Chemicals Emojis & Symbols

⠀⠀⠀⠅⠀⠈⡆⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟
⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⡟⠿⠿⠿⢰⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠐⠈⠐⠀⠀⠀⠀⠀⠀⢰⠀⠀⡆
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢀⡠⠃⠀⠀⠀⠸⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣆
⠀⠀⠀⠇⠀⠀⡇⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢸⣤⣀⣠⣤⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⣿⡇⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⢸⣿⣿⣿⣿⣸⣿⠀⠀⠀⠔⠀⠀⠀⠀⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢿⣿⣭⣿⣯⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡇⣿⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢀⣿⣿⣿⣇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠸⣿⣿⣿⣱⣿⣿⠀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⢻⠀⠙⠿⢻⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣸⠀⢀⣀⣸⠀⢠⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠿⠿⠿⡿⠿⠿⠿⡿⢿⠇⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣤⣼⣿⣿⣤⣼⣿⣷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣷⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢹⣿⣿⠀⢹⣿⣯⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣇⣀⣿⣿⣇⣸⡀⠀⠀⠀⠀⠀⠀⢀⣇⣘⣿⣟⣀⣘⣿⣏⣀⣘⣿⣋⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡀⠲⠗⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠒⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⠦⠤⢄⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠐⠧⡀
⠀⠀⠀⠀⠀⢀⠘⠁⠀⢰⠂⠀⠐⢦⠄⠐⠀⠀⠀⠀⠀⠀⠀⢠⣽⡆⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠮⠀⠒⠒⠀⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⣉⣤⠄⠀⠀⠀⠀⠀⠀⢆⠉⠓⠆⣄⡀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠢⠤⠤⠄⠀⠐⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⡀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠘⡶⢌⡉⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢴⡶⠖⠛⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⡠⠖⠉⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠬⠯⠄⠈⠐⢦⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣳⠒⠉⠛⣶⡀⠀⠁
⠀⠀⠀⠀⢀⡀⢠⣏⣀⣀⣀⣀⣀⣀⣀⣀⣆⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢷⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⢨⢇⣀⣀⣀⣸⣧⢰
⠀⠀⠀⡄⠻⢁⡎⠀⠀⠁⠈⠁⠀⠈⠉⠩⠉⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠃⠰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠁⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠡
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⣀⣀⣀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠀⠀⠂⠀⠀⠀⠀⠚⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠒⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢈⣯⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢻⠁
⠀⠀⠀⠁⠈⢳⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠨⣭⣙⡋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣷⠀⠀⠘⠛⠃⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠈⢣⣧⣀⡀⠀⠠⠴⣶⠿⠋⠀⠀⠀⠛⠧⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⢲⠦⠄
⠀⠀⠀⠀⠀⠦⠝⠁⠀⠀⠀⡀⠉⠀⠀⠀⠀⠐⠒⠒⠟⠄⠀⠀⠀⠀⠀⢠⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠒⠛⠿⡓⠂⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢲⡄⠉⠀⠁⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡰⠀⠠⠀⠀⠀⠀⠀⠀⢡⠿⡄⠀⠀⠀⢀⠤⠀⠤⠄⠀⠀⠀⠈⠤⠮⠂⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣤⣶⣤⣶⣦⣶⣤⡤⠁⠀⠀⠀⠀⠀⠀⡏⠀⣿⡀⢀⠆⠀⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡬⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢹⠈⠯⠠⡄⡄⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠀⠀⠀⢛⡄⠀⠀⠀⠀⠀⠀⠸⠀⡔⠛⢷⠏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⡤⠐⠈⠈⠁⠢⣄⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠐⠛⠓⠒⠒⠒⠒⠒⠛⠛⠂⠀⠀⠀⠀⠀⠁⠐⠒⢲⣤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣞⣛⣛⣛⣛⣛⣛⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⡀⠀⠀⠀⢿⠣⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⢐⡇
⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⣶⠀⠀⣼⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠢⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠠⡇⠀⡀⠀⣿⠀⢰⣿⢿⣿⣿⣿⣿⡆⠀⢀⣀⣀⣀⣀⣀⣀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⡀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣏⣉⡉⣉⣉⣉⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⣿⣼⣿⣽⣿⣿⣿⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠉⠉⠉⠁⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠭⡇
⠀⠀⠀⠀⠀⢀⡼⠇⠰⠆⠀⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣉⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇
⠀⠀⠘⣟⣿⣿⣿⣼⣿⣯⣿⣿⣿⣿⣿⡟⠉⠉⠉⠹⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠘⢾⣿⣿⣿⣧⣽⣿⣿⣿⢟⡟⠁⠀⠀⠀⠀⠙⠯⣿⣿⣿⣿⣿⣿⣿⡯⠟⠁⠀⠀⠀⠀⠀⢰⣯⣿⣿⣿⣿⣿⣿⣯⣷⠄
⠀⠀⠀⠀⠀⠙⠺⢽⣿⣿⣿⠽⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣆⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢉⣉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡌⢋⢩⠀⠁⠀⠀⠀⠀⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢸⠘⡄⠀⠀⠀⠀⠬⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣇⣃⣀⣀⣀⣉⣭⣁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⠹⠉⠉⠉⠉⠭⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠇⠀⠀⠸⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⡄⡇⠀⠀⠉⣭⠀⣿⡇⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠍⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢣⢱⠀⠠⠄⠈⠀⣿⡇⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠙⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠅⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⡸⡀⠀⠲⣶⠀⣿⡇⠀⠀⠀⠀⠀⢻⢴⠒⠒⢒⢶⠒⢒⣖⠚⣆⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⠀⠀⣇⡇⢀⣀⣒⠀⣿⡇⠀⠀⠀⠀⠀⠘⢯⣧⡀⠈⠉⣔⡌⢁⢜⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠅⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣲⣶⣾⣶⣶⣶⣶⣫⠜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠮⣷⣶⣾⡾⠷⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣷⣶⣶⣿⣽⣦⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠶⠶⢶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⠶⠶⠞⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡟⠉⠉⠉⠉⡟⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⣀⣀⣀⣀⡗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣀⣀⣀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠉⢉⣉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠶⣻⡼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠐⠒⣳⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠒⢚⣇⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠐⠒⣺⡜⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢴⠒⠒⢲⣶⠒⠒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠐⢒⣻⣹⣧⠀⠀⠀⠀⠀⠀⠀⠸⡾⡄⠀⠳⠼⠁⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠧⢿⡆⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠘⠿⠂⠾⠇⠀⠀⠀⠀⠀⣠⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⡢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢀⣀⣬⠄⠨⠷
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⣾⣛⣂⣠⠤⠞⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⢸⣿⣿⠟⠋⠉⠉⠁⠒⠂⠉⠭⠬⣤⣐⡤⣤⣶⣿⡥⠋⠀⠀⠀⠀⠀⠀⡔⠐⣦
⠀⠀⠀⠀⠀⠀⢘⣟⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠈⢿⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡷⠶⠋
⠀⠀⠀⠀⠀⢰⣿⡿⣷⠀⠀⠀⠀⠙⠲⢤⣄⡴⠃⠘⣷⡀⠀⠀⠀⢀⣿⠞⠁⠀⠀⣀⠀⠀⠀⢀⢠⡼⠁
⠀⠀⠀⢀⣴⢻⠛⣿⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠒⠋⠁⠀⠀⠀⡏⠉⣷⠒⠲⢇⣀⣿⡀⢀⣀
⠀⠀⢸⡿⣷⠧⣤⣼⠄⠤⢿⣿⡀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢀⣠⣼⠉⠀⠱⣇⢈⡷
⠀⠀⢻⣯⣿⣻⣿⣓⣖⠂⣹⣿⠃⠀⠀⠀⠀⠀⠙⠻⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣼⠇⠀⠀⠈⠉⠁
⠀⠀⠀⠉⠛⠛⠒⠶⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡿⠿⢿⠆
⠀⠀⠀⠀⢸⡿⢯⠇⢸⠯⠿⡇⢻⠿⣿⠃⠻⠍⢹⠂⢻⣿⢿⠀⠀⠀⠀⠀⠀⣈⣁⣀⣀⡀⠀⢠⡁⠀⢸
⠀⠀⢀⣰⢸⣶⣶⡆⢸⠀⢀⡇⢸⣿⠉⠀⢸⡄⣸⠀⢸⠉⠉⢰⣄⡀⠀⠀⠀⠙⠷⠚⢺⠃⠀⢸⠁⠀⠠⡀
⠀⠀⢨⣿⡿⣿⠿⢃⣸⣦⣴⢃⣸⣿⡴⠂⢼⢤⡼⠀⢹⣤⡴⢛⡇⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⢁
⠀⠀⠠⣿⢰⣷⢾⠞⢲⣷⣶⡏⢳⣶⠒⠂⢲⠶⢲⠓⢲⠛⢻⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⠀⠈⠄
⠀⠀⠀⣿⢸⡁⢸⠇⢸⠀⠀⡇⢸⣿⠀⠀⢸⠀⠈⠀⠘⠀⢀⢸⡇⠀⠀⠀⠀⢀⠀⠀⢸⡀⣶⣶⣶⢒⣒⣲⣦
⠀⠀⠀⢛⢸⠁⢸⡇⢸⠀⠀⡇⢸⣿⠀⠀⢸⠀⢠⠀⣰⠀⢨⢸⡇⠀⠀⠀⡠⠚⠀⠀⠀⠛⢯⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠠⣸⢸⠀⢸⡇⢸⠀⢀⡃⢸⡿⠀⠀⢸⠀⢸⠀⣻⠀⢸⢸⡇⠀⠀⣾⣒⣒⠒⠀⠀⠀⣒⣶⠀⠀⠀⠀⣴⣿
⠀⠀⠐⣿⢼⣆⣼⠇⢸⣤⣼⣇⢸⣅⣰⠄⢼⣄⣼⠄⣿⣀⣼⢼⡇⠀⠀⣿⣿⠉⠉⠉⠁⠉⢹⣿⣶⣶⡶⡧⠿⠟
⠀⠀⠐⣯⣤⣿⣽⣧⣤⣭⣭⣭⣤⣍⣥⣤⢤⣝⣯⣥⣬⣿⣿⣦⣷⡀⠀⠹⣿⣤⣆⡀⣀⣶⡾⠃
⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⡠⠲⡄⠀⠀⠀⠈⠉⠉⢒⣤⡄⠀⠄⢠⣀⣀⠀⢠⡤⠀⢠⡄⣀⠆⠠⠄⣔⣰⢀⡀
⠀⠀⣔⣿⡀⠀⠀⢏⠀⠈⠻⢧⡀⢘⠀⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠈⠀⠀⢀⣠⣤⡀⠀⣠⣤⣤⡀
⠀⠀⠀⣘⠇⠀⠀⣈⢦⠒⠋⠉⠉⢫⡉⠑⢢⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⡤⠘⠚⠛⡃⠀⢹⠑⣺⠀⠤⠀⢀⡀⡀
⠀⠀⢠⣿⠀⠀⢜⠁⠀⢹⣄⠘⠃⢠⠑⣄⠜⠀⠀⠀⠀⠀⠿⠯⢽⠀⠀⠀⠀⣃⠀⡁⠀⠠⠀⡇⠀⠀⠀⠠⠋
⠀⠀⠀⠘⣦⡀⠈⠹⠂⠸⠄⠓⠶⣞⠉⡱⠰⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⣯⣀⡇⠀⢀⣀⡇⠀⠀⠀⣶
⠀⠀⠀⠀⣡⠁⠀⠀⠀⡀⢆⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠢⡀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⡀⣿⡀
⠀⠀⠀⠀⠿⢆⠀⠀⠀⠁⠈⠉⠀⣀⣠⡤⢄⠀⠀⠀⢰⠁⠀⠀⠀⠀⢱⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⠈⠁⣿
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠒⠛⠉⠁⠀⠀⠈⡆⠀⠀⠈⠒⠒⠒⠒⠈⠁⠀⠀⣿⣿⡇⠀⢼⣿⡇⠀⢀⢠⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠤⠶⢢⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠠⠀⡞⠉⠉⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⢀⢀⣠⠀⠀⠀⡦⡀⠐⠒⠐⠄⠒⠂⠄⠻⠀⠀⠘⣿⠃
⠀⠀⠀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡀⠈⠉⠈⠉⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⢠⣤⡄⢀
⠀⠀⠀⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠆⠀⢀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠁⠀⠀⠀⣸⠀⠉⠐
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡊⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⡠⠊⠀⠑⢄⠀⡠⠊⠀⠑⢄⡀
⠀⠀⡄⢞⠒⠘⡄⠀⠀⢣⠀⠀⢀⣀⠀⠠⠇⠀⠀⠀⠠⠂⠀⠀⠐⠒⠎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢸⠀⠀⠘⢄⠀⠈⠆⠊⠁⠀⠀⠀⠀⠐⠆⣠⠡⠄⠗⢀⠀⠀⠘⡀⠀⠀⠀⢠⠃⢁
⠀⠀⠤⢸⠠⠀⠀⠀⠙⠢⠤⠤⢠⡄⠀⠀⠀⠀⠉⡄⠐⢨⡄⠂⠀⠀⠀⠰⠤⠀⠠⠜⠀⢠⠒⠂⢉⣥⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠂⠛⢢⠁⠀⠀⠀⠀⠐⠁⢰⣵⣕⠀⠀⠁⣀⠀⠸⢿⠟
⠀⠀⠠⣼⠠⠤⠤⠤⠥⠤⠤⠤⠤⠼⠤⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠅⠀⢠⠀⠉⠀⢀
⠀⠀⠐⠏⠀⠀⠀⠀⠚⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⡤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⠀⣀⣀⡀⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠐⠂⠣⢄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣷⣿⡿⠫⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣟⠉⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⣿⣿⢯⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⣀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠳⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠾⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡉⠀⠀⠀⠀⠀⠀⠀⠈⡉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⠑⠒⠒⠀⢀⠀⠀⣀⣤⠂⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⡔⢶⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠑⠒⠈⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠉⠻⣦
⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠂⠤⠤⠀⠒⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⣼⠏⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⣸⡏⠀⠀⠀⠀⠀⠸⠀⠤⠀⠀⠀⠀⠠⠀⢀⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⢸
⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⢀⣠⣿
⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠈⠙⢿⣿⣿⣶⣦⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⣶⠿⠟⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠹⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⡦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠲⠛⠈⠛⠋⠘⠷⣠⣶⣄⠞⠃⠙⠛⠁⠛⠆⣴⣶⡄⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠲⡦⣠⣤⣄⢠⠶⠙⠛⠋⠶⡄⣠⣤⡄⣤⠖⠃⠀⠀⢠⣦⣦⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠙⠛⠋⠶⣄⣠⣤⣄⠀⢀⣀⣀⣀⣀⣀⣀⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠈⣩⣭⣭⣭⣭⣭⡍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣶⣬⣭⡅⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣶⣶⣿⣿⣿⣷⣶⣬⣍⣛⣛⣛⣛⣛⣩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠩⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⠫⣤⢹⣿⣿⣿⣿⡿⢛⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣷⣶⣿⣿⣿⣿⣿⣇⠿⠗⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠙⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡑⡤⡀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡄⢠⡤⣤⠀⣤⢤⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠈⠂⠀⠀⡎⠀⠀⠀⠄⠠⠀⠀⠀⠈⠁⠺⢖⡄⠀⠀⠀⠀⠀⡇⠈⠀⠈⠀⠁⠀⡏⠈
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡤⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⡀⢠⠀⢸⠀⡇⢀⡄⡀
⠀⠀⢸⡏⠉⡆⠀⠀⠀⡇⠀⠀⡇⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⡅⠀⠀⠈⡀⠀⠈⡆⡶⠲⠂⢰⠀⢐⠀⡆⢀⠂⡆
⠀⠀⢸⡇⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⣌⡀⠀⢀⣀⡁⠀⠀⠀⡆⠉⠉⠁⡇⠀⠀⡇⡇⠀⠀⢸⠀⡆⠀⡇⢸⠀⡇
⠀⠀⢸⡁⢀⣇⠀⠀⠀⣇⡀⣠⠇⠀⠘⣆⡀⢀⡰⠃⠀⠀⢸⡁⠀⠀⠀⣧⠀⢀⠇⠱⠜⠀⠀⠦⠃⠀⠱⠜⠀⡇
⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠈⠃⠀⠋⠀⠀⠀⠀⢆⠉⢂⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⢐⡂⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⢜⠀⠠⡀⠑⠄⠀⠀⠀⣀⠴⡀
⠀⠀⠀⢀⠀⠀⠆⠀⠀⢰⣒⣒⣒⣒⣒⣒⣒⡂⠀⠀⡸⠁⠀⢹⡀⠀⠀⠀⠀⠀⠈⢣⡙⢦⠀⠀⠀⠀⡅
⠀⠀⠄⠁⠀⠀⠀⠀⠀⢰⠀⡇⢰⠀⡤⢰⠀⡇⠀⢠⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠑⣤⡷⠀⠀⡎⠽⠀⠈⡆
⠀⠀⡖⠀⠀⠀⠀⢰⠄⠸⠀⡇⢸⠀⣧⣸⠀⠇⠀⡟⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⡀⠀⡇
⠀⠀⠙⠦⠤⠤⠴⠋⠀⠸⠀⠈⠁⠀⠈⠉⠀⠇⠀⠳⠠⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠧⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⢷⡄⠀⠀⠀⠀⢰⡟⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⣸⠇⠀⣴⠛⢷⡌⠷⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠿⣧⣠⣤⣤⣀⣠⠞⠙⠛⠛⠉⠀⠀⠛⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢹⡇⠀⠀⠀⠀⠚⣿⠛⠛⢻⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⢀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣠⠞⠙⠛⠋⠉⢻⡶⠟⠶⣄⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠈⢿⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣠⡿⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⢠⡟⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣀⠀⠀⠀⠀⣀⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠉⠙⠛⠛⠛⠉⠁⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠀⡀⡼⠿⠄⠀⠀⠀⣠⠤⡤
⠀⠀⠀⠀⠀⠘⢶⢿⣿⡽⠿⣿⣿⠀⢠⠀⠀⠀⠀⣠⡞⡇⠀⣠⣶⣴⣾⡟⢦⡀⠀⠀⠈⠻⡵⠃⠀⠀⠀⠈⣁⣨⣦⠤⠤⠤⠴⠶⠒⠊
⠀⠀⠀⠗⠀⠀⢸⢷⠀⠀⠀⢽⣿⠀⠀⠀⠀⠀⣰⡷⠛⡄⠀⣻⣿⢟⣽⡓⡆⢳⠘⠤⡀⠀⠀⠀⠀⠀⠀⡎⢉⠁⠈⠲⣄⠀⣎⠀⡶⢀
⠀⠀⠀⠀⠀⢀⠎⢌⠀⠀⠀⣼⢺⠀⠀⠀⠀⠀⡷⠒⠚⣃⣀⠈⠉⠛⠶⠞⣁⣸⠀⠀⠀⠀⠀⢰⠶⠰⡶⠙⢄⠀⠀⠀⠀⠳⡀⠀⠀⠉
⠀⠀⠀⠀⠀⡜⣀⣬⣅⣤⣴⣶⣼⡆⠀⠀⠀⠀⢱⡀⣾⢋⣩⣳⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⡰⠚⠋⠑⠒⢿⣄⡐⣈⢀⡧⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠐⠅⠑⢌⡻⡿⠟⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⢀⡀⣧⡀⠐⠊⠀⠁⠀⠻⡉⠉⠀⠈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡠⣒⢦⡀⠀⠀⣈⠉⠉⠉⠉⢁⡤⣄⠀⠀⠀⠘⠛⣈⡶⠟⢛⡓⢶⡒⠒⠒⠚
⠀⠀⠀⠀⠘⢿⣿⣛⣿⣿⣿⣿⠿⠟⢱⢹⠧⢗⡇⠀⠸⣱⠗⠀⠀⠀⠘⠢⠚⠀⢰⣲⡀⠘⠉⠀⠐⠀⠀⠀⢱⠀⠀⠀⠖⠫⠰⠄⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⠀⣀⠀⢀⣀⡀⢀⣤⡘⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⢀⡞⠉⠀⢸⡄⠴⡀⢸⠤⠄⡰⣆⠶⡀⢸⠀⠸⢄⠀⠀⣏⠀⣤⢴⡁⠀⡏⠁⠀⠈⠉⢿⣾⡟
⠀⠀⠀⠀⣦⢴⢠⡆⣶⢠⠀⡄⣄⡄⣀⠈⠦⠤⠄⠘⠀⠀⠃⠘⠒⠀⠁⠉⠀⠁⠘⠀⠐⠋⠀⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠃⠈⠈⠀⠁⠈⠀⠀⠋⠃⠛⠰⠀⠀⠀⠀⢀⡀⢀⣤⣤⠀⠀⢀⣤⡀⢀⠀⢀⣤⣤⡄⣀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠲⠲⠶⢤⣀⣀⣀⠀⠀⠀⠀⢼⠀⢸⠀⠀⢸⠉⣿⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠘⠁⢸⠿⡏⠉⠉⢩⠉⡇⠈
⠀⠀⠀⠀⢀⠠⠄⣰⠋⠀⠀⠀⠈⠁⣀⢹⣇⠜⠁⠀⠀⠀⢹⢶⣾⠀⠀⢸⠀⣿⠀⠀⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠠⡇⡇
⠀⠀⠀⠀⠀⠁⢠⠃⠀⠀⢀⠀⠀⣪⡽⠟⡇⠀⠀⠰⢶⡶⢾⣾⣿⠶⠶⢾⣷⣿⠶⠶⠶⣿⣿⡷⢾⠖⠀⢻⡟⠀⠸⢉⣇⣀⣄⣼⣥⡇
⠀⠀⠀⠀⠀⡴⣻⣄⣐⠬⠔⠚⠉⠀⡴⢡⠇⠀⠀⠀⠀⡇⢸⣿⣿⠀⠀⠸⣿⡇⠀⢀⣀⣿⣿⣇⣸⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠛⠉⠙⠦⣀⣀⢀⣀⡠⠞⢁⣤⣤⠀⠠⢼⡷⠾⠿⠿⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⣦⠀⠀⠈⠻⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣭⣥⠀⠀⢸⠸⡮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣉⠇⠀⣀⣸⡋⠙⣳⠀⠀⢄⢀⠤⠒⢤⣌⣀
⠀⠀⠀⠀⠬⠁⠀⠴⢒⡚⠿⢍⣹⠋⢹⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⡷⠀⡀⠀⣡⠶⠛⠉⣂⠝⣀⡇⠀⠀⢰⠃⣠⣀⣀⠺⣗⠂
⠀⠀⠀⠀⠀⢠⠲⡛⠛⣻⠉⣇⠀⠐⠸⠀⠀⠀⢚⢠⠒⠁⢢⣴⠶⠺⣄⣀⠜⠀⠈⠉⡼⠋⡠⠞⠉⡝⢀⣽⠀⠀⠐⢸⠀⣧⡄⡞⣶⡟⠂
⠀⠀⠀⠀⠀⢸⠀⣉⠁⠀⠀⡇⠀⣀⢀⡇⢠⠀⠀⠉⠦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠠⢸⠁⡼⠁⠀⣶⡇⢸⣧⣄⠀⠀⠁⠳⣼⡕⣷⢟⠑
⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⢇⠀⠀⠀⡇⠀⠿⠃⠀⣀⣤⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠀⢇⡀⠀⠙⣤⡿⠜⠁⠀⠀⠀⠀⣸⢳⣇
⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⢸⣀⣀⡡⠜⠀⠀⢀⣼⣿⣏⣀⣰⣿⣃⣴⣮⣱⠀⠀⢿⠀⣶⣯⠙⠓⢻⡖⢢⡀⠀⠀⠀⠀⣿⣿⣿⢀⢀
⠀⠀⠀⠀⠀⢸⣀⡠⠤⠤⠤⠼⠁⠀⠀⠀⠀⠚⢻⣷⣆⠀⠀⢹⣷⡄⠉⠉⠁⠀⠀⠈⢷⣬⣅⣀⣀⣀⣱⠞⠀⠀⠀⠐⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠒⠒⠒⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠠⠀⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠒⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠤⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣄⡀
⠀⠀⠀⠀⡄⠁⢀⠄⢄⠀⠉⠀⠀⠈⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠉
⠀⠀⠀⡗⡁⠀⢈⠀⢈⠀⠀⡁⢈⠀⠀⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣁⡌
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠐⠐⡁⢸⢀⢀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠐⣇⣂⠿⡀
⠀⠀⠀⡇⠐⠄⢠⠀⠀⠀⠀⡇⢰⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣈⠛⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠂⠘⠈
⠀⠀⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠄⠘⠚⠀⠀⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⠄⠈⠁⠠⠭⠬⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠀⠀⡀⢀⣤⠀⣠
⠀⠀⠀⠀⢰⠋⠙⠦⠤⠤⠤⠤⠜⠋⢱⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⠖⠶⣧⠀⢀⡇⠠⡟⣋⡛
⠀⠀⠀⠀⢸⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡎⠑⠒⠢⠤⠄⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠨⢐⡂⢸⠁⢙⡀⢠⢣⣛⣸⠆
⠀⠀⠀⠀⢸⢀⣒⣒⣒⣒⣒⣒⣒⣒⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡁⢸⠀⠐⢅⢨⠀⡆⠒⡀
⠀⠀⠀⠀⢸⠀⠒⠒⠒⠒⠒⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⢘⢨⡅⢺⠀⠸⡤⠰⠀⠊⠯⠇
⠀⠀⠀⠀⢸⠀⠨⠭⠭⠭⠭⠍⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠄⢺⠀⠀⡇⢸⠀⢸⢻⡼
⠀⠀⠀⠀⢸⠀⠨⠭⠭⠭⠭⠍⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⣿⠀⢘⡇⢘⠀⢸⣶⣾⡆
⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠁⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠉⠉⠿⠆⠾⠇⠠⠀⠀⠯⠤⠇

⡿⢿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣿⣿⣻⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠰⡀⠀⠀⡀⢀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠆⠀⣂⠔⢢⢀⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⣩⠂⠤⡽⡓⠉⠁⠀⢴⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠫⠞⠀⠀⠀⠀⠀⠀⢼⡠⠇⠀⠀⢠⠛⠀⠀⠂⠂⠀⠀⡜⡙⠀⠀⢸⠀⠀⠀⠀⢉⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢭⠀⢁⡀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠒⠀⣾⡄⠀⠀⠃⠀⠀⢀⠄⠀⠀⠀⢸⣀⠠⠀⠀⡌⡤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣶⣀⣖⣤⢀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⢹⠉⣃⠀⠀⢰⠀⠀⠀⢀⡠⠖⢻⠿⠀⠀⠀⢘⠥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⡏⠀⠁⢄⢠⠂⡤⢠⠀⠀⠤⠀⣤⣤⠄⠘⠀⠀⠀⡾⠟⠀⠀⠐⠉⠀⠀⢸⠀⠀⠀⡛⡿
⠀⠀⠀⠀⠀⠀⠀⣞⠿⠑⠀⡠⠀⢈⠉⠀⠀⠡⠛⠓⣆⠀⠀⠀⠀⢨⢄⠐⠀⠀⠀⡀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢣⠄⠁⠈⢤⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠠⢀⠀⠈⠀⡆⢠⠜⣤⣤⡄⢰⠀⠀⠘⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠁⠀⠀⢀⠰⣶⠄⠀⠶⠾⠶⢾⡣⠄
⠀⠀⠀⠀⣀⣀⠄⠀⢀⡀⠀⠆⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢬⠀⠀⠉⠉⠀⠛⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠊⠀⠀⠀⠨⣳
⠀⠀⠀⢀⣀⣀⣾⣆⠀⣀⠀⠀⠤⡦⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠈⠀⠉
⠀⠀⠀⠈⠀⠀⣄⣀⣠⣶⣦⣿⠶⢦⣧⣤⠤⣤⣤⡤⠤⡤⡤⠄⠀⠀⢠⣼⡍⣁⣀⡀⣤⣀⡀⠀⣠⡤⠸⣦⣤⣤⣄⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠾⠿⠿⠲⠾⠗⠒⠒⠛⠀⠈⠓⠚⠛⠛⠉⠉⠃⠚⠛⠃⠈⠉⠙⠛⠉⠉⠉⠉⠉⠛⠉⠁⠁

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

⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣧⣤⣝⣶⠃⠀⠀⠀⠀⠀⠀⠀⣀⠛⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⠀⣰⣁
⢀⡜⠁⢰⣿⣞⠈⢦⡀⠀⠀⠀⠀⢐⣶⡿⠁⠀⠀⠀⠀⠈⠉⠙⢿⣷⣼⣿⡆⠀⠀⠀⠀⠀⠀⡼⡿⢿⠃⠀⠆
⠮⢴⣎⣀⣉⣀⣱⣆⣳⠀⠀⠀⢦⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢴⠦⠄
⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⠀⠀⣄⠀⠀⠀⡠⠋⢹⣿⡟⠑⢄⠀⠀⠀⠀⠀⢀
⠘⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⠀⠀⡇⠀⡱⠀⠀⣀⠀⠀⠀⢁⣤⣄⣽⣡⣤⣌⡀⠀⠀⠀⠀⠸⣷⠆
⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠈⠑⠁⠈⠲⠀⠀⠁⠉⠀⠀⠀⠺⡿⠋⠀⠙⠿⡟⠀⠀⠀⠀⢀⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠊⠁⠀⠀⠀⠀⠸⠿⣿⡿⠗
⠀⠀⠀⠀⡄
⠀⠀⣶⠀⡄⠀⠔⡀⠀⠀⠀⢀⣘⠁⣤⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣷⠀⡇⠀⠰⠇⠀⠀⠀⠘⠛⢄⣀⠶⠀⡶⠀⡀⠀⠀⠀⠀⠰⠿⠿⢆⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣶⠦
⠀⠐⠛⠂⡃⠀⢰⡆⠀⠀⠀⢀⣤⠜⢻⠂⠘⠛⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣰⣄⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠉⢀⡘⠗⠀⠀⠁⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⡆
⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢶⣤⣴⣧⣄⠀⠀⠀⠀⠀⠀⢀⠉⢁⡘⠙⣀⠛⢃⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣆⠀⠀⠀⢀⢞⡟⠉⠉⢙⠲
⠀⢰⣏⣠⣟⣀⡀⠀⠀⠀⠀⠸⠉⠉⠉⠈⠉⠁⠘⡃⠀⠀⠀⠠⣾⣷⡇⠀⣸⣿⠀⠀⠀⣤⠞⠳⠄⠰⠚⠳⡇
⠀⠀⢉⣿⡋⢉⢹⠆⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠂⠂⢿⣿⣿⠿⠃⠀⠀⠀⠠⡀⡀⢸⡀⣠⠀⠄
⠀⠀⠀⠙⠛⢻⡟⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⠀⠀⠀⠀⠈⠛⠋⠉⠑⠈

⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠒⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣞⣀⣈⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⢠⡞⠙⠉⠉⠉⠉⠀⠈⠉⠉⠉⢏⠃⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠒⠢⠴⠦⢄⣀⣀
⠀⠀⠠⡟⡀⠀⠤⠀⠀⠀⠀⠠⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠑⠒⡄
⠀⠀⠐⠑⡀⠀⠀⠀⠀⠀⠀⠉⠉⢁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⣠⡇
⠀⠀⠀⠈⠊⠢⠄⢀⡀⢀⣀⠀⠀⠁⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠉⢇⠀⢀⠠⠂⢈⠢⠀⢃⠀⢀⠀⠀⠰⣗⠀⠀⡠⠀⠀⠀⢪⡆⠀⠀⢀⡄⠀⢠⡄
⠀⠀⠇⡀⠁⢀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠑⠐⢤⡚⡤⠀⠀⠀⠂⣧⢀⠄⢠⠄⠁⠰⡈⠠
⠀⠀⠀⠀⠀⠈⠈⠁⡇⠈⠀⠀⠁⠐⠈⠐⠀⣀⣉⣃⡄⡀⡞⠀⠈⢇⡀⢸⠈⠀⠸⠁⠸
⠀⠁⠀⡀⠀⠀⠠⠤⠅⠤⢄⠀⡄⠂⠢⠀⠀⠐⠒⠄⠋⠇⠑⠀⠀⠁⠀⠈⠀⠂
⠚⠓⠚⠓⠚⠒⠒⠒⠒⠒⠚⠒⠛⠒⠚⠒⠚⠒⠒⠒⠒⠚⠒⠂⠀⠀⠄⠀⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠢⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠛⢋⡹⠋⠛⠛⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠠⠴⠄⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣿⣯⡿⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣀⣀⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠰⠶⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠛⠛⠃⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣼⠃⢀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡘⣷
⠀⠀⠀⠀⢀⡾⢃⡴⠶⠒⠛⠛⠋⠙⠉⠙⠛⠛⠶⠶⣄⡹⣦⠀⠀⣼⠇⣸⣿⣿⣭⣭⣽⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣭⣭⣽⣿⣿⡾⣧
⠀⠀⠀⠀⣼⣷⠟⡛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠋⢷⡘⣧⣴⠏⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡹⣧
⠀⠀⢀⣼⣻⠏⡼⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠏⣸⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣆
⠀⠀⣸⢧⡟⠰⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣆
⠀⠀⢹⣎⢷⣐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣸⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣆⢻⡆
⠀⠀⠀⠙⠷⣭⣛⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⢛⣛⡿⢠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠲⠒⠒⠒⠛⠛⠛⠛⠛⠙⣧⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⢃⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣉⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠟⢛⣩⣵⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠶⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⠶⠶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣒⣚⣉⣉⣉⣍⣉⣉⣙⣒⣒⣶⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⢞⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣷⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠓⠶⠤⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠤⠴⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⡶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⣴⡶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⡀⢠⠀⠀⠠⠄⠠⠀⠄⠠⠄⠠⠀⣉⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡾⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠎⠑⠠⢤⣤⣤⣤⣀⣀⣀⣀⣤⣤⡤⠤⠄⠀⠀⠈⢧⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠋⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡼⠁⠀⠀⠀⠀⢯⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⢦
⠀⠀⠀⠀⠀⠀⣠⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⡀
⠀⠀⠀⠀⠀⡰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢳⡀
⠀⠀⠀⠀⡼⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡱⡄
⠀⠀⢀⠞⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⣄
⠀⢠⢎⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣆
⠠⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠃
⣦⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠
⢯⠳⢭⣓⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⣋⡵⢫
⠀⠑⠦⣄⣉⠙⠒⠲⠮⠭⢭⣥⣒⣒⣒⣒⣒⣢⣤⠤⠤⠤⠤⠤⠤⠤⠒⠒⣒⣒⣒⣒⣒⣋⣩⣭⡭⠤⠶⠒⠚⣉⣠⠴⠋
⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⣤⣀⣀⣈⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣀⣠⡤⠤⠤⠶⠒⠚⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣂⠉⠩⠍⢁⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠊⠁⠀⠀⠀⠀⠈⢂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⢀⡀⢀⠀⠀⢀⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠡⡀⠀⠀⠀⠀⡨⢀⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡱⢌⡒⠶⠄⣊⠥⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠤⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠃⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢘⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠚⠂⠀⠈⠐⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠢⣀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠠⡂⢰⠀⢀⢄⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⡀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠐⢄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡋⠈⡐⡊⠉⠁⠀⠈⠀⠴⠄⠙⠊⠁⢙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠰⣁⡹⠀⠏⠀⠂⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢡⠀⠈⠀⠀⠀⡤⠀⠀⠀⠀⡤⢄⠀⠌⡌⠐⠀⠀⠀⠀⠀⠀⢀⠎⠀⠑⠤⡤⠊⠀⠒⠠⢄⡀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡀⠀⠀⠀⠀⡠⠀⠀⠀⠑⢀⠌⠜⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠱⡀
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⡄⠀⠈⠪⢕⠠⠀⡀⠦⠌⠀⠄⡊⠔⠁⠀⠀⠀⠀⠀⠀⠀⢰⢧⡀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠱
⠀⠀⠀⠀⠀⠘⠂⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠻⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡰⢀⣀⣆⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⢩⡍⣭⢩⣭⡍⡍⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀
⠀⠀⠀⠀⠠⠠⠉⠁⣀⠈⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠇⠄⠰⣰⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⡠⠁⢀⠌
⠀⠀⠀⠠⠡⠁⢀⠀⠈⠀⠘⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠔⠁⠑⠤⡀⢠⠎⠁⠀⠀⠀⠀⠈⠢⠊⠀⡠⠊
⠀⠀⠠⠡⠁⠀⠉⠀⠀⠀⠀⠈⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⡇⠀⠀⢠⠊⠐⡀⠀⠀⣷⠊
⠀⠠⠡⠁⠀⠀⠀⠀⢞⡱⠀⠀⠐⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⢀⠀⠀⠙⠃⠀⠀⠈⠂⠊⠀⠀⠀⡅
⢀⢀⠁⠀⠛⠂⠀⠀⠀⠀⠀⡈⠂⠑⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⣧⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣅⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀⡀⢀⠀⡀⠀⠀⠀⢀
⠀⠉⠀⠀⠀⠀⠰⠶⠀⠀⠀⠘⠄⠺⠃⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠘⢂⡀
⠀⠛⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⠀⠀⠀⠀⠀⠉⠀⠁⠈⠀⠁⠀⠉⠀⠀⠠⡰⢤⡞⠁⠀⢦
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠈⠁⠈⠀⠀⠀⠀⠀⢠⠀⠀⠉⠂
⠀⠐⠲⢀⠈⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠈⠃⢀⠘⢤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⣠
⠀⠀⠀⠀⠤⠀⡄⠀⠄⠀⠀⠀⠺⠗⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠂⠀⠐⠂⠓⠀⠀⠻⠉
⠀⠀⠀⣀⣀⠀⠀⠀⠤⠀⠃⠀⠀⡀⠀⠀⠘⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉
⠀⠀⠀⠋⠉⠀⢸⣄⠀⠉⠒⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡂⠀⢔⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠏⠙⠀⠒⠀⠀⠀⠀⠀⠀⠦⠀⠁⠀⡀⠀⠃⠀⠀⠀⠀⣠⠰⢶⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠐⢄⡀⠈⠉⢁⠀⣀⡆⢠⣤⣶⡄⠀⡁⠀⠀⠈⠁⠀⣤⠹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠈⠷⠶⣶⡦⠇⠀⠀⠙⠑⠀⠀⠘⠋⠉⠁⠀⠁⠀⠐⣄⢛⡆⠘⠂⠀⠠⠆⠒⠚⠲⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠢⠀⢀⠀⠀⢠⡀⠀⠈⡄⠀⡀⠀⣰⠃⣹⠶⢤⡦⢸⣿⠷⠈⠁⠀⠀⠀⠀⡀⠐⠂⠐⠒⠓⠂⠀⠰⢀⠸⠂⠘
⠀⠀⠀⠁⠀⠀⠛⠁⠀⠀⠹⢼⡈⠀⠈⠉⡀⠀⠘⠓⢁⡁⠀⠀⠂⠀⠀⠁
⠀⠀⠐⠁⠀⢀⠀⠰⠄⡀⠄⠈⢠⠀⠀⠘⠕⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠰⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠶⠀⠀⠀⠉⠀⡀⠀⢀⡤⠞⠁⠐⠆⠀⣀⠀⡀⠀⠈⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⢚⢲⡀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠉⠁⠠⠖⠁⡠⠀⠀⠂⡀⠀⠁⠀⠁⠀⠀⠤⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠈⠂⠉⠀⢰⠐⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠐⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠁⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⣖⡇⠀⢀⠀⠐
⠀⠀⡀⠁⠀⠀⠀⡏⢧⠄⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠈⠀⠀⠉⠀⠀⠠⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁
⠈⠠⣄⠀⠀⠀⠀⠠⠐⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠐⠀⠀⠟⠀⠀⠀⠈⠀⢀⡀
⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠘⠀⠒⠀⠀⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⠀⢸⡉⡿⠀⣠⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠀⠀⠙⠀⠀⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠃⠀⠀⠀⠈⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠦⣄⣀⣀⡤⠖⠒⠒⠲⢤⣄⣀⣀⣀⡤⠖⠚⠳⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣙⠲⢤⣀⣀⠀⠀⠀⣀⣀⣤⠴⢚⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠬⣭⣭⣭⡭⠤⠴⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠋⢻
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⣠⣀⣴⡶⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⢀⠜⢻⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⡠⠊⢀⡌⠈⠢⡄⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⣔⡁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⡄
⠀⣜⣀⣀⠈⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⣀⣠⣄⡀⢘⣆
⠀⢿⣿⣏⣹⣶⣦⣶⣾⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡄⠘⠂⢠⣬⡁⠘
⠀⠈⠻⣿⣯⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣈⣁⣀⣀⣈⣛⣁⣀
⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⢸⣿⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠬⠅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠘⠿⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠭⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣦⣤⡇
⠀⠀⠤⣤⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣿⡇
⠀⢀⣤⣿⣯⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡶⡇
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⢢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⢤⡀
⠣⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣹⣢⣖⣏⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢪⠀⢰⡗
⠀⠈⢢⠀⠖⢱⣶⣶⡶⠀⠀⠀⠀⠀⠀⢔⠉⢱⣏⠠⠄⣳⡏⠉⡶⠀⠀⠀⠀⠀⠀⡈⣆⢀⡟⠉⢉⡏⠁
⠀⠀⠘⣸⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⢛⡲⢞⡗⠙⡏⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⢸⠆⠘⠁
⠀⠀⠀⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⢆⡰⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡇

⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢠⣿⠷⠀⠀⣄⡀⢀⣠⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠚⠀⡀⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⣀⣀⣠⣤⣄⣀⣀⣠⣤⣠⣤⣤⣤⣄⠄⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⢠⡏⣶⡟⡙⢹⠼⡇⡁⡇⠦⢗⣧⣰⣲⡏⠒⡀⢀⢀⡀⠠⢶⠶⠀⠀⠀⢀
⠀⠀⢲⡄⠀⠀⠀⠀⠰⠁⠀⠐⠊⠛⠶⠿⠛⠿⠾⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⠀⠸
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠠
⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⡳⣇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⣰⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠂⢀
⠀⡄⢁⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⡆⠀⠁
⠀⠀⡄⠠⠌⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢄⣴⣢⠀⠀⠀⠀⠀⠘⠢⠐⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡄⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠘⠻⠟⠁
⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⡀
⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢈⣉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡇⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⢃⠀⠀⠀⡠⠐⠉⠀⡀⠀⠀⢤⠀⠉⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢆⡔⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠠⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢈⠀⠀⠘⡄⠁⠀⠒⠀⠀⠀⠀⠀⠆⠈⡂⡽⠒⢄⠐⠕⡠⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡸⢃⡀⠅⠹⣄⡔⣉⣂⣄⣢⣠⣠⣄⣱⣤⣇⣁⣀⢑⢿⣋⣡⣴
⠀⠀⠀⠀⠀⠀⡐⠠⠊⠬⠾⠤⠲⢵⢬⣔⠷⢦⢹⡉⠑⢁⡬⠆⠄⠀⠀⠸⡬⠐⠒⢔⠀⠀⣊⡴⠇⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⢀⡴⢻⠜⠣⡪⡧⢯⡁⢕⣙⠒⠲⣶⠀⢐⣌⡪⣐⣗⡡⠪⠂⢕⢇⠁
⠀⠀⠀⠀⡰⠀⠀⠀⠈⠂⠊⡤⣨⡂⢕⣕⣄⡪⢐⣎⡗⠻⣕⠀⠀⣀⠀⡋⠀⠉⠖⡡⢈⢔⢕⡽⠸
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⢍⠪⣺⣇⢠⡿⡊⣽⡿⣤⣷⡑⠉⢊⠤⡱⢂⢖⠭⡪⡱⢗⠵⡡⠁
⠀⠀⢠⠁⠀⠀⠀⠀⢅⠌⠀⠸⣋⣌⠞⡊⣕⠄⡪⢐⢡⣱⣹⡶⡋⢕⠅⡪⢚⢕⠈⣊⡔⢁⠔⠁
⠀⠀⠈⢔⠄⡀⠀⠀⠀⠀⠀⢨⠢⠐⠍⡪⠐⢅⢨⣲⡋⢇⡗⣬⣪⣕⡥⢪⠄⠵⠊⣉⠔⠁
⠀⠀⠀⠀⠈⠉⠀⠘⠁⠰⠶⠷⠾⠶⠿⠾⠿⠥⠉⠐⠊⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠠⡀⢀⠄⡀⢄⢠⠠⢀⠀⡀⡀⠄⠠⡀⢀⢀⠀⠀⠄⡀⠄⠀⡀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠐⠁⠊⠀⠑⠁⠊⠂⠅⠊⠐⠀⠐⠑⠨⠀⠅⠊⠔⡩⠂⠕⠨⢂⠕⠪⠐⠡⡪⠠⠃⠔⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠉
⠀⠀⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⣤⣀⡀⠀⠀⢀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠙⠉⠑⠲⡀⠀⠀⠠⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠐⢻⡁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⡆⠀⠠⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠅⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⡦⣀⠄⠀⠘⠛⡀⠀⠀⡤⠤⠶⠶⠶⢷⡤⠴⡏
⠀⠈⠀⠀⠢⡀⠀⠀⠀⠀⠀⠈⠃⠱⠠⠀⠐⠃⠨⠃⠀⠀⠀⣀⣈⣉⣀⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠡⠋
⠀⠀⠀⠀⣰⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⢠⢁⣀⡄⠉⠩⠋⠊⠑⠀⠀⠀⠃⠀⣸⠀⠀⠀⠀⠀⣿
⠀⡤⠄⢠⣃⠀⠒⠂⠀⠀⠴⠶⠄⠀⠀⠀⠠⠤⠌⣀⠀⣀⡀⢀⠀⠀⢀⣆⠤⠬⠤⢬⠂⠉⠒⣐⣀⣀⣰⡿⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⣀⡤⠶⠖⠛⠛⠉⠉⠉⡁⠒⠀⠄⡀⠀⠀⠄⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⠴⣯⢀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠈⠑⠠⣀⠉⠒⢄⣀⣀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠠⠁⠀⠠⠊⢁⠈⠁⠀⠈⢦⡈⠐⠂⠄⠀⠀⠀⠀⠀⠙⠂⠄⡀⠁⠂⠤⢈⠐⠈⡂⠀⠀⠂
⠀⠀⠀⠀⠀⡄⠀⠀⡄⢠⠂⠀⢀⠄⠀⢀⡽⢦⣀⠀⠀⠉⠐⠠⠄⣀⠀⢀⠀⠉⠐⣂⣠⠼⠛⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠠⠊⠀⠠⠈⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⠐⠘⠛⣉⠴⠶⣭⣾
⠀⠀⠀⠀⠀⠁⠐⠢⡤⢄⠅⠠⠐⠋⠀⠀⠀⠀⢴⠋⡉⣒⡉⠉⠗⠚⠛⠓⠊⠉⠁⠠⠀⠠⠄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⡀⠀⠀⡜⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠈⡄
⢀⠀⠠⠘⠀⠀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠄⠀⠘⠄⣀
⠣⢀⣀⡀⠤⠊⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠈⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠠⡁⣰⠂⠀⠤⣄⠺⠆⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠠⡱⠁⠈⠂⠄⣀⠀⠈⠙⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢡⠛⠃⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⣞⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⢂⢅⢀⠐⢢⠀⢰⡈⠵⣶⠒⢄⠀⡰⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⡞⠉⠀⠀⠀⠀⡄⠱⠞⠹⠀⠀⠈⠳⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⣉⢏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣀⣀⣀⠡⣀⡀⠀⠀⢤⠄⠏⣥⠀⠀⠀⣀⣜⡀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢍⡀⠀⠀⠀⠉⠐⠒⠀⠀⠒⢒⠾⠯⡍⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡈⠑⠒⠤⣀⠀⠀⠀⠀⢀⠪⠁⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⡀⡿⠀⢔⠒⣽⠲⣤⣀⣲⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⡇⠀⠀⠀⢸⠀⡆⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⢀⡆⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣶⣾⡽⠄⡀⠈⡀⠏⠀⡇⠀⡟⠀⠀⠀⣀⣀⣤⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠄⠠⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠡⠤⠤⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣽⣳⣒⣛⣯⠁⡏⢨⣭⣷⠶⠾⢽⡋⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡄⠀⠀⠀⣄⡘⠯⣂⠄⠀⣀⠀⢀⡰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣤⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠶⠶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⡟⠀⠀⣶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣼⣟⣒⣒⣒⣒⣷⣤⣤⣿⣻⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣅⣉⣉⣉⣉⣉⣭⣁⣀⣀⣀⣠⣍⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢰⢶⠷⢶⡶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠟⠹⠀⠀⠀⠀⠀⣸⡀⠀⠀⢠⠀⠀⠀⠸⠀⢀⣷⡀⠀⢠⣿⣬⣠⣀⡴⡟
⠀⠀⠀⠀⢀⡄⠀⠀⢰⣷⣍⠁⢀⠘⠀⠀⠀⠀⢀⡟⢃⠀⠀⠈⠀⠀⠠⠌⢅⣼⡿⠷⠆⠘⢏⣈⣉⣉⣡⡗
⠀⠓⠃⠀⠀⠁⠀⠀⢸⡟⠀⠿⣿⣆⠀⠀⠀⠀⡘⢠⣞⠞⠀⣀⡀⠀⢀⠀⠀⠙⠁⠀⠀⠀⠀⠉⠙⠃⠈
⠀⣤⡆⠀⠀⠆⠀⠀⢸⡇⢀⠀⠈⠉⣁⠀⠀⣠⣤⠞⠉⡷⠞⢣⡙⠈⠁⠑⠰⠾⠁
⠀⢠⣤⣤⡤⣦⣤⢶⡾⣷⡈⢻⣷⣾⡎⠳⠞⠿⠋⢀⡀⢱⣶⡞⣷⢰⡇⣤⡀⠛⠂⠀⠀⡀
⠀⠘⠋⠹⠇⠀⠹⠀⠈⠿⢁⠀⣿⣻⡧⠐⠃⠘⠘⠃⢠⢨⣿⠇⢸⣿⠀⡆⠿⠳⢦⣄⡘⠃
⠀⠀⠀⢀⣀⣀⣀⣀⠀⣰⠫⢏⡿⣿⣧⣤⣤⣤⣴⠀⠀⠰⠀⠀⢠⡟⢂⡀⠖⠀⠀⠈⠹⠓⢤⣀⠙⠉
⠀⠀⠀⠀⠠⠀⢾⠋⠀⣿⠀⠈⠃⣿⣷⣿⣟⣿⣿⠀⡀⠀⠀⠀⠀⠖⠛⠛⠀⠐⠓⠀⠄⢀⠀⠀⠗
⠀⠀⠀⠀⢀⡌⠆⠀⠀⣿⠂⠀⠀⣿⣿⣜⡟⠋⢸⢠⣼⣄⠀⠄⠀⠀⠀⠀⠀⢆⣤⡀⠀⠈⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⡇⢀⣿⣷⠒⣿⣼⡟⡧⠀⠀⠀⠀⠀⠀⠀⢤⡉⠁⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⠇⣤⠛⠩⠋⡃⢸⣟⠃⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠸⢄⣧⠀⠀⠘⠁
⠀⠀⠠⠠⠄⠀⠄⠚⠀⠿⠄⠀⢹⢠⠇⠀⠒⠒⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠀⠀⠀⣀⡀⠘⠛⠁⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣿⣾⠟⣻⣏⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠻⠛⠓⠲⠷⡶⠂⠀⢸⠦⢿⠿⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢁⣁⢀⠀⠀⠁⣁⠀⣤⠶⠀⠀⠀⠄⠠⠐⠒
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡖⠳⡀⠈⣿⡇⠀⠀⡐⠿⠀⠀⠀⣀⠰⠷⢽⡄⠐⢀⢈⣔⣁
⠀⠷⠖⠂⣀⡈⡅⠤⠀⠀⡿⠂⣄⠠⣟⡂⠀⠚⠋⠏⢹⢯⠀⢈⣾⠃⠒⠂⢀⡀⠀⠋⠁⠀⠀⠀⠀⠂
⠀⣤⣠⡸⣰⡇⠀⢠⢠⡤⢷⣁⡋⠀⣿⡗⠃⠀⠀⠁⠘⢆⢙⡎⣻⠇⠀⠀⣶⠀⠀⠀⡤⠀⡄
⠀⠛⠇⠙⠁⠘⣇⣈⣥⣴⢼⡏⡜⠀⠁⠉⠈⠈⡄⠑⣖⣀⡄⣠⣿⠂⠀⠀⣼⠄⠀⠀⡘⠆⠀⠘⠅⠴⠲⠆⢠
⠀⠂⢰⣶⣾⣿⡟⡟⠉⠻⠉⠁⠀⠘⠀⠀⠀⠀⠓⢀⠉⡜⡿⠽⠿⠧⠀⠀⠘⠁⠀⡀⠉⠈⠙⠂⠐⠂⠐⠲⠅
⠀⣿⠸⠟⠋⠛⠃⠁⠀⢸⠛⠋⠛⠛⠋⠉⠉⠉⠉⠹⡏⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⡀⠀⠀⣿⣶⣄
⠀⠁⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠂⡇⠀⠀⠛⠙⠋
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠔⠋⠁⠙⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡤⠶⢽⡆⠀⠀⠀⠀⠀⠀⢠⣾⠓⠒⠒⠒⠦⢌⡳⣄⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⡴⢋⡽⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⢠⠀⠀⣀⠉⣮⣱⠞⠳⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢸⣻⣧⠀⠀⠀⠀⠀⠀⠸⡏⠓⠾⠲⢄⣉⣠⠃⠀⠀⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⢱⣻⡀⠀⠀⠀⠀⠀⠀⣷⡀⢠⣄⡠⠀⠀⠀⣼⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣷⣳⡀⠀⠀⠀⠀⢀⣇⣙⣢⣤⡤⠤⠔⠋⢸⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⠓⣒⡩⡇⠙⠁⠀⠀⠀⢀⡴⢚⠟⢩⠟⢢⡀⣠⠴⢚⡆⢹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⣿⢠⣖⣲⣄⠔⠁⠰⣅⡀⢸⣄⣾⢿⠀⢀⡜⠀⠈⡏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢼⡅⢸⡇⡀⠀⢠⡞⠁⢸⠈⣸⠀⢓⠟⢀⣀⣀⡧⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢀⣷⡾⠍⠉⠉⠒⠷⣄⣸⠀⡇⢠⠏⠀⠈⢣⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⡯⣒⣂⠀⠀⠀⠀⠀⠹⣄⡷⠃⠀⢀⠔⠉⠀⣠⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢀⣀⣠⣼⠛⠓⢶⠶⢶⠶⢦⡀⠀⠈⡳⣄⡐⠁⠀⠀⡴⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣰⠃⠀⠀⠀⠳⣼⠀⠀⠙⢦⠚⢁⠎⠉⠳⣄⡼⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣀⣀⡀⢹⠀⠀⠀⣸⢳⠎⠀⠀⠀⠈⠳⡄⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠥⠤⠤⠤⠭⢾⡇⠀⠰⡇⠋⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⣠⠞⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠉⠉⠉⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠄⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢰⡁⠀⠀⠀⠤⠠⠤⠐⠈⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠠⠸⠅⣀⠀⠀⠀⠀⠀⡀⣀⠀⠠⠤⠌⠂⣰⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠠⣆⠀⣤⡄⠀⢀⡀⠀⣠⣄⠀⢀⠔⠈⠁⠀⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠌⠀⠩⠡⢀⠋⠈⠂⠈⠁⠐⠁⠀⠀⠒⠈⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠜⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠀⠀⠃⠀⠀⠑⠠⣀⠀⠀⣀⠠⠔⢡⠁⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠄⠠⠀⠠⠀⠠⠀⠀⠀⠃⠀⠀⠀⠐⡀⠀⠀⠀⠐⠠⠀⢐⠀⠀⡠⠃⠇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⢁⠀⠀⠀⠀⡑⢄⠸⠀⠎⠀⠰⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⢰⠒⠲⠲⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⢂⠀⠀⠀⠡⠀⠑⡇⠀⠀⡄⠀⠀⠀⠠⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡱⠶⡈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢂⠀⢀⠀⡐⠀⠀⠀⢀⣆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⢰⠀⠀⠀⢀⡀⡇⠀⠇⣀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢡⠀⢲⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉⠏⢸⠀⠠⠤⠰⠀⠀⠀⠀⠈⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣀⢀⠀⠠⠀⠈⠢⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠒⡀⠱⡀⠀⠈⢂
⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠂⠐⠀⠁⠀⠀⠀⠑⢄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⢀⣀⣀⣀⡀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠔⠋⠁⠀⠀⠀⠈⠓⢤⡀⠈⠓⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⢤⡉⠉⠉⠉⠉⠉⠉⠙⠒⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⠏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠭⠒⡹⡟⢹⢹⡏⡏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⠁⠀⢸⢱⡇⣼⢸⡇⣷⢸⡎⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣼⡺⣇⣿⣸⣇⣿⣼⣷⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞
⠀⠀⠀⠀⠀⠀⢣⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⠦⣀⣼⣥⣤⣤⣤⣤⣤⣤⣬⢧⡀⠀⠀⠀⠀⠀⢰⠁⠠⡃
⠀⠀⠀⠀⠀⠀⠸⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠗⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠛⠢⢤⡀⠀⠀⠀⢇⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⢳⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⢦⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢣⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⢇⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢣⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⣘⡀⣀⣀⠀⢀⣀⣀⡀⣀⠀⣀⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣇⡎⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡏⠈⠁⡼⠛⣌⠉⠈⠈⣡⠟⢣⡈⠈⠉⢉⡼⠻⣄⠀⠀⠀⣡⠛⢯⠈⠀⢹⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⣠⠞⠀⠀⠈⠳⣀⡴⠁⠀⠀⠙⢄⣠⠊⠀⠀⠈⢣⣀⠜⠁⠀⠀⠱⣄⢸⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠛⠛⠛⠛⠛⠉⠛⠛⠛⡟⠛⠋⠙⠛⢻⠛⠛⠛⠉⠛⠛⠛⠛⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠓⠒⠒⠒⠒⠚⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠠⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠖⢲⠎⠀⠀⠀⢹⡤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢒⠒⠒⠒⣶⡒⠒⠒⠒⠒⠒⠒⠒⠺⣄⠀⠀⢀⡼⠓⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠰⡻⠆⢤⣄⠿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠈⣷⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠐⠂⠀⠀⡔⠂⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡈⠄⠠⡀⠐⣂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠪⠴⠁⠈⣦⠟⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣤⣀⣀⣀⣀⣀⣠⣔⣁⣀⡀⠀⠀⠀⠀⢀⡽⠒⠿⡀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠞⠭⠭⠭⠭⠁⠸⣀⠀⣀⠛⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡈⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣄⣀⣠⠄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠨⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⣨⡤⠖⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣧⣤⣚⣡⠤⢀⣀⣀⠀⠀⠀⠀⢀⣠⢴⡶⠾⠗
⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠘⣿⡟⠋⠀⠀⠀⠈⠉⠉⠈⠛⠒⢶⣖⣾⣿⡿⠊⠀⠀⠀⠀⠀⠀⣏⢈⡧
⠀⠀⠀⠀⠀⣠⣾⣤⠀⠀⠀⠙⢧⡀⠀⠀⣰⠟⣦⠀⠀⠀⠀⠀⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉
⠀⠀⠀⠀⣠⣿⣿⡿⣧⡀⠀⠀⠀⠉⠙⠛⠁⠀⠘⢧⣄⣀⣀⠼⠛⠁⠀⢠⠔⢦⣀⣀⡔⠈⣯
⠀⠀⣴⣾⣡⣁⣘⡆⢈⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠦⠜⠁⠀⣸⠖⠛⢢⠎⢳⡄
⠀⠀⣿⣳⣷⣾⡿⣥⠄⢸⣿⠇⠀⠀⠀⠀⠙⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣹⡆⠀⠈⠓⠚⠁
⠀⠀⠈⠛⠻⠿⠿⠿⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣶⠶⣶⠆
⠀⠀⠀⠀⢿⠿⠟⠘⡿⠿⡇⢻⢿⣿⠀⡟⠋⡗⢘⣿⣿⠃⠀⠀⠀⠀⠀⣨⣤⣤⣀⠀⠀⡇⠀⢸
⠀⠀⣠⣆⣺⣶⣇⢀⡇⠀⡇⢸⣿⢉⠀⡧⣤⡇⢸⡏⠉⢰⣦⠀⠀⠀⠀⠹⠓⠛⡏⠀⠀⡇⠀⠰
⠀⠀⠺⣿⢻⣟⣃⡴⣷⢶⣣⡾⠿⡞⠀⠓⡶⣃⠘⣷⣾⣋⡇⠀⠀⠀⠀⠸⠀⠀⡇⠀⡰⠀⠀⠀⢀
⠀⠀⢚⡏⣿⠟⡏⠈⡟⠛⡇⢸⣿⠉⠀⡟⠉⡏⢸⠋⠙⢹⡇⠀⠀⠀⠀⢠⠀⠀⡇⢠⠁⢀⠀⠀⠈⠄
⠀⠀⠀⡗⢸⠀⡇⠀⡇⠀⡇⢸⣿⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢀⡼⠀⠀⢧⣾⠛⠛⠠⠒⠟⢳
⠀⠀⡄⡇⣀⠀⡇⢀⡇⠀⡇⢸⡿⢠⠀⡇⠀⡆⢸⠀⢰⢸⣇⠀⠀⣔⣁⣀⡀⠀⠀⡈⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠥⣧⣤⢀⣇⢀⣇⣠⡇⢸⠇⢘⠀⣧⢀⡇⢸⡇⢸⣸⡇⠀⢸⣿⡖⠒⠂⠐⠒⢲⣿⣧⣤⣤⣜⣿⡗
⠀⠀⠴⣏⣹⣿⣷⣀⣙⣛⣛⣈⣻⣏⣀⣙⣿⣓⣈⣻⣿⣎⣧⠀⠈⢿⣧⣠⠀⠀⢰⣴⡟⠉⠉⠉⠁
⠀⠀⠰⠋⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠻⠄⠀⠀⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢄⡀⠀⣀⣀⣴⡶⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⠤⠠⠄⠤⠤⠶⠤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢀⣤⣤⠤⠤⡖⣶⠔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠁⠘⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠉⠀⠀⠈⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠐⠂⠀⠀⠄⢣⠀⠀⠀⢀⡴⠊⠁⠀⠀⣠⠀⠀⠀⠰⠆⠁⠂⠄⡉⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣀⠀⠀⠈⢇⢠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⢔⡠⢀⠃⠀⠁⢂⠄⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⡀⠀⠀⠉⠅⠀⠠⠘⡇⠰⠂⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⠀⢂⡡⢚⣇⣀⡀⠩⠔⡡⢈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⠀⠀⠈⣴⠀⠀⡆⠸⣌⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⡠⣀⠊⡽⠡⠀⡌⣆⡩⢖⣵⣤⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⣀⠀⣀⢀⠀⣠⠒⣢⠄⡓⠀⠹⡔⣾⣠⠄⡽⢾⡭⠶⠶⠶⠾⠤⣽⠶⡧⢬⠤⠤⠤⠽⣿⢤⠦⢷⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠼⠥⠤⠽⠥⠬⢻⠽⡦⣡⢖⡾⢲⣄⢻⣔⠕⣊⢔⣩⠖⠢⡀⠀⢐⡠⠽⣭⢔⠭⣊⠔⡣⢊⠔⣋⢔⢽⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣀⡀⠀⠀⠕⡩⣰⢏⣨⠖⡡⣚⡌⣷⡫⠔⡡⠞⢄⡤⣴⢦⣈⠁⡩⢒⠵⣪⠴⣫⠖⡡⢚⡕⣣⢺⢀⠁
⠀⠀⠀⠀⠀⠀⡰⠁⠐⠀⠀⢸⠀⣀⡇⠀⠩⢊⠤⣊⠔⡩⢚⠵⢋⡘⣖⣩⡲⢕⡂⠀⠈⢟⡿⠰⠞⠛⠺⠿⢻⠷⢋⠴⠫⢞⣵⣿⣾
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠉⠉⠰⣉⣽⠥⣊⢕⡭⠶⣥⢊⠥⣻⣸⡉⠙⡧⢂⠀⣈⠤⣺⠥⡀⠀⠠⡼⢣⠴⠣⠄⠴⠧⠿⠳⠇
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠕⡨⢔⣹⡁⠠⣸⠗⡫⢔⣧⢳⣤⣯⣔⡩⢀⠉⡿⢖⡴⢲⡶⣿⠶⡢⢶⠶⣢⠶⢢⠖
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢼⠁⣈⠂⠀⣲⠜⢒⢭⡺⠝⡫⢔⡩⢒⡡⢚⢈⢧⢚⡾⣲⠟⡩⢒⡡⣚⠵⢊⠔⡪⠖⡡⠚⠁⡠⠋
⠀⠀⠀⢸⢠⠠⠀⠀⠀⠀⠀⠉⠁⠀⠀⠕⡪⢕⡩⢔⡫⢒⡡⢒⡭⣒⢵⡿⡎⢟⡫⢔⡩⢒⡩⢚⡡⢚⠥⣊⠴⠯⠚⡠⠞
⠀⠀⠀⠀⠓⢝⡢⠤⠂⠐⣀⡀⠀⠀⢀⠭⢒⡭⢒⡥⢒⡥⣚⠕⣪⠵⠥⢚⣡⣎⣚⡓⠶⠃⠖⠋⠚⠓⣚⣋⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠐⠒⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⣀⠀⣀⠀⡠⠀⣠⢀⡀⢀⡀⠀⡀⠀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡀⠀⣀⠀⡀⠀⡀
⠀⠀⠀⠁⠋⠔⠉⠔⠉⠖⠡⠚⡡⠒⡡⠒⠥⢊⠵⢊⠔⡨⢔⡭⢒⡡⠒⣁⠔⢈⠔⣊⠔⣈⠔⢊⠥⢊⡥⢚⡡⢒⡡⢒⡡⢚⡡⠒⡩⠔⡡⢒⠴⡢⢂⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠀⠈⠁⠈⠁⠈⠀⠊⠁⠒⠁⠐⠉⠚⠁⠚⠁⠒⠉⠐⠋⠐⠊⠔⠁⠊⠐⠁⠈

⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢀⣆⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠰⢸⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡢⠀⠈⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡠⠞⠁
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠁⠂⠈⠀⠀⠀⠀⠘⡂⠀⠂⡀⠤⠄⠀⠀⠠⠄⠀⠀⠤⠁⠪⠀⢀⠃⠀⠀⠃⠀⢨⠀⣠⠾⠀⠄
⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠚⠁⠀⠀⢀⠀⠀⠈⠂⠀⠀⡈⢀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠡⠤
⠀⠀⠀⠠⡀⠀⢀⡀⠀⠐⠒⠒⠒⠒⠚⠂⠧⠀⠀⠂⠀⠁⠀⠀⠀⠄⠀⠐⠂⠀⢀⠀⠀⢀⡇⡤⠄⠀⠀⠀⠀⠀⠀⠰⠐⠂⠖⠒
⠀⠀⠠⠤⠤⠜⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠂⠀⠙⠈⠀⠀⠘⠁⠈⠀⠀⠑⠂⠀⠀⠀⡄⡆⠀⠀⠀⠀⢈⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠑⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⠘⠂⠀⠀⠀⠠⡀⠀⡈⠀⠀⠀⠀⠐
⠀⠠⠐⠐⢊⠁⠀⠂⠐⠀⠘⠋⠉⢩⢍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠑⠂⠀⠀⠀⠀⠠⠍⠀⠀⢀⡀⠀⠀⠀⠄⢂⡠
⠀⠀⠀⢀⠄⠀⠀⠀⡤⠠⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠒⠀⠀⠂⠀⠀⠀⠀⣡⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠔
⠀⠀⠀⡀⠀⢀⠀⠀⠙⣾⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠒⠚⠀⠠⠀⡤⠀⡐⠁⢨⠓⠀⡉⠂⠀⠀⠀⠀⢀⡄
⠀⠰⡠⠀⠁⣌⠁⠀⡴⠀⠐⠻⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠐⠓⠀⠀⠁⠀⠀⠀⠀⠒⡒⠂⠈⢢
⠀⠀⢉⠠⢄⠊⢀⡄⠀⠀⠀⠀⠠⠟⠣⠤⠤⠤⢤⡦⠀⢠⣖⡀⣔⣂⠀⠀⠀⠀⠀⠠⠀⠀⡦⠄⠄⠀⡇⠀⠀⠀⢨⠉⠀⠀⠊
⠀⠀⠀⠀⠉⠀⠈⠀⠂⠀⠂⢀⣀⠀⠀⠠⠀⠀⠀⠠⠀⢨⠉⡄⡍⠡⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠁
⠀⠀⠉⠀⠉⠀⠀⠀⡀⠀⠰⠥⠤⠤⠤⠤⠕⠀⠀⠀⠀⠀⣄⠇⢘⡀⠀⠀⠀⢋⠋⠀⠀⠀⠀⠀⠄⢂⠀⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣈⡁⠁⠀⠀⠀⠀⠀⢸⠀⠁⢰⠀⡆⠈⠀⡀
⠀⠀⠀⠀⠀⡘⠀⠀⠁⠀⠀⠀⠒⠒⠐⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣀⣄⣈⣀⣀⠈⠉⠁⠀⠉⠁⠤

⠀⠀⠀⠀⢀⠠⠐⠀⢈⠉⢉⠀⠀⢄
⠀⠀⠀⠔⠁⠐⠀⠀⠀⠄⢀⠀⠐⠀⠡
⠀⠀⠈⠀⠀⠠⠀⠔⠀⠀⠢⠐⠄⠀⠀⠁
⠀⠀⡄⠀⠀⠇⠘⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠐⠀⠀⠈⢄⠑⡤⠒⣁⠔⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠆⠘⠈⠀⠀⠀⠀⠀⠀⠠⡀⢀⡶⠶⢲⡀⠀⠀⢠⠶⠴⢦⡀⠀⠀⡰⠶⠴⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢁⣀⡀⢀⡁⠀⠀⣀⣀⡀⢸⡁⠀⢀⣀⣀⠀⣌
⠀⠀⠁⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢨⠈⢀⠁
⠀⠀⠀⠀⠀⠀⠡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⠁⠈⡄
⠠⠀⠀⠐⠀⠀⡔⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⢄
⠈⠀⠒⠚⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠠⠀⠁⠀⠀⠈⠦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠑⠤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠠⠀⠀⠄⠀⠀⠀⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠀⠉⣍⠉⢉⠉⠉⠉⠉⡍⠉⠉⠉⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠅⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⡠⣤⡊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⠄⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠇⠀⡄
⠀⠀⠀⢀⣎⠞⠁⠘⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉
⡄⠀⠀⢚⣛⡂⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⣀⣀⣀⣀⣠⠔⠂⠉⠉⠉⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠈⢿⠉⠀⠀⠀⠈⠉⠉⠓⠤⡀⠀⠀⣉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠲⡉⠁⡀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠈⡶⠋⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠚⡦⣀⠀⢀⠇⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢰⠃⠈⠑⠊⠀⢳⠈⠓⠤⣀⣀⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⡠⠽
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠤⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⠛⡄⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣭⠥⢤⣄⣀⡴⠚⠉⠉⢹⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⡄⠀⡸⢯⡄⢳⠠⠦⠤⣀⠀⢸⠶⠾⡏⠀⠀⣄⠀⢸⠁⢧⡀⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠈⠻⡔⣧⠈⠓⠃⠀⠀⠹⣄⣀⣀⡠⢏⡀⢀⠝⠒⠒⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⠦⢤⣤⠤⣤⣤⢤⡴⢮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠑⠢⢷⡁⣢⣇⣀⡕⣸⠀⠀⢰⡒⠛⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠙⠣⡃⠀⢱⣇⣳⣀⠜⢳⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠈⠟⠉⠁⠀⡇⠀⠀⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⢇⣀⡤⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿⠉⠒⠶⠤⠤⠤⢶⡺⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠰⢹⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡿⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠠⠇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⢀⣠⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣀⣀⠿⠈⠁⢄⠒⠒⠒⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢤⡤⠤⠤⠴⠗⢶⠒⠒⢻⠋⠁⠀⠀⠀⠀⢸⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⠔⠉⠳⡀⠀⠐⢰⢧⣀⣉⣸⡀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠸⡀⠀⠀⣠⠚⠁⠓⣄⡀⠈⠒⢒⣧⢀⣀⣠⠴⢧⣀⠀⠀⠀⠀⣸⠀⠀⠸⣀⠀⠀⠀⠢⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢡⠀⠠⠃⠀⠀⠀⠸⡉⠉⠉⢿⡄⠀⠙⢤⢠⠜⠈⠢⡀⢠⠊⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠑⠦⠴⠋⢱⠀⠀⠀⠀⠀⠀⢠⠇⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⢀⣀⡠⠔⠃⠀⠘⢄⠀⠀⠀⠀⠀⡴⠀⢠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠲⠤⣀⣀⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⣤⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⠽⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢶⣶⣾⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄⢐⣶⣀⠀⠀⠀⠀⠀⠀⠘⠳⡌⣿⣿⣿⣟⣛⣥⡀⠀⠀⠀⠀⢶⠒⣶⣶⣶⣶⣶⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⣀⣀⣠⢮⢿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠀⠈⠛⠛⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢻⣶⣶⣶⣦⡆⢸⣧⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣿⣿⣷⣾⡇⣻⣿⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣿⣿⠇⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡿⠛⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣆⣿⣻⣿⣿⠁⠀⠀⠀⣿⣿⣿⣶⣶⣦⣶⣶⣶⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣥⣄⣽⣿⣟⣴⠟⣛⣟⣟⣛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⣿⠃
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡏
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟


⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⠞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⡴⠛⠁⠀⣆⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⡎⠉⠉⠉⠉⠉⠁⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠃⢀⠴⠊⢁⡤⠛⠁⠀⠀⠀⠀⠈⠁⠀⢴⢿⠆⠀⠀⣠⠀⡀⠀⠱⡀⠀⠀⠀⠀⢀⠜⠀⠀⠠⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠆⠀⡇⠀⠈⠉⠉⠀⠀⠁⠀⠇⠀⠀⠈⠒⣤⣴⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢺⣀⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣁⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠂⠉⠰⠦⠀⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡮⠉⣻⠚⢁⠀⠂⠂⠀⠀⠙⠋⡼⢉⣹⠂⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠊⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢱⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⠀⣽⢒⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢰⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠘⣄⡜⠀⠊⠀⢀⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣐⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠠⡞⢶⠀⠀⠀⠀⢾⣁⣀⣀⡤⠆⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠛⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣅⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡄⠀⠀⠀⠀⠀⣤⠀⠀⠘⠂⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠠⠚⢧⠀⠀⠈⢛⣦⣄⣼⠆⠀⡀⠀⠀⠀⠀⢹⢻⣷⠘⣇⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⣁⣹⠀⠀⠘⠉⠈⠀⠀⠠⠈⡼⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢠⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠖⢃⣘⡛⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠇⡇⣀⡤⠒⠁⣠⣀⠀⢸⠀⠉⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡇⠀⠀⠀⠀⠀⠀⣀⡀⠤⠶⠶⠤⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢰⠀⠀⠛⠋⠉⠉⠙⠓⠤⠤⠤⠤⠜⠋⠉⠁⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⢄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠔⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣥⣦⣵⡞⠁⠀⠀⠀⠀⠀⠀⢠⡉⠟⠀⠀⠀⢰⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠘⠆⣠⣃
⢀⠎⢀⢹⣿⢇⠘⢆⠀⠀⠀⠀⠈⣷⣿⠉⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⡀⠀⠀⠀⠀⠀⠰⠿⠻⠃⠄⠒
⠳⠼⠧⠤⠤⠤⠽⣮⠇⠀⠀⠐⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣷⡄⠀⠀⠀⢀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣀⡀⠀⠀⠀⠀⠐⠛⠂
⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠄⠀⡄⠓⢄⡀⠀⠶⠀⠀⠀⠎⠀⢹⣿⠃⠉⢄⠀⠀⠀⠀⠀⣤⡀
⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠤⡀⠥⢀⠘⠁⠀⠦⠀⠀⠘⢰⣶⠖⠓⣶⣶⡎⠀⠀⠀⠀⠀⣻⡃
⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⣀⠀⢈⠻⠁⠀⠀⠀⠀⣶⣿⣿⣦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⣀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⡏⠈⡇⠀⣼⠀⠀⠀⠐⠿⡂⠉⢠⡀⢠⠈⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣤⣀
⠀⠠⠿⠄⡇⠀⣤⠀⠀⠀⠀⢀⣈⢶⠎⠀⢶⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⢀⡀⠀⢀⡇⠀⠋⠀⠀⠀⠀⠙⠁⠀⣦⠀⠀⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢻⡆
⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⢶⣤⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⠛⣀⠛⠃⠘⠓⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⡰⡺⠉⠉⢓⠢
⠀⢰⣋⣰⣏⣀⡀⠀⠀⠀⠐⠋⠈⠉⠀⠉⠑⠚⠃⠀⠀⠀⠠⣶⣾⡄⠀⣿⡇⠀⠀⢀⡴⠻⠦⠠⠞⠳⡆
⠀⠀⢩⣟⠉⡉⣿⠀⠀⠀⠀⣀⢀⠀⡀⢀⡀⢀⡃⠀⠀⠀⠀⠠⣿⣿⡿⠟⠁⠀⠀⠀⠄⢀⢀⣇⣠⠀⠄
⠀⠀⠀⠉⠛⣻⠋⠁⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣴⣿⣾⣿⣷⣶⣆⠀⠀⠀⠀⠉⠋⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⠙⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⢠⡞⠲⣽⣍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⣼⠀⢀⡬⣅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⣸⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⣛⣉⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉⠀⠀⢀⣨⠿⠖⠒⠲⢦⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⣴⡆⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠹⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠘⠁⢠⡶⠛⠛⠒⠦⣏⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡆
⠀⠀⠀⠀⢀⡤⠤⢤⣀⣠⢼⡇⠀⠀⠀⠀⠀⠀⣾⣤⣄⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⣔⣷⡆⠀⠀⠀⠀⡟⠀⣷⠀⠀⠀⠀⡏⠉⠙⡇
⠀⠀⠀⢰⡏⠀⠀⠀⠀⡏⣰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⢶⣄⠀⢹⡄⠀⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⢀⡼⠁⠀⣿⠀⠀⢀⣤⡇⠠⡞⠓⢦
⠀⠀⠀⢸⡇⠀⠀⠀⢼⠳⣏⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣧⠀⣻⣄⣀⣀⠀⠀⠈⢹⠷⠤⠤⢖⡯⠤⣄⠀⣿⠀⠀⣯⢠⡇⢠⠼⠧⣾⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠈⠳⣝⡛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠘⣇⠀⠀⠀⠈⠙⢦⣤⠞⠀⠀⠀⠜⠀⢀⡼⢰⠇⠀⠀⠸⣼⡇⢸⠃⠲⡼⠃
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣉⣉⡉⠀⠀⢀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡟⠀⠀⠀⢀⣽⡇⠈⢹⣦⠞
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⡇⠀⠞⠓⠛⠉⡀⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢠⡞⢹⡇⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⣤⣤⠴⠋⠹⡄⢸⡧⠝⣦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⠋⠀⢸⡇⠀⣾⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠰⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠷⠛⠁⠉⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠀⠀⠸⠦⠤⠟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⡠⡾⠃⢸⡄⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⡾⠀⠀⢀⣠⠶⠋⠀⣀⡤⠚⠉⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⡏⠳⠶⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡷⠤⢰⠋⣷⠖⠒⠉⠁⠀⠀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢥⡀⢣⠀⡼⠀⣼⣆⡠⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢺⡀⢸⡀⠇⢠⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⣒⠒⠒⢒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⠀⣿⠀⠘⠀⠀⠀⠀⠀⠀⢫⠍⠉⢡⠝⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⣸⡀⠀⢸⡄⢠⡋⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠀⣴⠃⠀⠀⠀⠹⡇⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠷⠶⠖⠛⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⡾⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⡗⠚⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠶⠤⠤⠤⠤⠤⠤⠶⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡠⠶⠊⠻⠟⠃⠶⡄⣠⣤⡀⡴⠆⠻⠿⠃⠲⡤⣠⣤⡀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⣤⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢣⣄⠀⢀⣀⠀⣀⡌⠿⠿⢇⣄⡀⢀⣀⠀⢀⣤⠄⠀⠙⠛⣛⣛⣛⣛⣛⣛⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⣿⡇⠉⠀⠀⠀⠀⠈⠁⣿⣿⡇⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠈⠙⠃⣾⣿⡆⠀⠰⠶⠶⠶⠶⠶⠶⠶⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⣙⡛⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡆⠛⣛⣛⣛⣛⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⢿⣶⣶⣬⣭⣭⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⢿⣿⣅⣢⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⠾⢈⣿⣿⣿⣿⣿⢋⣭⡻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠈⠙⠛⠛⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠖⠒⠒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⢲⠂⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣶⣶⠆⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠄⢄
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢣⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⣿⣿⠿⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⣿⣿⡟⣻⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⣿⣽⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠯⠭⠽⠽⠽⠭⠊⠀⠀⠀⠀⠀⠀⠀⠑⠽⠿⠿⠿⠿⠿⠿⠿⠑

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡇⢼⠀⠀⠀⠀⠀⠀⠈⣤⠈⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⣹⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠻⠿

⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⡈⠀⢁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠔⠁⠀⠈⢢⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢜⣀⣀⣡⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡇⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢞⣿⢿⣿⣿⡳⠀⠀⠀⠀⠀⢯⠇⠀⠀⠀⠀⠀⠻⠿⣿⠿⠋⠀⠀⠀⠀⢿⣿⣿⡿⠇


⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⡤⠤⡄
⠀⠀⠀⠀⢀⠤⠃⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢣⠀⠀⠀⠀⠀⢀⠃⠀⠃
⠀⠀⠀⠀⠎⣀⣀⣀⣀⣰⠀⠀⠀⠀⠔⠀⠐⠄⠀⠀⠀⠀⠀⣧⣤⡜⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠈⢴⣶⣶⠜⠀⠀⠀⠀⠀⢿⣿⡧⠀⠀⠀⠀⠀⡾⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⣠⠖⢉⠗⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡇⠀⠀⠀⣠⠞⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣇⣸⠓⠒⢦⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠉⠉⢀⡴⢁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢳
⠀⠀⠀⡴⠒⠲⢄⣀⣀⣀⣀⣀⣀⣀⣞⡀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢶⠋
⠀⠀⢸⠀⠀⠀⣸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⠆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠑⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠖⢺⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡉⠀⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⣻⠆⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣦⠤⠤⣄⡀⢀⡴⢋⡴⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢳⣼⡆⠀⠀⠙⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡟⣷⣤⠴⠋
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠲⡤⠤⠄⠀⠰⠮⣁⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠘⡀⠀⠀⠀⠀⠀⠉⠢⣄⠐⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠔⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⢸⠦⣀⣰⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣸⠀⠀⠀⠀⢣⠈⠑⠒⠓⠒⠠⠤⠤⠖⡐⠒⠖⠈
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢋⠀⠀⠀⠀⠘⡄⠀⢀⣐⣂⣀⣀⣠⠴⠒⠒⣷⠆
⠀⠀⠀⠀⠀⠀⠘⠶⡀⡰⢣⡄⢆⡴⠤⣄⢀⠶⠺⡏⠀⣠⠀⡏⠹⡀⠘⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠣⣗⠀⠉⠀⠀⠑⠤⠤⠚⠠⡤⠈⠉⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⠀⢀⣀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠽⡅⢠⣏⣹⢨⠀⠀⡔⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠳⢅⢀⡯⢵⡤⢚⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢄⠀⠀⠀⠈⠁⠀⠀⡄⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠒⠤⣀⣀⣀⣀⡿⠋⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠄⡆⠀⠀⠀⠀⠘⡄⠀⠀⠀⡮⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⡆⠀⠀⠀⠀⡜⠀⠀⠀⠂⠇⠀⠀⠀⠀⠀⠱⠤⡀⠴⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡇⠀⠀⠀⠰⢁⠀⠀⠀⢀⣒⣀⣀⠠⡤⠄⠚⠁⠀⢢⠄⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⠀⠀⠀⠀⢀⠜⢫⡉⠁⢀⣌⠀⢂⡇⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡀⠀⢠⠚⠑⢢⣀⡉⢂⡺⠀⣈⠡⠶⣄⠀⠀⠀⡸⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⢇⠉⢉⢇⠀⠐⠂⠒⠈⢣⠀⠂⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠆⢸⡀⠀⠀⠀⠉⠁⠈⡆⠀⠀⠀⣀⠎⠀⡄⠀⠀⠀⠀⡸⠀⡄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠁⠀⠑⠤⣀⣀⣀⣀⠔⠉⠉⠉⠉⠀⠀⠀⠈⠂⠤⠤⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡃⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⢬⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠲⠬⣌⡒⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⡀⣀⣉⣀⡀⣌⢑⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⢉⠙⠃⠀⢴⡦⣄⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⠛⠑⢄⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠒⠊⡉⠥⠴⠒⠉⠁⠀⢀⣠⠔⠊⠀⠀⠀⢀⠔⠁⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⣀⡤⠖⣉⠄⠀⠀⠀⣠⠔⠁⠀⠀⠀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣠⠴⠚⠁⠔⠈⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⠜⠀⠈
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣶⢦⡀
⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⢆⡆⠀⠀⠀⠀⣹⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⣠⠞⢵⠀⠈⠢⠈⠓⠤⣄
⠀⠀⢀⠀⠀⢘⣆⠀⠀⣘⣙⣻⡄⠀⠀⠀⡇⢘⣿⠀⠀⠀⠀⢸⣏⠀⠀⠀⠈⢰⠞⠁⠀⠀⠀⠐⢆⠀⠈
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⡑⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⣀⢀⡀
⠀⠀⠀⢰⡶⣒⢿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡇⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⢸⣿⢿⠿⣿⠀⠀⠉⠉⠘⡇⠀⠀⠀⢐⠶⠖⠀⠀⢠⠄⠀⢤⠀⠀⠀⡇⢸⠈⡇⠀⢀⠔⠋
⠀⠀⠀⠚⠋⠉⠉⠛⠀⠀⠀⢐⠊⠀⠀⠐⠒⠒⠒⠒⠀⠀⠙⠒⠒⠚⠃⠀⠀⠁⠀⠚⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢜⡆⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⡀⢀⣨⡇⠀⠀⣀⠠⢚⡃⠀⠀⠲⠲⢔⠶⡲⢖⠶⡲⢲⠆⠀⠀⠀⢈⠀⠀⣹⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠀⠁⠈⠀⠁⠉⠈⠀⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉
⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⡤⢤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡄⠀⠠⡄
⠀⠀⠀⢜⠓⠂⠀⢠⡄⠀⠃⢸⠀⢱⠀⠀⠸⠛⠛⢩⣧⠀⠀⠖⠀⠀⢸⠄⠀⠀⢠⡾⠛⠁⠀⣴⡇⠀⢸⡇
⠀⠀⠀⠘⠦⠀⠠⠞⠁⠀⠀⠸⠀⠀⠄⠐⠶⠒⠒⠚⠲⠆⠀⠰⠤⠤⠞⠀⠠⠊⠈⠀⠀⠀⠈⠀⠁⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴
⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠈⠀⠴⠂⠉⠒⢊⡉⠕⠀⠢⠢⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠈⠈⠀⠀⠀⠄⠤⠠⠀⠄⡄⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠠⠀⠀⢀⡀⡀⣀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣍⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠠⡐
⠀⠀⢿⣿⣿⣿⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠥⠎⠃
⠀⠀⠀⠉⠉⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡄⢦⠦⡖⢲⣆⠔⠀⡖⠐⠖⠂⠠⢰⠀⠐⢦⠀⠒⠀⠀⠀⠐⠠
⠀⠀⠠⣶⠒⣲⠆⢲⡶⢶⠄⣶⠀⠀⠀⠀⠸⡀⣸⡄⡆⡞⠸⠀⡧⡏⣬⢩⠁⢼⡬⠀⠀⠸⠄⠘⠃⡀⠀⠀⠠
⠀⠀⠂⠘⠃⠋⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠈⠀⠈⠉⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⢀⠀⠄⠀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣻⣷⣄⠀⠀⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠠⠀⠀⡄⠀⡇
⠀⠴⠾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⡞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⡴⠛⠁⠀⣇⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠛⢀⠴⠊⢁⡤⠟⠁⠀⠀⠀⠀⠈⠁⠀⢸⣿⠇⠀⠀⣠⠀⡀⠀⠹⡀⠀⠀⠀⠀⢀⠜⠀⠀⠰⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠦⢐⡇⠀⠈⠉⠉⠀⠀⠁⠀⢇⠀⠀⠈⠓⣤⣦⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢾⣠⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣉⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠊⠉⠰⠦⡄⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡾⠉⣻⠞⢁⠀⠂⠂⠀⠈⠙⠋⡽⢉⣽⠂⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠛⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢻⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⡀⣹⢖⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢸⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡅⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠸⣔⡝⠀⠊⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣒⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠤⡞⢶⠀⠀⠀⠀⢾⣁⣀⣠⡴⠂⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠟⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣍⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡆⠀⠀⠀⠀⠀⣤⠀⠀⠘⠒⠃⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡚⢧⠀⠀⠘⣛⣦⣄⣼⠇⠀⣀⠀⠀⠀⠀⢱⢻⣷⠸⣇⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⡁⣻⠀⠀⠘⠉⠀⠀⠀⠠⠈⡜⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢨⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠈⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢐⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠒⢃⣘⡟⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡆⡇⣀⡤⠒⠁⣠⣀⠀⢸⠈⢩⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡆⠀⠀⠀⠀⠈⠀⣀⡀⠴⠶⠶⠦⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢸⠀⠀⠛⠉⠉⠉⠙⠳⠦⠤⠥⠤⠼⠋⠉⠀⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⣄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠖⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠰⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠴⣄⡀⠀⠐⠂⠀⠈⠁⠡⠐⠤⡀⠀⠀⠀⠀⠠⢀⣀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⣀⡠⠤⠐⠊⠁⢊⠀⠠⣂⠉⢐⠄⠀⠉⠑⠦⣄⡀⠀⠁⠂⠀⠀⠉⠑⠢⠀⠀⠈⠀⡀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠂⠂
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠀⡀⠀⠀⢀⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢀⣀
⠀⠀⠀⠀⠙⠆⠀⠀⠈⠀⠀⠄⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠊⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡤⢀⡄⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡇⢠⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠄⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣒⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠒⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠈⠤⠤⠤⠬⠥⠁⠠⠤⠤⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⢀⠈⠐⢀⠀⠀⡄⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠤⠄⠈⠀⠐⠂⠄⠆⠐⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠀⠰⠀⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢈⡔⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠜⠀⠁⠉⠉⠉⠜⠀⠉⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⢤⠀⠀⢠⠤⠄⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⢀⠀⠀⢀⡀⠀⢀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠈⡁⠁⠀⠀⡆⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢘⠀⠀⢐⡃⠀⢘⡀⠀⢘⡃⠀⣚⠀⠀⢘⡂⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠀⠠⠀⡀⠀⠁⠀⠀⠀⠁⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠈⠇⠀⢸⠀⠀⠀⡇⠀⢹⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠁⠙⠀⠀⠀⢤⠀⠀⠙⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⠀⢈⢈⠁⠀⡆⠀⢸⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⠂⠁⠀⠀⡇⢸⠀⠒⠐⡄⠀⢸⠀⠀⠀⡇⠀⢸⠀⠒⢂⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠈⠉⠉⠉⠀⠐⠀⠀⠀⠀⡄⠀⠚⠀⠀⠀⡇⠈⠧⠤⠤⠁⠀⠀⠦⠤⠔⠁⠀⠀⠦⠤⠜⠀⢸
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢂⡀⠀⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠁⠤⠤⠠⠄⠤⠤⠤⠤⠤⠠⠄⠄⠀⠤⠀⠀⠀⠈⠤

⣾⣿⣷⣾⣶⡷⢿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣷⣶⢷⡶⠶⣶⠶⠶⣶⡿⠶⠷⢾⠷⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⢒⠒⣦⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠉⢹⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣀⣴⣶⣶⣦⣀⢀⡀⢻⠀⠀⠀⠀⣰⠃⣤⣶⣦⣤⡈⢧⠀⠀⠀⠀⠀⡇⢸⣹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⡁⣹⣿⣿⣿⡇⢸⠀⠀⠀⢰⠇⣼⣿⣀⣸⣿⣷⡈⢧⠀⠀⠀⠀⡇⢸⡿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠹⢿⣿⣿⣿⣤⠟⣠⠎⠀⠀⠀⡏⢸⣿⣿⣿⣿⣏⣿⣷⠘⡇⠀⠀⠀⡇⢸⣷⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣬⣭⣭⠴⠞⠁⠀⠀⠀⠀⠳⢬⣭⣭⣭⣭⣭⣭⣥⠾⠁⠀⠀⠀⠹⢤⣭⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠩⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⢩⣭⠗⠀⠀⠀⠀⠀⠺⡍⠉⠉⣭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣀⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇⢰⣦⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣴⣿⣿⣿⣷⣤⣤⡄⢹⠀⠀⠀⠀⡼⢁⣶⣿⣷⣶⣆⢹⡄⠀⠀⠀⠀⡅⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣿⣿⣿⣿⣿⣿⣿⠇⣼⠀⠀⠀⣼⢁⣾⣿⣿⣿⣿⣿⣆⢳⡀⠀⠀⠀⡇⢸⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⠿⢿⠿⠟⣃⡼⠁⠀⠀⠀⣇⠺⣿⣿⣿⣿⢿⡿⠿⢀⡇⠀⠀⠀⣇⠸⠿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠒⠚⠁⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠒⠋⠀⠀⠀⠀⠈⠓⠖⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⢤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣈⣿⣈⣉⣉⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠠⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠐⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠠⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⢀⣀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠣⠤⠤⠄⣀⣀⣀⣀⠬⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣴⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠷⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠳⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁


⣿⣿⡿⠻⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣀⣀⣀⣀⡬⠀⠀⠀⠀⠀⠀⢏⣉⣉⣉⣉⣉⡕⠀⠀⠀⠀⠀⠀⠸⣉⣉⣉⣉⣉⣹
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠠⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⢧⢤⠤⠤⠤⠤⢤⡀
⠀⠀⠘⠂⠀⡖⠆⠀⠐⠒⠐⡖⠒⠒⠒⠐⡖⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⡖⠒⠒⠒⡖⠖⠒⠁
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⡀
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⡇⠀⠀⠀⢷
⠀⠀⠀⠀⠸⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⢸⣥⣤⣤⣤⢤⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢰⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠇⠀⠀⢸⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠢⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠊⠀⠀⠀⠸⢸
⠀⠀⢠⠀⠘⠚⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠁⠈⠈⠁⠀⠈⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠐⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⡂⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⢿⡿⠂⠸⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠐⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⢀⠄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠁⠀⡁⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠠⠨⢅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠤⠤⠤⠤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠒⠒⠒⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⡆⠀⠲⡆⠀⢰⡀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⢓⠀⠛⠇⠈⠙⡇⠛⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠴⠀⢀⣀⠀⡀⣀⣓⡇⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⡇⠀⠀⠋⠀⠀⠨⢽⠛⠛⠩⠉⠍⠃⠒
⠀⠀⠀⠀⠀⠀⠀⢤⠈⢭⠀⣨⢽⣈⡳⢗⣐⠆⣎⡋⣧⡇⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⢫⣈⣉⠉⠈⠉⠉⠸⠭⢆⡋⣱⣬⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠈⠁⠈⠀⠁⠈⠉⠀⠀⠀⠉⠄⢀⣃⠀⠀⠀⠀⠀⠄⠀⠐⠀⠸⢄⠉⠉⠉⠉⢩⣀⣀⣀⣀⣨⣀⡀⠀⣀⣀⢠⣄⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣠⣤⣤⣶⣒⣒⡒⠒⠒⢀⣐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠸⣇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠛⠿⠿⠻⠛⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠃⠋⠉⠉⠉⠉⠉⠉⣉⣉⡉⣁⠤⣧⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣥⡀
⠀⠀⠀⠀⠘⠀⠀⠄⠤⠠⠤⠤⠇⠰⠒⠛⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⢄⣄⣀⢀⡀⢀⢀⠀⠀⠀⠀⠀⢀⣠⣠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠊⠐⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⣄⢴⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⣸⠀⠀⣙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠴⠋⠀⣸⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠛⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠞⠋⠉⠀⠀⠀⡋⠥⠤⢤⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣤⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠈⠳⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠰⠋⠁⣠⠴⠒⠢⠄⡌⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣿⠀⠀⠀⠀⠀⠀⢰⣇⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢳⣤⣶⡄⠀⠀⠀⠀⣾⠀⣷⠀⠀⠀⠀⡖⠂⠒⡆
⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⢃⡾⠃⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⢦⣄⠀⠸⡇⠀⠀⠀⠀⠀⢀⣻⡛⠁⠀⠀⠀⣰⠃⠀⣿⠀⠀⢀⣀⡇⢠⡶⠓⢀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⣄⠀⠀⠀⠀⠈⠙⡧⠤⡤⠴⣚⣡⡀⠀⣿⠀⠀⣏⢈⡇⢀⠽⠆⡼
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⢮⡛⠚⠛⠛⠛⠉⠉⠉⠙⠛⠒⠦⣄⠀⠈⢣⠀⠀⠀⠉⠑⠢⣀⠼⠁⠀⠀⠸⠁⠀⡸⢠⡇⠀⠀⠸⣼⡇⣸⠆⠀⡼
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠳⢤⣀⡀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠉⠉⠀⠀⠀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠈⢀⡞⠀⠀⠀⠀⣽⡇⠈⢱⣀⠄
⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢾⠀⠐⠃⠐⠋⢀⠀⠈⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢀⡞⢁⠀⠀⢸⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠦⣀⣀⡤⠖⠙⡄⠀⣧⠜⢤⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡠⠋⠀⢸⠀⠀⠘⠢⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢳⠞⠁⠈⠀⠀⠀⣀⠔⠁⠀⠀⡠⠞⠁⠀⠀⠘⠦⠤⢂⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⣠⠖⠁⠀⢀⡤⠊⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣷⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣼⠃⠀⠀⣠⠴⠋⠁⣀⡤⠞⠉⠀⠀⠀⢀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢘⠘⠒⠒⠋⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠷⠠⢤⡏⢱⠖⠒⠋⠁⠀⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⠤⠤⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠧⡀⢸⠀⢰⠁⣼⠇⠠⠤⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠇⠀⢀⠟⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢘⠛⠛⣓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⡄⠀⠀⠀⠀⠀⠓⠀⠈⢡⠞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⢠⡄⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⣸⡄⠀⠸⡇⣰⣇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠛⠓⠒⠚⠛⠛⠓⠛⠛⠛⠛⡿⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠀⠀⠀⠀⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⢀⠀⠆⠄⠀⠂⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠇⠰⠘⢻⠰⠘⠃⠋⠀⠈⠈⠃⠃⠀⢀⠠⣦⣠⠄⠀⠀⣀⠳⣄⠀⡜⠁⠀⠀⠀⢠⠀⢠⣜
⠀⠀⢣⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠸⠧⠎⠀⠀⠀⠀⠁⠀⠈⠀⢧⠀⣀⣀⡤⠎⠀⡇⡟⠀⠀⢀⡀
⠀⢠⡈⢧⠃⠀⠀⡰⠢⣎⠀⠀⠈⠓⠀⠢⣀⣀⣀⠀⢀⠀⣠⠀⠀⢠⠞⠉⠉⠈⠉⠻⡉⠀⠀⠀⠀⢇⠣⠤⠚⣻⠄
⠀⠀⠘⢼⠄⠀⢛⡀⠀⢹⠀⠀⢀⡀⡠⠊⠁⠀⠀⠈⠙⠁⠉⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⢀⣀⡀⠀⠈⠓⠒⠊⠁
⠀⠀⠀⠈⡇⠀⠁⠘⠛⡍⠀⠀⠈⠁⠀⠀⡄⠀⠀⠀⣠⡼⢀⡤⠤⠤⠵⢤⠐⠤⠒⠋⡰⡟⠉⢠⢪⢂⢆⠀⣀
⠀⠀⢀⡀⢡⠟⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠚⠋⠀⢯⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⣉⠷⣇⡈⢁⠆⠸⣿⡇
⠀⠀⠀⠱⣾⠀⢰⠉⠉⡱⠚⢄⣸⠀⠄⠤⠶⠋⠉⠉⠓⠒⠶⢷⠤⠤⠴⠖⠚⠀⠀⠀⠀⠀⠈⠁⠘⢪⡤⡄
⠀⠀⠀⠀⠹⠀⠀⠳⣔⠁⠲⢀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⣤⡄⠠⣤⡄⢠⣤⠀⠀⢸⡂⡄
⠀⠀⠀⠀⠘⠀⠈⢀⡃⢑⡲⠮⠀⠴⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⢰⡆⠀⣶⠀⢸⢷⠀⠀⢸⠄⡇
⠀⠀⠀⠀⢀⣀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠐⠆⠀⠀⡔⡲⡀⠀⢸⡇⠀⣿⠀⢸⣾⠀⠀⢸⠀⡇
⠀⠀⠀⠠⠘⡍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢓⠃⢀⠀⠀⡯⣹⡁⠀⠘⠃⠀⠛⠀⠘⠛⠀⠀⠸⠤⠇⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡟⠻⡃⠀⠀⣐⠃⢱⡆⢐⠆⠣⠔⠁⠀⠀⡸⠁⠀⠀⢀⣄⠀⢀⠴⢆
⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⡰⠀⠀⢡⠀⠀⠉⠀⠀⠀⠀⣀⡀⢀⠀⠀⠘⠓⠠⣶⠊⠀⠀⠱⠃⢀⠀⠙⠆
⠀⠀⠀⢠⡪⢌⡆⠀⠀⠀⠀⢠⠃⣠⡀⡀⣆⠀⠀⠛⢸⠂⠀⠀⡄⠸⠄⠀⠀⠀⢀⡀⠳
⠀⠀⠀⡏⠀⠉⢹⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⡀⠀⠀⣷⠀⣦⠀⣺⠀⠀⠑⠂⠀⡤⠤⢴⠀⠀⠴
⠀⠀⠀⠙⠲⠶⠊⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⠀⠀⠀⣿⠀⠻⠀⣿⠀⢸⡇⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣄⣀⡘⣧⣀⠬⢿⡬⠤⠄⠀⠀⠀⠠⢸⠄⠀⠀⣟⠀⠀⠀⢿⠀⢸⠁⠀⠀⣿⠀⢸⡇⠀⢴⡄
⠀⠀⠀⣶⠖⠈⠉⠟⠀⠘⠋⠀⠘⠁⠀⠀⠀⠐⡆⠒⠺⠓⠒⠚⡛⠚⠛⠒⠛⠒⠚⠞⠒⠲⠛⠃⠛⠃⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣀⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣧⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⡿⠛⠛⠻⣿⣿⣿⣿⡿⢸⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⡇⣼⡇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣷⣤⣠⣴⣿⣿⣿⣿⢀⣿⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⠇⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⢋⣼⠏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣶⣿⣿⡿⢃⣾⠏⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⡿⠋⣴⡿⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡙⠿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⠿⢋⣴⡿⠋⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣤⡾⠟⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⡂⠉⠉⠉⠉⠉⡉⠉⠁⠐⠒⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠘⠲⠦⠏⢀⡀⣀⣠⣄⣇⣀⡀⠰⠶⠖⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⢲⠄⠤⠤⢤⠤⡤⢠⠤⡤⠤⢤⠤⣴⠒⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠄⠀⠀⡆⠀⠀⠀⡗⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡀⢰⠀⡄⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⡀⠀⠀⢠⠀⡇⢸⠀⡇⠀⠀⠆⡐⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠁⠀⠀⢸⠀⡇⢸⠀⠁⠀⠀⠸⠃⠃⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠃⡄⠀⠀⠀⠘⠀⡇⠈⠀⢰⠀⠀⠀⠘⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠆⠰⠀⠀⠀⠀⡄⠀⡇⠀⠀⢸⠀⠀⠀⠇⠇⠀⠀⠆⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠂⠀⠀⠀⠀⡇⠀⠁⠀⠀⠈⠀⠀⠀⢰⠸⠀⠀⠐⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡌⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⡀⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠇⠀⠀⢠⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⢠⠀⠆⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⡄⠐⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠃⠀⢡⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡌⠀⠀⠂⠀⣀⠀⢀⣀⣀⢀⣀⣀⣀⣀⢀⡃⠀⠀⡀⠀⠀⠀⠰⠆⠈⡄⠀⠀⠀⠆⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠖⠒⠻⠛⠻⠋⠉⠉⠉⠉⠉⡉⠉⠉⡍⠉⣍⠀⢈⣍⢀⣀⣀⠘⣷⠶⢷⡤⣶⣤⣤⣀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢂⣧⣤⣤⣁⣀⡄⠀⠀⠀⠀⠀⢠⡅⠀⢠⡦⠠⣷⠀⠒⣿⠒⠒⠒⠒⣿⣆⠻⣯⠉⢻⣐⣯⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⣼⣿⡟⢋⡙⢩⠉⠛⠛⠒⠶⠶⣶⣦⣤⣴⣦⣤⣼⣤⣤⣤⣤⣤⣤⣤⠽⣷⢶⣿⣾⣿⣿⣯⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⣿⡿⡀⣮⠁⡌⠀⠀⠀⠀⠀⡦⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠘⣿⣿⣿⣿⣿⣿⣯⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢰⣿⣿⢣⣱⠇⢠⠀⠀⠀⠀⠀⠀⠇⣿⣿⡟⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⢿⣿⣿⣿⣿⣿⣻⡜⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢠⣿⣿⠏⢆⠏⠀⠄⠀⠀⠀⠀⠀⢸⢰⣿⣿⡇⢸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣷⢳⢹⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⢁⣾⣿⡟⡘⡜⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⡇⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠀⣿⣿⣿⠿⣿⢿⡎⣇⢻⣿⡄
⠀⠀⠀⠀⠀⢠⣿⠃⣼⣿⡿⢃⣱⠁⠠⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡄⢸⣿⣿⡆⢻⡌⣿⡸⣆⢿⣿⡀
⠀⠀⠀⠀⢀⣿⠏⣸⣿⣿⠁⣰⠇⠀⠆⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⡇⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡇⠀⣿⣿⣿⠈⣷⠸⣧⢻⡌⣿⣧
⠀⠀⠀⠀⣾⡏⣰⣿⣿⢧⢻⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⡇⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣇⢹⡇⢿⣇⢳⡘⣿⣆
⠀⠀⠀⣼⡟⢠⣿⣿⡏⡞⣾⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠀⣿⢰⡿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⣿⣿⣿⡄⢻⡘⣿⡌⣧⠸⣿⡆
⠀⠀⣼⣿⢁⣿⣿⡿⢰⣸⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⣿⣿⣿⠀⣿⢸⡇⣿⠘⣧⢸⡟⣿⡿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣇⠀⢇⢹⣷⠸⣆⢻⣿⡄
⠀⢰⣿⠃⣾⣿⡿⢡⢧⠏⣼⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠀⣿⢸⡇⣿⠀⣿⢸⣷⢻⡇⢻⣿⡇⣿⠀⠀⡀⠀⣿⣿⣿⡄⠘⡄⢿⣧⢹⡄⢿⣷
⠀⣿⡏⣸⣿⣿⢣⣏⡞⢰⠇⠠⠀⡆⠐⠀⡆⢸⠀⠁⣼⠇⢸⣿⣿⣿⠀⡿⢸⡇⢸⠀⣿⠀⣿⠸⣷⠸⣿⣧⢸⡇⠀⠁⠀⢸⣿⣿⣇⠀⢣⠈⣿⡆⢷⡘⣿
⠀⠻⣿⣿⣿⣏⡾⣼⢁⡟⠀⠀⢠⠀⠇⠀⠀⡄⠸⠀⣿⠀⣾⣿⣿⡿⠀⡇⢸⡇⢸⠀⣿⠀⣿⠀⣿⠀⣿⣿⠸⣇⠀⠰⠀⠀⣿⣿⣿⡄⠀⠁⠸⣿⣌⡷⣻
⠀⠀⠈⠻⣿⣿⣼⡃⣼⠁⡄⠀⡀⢸⠀⠃⢀⠁⡄⢰⡿⠀⣿⣿⣿⡇⠀⡇⢸⡇⢸⠀⣿⠀⣿⠀⣿⡆⢻⣿⡀⣿⠀⠀⡄⠀⢸⣿⣿⣧⠀⢀⣠⣿⣯⡵⠋
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣄⣰⠁⡆⠘⠀⠸⠀⠃⣸⡇⠀⣿⣿⣿⡇⢸⡇⢸⡇⢸⠀⢿⠀⢸⡄⢻⡇⢸⣿⡇⢻⡀⠀⠃⠀⢠⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣷⣷⣤⣄⣰⣀⣿⡇⢰⣿⣿⣿⡇⢸⡇⢸⡇⢸⡇⣸⣀⣸⣇⣼⣧⣼⣿⣧⣼⠷⠶⢛⣛⣫⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠷⠶⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡠⠊⠀⠀⠀⠀⠐⠀⡵⠂⢓⠉⠂⠀⠀⠀⠀⠉⢩⠁⠁⡀
⠀⠀⠀⠄⠀⢉⠄⠀⠀⠀⠀⠀⢀⠀⡀⠁⠈⠀⠀⠀⠀⠀⢐⠡⠊⠀⠀⠀⠀⠀⠀⢠⠑⡆⢀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠂⠈⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠜⠢

⠀⠀⠁⡅⠁⡄⠀⠄⠀⠀⠀⠀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠁⣂⠄⠙⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠘⠑⠀⡄⡄
⠀⠠⠄⠇⠄⠣⠄⠳⠄⠀⠀⠀⠀⢯⠐⢨⠇⠀⠀⠀⠀⠀⠁⠀⠐⢢⢀⠀⠀⠀⠀⠐⠢⠁⠈⠤⡖⠢⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠷⠟⡂⠄⠀⠀⠀⠀⠀⠀⣨⠉⠀⠁⠀⠀⠀⡔⠐⠁⢇⠀⠀⠀⠀⠀⢀⠈⠂⢀⢀⠠⠊⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠀⠀⡄⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠠⢀⢀⡠⢄
⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡠⢁⠁⡀⠀⠀⠀⠀⡊⠀⠲⣀⠑⢄⠀⠀⠀⠀⠀⠀⢰⣤⡂⠀⠀⠀⠀⠐⢅⠀⢀⢵⡀⢀⠕
⠀⠀⠠⡄⢠⠀⡇⠀⠀⠀⠀⠀⠀⢰⢤⠤⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⢠⠌⡀⠀⡀⠀⠀⠀⠀⠀⠈⠇⠉⢈⠅
⠀⠀⠐⠤⠀⠀⠃⠀⠀⠀⠀⠀⠈⠄⠑⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠡⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⡆⠀⢁⠀⠀⠀⠀⠐⠀⠢⠄⠨⠢⠀⠀⠀⠀⠀⠀⠀⠉⣆⠀⠀⠀⠀⠀⠀⠈⢆⠀⡐⠁⠀⠀⠀⠀⢈⠔⠠
⠀⠀⡠⠂⠁⠀⠈⡇⠀⠀⠀⠈⢀⣙⠷⡟⣁⠈⠀⠀⠀⠀⠰⣠⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠉⠀⠀⡂
⠀⠀⠁⠈⠁⠁⠀⠃⠀⠀⠀⢀⣀⡀⠿⠃⡀⣀⠀⠀⠀⠠⠒⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠈⠠⠠⠄⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄⠛⠿⣿⣿⣿⡿⠃⣼⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣌⠛⠟⠀⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⡙⠻⣿⣿⣿⣦⣄⠀⠀⠀⠈⢻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣶⣌⡙⠿⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀
⣠⣶⣶⡄⢠⡤⠦⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣌⠛⢿⣿⣿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄
⢿⣿⣿⠟⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠰⣿⠟⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠶⣶⣶⣤⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⡏⢰⣶⡌⣿⣿⣿⣷⣄⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄⢀⣾⣿⣿⣿⣿⣷⣤⣭⣴⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠄⠀⠀⠃⠄⠀⠀⠀⠀⠀⠄