣶⣿⣧⣼⣿⣍⡃⣹⣦⣉⠙⣽⣿⣿⣿⣳⣿⡟⡋⠡⠌⠉⠈⠿⠙⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡗⠺⡿⣿⣿⡟⣿⣿⣿⣿⣿⢟⣽⣿⣿⣧⣶⡞⠄⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠊⠋⢀⣹⣮⣿⣿⡇⣿⣿⢿⡿⢟⡠⠀⣤⣸⣷⣄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢾⣿⣿⡿⢷⡇⢻⣿⣿⣿⣿⣟⠒⢻⣿⠛⠛⢿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⣿⣶⣾⣐⢲⣟⡏⠃⠈⣿⣘⣍⠹⢛⣻⡟⠒⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡾⢺⣯⡏⢛⣿⠛⢻⡶⠀⣿⣽⠿⡵⣏⣿⣿⣿⡧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡚⠉⠀⠈⠁⠀⣿⡇⠀⠀⠈⠫⠥⡍⠈⠛⣿⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠁⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣚⣛⣛⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡿⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣛⣟⣜⢳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡞⠋⣩⠉⠙⢿⣧⣽⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⠻⣦⡀⠠⠀⠀⠈⠡⢘⡁⠄⠙⠻⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⡀⢀⡔⠒⠰⠂⠀⡠⢾⣿⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠟⠿⣿⣿⡋⠀⡀⢴⣼⠿⠛⠋⠉⠹⣿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡆⢈⠟⠈⠀⢀⠻⣤⠃⠀⢀⠀⣄⢘⠁⠆⡜⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⡺⠀⢸⠛⣄⠸⣏⢸⣎⢺⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠠⡄⢿⠑⢿⡕⠬⣿⣽⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠈⢀⡘⠳⡄⣻⣄⣻⣮⣽⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠴⡶⠹⣦⡀⠻⣿⣏⣺⣿⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣄⣠⣴⣷⣄⣿⢻⣶⣿⠙⣿⣻⢟⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡍⣿⡿⠿⣥⡾⠹⣷⣴⣿⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⣷⠟⠛⢾⣼⠷⣎⠻⢽⣿⣾⣼⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣼⢟⣄⣀⣾⢻⠛⠿⢿⣵⣶⣭⣻⣿⣟⠻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢹⡟⠛⠠⢄⠀⠉⠛⢿⣿⣷⣬⣵⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣶⣂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡼⠛⣿⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢢⣧⢸⣿⣇⣿⣏⣿⢻⣿⡗⠯⡂⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠡⢹⡿⠋⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠐⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢿⣏⣠⡤⠶⢿⣿⣟⣒⠒⠶⣶⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠄⠈⠙⠺⠧⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼⣿⣥⣤⡀⠈⠻⣿⣿⣷⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢐⠀⠀⠀⢹⡀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠘⢿⣆⢀⡎⠀⠈⠻⣿⣿⡄⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠵⢀⠀⠀⠀⠀⠂
⠀⠀⠀⢶⣤⣄⠀⠙⡿⠀⠀⣀⣤⣤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠥⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢻⣿⣇⠀⢡⢠⡼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⢛⡁⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠉⠉⠙⠻⡏⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⠀⠀⠘⠡⠂
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡘⢄⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡀⢢⠸⡅⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣻⠀⠀⠀⠀⠀⠀⠐⠪⠅⠳⡗⡨⠊⡁⠀⠀⠀⠀⠀⠹⣦⡄⠸⡇⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣦⠀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢅⠀⠶⡗⢐⠄⠄⠀⠀⠀⠀⠀⠀⠘⢿⡄⣇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡆⢀⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠑⢤⡷⠥⡐⢥⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡇⡼⠋⢀⣀⣀⣀⡀⠀⠀⠀⠀⢈⢢⡀⢐⣠⡧⠊⠀⢐⡀⠀⠀⠀⠀⠘⣿⡆⠀⢹⡇⠀⣠⣴
⠀⠀⠀⠀⠀⠀⡾⢆⠀⠀⠹⣾⣞⡥⠚⠉⠀⣠⠜⠁⠀⠀⠀⠀⠈⠂⠀⠠⣄⣧⣐⠈⠄⠊⠀⠀⠀⠀⠀⠈⠻⣄⢸⡇⢠⡿⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠳⡄⢠⠟⠛⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣬⣧⠐⠀⠈⠩⠀⠀⠀⠀⠀⡀⠀⠘⢾⣇⡞⠁
⠀⠀⠀⠀⠀⠀⢧⡀⠀⣷⠏⣀⡠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠐⠠⣀⡇⠄⠀⠀⠰⠀⠀⠀⠀⠀⣿⣦⠀⢸⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⣚⣁⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠊⠉⠠⣁⠈⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⣦⢸⠃⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠙⡟⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣾⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⡟⠃⠠⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⠖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣷⠀⡑⠀⠙⢴⡕⠁⢀⠶⢁⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢌⢀⠠⠜⢺⣤⣄⣄⡗⠟⠁⡠⠄⢈⠤⣲⣀⡀
⠀⠀⠀⠀⠀⢦⡀⡀⠀⢠⠀⠶⡀⠀⠛⠀⠤⢤⡱⣿⣮⢳⣇⡞⠀⠠⣨⠒⡋⠉⠠⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠐⠱⣿⡄⡀⠂⠀⢸⡦⣠⡀⠀⠀⠀⢽⣿⣿⡯⠀⣠⡞⠛⠍⡄⠁⠀⠀⠀⣾⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣓⣳⡄⠠⠥⣽⣶⡀⠀⣸⣹⣿⣧⡽⢯⠗⡀⠌⣁⢀⣠⠶⠊⣀⡠⢞⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⢀⣻⣦⡱⢿⣝⣷⣤⣈⣹⣿⠏⠀⠈⣶⠿⠶⠄⣠⣖⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣤⠶⠛⠿⢿⣿⣿⢿⣿⣽⣿⣤⣶⣶⡟⢀⣴⣾⡅⠈⠉⡉
⠀⠀⠀⠀⠀⠀⠈⠹⠟⠊⠉⠈⡉⠰⠲⣶⠶⠿⣧⠻⣿⣿⣻⣿⣿⣿⠛⣽⡿⠷⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡶⠖⠾⠷⣾⣿⡏⣿⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⠶⠶⠥⠼⠾⣝⣂⡀⢿⣷⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⢤⣤⠠⢤⠼⠷⠦⠐⠀⠀⠈⠀⠉⢙⠩⠍⠙⠙⠛⠛⠛⠓⠲⠲⠦⢀⡀⠠⠌
⠀⠂⠡⡄⡐⠀⠀⠘⠃⠀⠀⠠⢁⠀⣀⣀⢀⠦⠤⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲⣀⣀⣤⣤⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡻⣭⠩⠁⠁⠄⠤⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⣱⡟⣌⢧⡛⣀⣀⢀⣀⠁⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢻⣛⠛⠁⠛⠃⠻⠎⠻⣦⣀⣠⣴⣤⣤⣤⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⠏⢻⣿⣥⢿⣄⢦⡸⣟⣼⢿⣏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢹⡋⠈⠉⠂⡅⣿⠃⠀⠻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⠀⠀⠀⠘⡧⠶⣶⣦⠀⡇⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⣀⡀⢿⣠⢤⠀⢠⡏⠀⣽⡟⠀⣷⣀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢉⡕⠛⠶⣾⣿⣿⣿⠐⣻⣿⣇⣿⠿⠿⢛⣻⣧⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣦⠚⣻⣤⣶⡖⣫⣿⣷⣶⣐⣶⣾⣭⣿⣿⣿⣿⣏⡉⢈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢩⣿⣧⠀⠄⣧⠀⠀⠈⠉⣙⣇⢉⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣉⠀⠉⠻⠂⠀⠛⠀⠰⡶⠶⠛⢟⣻⣿⣿⣿⡟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⢆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠜⠀⠀⠱⡀⠀⠈⠓⠁⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⡀⠀⠀⠱⡀⠀⡄⠀⠀⢣⢀⡠⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠈⠢⡀⠀⠱⠀⠁⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⠀⠀⠀⠀⠈⠀⠀⢳⠀⠀⠀⠀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡄⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠆⠀⠀⡘⠀⠀⡴⠉⠢⠔⠉⠀⢀⠔⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⡄⠀⡄⠀⠀⠄⠀⡰⠃⠀⠀⠀⢀⠐⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠱⠀⠀⠀⡐⠀⢠⠃⠀⠀⢀⡐⠡⠐⠀⠀⠠⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡁⡠⠁⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠒⠢⢄⠈⠐⢄⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠸⠃⠀⠀⡤⠀⠀⣠⠔⠉
⠀⠀⠀⢀⡠⠖⠒⠂⠈⠀⠀⠀⠀⠀⠀⠉⠢⢄⢑⠄⠀⠀⠀⣇⠀⠀⠀⠀⠠⢁⠠⠀⠀⢀⠤⠊
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠀⠀⠀⠉⠀⠀⠀⠀⠘⡀⠀⠀⠀⠋⠀⠀⢠⠖⢁⠤⠔⠒⠒⠂⠤⣀
⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠶⢄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠎⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⡱⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠓⢄⢣⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠠⠴⠨⠁⠀⢀⠠⠚
⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠀⠀⢀⠖⠈⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠤⠤⠤⢄⡀⠀⠈⠐⠀⢤⠸⣆⣧⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠁⠀⠀⠀⠛⡠⠆⠒⠒⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⠔⠉⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠂⠉⠀⠀⠀⠀⠀⡇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠋

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⡄⠀⢀⡄⠀⢠⡆⠀⠀⡆⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⣰⣿⣆⠀⠀⠀⣏⠀⠀⠀⠀⠀⣾⠇⠀⢸⣿⠀⠀⡇⠀⠀⠀⠠⠀⡊⢑⠄⠄⠀⠀⠹⣦⣄⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠘⠻⣿⠟⠂⠀⠀⠛⠀⠀⠀⠀⠀⠈⠃⠀⠈⠋⠀⠀⠣⠀⠀⠀⢐⠂⠈⡁⠐⡇⠀⠀⠀⠰⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣐⠀⠀⢸⡇⠀⠀⠀⠀⠘⠙⢷
⠀⠀⠀⠂⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠀⡆⠂⢀⠂⢐⠂⠀⣰⠀⡄⡆⠂⠀⠀⠀⡇⢉⣿⣷⠈⢧⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠁⠀⡆⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠹⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣦
⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠻⠏⠉⠟⠇
⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠸⠀⠀⠀⣠⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⣀⠀⠀⠀⢸⠁
⠀⢰⠋⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⣾⣟⡝⢾⡗⡀⠀⠀⠂⠀⣄⠀⠀⠀⠀⣀⠠⠂⠀⠀⠐⢿⡿⣜⣿⣦⠀⠀⠐⠄⠀⣰⣾⣿⣿⣿⣿⣆
⠀⢠⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣽⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⣼⣿⡅⠀⠀⢈⣤⠀⠀⢨⠟⡏⢙⡟⣯
⠀⠘⢄⡀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠂⠀⠀⠀⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⣸⡿⠋⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠒⡀⣠⠒⠀⠀⠀⣆⠀⠀⠀⠀⣠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣦⠀⠀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣽⡄⠀⠀⢀⣿⡄⠀⣿⠀⠀⠀⣤⡤⠈
⠀⠠⠴⠶⠶⠶⠿⠶⠤⠤⠀⠀⠀⠻⠃⠸⠿⠀⠀⠿⠁⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⠻⠀⠀⠘⠻⠀⠀⠁⠀⠀⠀⠛⠇

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣣⠊⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡀⠀⠀⠈⢇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡌⠀⠀⢀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢱⡌⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⡴⠃⠀⡜⠀⠀⠀⠈⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠆⠔
⠀⠀⠀⠈⢣⡀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⠀⠀⠀⠀⠰⡆⢠⠏⠀⠀⠀⠀⢄⠀⠀⠀⠀⠸⣸⠂⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠙⢄⣼⠃⠀⢀⠀⠀⠀⢠⠂⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⢹⠏⠀⡄⠀⠂⠀⠘⠇⠀⠀⠃⠀⣷⠀⠀⠀⠀⠀⠆⠀⠙
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⣇⠁⠀⠸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠁
⠸⠇⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣛⣛⢻⡛⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⢄
⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢹⠀⡀⣀⠀⠀⠀⠀⠆⣊⠑⣢⢉⢛⠐⢺
⠀⠀⠀⠀⠀⠀⠈⢳⣿⡒⠂⠀⠁⠀⠀⠀⠀⠀⣄⣀⡈⠢⢄⣿⣷⠲⠋⠀⠀⠀⠈⠸⠬⣱⣇⠸⢸⣂⠉
⠀⠀⠀⠀⠀⠀⠠⠊⠃⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣡⡦⠤⣀⣄⡄⠀⠀⠘⠒⠋⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠖⠀⣄⣬⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠘⡳⠤⣤⡀⠪⠑⠂⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠢⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⣨⠆⠁⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠈⠑⣃⠴⢁⠂⠐⣢
⠀⠀⠀⠀⣐⠀⠀⠑⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡛⣫⣕⣶⡆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣞⣀⣣⡊⠑
⠀⠀⠀⢐⣀⡀⠠⠑⠖⢨⠁⠀⠀⠀⠀⠀⢀⣀⢉⡚⢬⣭⡼⢿⣜⣇⠀⠀⠀⠀⡠⡀⠓⣤⢵⣿⡿⢇
⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⢴⣿⠟⡁⡏⢩⡟⠈⠀⠀⠀⠀⠀⠜⠐⢋⣱⠗⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠩⠀⠖⡀⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⠀⠀⣀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⣴⣽⣤⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⢀⢴⣿⣿⣿⣀
⠀⠀⢀⣼⣿⣿⣷⣿⣤⢀⡀⢰⣿⢿⣾⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣭⣿⣫⣍⠛⢿⣶⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢱⣿⣿⣿⢿⠉⠯⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⢀⣠⣶⡄⣘⣿⣿⣿⣟⠻⢿⣿⡿⠟⠿⠆
⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣥⣶⠿⠓⠲⠶
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢬⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣷⣴⣾⡟⣰⣆
⠸⣿⣿⣿⣿⣽⣿⣼⠿⣿⣿⣿⣿⣿⣿⣤⡇⠺⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡛⠓⣿⣾⣿⣿⣿⣿⣿⡏⢹⣏⣿⢋⣹⣿⣿⡇
⣤⣿⣿⣿⣿⣽⣯⣾⣻⡟⢻⣿⣿⢿⢿⠉⡇⠀⣿⠉⢹⡟⣿⢹⣿⣿⣻⣿⣿⣿⠷⡿⢛⡃⣼⣿⣿⡿⠀⢸⡭⢽⣼⣿⣿⣿⣿
⠈⠙⢛⣿⣿⣿⡿⢼⢛⡇⢺⠻⢭⢴⢺⢹⠃⠘⢿⡇⢈⡟⢿⠙⢻⡟⣙⡏⣿⠁⠀⡇⢸⠀⢸⣟⣉⡟⠀⢸⡄⣼⣹⣿⣿⡟⣧
⠀⠀⠠⣿⡏⢙⡇⣻⢀⡇⢸⣾⠀⢸⢸⢸⠁⠀⢸⡇⢐⡇⢹⠀⢸⠀⠉⡇⣸⢰⡂⡇⢸⠀⢸⢨⠀⡇⠀⢸⠀⢸⢸⣿⣿⡗⡃
⠀⠀⠀⡋⣇⠈⡇⢹⠀⡇⢸⣿⣶⢸⢸⢈⠀⡇⢸⣷⣼⣇⢸⢸⣸⠀⠀⡇⣾⣿⣇⡇⢸⠀⢸⣤⠀⡇⠀⢸⠀⢸⠈⠹⠿⡇⠃
⠀⠀⠀⣇⡇⢠⡇⣼⣤⣷⣼⣿⣿⣼⣼⣷⣾⣿⣼⣿⣿⣷⣾⣼⣿⣿⣇⣷⣿⣿⣿⣷⣸⣇⣸⣿⡄⣷⣴⣸⠀⢸⠀⣀⡚⡇⠃
⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠙⠛⠋⢻⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠈⠉⠉⠙⠋⠙⠀⠈⠻⡿⠛⠛⠉⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⠀⠀⠀⠈⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠂⠒⠀⠈⢆⠀⢀⠎⠀⠘⠒⠐⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠈⢲⠎⠀⠀⠀⢀⠀⠘
⠀⠀⠀⡠⢄⣀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⡄⠀⠀⠀⢀⣀⠤⡀
⠀⠀⠀⠐⡀⠀⡉⠐⠀⠘⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠘⠆⠐⠈⡡⠀⡰
⠀⠀⠀⠀⢱⠀⠈⠑⢄⡀⠀⠘⡀⠀⠈⠐⠢⠜⠀⠀⠀⠀⠱⡀⠀⠀⡰⠁⠀⠀⠀⠐⠤⠒⠉⠀⠀⡈⠀⠀⢀⠔⠉⠀⠰⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠙⢦⡀⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⣄⡔⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠃⣠⠞⠁⠀⠀⢠⠃
⠀⠀⢀⡀⠀⠠⠂⠀⠀⠀⠀⠙⢦⠀⠀⠀⡀⠀⠀⠘⠄⠀⠀⠀⠈⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠢⠀⠀⣀
⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠱⡀⠀⢰⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠀⠀⡰⠁⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠉⠐⠂⠤⠀⡌⣄⠀⡀⠀⠀⠀⠰⡀⠀⠀⠀⠀⡰⠀⠀⠀⠀⡀⢀⡌⡤⠠⠄⠒⠈⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡇⠀⠀⠀⠀⠑⡄⠀⠀⡐⠁⠀⠀⠀⠀⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⣀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠘⠃⠀⠀⠈⠉⠁⠀⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠒⠂⠈⠉⠉⠀⠀⠀⠛⠠⠄⣀
⣀⠤⠐⠂⠉⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠒⠠⢄
⠈⠢⢄⠀⠀⠀⠀⢀⣀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⢀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠉⡩⠖⠀⠐⠒⠒⠒⠒⠀⠀⠀⠄⣨⠷⢯⡤⠄⠀⠀⠀⠒⠒⠒⠒⠀⠐⠮⡉⠁⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡼⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⡠⠊⢀⠔⠁⢸⠀⠑⢄⠈⠢⡀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠔⢊⠤⠊⠁⠀⠀⠈⠀⠀⠀⠉⠢⢌⠒⢄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠇⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠧⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣠⢠⣾⢀⡄
⠀⠀⠀⠀⠀⢠⡦⠀⡀⠀⡜⠛⠀⠀⠀⢰⡇⢿⣇⡞⢀
⠀⠀⠀⠀⠀⠋⢤⠀⠛⣾⡟⠆⠀⠀⠀⢸⣃⣇⢸⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⡧⠀⠀⠀⠀⠘⡋⠉⠻⣣⣾⣀⡀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡇⠀⠀⠀⠀⠀⠁⠀⢠⠈⠹⠿⠃⠀⠀⠀⠀⡠⠊⠁⣀⠴⠂
⠀⠀⠀⡤⢀⡀⣿⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⢀⣼⠋
⠀⠀⠀⠀⣀⠙⡷⣴⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣤⡐⠀⠀⢠⣼⠉
⠀⠀⠀⢱⠋⣼⣿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠝⠛⠙⠀⠀⠈⠊⢅⣀⣀⣠⠤⠐⠀⠀⠂
⠀⠀⠀⠘⣰⡟⢻⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⡵⠂⠀⠀⠀⢤⣤⣤⣬⣿⣿⣧⣀⠀⠀⠀⠈
⠀⠀⠀⢰⡏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣏⣹⠛⢿⠷⠤⠄⠀⠀⢀⠠
⠀⠀⠀⢸⢷⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⡠⠐⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡇⠀⡜⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠢⣀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⡃⠀⡃⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⣽⠾⠧⠇⠀⠀⠀⠀⠀⠀⣶⣥⡒⠂⡐⢾⣶⢄⣀
⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠛⠛⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢸⠀⠀⠛⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠉⣴⣯⡆⠀⠀⠀⠀⠀⠰⣀⠿⣿⣦⡟⡂⢴⠈⠖
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠂⠋⠈⠁⠀⠄⠱⠈⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠤⡀⠈⠁⠀⠀⠀⣠⠱⢦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠁⠀⠀⠀⠀⠀⠸⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠤⠄⠄⠀⠀⡀⠀⠀⠀⠴⠖⠿⠙⠻⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠩⠄⠀⠀⠀⠀⠺⠋⠀⠀⠈⠀⠀⠀⠀⠽
⢠⣀⣀⠀⠀⢀⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠤⡀⠀⠛⠃
⢨⡙⠉⠫⠽⣾⢋⣿⣯⡀⠀⠀⠀⠰⠛⠵⠂⠐⠿⢇⣠⢴⣶⠀⠀⠀⠐⢄⡀⢀⡀⠀⠀⠀⠀⣘⣿⠀⠛⠀⠀⠈⠀⠀⠀⠂
⠈⠁⠓⠂⠀⡿⠟⠋⠁⠁⠀⠀⣀⢠⠀⠀⡆⡰⠀⠀⠁⠀⠀⠀⢠⠆⠀⠀⠋⠉⠉⣠⣄⠀⠀⠀⠁⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠓⠀⠈⢹⡦⠄⡏⢣⠀⡆⠰⡄⠐⡄⠈⠤⡀⠴⠀⠀⠾⠿⠃⠸⠃⠀⠒⠚⠋⠀⢀⣿⣧⠀⣼⣧⡀
⠀⢰⣍⣿⣿⡾⢂⡄⠀⣀⣀⣀⣀⡄⠀⡀⠀⠀⠀⢠⠆⠀⠀⡀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠄⠀⠀⢸⣿⣿⢸⣿⣿⡇
⠀⠀⠙⠉⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⢶⠘⠄⠀⠃⠙⠀⠳⠀⠃⠈⠂⠓⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠈⠀⢸⣿⣿⣧
⠀⠠⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⡿⠻
⠀⠀⠀⠀⠀⠀⠈⠃⠀⡏⠀⠀⠀⢀⠴⠤⡀⠀⠀⠀⠀⢀⣠⠀⢀⣄⠀⠀⠀⠦⣄⠀⡀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡰⠀⠁⠀⠀⠀⠿⠏⣸⠳⠀⢠⠁⡀⠻⠃⢀⣄⣄
⢠⠀⠀⣀⠀⠀⠀⣼⠇⢀⣷⣿⣿⠀⠀⣢⣀⡀⣤⠀⠠⠀⠖⠀⠀⠦⠀⠄⠀⠀⠀⠀⠀⠀⠰⣤⣾⣦⣤⢀⢸⣿⣧⣿⡄
⠀⢀⠔⠁⠀⢰⡐⠋⠀⠀⣱⢛⡄⠘⡾⠉⠛⠛⠁⠀⠀⢢⠀⠀⠀⢀⠞⠀⠀⠐⠂⠛⠃⠀⠀⣼⣿⠻⠟⣾⠏⣿⣿⠀⠙⢷⡄
⠀⠸⡄⠀⠀⣸⠃⠀⢠⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠰⣰⡟⠀⠾⠟⠀⠀⠀⠃
⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠁⠀⠀⠀⠀⠈⠀⢠⡤⠄⠀⠀⠀⠂⠀⠀⠀⠉⠠⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢺⣦⠙⣴⡾⠀⠀⢠⣆⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠰⣶⡜⠟⣁⣀⠀⠀⠉⠁⠉⠀⣰⡄⠘⢏⣯⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⠶⣋⣋⠀⢀⠉⠉⠘⠛⠋⠀⠀⢀⡇⠀⠀⣟⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠀⠀⠈⠒⢦⡀⠀⠀⠀⣼⡥⠚⠉⠀⠀⠀⠀⠀⠀⣄⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⣀⢀⣙⣆⠀⢰⡟⠀⢰⣷⢀⣤⠀⠀⠀⠀⠻⠫⠷⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢫⡾⠀⠀⠀⣴⡿⠈⠹⣧⣿⠁⢶⣦⡟⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⣤⡀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⢻⣿⠀⠀⠉⠀⠀⢀⣀⠤⠤⠖⠀⠀⠀⣉⢽⣦⣄
⠀⠀⠀⠀⠘⠿⠿⣎⣙⠀⠀⠙⠇⠀⠀⣤⣤⡻⢇⣶⠆⠀⠀⢸⣿⠀⠀⢀⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠻⠇⠉⠁
⠀⠀⠀⣤⡀⠀⠚⠛⠁⣀⣠⣤⣬⣴⣤⣈⣛⡛⠈⠁⠀⠀⠀⢸⣿⡄⣰⠏⠀⠀⠀⣀⢼⡇⣀⠀⠀⠀⠀⣴⣠⣶⠇⠀⠀⣀⣤
⠲⣶⣤⠛⠃⢀⣠⣀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣷⣄⡀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠻⠇⠟⠋⠀⠀⠀⠀⠙⠱⡶⠆⠀⠀⢛⠣⣶⣶
⠀⢀⣾⡟⠀⢸⠏⠻⠀⠀⠀⢦⣤⡀⢀⡠⠒⠚⠛⠛⠿⣿⣦⡀⣿⣿⠀⠀⠀⠀⣀⣴⣶⡶⠶⠶⣶⠒⠲⠒⠒⣒⠈⠀⠀⠘⢿
⠀⠀⠁⠀⠀⠈⠀⠀⠘⠻⣳⡄⠉⠉⣴⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⣄⣻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠱⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⣤⠴⣤⡁⠂⢄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡤⢾⣦⡰⡟⠻⡉⠉⠙⢦⢌⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⠁⠈⠁⠈⠛⠒⣻⢏⠎⣂⢰⠀⠀⣼⠀⠑⡈⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠒⡄⠀⠀⠀⠀⠎⢀⠇⠯⡀⠘⠔⠁⠀⠀⠀⠈⡄⢂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⠀⠀⠀⠀⠉⠀⠖⠺⠀⠀⠀⠀⠀⠸⣮⠿⡀⡀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⢀⠀⠀⢄⠀⠀⢀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠾⡇⠁
⠀⠀⠀⠀⡀⠨⠰⠉⠉⠉⣷⠨⠀⡀⠈⠓⢄⣇⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡄⡀⢀
⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⡉⡄⠀⠀⠀⠙⠶⠒⠂⠀⢀⠀⠀⠀⠀⠀⠑⠂⢲⢁⠁⠈
⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠵⠤⠤⠤⠤⠤⡧⠾⠴⠓⠲⢟⣚⡛⢍⠉⠙⠛⠛⢋⠆
⠀⠀⢰⠀⠘⠠⡷⠀⠀⠀⠰⡧⠈⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠈⢻⡆⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⠄⠁⠰⢢⢀⠀⠀⠀⠀⠰⠀⠀⡠⢄⠙⠒⠚⠁⠃⠀⠀⠀⠀⡔
⠀⠀⡄⠀⡠⠐⠒⠒⠒⠒⠒⠒⠠⠀⠀⡷⢤⡁⡐⠂⠀⠒⠀⠒⣘⡜⡠⠀⠡⠄⠀⠬⠅⠀⠀⠈⢆⠀⠀⠠⠀⠀⠀⠀⠀⡠⠂
⣆⠀⠀⠀⠃⠤⠤⠤⠤⠤⠤⠤⠄⡆⠀⠂⢀⠧⠀⢀⡀⠀⠀⡀⠠⠖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠦⠀⡖⠐⠀⠂⠈⠀⠠
⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠠⠀⣠⠑⠶⣷⣴⡀⠀⠀⠀⠀⠀⡔
⠣⣘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡠⠂⠐⠒⠓⠒⠒⠓⠒⠀⢀⠀⠀⠀⠀⠀⢀⡤⠊⠈⠁⠐⠃⠀⡀
⣀⣈⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣌⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣎⣶⣶⣶⣦⣬⣤⣦⣤⣖⣒⣒⣚⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



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

⠀⠀⠀⠀⠀⠀⠀⢰⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠙⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⣴⣀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠳⣤⠀⡀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡘⠷⣧⣴⡂⣀⠻⡇⠀⠀⠀⠀⠘⠠⡀⠀⠘⠶⢦⣴⣿⡧⠔⠁⠀⠀⢳⣸⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠻⣥⣈⣻⣿⣿⡾⠀⢠⠤⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣗⠀⠀⠀⠀⢹⣿⣃⡠⠉⠙⠋
⠀⠀⠀⠀⠀⢠⢁⡤⠴⠆⠶⠶⠿⣿⠿⣿⣧⡠⣷⠀⢀⠀⠀⠁⠀⣠⣤⠶⠋⠀⠀⠛⢆⡀⠀⣤⣾⣿⢻⣍⢛⠠⢄
⠀⠀⠀⠀⠀⠈⠈⠒⠤⠀⢀⣤⠤⠾⣄⠀⠉⠧⢿⣄⡽⠒⠀⠂⠀⠑⢆⠀⠀⠀⠀⠀⠈⠁⠀⠘⠿⠿⠏⠉⠙⠷⠬⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣟⢠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡄⡄
⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢣⠈⣄⠀⠀⠀⡞⠀⡄
⠀⠀⠀⠀⠁⢀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣼⡀
⠀⠀⣀⠀⠀⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⢨⣀⣴⣿⠷⣠⠀⣠⠔
⠀⠈⠀⠀⣀⠀⠀⢧⠀⠀⠀⠀⠐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⢀⣄⠤⣙⣿⣿⣿⣷⣶⡈⠀⠀⠂
⠀⢀⡠⠜⠁⠀⠀⠼⡖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡇⣆⡏⠀⡀⠀⠀⠀⠐⠂⠀⠉⠿⡿⠟⠿⠿⣿⡂
⠀⠸⠀⠀⣄⠍⠀⠀⠉⠀⡀⠀⠀⠲⠄⠀⠀⠀⢀⡃⢀⠹⣿⣠⣨⣾⡶⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠁⠀⠀⢀⠀⢁⠉⠚⠉⠀⠀⠀⠀⠀⠰⢄⡪⣤⣰⢳⣿⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⠈⣑⢿⡻⡘⣿⣗⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡇⠀⢸⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⣿⠇⢇⠘⢻⣃⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⡀
⠀⠀⠀⠀⣤⡀⠆⠸⠀⢐⡤⠂⢐⠀⠀⠀⠀⠀⠠⠄⠉⠙⢳⠄⢧⡘⡵⢊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⣸⣿⣰⠁⡠
⠀⠀⠂⠀⠨⣍⠳⡟⢤⣠⣦⠄⠚⠚⠀⠘⠁⠀⠀⠀⠄⠚⣉⡥⠄⢣⣘⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⣿⣇⠎
⠀⠀⠀⠀⢢⣝⣦⣶⠈⣿⣡⣴⣷⡶⠂⢀⠀⡀⠀⠀⠀⠈⠐⠚⠿⠶⣛⠅⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢈⣻⣷⣿⠃
⠠⠀⠀⠀⠀⢉⡽⠿⠿⣿⡿⠑⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠬⢝⣿⡏
⠀⠀⠀⠀⠀⠨⣀⠀⠠⡿⠛⣦⣤⣴⣶⣍⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠴⠾⢿⡦⠂
⠀⠀⠀⠀⠀⠀⣦⠀⠀⣏⠉⣡⠋⠯⠙⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣥⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿