Kite Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁⠈⠦⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⣷⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠴⠥⠤⢤⠤⠤⠼⠦⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣐⣛⣛⣛⣛⣃⡈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⣛⠋⠉⣉⣏⡉⠙⣛⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠰⡍⠀⠀⠀⠀⠀⠀⣠⠋⠱⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⢜⠁⢹⣿⣿⣿⣿⣏⠀⢱⠀⠀⠀⢩⠆
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢴⡊⠁⠀⠀⠈⣑⠦⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠾⠛⡛⠛⠿⡿⠛⢛⡛⠳⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠳⡜⢦⠊⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣼⣿⡄⠀⡇⢠⣾⣷⡀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠠⣔⠊⠀⠀⠑⣤⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠹⡿⠁⢀⣇⠀⠻⠟⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢑⡜⢶⠋⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⡧⠼⡀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⢏⠀⠀⡝⠂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢈⠦⠴⣇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠆⡸⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠸⣄⣀⠞⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠤⣀
⠀⠀⠀⠀⣀⡄⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⢠⣀
⠀⠀⠀⡠⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠧⢄
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠔⠒⠒⠒⢉⡟⣄
⠀⠀⢺⠭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⣆
⠀⠀⠈⡆⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠸⠀⠀⠀⠈⠑⠦⣀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢑⡾⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠎⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠱⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⢇⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠘⣞⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⣱⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠓⠒⠒⠒⠒⠚⠳⢤⣀⠀⠘⣅⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠿⡓⠦⣄⡀⢀⡴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠇⠀⣀⠽⣻⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠊⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠭⣿⣖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠠⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠂⠄⡀⢀⠂⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠠⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢑⠧⣄⢌⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡰⠁⠀⠀⠀⢉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⢁⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⡨⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⢀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣤⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⢠⠀⠀⢀⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣅⠀⠡⣿⡇⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡼⢊⠀⠀⢜⡛⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠗⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⠂⠒⠠⡀
⠀⠀⠀⠀⠀⠺⢿⣷⡆⠒⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢟⡠⠑⠠⠤⠃
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠆
⠀⠀⠀⠀⡳⠿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠾⢁
⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣯⣿⣿⣿⣿⣯⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠈⠉⠛⠿⢶⣤⣄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡶⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⡶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⣴⠟⠁⠀⠀⠀⣀⣀⣠⣤⣴⣶⠾⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣴⠶⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠏
⣠⡶⢶⣤⣀⠀⢸⡟⢀⣠⣴⡶⣶⡄
⣿⡇⠀⠉⢛⣿⣿⣿⣟⠋⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠿⣦⣀
⢿⣧⣴⡾⠟⠋⢿⡏⠛⠿⣶⣤⣾⠇⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢈⣿⠆
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠉⢹⡷⠀⠀⢀⣀⣠⣤⣄⣀⣸⣯⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠸⣷⠀⣴⣟⣡⣴⠾⠛⠋⠉⣉⣽⣿⣿⠿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⣀⣿⣿⡿⠟⠋⠀⠀⠀⣴⡿⠛⠁⢰⣿⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢛⣿⠿⣿⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣼⡏⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⢿⡆⠀⣠⡾⠛⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣤⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣼⣿⣾⡋⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢀⣼⣿⣿⠛⠛⠛⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⡿⠋⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠻⣷⣄⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣀⣹⣷⣾⣯⣴⣶⠶⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠋⢻⡟⢿⣦⡀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠻⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⢟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⡷⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣟⠦⡀⠀⠀⠀⠀⠀⣀⣴⡫⠞⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⢮⡢⣄⣀⡤⣺⠕⠋⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣳⣾⣿⣞⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡴⣫⠔⠋⠙⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣠⢞⡷⠚⠁⠀⠀⠀⠀⠙⢮⡳⣄⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣙⣟⠁⠗⠒⠀⠀⠀⠀⠀⠁⠀⠙⠯⡓⢄⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠈⠢⣑⢦⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⣠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣈⣳⡽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢇⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣷⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⣤⣧⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⠏⢣⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⣶⣿⣾⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⡿⣫⡿⣦⣿⣿⣿⡟⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣾⣥⣴
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡻⠿⣿⡿⢿⣿⡏⣰⣟⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣹⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣶⣿⣾⣾⠵⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⠓⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠛⠁⠀⠀⢀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠴⠜⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡗⠒⢻⠀⠀⠀⠀⠀⣀⣴⡴⠶⠀⠐⣦⠶⣲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡃⢸⠀⡇⠀⠘⠦⣄⠀⢼⣼⡿⣥⣤⠀⠠⠞⠋⠉⠁
⠀⠀⠀⠀⣀⣀⠤⠤⠈⠋⠁⠘⠛⠳⠾⠷⠛⠛⠀⠘⠛⠀⠉⠉⠋⠓⠂⠈⠉⠉⠉⠉⠉⠁⠒⠒⠒⠂⠤⠤⢄⣀⡀⠀⣶⡤
⠀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠶⢤⡀

⠀⠀⠀⠀⠀⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣽⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⣿⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠙⠓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⠀⠀⠀⠙⢦⡀⢹⡄⠀⢸⡟⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣙⣾⣧⠀⢸⡇⠀⠈⠙⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣳⣾⣄⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣶⠛⠉⠀⢸⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠉⠉⣹⠟⠀⠀⠀⠀⠀⠉⠳⢦⣄⢸⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣤⣤⣀⣻⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠻⡟⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⠤⢀⣀⣠⣤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣍⡛⠛⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣠⡤⠈⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⠄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠘⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⢻⣆⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠈⠉⠁⠀⣀⣤⣬⣉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠁⠀⢀⠀⢀⡀⠀⢠⠄⢈⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⢀⡀⢐⡖⣀⣴⣳⡅⢋⣱⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢤⣤⣄⣲⣤⣤⠛⠉⠀⡠⣀⣄⣽⣿⣿⣿⣾⡯⣾⣶⣿⣿⣷⠁⠹⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⣿⣿⣿⡿⣿⣿⣿⣭⣿⣿⣿⣄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣽⣿⣿⣷⣟⡿⣟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⣿⣻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣾⣻⣿⣿⣞⣛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣶⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣽⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣥⣴⣶⣶⣶⣶⣤⣌⡛⢿⣷⡀
⠀⠀⠀⢰⣿⣿⡿⠛⠛⠻⢿⣿⣿⡿⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⢀⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⣣
⠀⠀⢘⠋⡎⠉⠀⠀⠀⣦⠀⠀⠀⠀⢰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠚⡉⠀⠀⡀⡀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠆⠀⢀⠀⠀⠀⠘⣲⠺⠂⠀⠀⠀⠀⠀⣸⡇⠘⠂⠻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠈⠡⠀⠋⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠰⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠑⢄⠙⠻⢿⣷⠀⢰⣿⠿⠛⢉⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠒⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⢀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠸⠿⠗⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠮⣹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠐⠀⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⠀⠀⠐⠲⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠴⠈⠄
⠀⠀⠀⠀⣠⠀⡠⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⢁⣠⠼⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⢀⢤⠊⠀⠩⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⠀⢀⠀⠀⣠⠐⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠹⡨⠄⠉⠁⠀⠀⠀⠄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡀
⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠃⠌⠠⠀⠀⣀⣀⣀⢠⡀⠀⠤⠆⢒⠀⠀⠀⠀⠔⡀⠌⠀⠀⠁⠘
⠀⠀⠀⢀⡌⡄⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⡠⠁⠐⠤⠀⠀⠀⠂⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⠀⠊⠐⠠⡀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠘⠀⠀⢂⣠⡀⢠⣀⠂⠀⢸⠀⡐⠀⠀⠄⠀⠀⢀⠈⢂
⠀⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⢩⣆⠀⠀⣶⡙⠀⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢃⠀⠀⡀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠉⠁⢀⡃⠐⢤⠄⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠆⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠑⢤⣀⣀⣀⣀⠴⢋⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠿⠿⠛⠛⠛⠉⢁⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠂⠀⠀⢀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠊⡉⠀⡤⠀⠀⠀⣲⣦⣴⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⢁⠀⠈⢠⣬⠀⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡶⠖⠄⣀⡐⠁⠀⠁⡖⢡⣎⢄⡰⠃⠀⠂⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⡶⣷⡞⠁⠉⠡⣮⢔⡫⣕⡠⣻⠟⠁⠀⠀⠈⠀⠂⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠙⢋⣀⣤⣴⣿⣷⣾⣭⡵⠋⠀⠀⠀⠀⠀⠀⢄⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡡⠶⠀⠳⠬⣿⣿⣯⣿⣿⣿⡏⠉⡀⠀⠀⠀⠀⠀⢐⣵⠛⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣶⣶⠿⠶⠾⡶⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⢀⠐⡶⠛⠀⠀⡠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠤⠞⠍⠿⠠⣷⠾⡄⡀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠞⠛⠛⠛⣦⡴⢊⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⣼⣯⣵⣿⠃
⠀⠀⠀⠀⠀⠀⣀⠔⠮⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢀⠠⣪⠾⠋⠉⠃
⠀⠀⠀⣀⢔⡪⢖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣦⣶⠋⠁
⢀⣴⣿⢟⠟⣨⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⠿⣿⠿⠟⠉
⠈⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢈⠃⠀⠀⠀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⡆⠀⠀⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡄⠀⠀⢨⠀⠀⠀⠑⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠘⢆⠀⠈⠂⠀⠄⠘⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠣⠘⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⢄⠀⠱⡄⠰⡄⠈⠀⢃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠘⠃⢀⠰⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡄⠑⢄⠀⠈⠳⡀⠈⠢⣑⡀⠀⢪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢃⠀⠀⢂⠃⠀⠠⠀⠀⠀⠀⣀⡞⢰
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠈⠀⠀⠁⠀⠀⠙⠦⡀⠈⠳⠀⠀⠙⠀⠀⠠⠀⠀⠀⠀⠀⠀⠳⠰⡀⠀⢃⠀⢢⠀⠈⠡⡀⠀⣰⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠑⢤⡀⠄⡀⠀⠐⠢⠀⢀⡀⠀⠐⠄⠀⠀⠀⠱⡀⢳⠀⠀⠀⠀⠀⣣⠀⠀⣂⠀⢾⢣⠀⢡⠀⢿⡿⣾⠃
⠀⠀⠀⠀⠀⠀⠰⣦⢀⣈⠠⠀⠈⠃⠀⠠⣀⠀⠀⠀⠉⠓⠢⠄⢀⠀⢠⣀⠈⢦⠀⠀⠀⠀⢢⠘⢗⣄⠈⠆⣸⠀⠀⠀⡆⠘⠁⠹⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⠙⠓⠆⠠⠄⠈⣁⡁⠀⠀⠀⠀⠀⠀⠁⣀⣯⠀⠈⠣⡀⠀⠀⠈⡗⠀⠪⡀⠐⠈⠃⠀⠀⣡⠀⠂⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠓⢀⡁⡘⠂⠡⠀⠹⣄⠀⠐⡟⠂⠀⠀⠊⠀⠀⠀⠀⢀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⡐⠲⠙⠁⠀⣤⠀⠀⡹⠄⠀⠁⢀⠻⠿⡀⠁⢀⣴⠁⠀⠀⠀⠀⠀⣸⣷⡀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠛⠉⠉⠀⠀⠈⠁⠀⢀⡀⠠⠀⠂⠀⠐⢋⣶⣀⠀⢁⠂⠀⠀⠀⠁⠀⢧⡀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠉⣠⠤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠒⠒⠂⠈⠁⠀⠀⠀⠄⠊⠀⠀⠠⢹⠃⢄⡈⡁⣄⠀⠒⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⠦⣀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀⣠⣤⡠⠆⠀⠀⠀⢀⡠⠊⠀⡀⢸⠂⠆⠈⢠⠤⠀⢉⠄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠔⠉⡠⠀⠀⢀⠃⣠⠀⠀⠀⣁⠀⠁⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⠈⠀⠐⠀⠀⠀⠁⠀⡆⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠓⢂⠀⠠⠄⠀⠀⢠⠃⡈⢣⡎⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⢀⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠀⠀⠛⠈⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣂⠠⢔⡄⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣄⠤⠒⠀⠁⠀⠀⠀⢿⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠟⠋⠴⠋⠀⠈⠀⠀⠀⠉⠉⠙⠀⠬⠛⠒⠲⣶⠒⣢⠄⠈⠁⠄⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣀⣤⠴⠞⣋⣥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠴⠚⠚⢉⡡⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⢤⠞⣹⠇
⠀⠀⠀⠀⡝⠃⠤⠀⠴⢚⣀⠤⠒⣈⣡⠄⠀⢀⡴⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⢀⠀⠀⠈⠂⠐⠀⠡⠌⠱⠂⠀⠌⢀⣤⠆⠁⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠒⠊⠡⠁⠒
⠀⢨

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⡄⠀⠀⠀⠀⠴⢿⣆⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡿⠤⠠⠀⠄⠀⠀⠈⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢈⢁⡤⢏⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠃⠀⠀⠈⠳⢄⠠⠤⠄⠆⠀⢂⡈⠁⢢⡀⠈⢧⡀⠀⡀⠠⣀⠁⡀⠀⠡⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠁⢈⠀⠀⠀⣂⢀⠂⠀⠀⠀⠒⠦⡀⠀⠀⠀⠀⠑⡌⢀⠊⠀⠀⠈⠀⣀⣀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⢀⠂⠐⡰⠇⠄⠀⠀⠈⠱⡀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢰⠀⠀⠀⡠⠤⠀⠠⣄⠑⢆⠀⠰
⠰⣄⡆⠀⠀⡅⠀⠀⠀⢀⡤⡄⠀⢤⡄⠀⠀⠀⠀⠀⡆⠀⠀⠚⡅⠀⠀⡄⠀⠀⠀⡄⠀⠀⠰⠘⠲⠠⠄⠉⠀⢸⠀⡘
⠚⠻⣿⠋⠀⠁⠀⠀⠀⠀⣤⡄⠀⣄⡌⠀⠀⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⢊⡀⠀⢰⢤⡀⠈⢠⣀⠀⠉⡡⠀⠀⠃⡐
⠀⠀⠈⠳⠦⠴⡀⠀⠀⠈⠘⠀⠐⠒⠀⠄⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠿⠀⢰⣦⣤⡼⠁⡀⢡⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠤⢒⣿⠀⠀⠀⠀⢠⢷⠀⠀⠡⢄⠀⡠⠄⢀⣼⣿⣾⢇⠀⠘⠒⠊⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⣵⣤⡄⠀⠈⠋⠑⢀⡤⢄⡠⢴⣋⣿⠀⠀⠀⠀⣀⠀⠀⠀⣠⠋⢀⣨⠦⢀⣀⣀⡠⢒⡏⣀
⠀⠀⠐⢦⣤⣀⣻⠀⠉⠉⠒⠦⢖⠒⠉⡇⠀⠀⠀⠞⠟⠓⠂⠰⡎⡼⠁⠒⠈⠀⠰⠯⠥⠤⣤⡄⠀⢳⠈⠳⠟⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡟⢧⣰⡇⠀⠀⠀⠀⠀⠀⠀⣠⠿⠴⠶⢲⡆⠀⠀⠀⣀⣴⠟⠁⠀⠈⠷⠤⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣥⣤⡀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠠⣄⡀
⠀⠀⠈⢯⣕⡢⢄⣀
⠀⠀⠀⠀⠉⢶⡩⠘⣙⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣔⣐⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⠤⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡄⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢴⠢⠄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠅⠀⠀⠀⠀⠻⣦⡀⠀⢀⡴⠊⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠬⠄⠀⠀⠀⠘⠷⣤⠋⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣤⣼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠦⡤⠴⠶⠶⠾⠮⠾⠮⣮⣴⣴⣵⣵⡵⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠙⢷⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⡟⠻⣧⡀⠀⠀⠀⢰⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣯⠑⢾⣄⠈⠻⣦⡀⠀⢿⠻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣄⠙⠳⣄⠈⠙⢦⣸⡄⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣈⠓⡤⠀⠙⠿⣄⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⠦⣄⡈⠙⢷⠀⠀⠀⠈⢳⡈⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠀⠈⠉⠚⢷⠂⠀⠀⠀⣿⢌⡢⠙⢷⡀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠛⠒⠒⠚⠳⡆⠀⠀⠹⣮⣕⡀⠀⠹⡄⠀⠀⣀⡼⠋⠀⣠⣦⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠋⠉⠉⢉⡹⣅⡀⠀⠙⢿⣄⠀⠀⠙⠏⠉⠁⠀⠀⠀⠙⠛⠀⢀⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣍⣉⣀⠤⠚⢢⠤⢀⠀⠉⠳⠶⠄⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⣤⠔⠊⢁⡤⢚⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣞⣁⡠⠯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣭⠎⠀⡴⢩⡟⣠⣶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠛⢉⣠⣴⠟⠁⡰⠃⡻⢛⠟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡿⡻⠟⠁⣠⠎⢀⠜⢠⠎⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠟⣫⠊⠀⢀⡜⠁⣠⠊⢠⠏⣰⠋
⠀⠀⠀⠀⠀⠀⠠⣞⣋⣠⣴⣇⣠⡴⢿⣀⡴⠁⣠⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⣿⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⣿⣿⣿⣷⢻⣎⠻⣮⣿⣆⠳⣌⠛⠷⣶⣶⣽⣿⣿⣿⣾⣿⢃⣴⣿⡿⢟⣫⣾⣧⣾⣿⢟⣠⣿⣵⠏⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡄⢻⣧⡀⠹⣿⣿⣿⣿⣶⣄⡈⠙⣿⡎⢻⣿⣿⣾⣿⣯⡾⣫⣭⣿⣿⣿⣿⣿⣿⠏⣠⣶⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢻⣷⠀⣿⢇⣤⣌⡙⠻⢿⣦⣹⣧⣾⣿⣿⣿⣿⣿⣴⣿⡿⠛⢉⣡⣤⣸⣿⣾⡿⠋⣠⡿⢣⣿⣹⣿
⣿⣿⣿⣿⢿⣷⡀⢻⣷⣿⣸⢳⣎⣙⢦⡀⠙⠿⠛⠋⠉⠉⠉⠙⠛⠿⠋⢀⡔⣋⣥⠸⡇⣿⡟⣠⣾⠟⠁⣼⢣⣿⣿
⣿⣯⢻⡟⣧⡹⣿⣌⣿⣏⣿⢸⣙⡾⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡰⣿⣿⡃⡇⣿⣿⠟⠁⣠⣾⣿⡿⣿⣿
⣿⣿⣎⢿⣌⠻⣿⣿⣿⣿⣾⡘⣛⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢣⣷⣿⣯⣴⣿⣿⢟⣩⣾⣿⣿
⣿⣷⣿⣾⣿⣦⣌⣻⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢟⣿⣿⣯⣶⣿⢟⣱⣿⣿
⣿⠶⢈⣙⣻⣿⣯⡉⠉⠁⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⣉⣽⣿⣿⣿⡿⠛⢻
⣿⣫⣭⣭⣿⣟⣛⣛⡶⡄⠀⠀⠀⠀⡞⠀⢰⡏⠳⡄⠀⠀⠀⢠⠞⣽⠀⠈⡧⠀⠀⠀⠀⠀⢾⣛⣿⣿⣿⣿⣿⣿⣻
⣿⡿⢟⣿⣿⣫⣭⠍⠁⠀⠀⠀⠀⠀⠸⡄⢸⡇⠀⡇⠀⠀⠀⢸⠀⢿⡇⣠⠃⠀⠀⠀⠀⠀⠈⠭⣭⣛⣿⣯⣟⡻⢿
⣿⣴⢟⣿⣿⠟⠁⢀⣀⣀⣀⠀⠀⠀⠀⠈⠚⠓⠊⠀⠀⡤⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⣀⣀⣀⡀⠈⠻⣿⣿⣷⣭⣻
⣿⣶⣿⣿⢇⡴⢋⣭⠿⠛⠉⣿⡷⢦⣄⡀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⠉⠙⠻⣍⠛⢦⣹⣿⡿⣿⣿
⣿⣾⣿⣿⡟⢀⡾⠁⠀⢠⠾⢫⡇⠀⠈⠙⠳⠦⠤⣤⢰⣿⣂⡤⠤⠴⠚⠋⠁⠀⢸⡙⠧⡀⠀⠈⠳⠀⢿⣿⣿⣿⢻
⣿⣿⡇⢹⣧⠸⠁⠀⠀⠀⠀⢚⣇⠀⠀⠀⠀⠀⠀⢀⡏⡇⢯⡀⠀⠀⠀⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣾
⣿⣿⣧⠈⢿⡄⢤⠀⠀⣀⡤⢟⣿⠀⠀⠀⠀⠀⢀⡞⣠⣿⡌⢧⠀⠀⠀⠀⠀⢸⣿⠳⢤⡀⠀⠀⡄⢠⡟⠟⢸⣿⣿
⣿⣿⣿⣷⡈⠳⠸⡷⠤⣤⣴⡿⢻⣷⠀⠀⠀⢀⡞⣰⠃⡇⠹⣌⢧⠀⠀⠀⢸⣾⠟⢷⣤⣤⠴⣾⠇⠟⠀⣠⣿⣿⣿
⣿⣿⣿⡿⢿⣷⣶⣿⣷⡿⢯⣤⡀⢿⣴⠀⠀⣼⡼⠁⠀⡇⢀⠘⢮⣧⠀⠈⣾⡟⢀⣤⡽⣿⣾⣷⣶⣶⡾⢿⣿⣿⣿
⣿⣮⠻⣷⡀⢠⣾⣿⣿⣿⣶⣌⢻⡌⣿⡀⠀⣿⣇⠀⡀⠟⠀⠀⣼⡿⠀⢀⣿⢠⡟⣡⣾⣿⣿⣿⣷⡄⢠⣿⢏⣵⣿
⣿⣿⣧⠘⣷⣿⣿⡸⣿⣼⣿⢿⣾⣇⣿⠙⢆⢸⣿⠀⠀⣤⠀⢀⣿⠇⡴⠋⣿⣾⣾⡿⣿⣷⣿⢡⣿⣿⣾⠃⣾⣿⣿
⣿⣿⣿⠀⢸⣿⠹⣿⣿⢿⣿⣸⣿⣿⠇⠀⠈⢿⣿⡆⡦⠀⠄⢸⣿⡾⠀⠀⢻⣿⣿⣅⣿⡿⣿⣿⠫⣿⡇⢠⣿⣿⢻
⣿⢻⣿⣇⠈⣿⣷⡿⣃⠘⣭⣿⣿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⣿⣿⣭⠁⡛⣿⣾⡿⠀⣼⣿⠏⣸
⣿⣶⣿⣿⣷⣬⣝⣛⣻⠿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⡿⠿⣛⣋⣭⣤⣾⣿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⢠⣶⣆
⠀⠀⠀⠀⠀⠀⣾⠀⢿⡀⠀⠀⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠈⢷⡀⠀⣇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿
⠀⠀⠀⠀⠀⣠⡈⢷⠀⠈⢻⣄⢻⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⠃⢠⡟⣀
⠀⠀⠀⠀⠀⣿⠙⣾⣧⡀⠀⠙⢿⣷⡀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⡾⠁⢀⣾⡾⢻
⠀⠀⠀⠀⠀⢻⡆⠀⠙⢿⣄⠀⠀⠙⢷⡄⠀⣸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣼⠏⠀⢀⡾⠋⢀⡿
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠈⠻⢦⣀⠀⠉⠳⣿⣆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⡴⢿⠁⢀⡴⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⢸⡷⠾⣿⣦⣀⠀⠀⠉⠓⠦⣄⣿⡈⠳⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠔⠉⣰⣯⠔⠁⠀⢀⣴⡿⣶
⠀⠀⠀⠀⠀⠈⢻⣄⠀⠉⠙⠓⠶⢤⣄⣀⡀⣾⠻⢆⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⡀⠐⠈⣼⣃⣠⠴⠚⠋⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠈⠉⠙⢧⡀⠙⠲⠄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡧⠶⠶⠶⣤⣤⡞⠉⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠛⠛⠓⠒⠒⠒⠒⠒⠛⠳⢦⣤⣀⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣤⣀⣀⠈⠻⣶⠚⠛⠛⣻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣠⣤⡤⠤⢠⣼⢧⣤⠀⠀⠀⣿⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠈⠑⡄⠘⣧⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⡤⠤⠤⠤⠤⠤⠺⣧⣀⣀⣀⠀⠀⠘⢷⣄⣀⣠⡟⠀⠀⠀⠀⠒⠾⣿⣿⠀⠀⢸⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⠤⠄⢾⡉⠀⠀⠀⠀⠀⠙⢿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠉⠁⠀⠀⢀⣨⠷⣄⣀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢶⡖⠋⠁⠀⣀⠌⠋⢙⠛⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣖⠋⢁⣠⠖⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⡋⠀⠀⠀⠀⠀⢻⡖⠀⠀⣀⣤⣞⣀⣤⣤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣏⡡⠀⠀⢀⡔⠀⠀⠀⠀⣾⢷⠾⡏⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⡿⠛⡁⠄⢀⡴⠃⢀⠌⠀⡌⢰⣿⢸⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠟⠉⠄⠀⢀⡴⠋⠀⡰⠃⢀⠞⢠⡏⣿⠘⡇⢿⡀⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣞⡁⢀⣀⣠⡶⠋⠀⣠⠞⠀⣠⠏⢀⡿⠀⠹⢦⡿⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⣼⠁⣀⣴⠃⢀⣴⡏⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⢿⠶⠟⠛⠷⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣴⣿⣵⣿⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢛⡿⣻⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣻⣄⠁⢀⡩⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠋⠁⠀⢈⣿⠁⠰⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠬⠁⡙⣭⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡰⠷⠆⣰⣞⣷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠀⣀⣼⠳⣶⡻⢮⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢠⠀⠸⣿⣿⢄⠛⣬⣙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡐⠃⠀⢸⣿⢠⡈⢻⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣀⣠⡞⠃⠀⢠⣿⣿⣷⣼⣻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣥⣀⣀⡀⣀⡘⣯⡄⢉⣻⡗⠠⣾⣿⣿⣝⢷⡼⠋⠀⠀⠀⠀⠀⠈⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢿⣿⢉⠘⠛⠛⠻⣿⣿⣿⣿⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣦⣠⣿⣿⡠⡀⡄⠀⠀⠈⠻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠆⠛⠉⠉⠀⠉⠛⠻⠉⠻⣥⣡⡀⠀⠀⠀⠀⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⣀⡀⠤⠒⠉⣀⣤⣔⣾⣾⣷⣦⡌⠡⣄⢘⠅⠀⡄⣥⡁⠑⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠁⠈⠀⢰⣦⣴⡒⢘⡷⣺⣿⡿⠛⠉⠀⠀⠘⣿⣿⣿⣠⣼⡧⢀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠘⡿⣇⢀⣀⣴⣤⡶⢿⢿⣿⣿⣧⣿⠞⠋⠀⠀⠀⠀⠀⠀⠨⣷⠙⠛⣳⠼⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣷⣠⣸⢾⡇⡛⡽⣿⣿⣾⣝⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣉⢿⣾⣾⣽⣾⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⣠⠞⠩⢀⡤⠶⣾⣷⠶⣄⠀⠀⠀⠀⠀⢀⠀⠌⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡾⠁⠀⣰⠋⠀⠀⠈⠻⣷⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⣼⠃⠀⠀⠀⠀⠀⠘⣿⡌⢧⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡄⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⢰⣦⡀⠀⠀⣿⢸⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠈⣧⠀⠀⠀⢸⣿⡝⢦⡀⠏⢸⠇⡁⠀⡁⠀⠀⠐⠀⢸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⠀⣸⠘⣷⡀⢹⡇⢹⠀⠈⡊⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠹⣎⣡⠙⢦⡀⡟⣶⣿⣧⣼⠀⠸⡆⠀⠀⢆⡀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠐⡆⠀⡀⠀⠀⠀⠀⠀⠈⣻⣷⣤⣉⣓⣟⣉⣵⡇⠀⠀⢧⠀⡓⠒⠒⡄⠀⣀⡀⠀⠀⠀⠀⠙⢀
⠀⠀⣰⣇⠈⡏⠀⠀⠀⡐⠈⠀⣤⣇⠼⣟⣿⣯⣿⡋⡜⠀⠀⠀⠘⣆⠀⠀⠀⡇⠉⣄⠙⠋⠐⠒⠲⠄⠤
⠐⢠⠇⠸⡄⣇⠥⡀⠇⣘⠀⠐⠿⠿⣽⣧⣟⡗⣏⠟⠁⠀⠀⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⣌⡉
⣠⡏⠀⠀⢹⡇⠃⠐⠀⠄⠾⠂⢼⡆⣼⣙⡮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡁⠀⠀⠉⠈⠒⠂
⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠃⠈⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⢂⡡
⠈⠓⠤⠔⠊⠀⠀⠀⠀⠀⠐⠆⠠⡶⠖⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢶⣤⡼⢃⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣀⣀⣡⣤⣔⣀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢧⣼⣿⣿⣿⣿⣧⣼⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⢻⡿⠀⠀⠀⠀⠀⣀⠀⣠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢧⠚⠁⢠⢄⠀⠐⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⠉⠀⠀⠀⡠⠔⠒⢂⠎⣸⡖⠁⣴⢦⣄⠈⠙⣿⣿⣤⡀⠀⡌⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠩⣐⣚⡁⠀⡀⠠⠘⠁⠘⡄⠙⠚⠿⣿⠦⣼⠛⠿⠛⠀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣹⠇⡀⠄⢇⠀⢠⡁⣤⠔⠊⠀⢡⠈⡟⢂⠀⠀⡉⠀⠀⢠⡾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⡻⢃⡀⣴⡆⠱⡀⠀⠸⣉⠦⠒⠋⠺⠁⠺⣦⡐⠸⠀⢀⣩⣴⣿⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⠆⠻⢯⣬⣿⣾⣏⢀⣀⠃⠀⡀⡀⠀⢠⡀⠈⠈⢇⠀⠀⠀⠈⠻⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣂⢠⣠⡄⠐⠒⢩⠛⠉⣔⡄⠀⣉⠲⡄⠃⣀⣠⣤⠀⡠⢀⠉⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡁⡨⢣⡀⢰⠁⠀⠀⡽⠧⠛⠃⠀⡎⢁⡮⠛⠃⠪⢄⣨⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠅⠀⡋⠉⠲⠏⠉⠋⠀⣼⡀⡠⠒⠉⠉⠁⠲⡷⢃⢠⡕⡀⣧⠕⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⡀⠙⠢⢭⣳⠀⡄⠀⠰⠆⠀⢹⠀⠰⡆⡴⠶⠖⠘⠇⡸⠱⢡⣏⣀⡊⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠂⢐⡡⠚⡇⠀⢠⣤⣴⡄⠀⠀⡀⠄⠠⠀⣤⠀⠀⡟⠀⢀⠸⡃⡐⢍⢣⡊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣈⣏⣀⣈⣑⣉⣀⣀⣀⣇⣑⣘⣘⣛⣀⣀⣃⣀⣈⣀⣇⠠⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⣀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⠀⢀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⠀⠘⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠒⠒⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⡗⢦
⠀⠱⣄⣦⠀⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡀⡀⠈⡓⣄
⠀⠀⠘⢿⡷⠾⢷⡢⣳⣦⣀⣦⣤⣀⣀⣀⣀⣀⠬⠿⠍⢛⣉⣉⣉⣙⣓⠲⣄⣀⣀⣤⣤⢔⣊⣥⠎⠸⢱⡀⠀⠘⢆
⠀⠀⠀⠀⢳⡑⢄⠈⠢⢬⣉⣉⡁⢨⣍⣋⠀⣀⠠⠶⢚⣉⡤⠴⠒⢦⡤⠐⠈⠉⠀⢶⣝⡉⠉⠅⠀⢨⠘⢿⣄⠈⡈⡆
⠀⠀⠀⠀⠀⠻⣦⡀⠐⠠⠉⠻⣦⣄⣈⣱⣤⣬⣴⣤⣠⣤⣴⠾⠿⠏⠀⠀⠀⠀⠀⢠⡿⠿⠛⢁⡠⠁⠀⠄⢻⢆⣻⢷
⠀⠀⠀⠀⠀⠀⠈⠒⢅⣘⣶⢀⣒⡂⠙⠉⠁⢀⠤⠊⠵⠟⠁⣴⠿⠀⡠⢤⣤⣀⠒⠦⠄⠀⠀⠋⣰⠃⠀⠃⢀⠀⢳⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠤⢬⡭⣤⡀⢀⣠⣔⠀⣐⣝⠁⠀⠐⠀⠠⠃⠈⠹⠮⡑⠒⠋⣊⡵⢂⣠⠀⡀⢀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠿⠭⠥⢤⢠⣄⣀⣀⣀⠀⠀⠈⡄⣸⣯⣰⡿⠿⠞⡁⣺⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⡂⠭⣉⣉⣷⡿⠿⢖⡂⠈⠀⡴⣛⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣭⠯⣉⡷⢘⣧⣤⣿⣿⣿⣿⠄⡜⣟⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢚⡆⡼⢷⣿⡿⠿⠋⡡⠋⠋⢺⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣏⡵⢂⠌⠠⠂⢀⠆⢸⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⡞⢰⠁⢠⠎⠀⡄⠰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢛⢠⢿⢀⢾⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⠘⠇⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡷⣾⠟⠉⢣⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢾⡿⣯⣏⣀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠈⡏⠸⠟⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢀⣄⣴⡏⣾⣷⣴⢤⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠀⠟⠀⠋⠈⢱⡈⣱⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣌⢻⡷⠞⠢⠄⢀⣸⠇⢹⢇⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⠛⣿⣿⡈⠃⠀⠀⠀⠀⠀⠀⠈⢈⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠛⣡⣞⣿⢿⣷⠀⢿⠀⠀⢀⣦⠀⢀⠋⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡘⠷⢸⡟⠸⠟⢹⣿⠿⠀⠀⠀⠀⢸⡟⠘⠛⡀⢘⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠼⠛⢇⣉⣥⠆⠀⠀⠀⠀⠈⠀⢡⣾⡇⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡤⠀⣠⡴⢯⡼⠇⢀⣀⣙⠀⠀⠀⢀⡼⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣤⠀⠿⠁⣼⢟⣾⣿⣿⠀⣜⠉⠁⢰⡆⠀⠀⣠⡿⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⣡⡟⠸⠇⣠⣾⣿⣿⣿⠀⠟⠋⠀⠠⡤⠄⠀⠉⠁⠘⢿⣿⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠻⢠⣾⣴⣿⣿⣿⣿⠃⣸⠖⠂⠀⠀⠀⠀⠰⢀⡄⠀⢶⡟⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢸⡷⢠⣼⡿⣿⣿⣿⡏⣸⣟⡛⠁⣰⠀⠈⢹⡄⠄⠀⢆⣈⠳⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠘⠁⢈⠻⣷⣿⣿⣿⣿⡟⡟⠉⠀⠈⠀⠀⠀⣤⡄⢀⣸⠇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣦⠀⠈⢱⡞⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠈⠉⠀⣼⡁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣏⠘⡿⣾⣤⣿⣿⣭⣾⣿⡿⠖⠀⠂⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⡜
⠀⠀⠀⠀⠀⠀⢠⣿⣹⡶⠃⠙⣿⣿⣿⣿⣿⣿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⡏⢩⣥⢀⡀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠟⠧⠘⣿⣼⡇⣿⣿⣿⣿⣿⠉⠋⠀⠀⠛⠠⠀⣠⠋⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢠⠀⣀⡸⠃⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⢀⡄⠁⠀⠀⣰⠏
⠀⠀⠀⠀⣸⣿⣍⠀⣹⠇⣼⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣴⠋⠀⠀⠀⠰⠋
⠀⠀⠀⢰⣿⣿⠃⠀⣿⣾⣿⣿⣿⣿⣿⡿⢀⡀⢀⣶⣿⠟⠀⣠⣷⠘
⠀⠀⠀⠸⠛⠁⠀⡄⣿⣿⣿⣿⣿⣿⣏⡿⠟⣻⣿⠁⣿⣯⣾⠟⡿⠀⢀
⠀⠀⠀⠀⠀⠀⠰⢁⣿⣿⣿⣿⣿⣳⠏⡀⢠⣿⠷⢀⣈⠛⠓⣶⣷⣤⣀⣀⠁⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⢍⢤⡛⢹⡤⣶⡏⠉⢉⠉⢉⢙⡁⠈⡏⢉⠉⠍⠉⠛
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢀⡜⣀⠀⠉⢰⣿⡇⠀⠀⠁⢸⡎⠁⠁⠁⢹⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣹⣿⣼⣿⠀⠀⠀⢿⡇⢰⣀⡇⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢀⣿⣿⣿⡿⠀⠀⠀⢸⡇⠈⢿⠃⠘⣿⢠⠀⠀⢸⡀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⣿⣿⢿⣿⠇⠀⠈⠀⠘⣧⠀⣸⠁⢰⣿⡇⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⣾⡏⠀⣼⡟⠡⣬⡟⠀⠀⣸⠇⢀⣿⠀⠁⠀⣸⢹⡇⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢀⡿⠀⣸⣿⠃⣴⠃⠁⠀⣸⡏⠀⡼⢿⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢸⡇⠀⣿⡏⡸⣏⠀⠀⠀⢻⣿⣶⣧⣼⠀⠰⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣼⠀⣰⡟⢠⠃⠈⠀⠀⠀⠈⣿⠁⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠘⠀⠾⣧⢆⠀⠀⠀⠀⠀⠐⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢠⣿⠏⠀⢠⣿⠃
⠀⠀⠀⠀⣤⡀⠀⠀⣿⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⣼⠇⠀⣴⣿⡇⠀⣠⣿⣧
⠀⠀⠀⠀⢻⣧⠀⠀⣿⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢹⣿⠟⣠⡾⣫⠟⢀⣼⠟⢸⡿
⠀⠀⠀⢠⣦⣽⣷⡄⠸⣇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣸⣯⡼⢋⠴⢃⡴⠟⠁⢠⡿⠁
⠀⠀⠀⠸⣯⠈⠛⠿⣷⣽⣆⠀⢷⡀⢠⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⣁⠀⢠⡿⣫⠖⣡⠶⠋⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠉⠛⠷⣦⣿⣼⣧⡀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⣿⣰⢟⡫⠴⠋⠁⢀⣤⣶⡛⠁
⠀⠀⠀⠀⠀⣨⣿⣦⣄⣀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣼⠟⢋⣁⡤⠴⠖⠛⣉⢩⣽⡟
⠀⠀⠀⠀⠀⠻⣧⡀⠉⠙⠛⠓⠶⠶⠤⢽⣷⣤⣄⡀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⣿⠭⠥⠤⠤⠤⠤⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⣀⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣿⣒⠒⠒⠶⣶⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⣛⡉⠉⠉⠉⠉⠩⠽⢷⣤⣤⠀⠀⠀⠻⣦⣀⣤⡾⠃⠀⠀⠀⠀⢀⣴⠿⠟⠛⠛⠿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣤⡤⠤⠶⠒⠻⣧⡀⠀⠀⠀⠀⠈⠻⣧⣤⣤⣤⣤⣤⣴⠟⠁⠀⠀⣀⡀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⠴⠖⢚⣉⠿⢦⣤⣀⣀⡀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⢒⣊⣡⠤⠒⣉⡤⠛⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠶⠚⢉⣡⠴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣯⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠋⣠⠖⢁⡤⠀⡀⠠⣿⡆⠀⣴⣟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠋⢀⡴⠊⠀⡠⠊⢀⡞⠁⣰⠏⠹⣦⠹⣟⣷⣶⠶⠄
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⠞⠉⠀⡠⠊⠀⣠⠋⠀⣴⠏⠀⠀⢸⡷⢿⣏⠛⠃
⠀⠀⠀⠀⠀⣩⣽⣿⣿⣿⣿⣁⣀⡴⠋⠀⢀⡜⠁⢀⣼⠏⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠙⢋⣽⣿⣿⡿⣿⣏⢀⣠⣴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⢴⣿⡿⠟⣿⣿⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⣿⠏⠀⠀⠀⣴⣾⣿⣦⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣿⡏⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠸⠿⠿⠛⢀⠶⠄⠘⢿⣉⠀⠀⠀⠀⠀⢠⠃⠀⣿⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣼⡿⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠈⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠀⠐⡡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠋⠀⢀⣤⠟⠀⠹⣿⣿⣿⣶⣶⣶⠆⠀⣰⠀⢀⡷⠀⢸⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣶⠿⠋⠉⣿
⠀⠀⠀⠀⢀⣠⣿⡋⠉⠀⢠⣾⣿⣄⣀⣠⣀⡙⠻⠿⠿⣿⣿⣦⣤⣿⣤⣼⣿⣤⣾⣿⡋⠀⢀⣀⣠⡾⠿⣦⡀⠀⠀⠀⠀⠀⣴⡿⣿⠀⠀⠀⠀⠀⣰⡟
⠀⢀⣴⠾⠛⠉⠉⠉⠻⣆⣸⡟⠀⠉⠉⠙⠛⢿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⡿⠿⠿⣧⠀⠘⢷⣦⣤⣤⣤⣰⣿⠀⠘⠷⠶⣶⡶⠟⠋
⠀⣾⡇⠀⢀⣤⣤⡀⣀⣿⠟⠁⠀⠀⠀⢠⡄⠀⠙⢷⣿⣟⠛⠛⠛⠻⣿⡟⠹⣿⣛⣉⣀⣀⣠⣤⣶⣿⣶⣦⡄⠉⠁⢨⡿⠟⠃⠀⣠⣶⡾⠟⠀⠴⠂⠄
⠀⠈⠛⠛⠋⠉⠈⠙⡛⠁⡀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⠿⠿⠷⠶⣾⣿⠃⠀⣿⡛⠉⠉⠉⢉⣉⣉⣿⠇⠹⣿⣀⣴⣿⣦⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠀⠀⢠⠀⠻⢷⣦⣤⣄⣠⣤⣴⣿⠀⢸⣿⣟⡛⠛⠻⠿⣿⣿⡁⢀⠆⠙⠛⠋⠀⠹⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⣉⣽⣿⡄⢸⣿⡛⠿⣿⣷⣶⣤⣽⣿⢠⡇⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠟⢋⣩⣿⣷⣿⣿⣿⣦⣄⡙⢿⣯⡉⠀⠈⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣯⣴⡾⠿⣿⣿⣁⣠⣿⣿⡿⠿⢿⣷⣿⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠿⢿⣶⣤⣶⠟⠙⠷⣦⡤⡈⠙⣿⠟⢁⣤⣶⠟⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⣦⡀⠀⠀⠈⢀⣀⡀⣠⡿⠀⠀⣠⣿⠀⠈⢻⣇⠀⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠁⢸⣿⣤⣤⣾⠿⠛⠛⢿⣤⣴⠾⠋⠙⠷⣦⣤⣿⣦⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⠻⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠈⢻⣧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠈⠙⢻⣦⣤⣄⡀⠀⠀⠀⠘⠟⠀⠀⠀⠀⣿⡷⠾⢿⣷⣾⡏⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠛⣿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢈⣩⣿⠆⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⠃⢰⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣾⠟⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⢷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣤⣄⡀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢳⡄⠈⢹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣧⣀⠀⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣀⣠⠴⠶⠶⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡀⢀⡤⠖⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⠟⠹⣶⠋⠀⠀⠀⠻⣄⠀⢀⠀⠀⢠⡴⢰⣾⣇⡼⢧
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⢠⣌⠳⠖⠋⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⢀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠟⠀⠀⠀⢹⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠸⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠛⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢷⣿⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠙⠿⠁⠀⠀⢀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢻⣆⠀⠀⠀⠀⠰⣤⡀⢀⣠⡄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⢳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⢷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠀⢠⣀⠀⢉⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣾⣇⠀⠀⢿⣷⣤⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠉⠉⠛⢳⡶⠤⠶⠚⠛⠉⠀⠀⠘⣏⠀⠴⠤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⠤⠚⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠃⠀⠀⣿⡉⣹⠏⠉⠉⠉⠉⢁⣀⠀⣼⠿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠏⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⡏⢉⣿⣿⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⢋⡴⠲⡄⠀⠀⣠⠖⠲⡄⠀⠀⠀⠉⠊⢹⡟⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⠈⠳⠞⠃⠀⠀⠛⣤⠾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⣄⠀⠘⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⠋⢙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡴⠇⠀⠀⠀⢳⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⡀⠀⠀⠙⠓⠋⠀⠀⠀⢠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡸⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⡷⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠉⠉⠀⠀⠀⠺⣅⣿
⠀⠀⠀⠀⠀⠀⢸⡿⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠿⠀⠀⠀⠀⠀⠀⢀⣀⢼⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠙⣿⡽⣟⠓⣂⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⠾⣿⠛⠊⢳
⠀⠀⠀⠀⢠⡎⠀⠀⢰⡟⠀⡏⠀⠀⠀⠀⠈⠘⡿⢻⡄⠈⠉⠉⠉⠛⠛⢻⣿⠹⠉⢻⠀⢹⠀⠀⠘⡆
⠀⠀⠀⠀⠘⢧⣄⡀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢃⢸⡇⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠹⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⣀⣠⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠿⠶⠶⠶⠶⠾⠿⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⣠⡀⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⠁⠀⠈⣻⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣺⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡜⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⣨⠟⠛⠷⣤⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣅⣀⣀⢀⣀⣈⣉⣉⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⣿⠿⠿⡿⠿⠿⢏⠹⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⡟⣻⣛⠛⠛⠛⣛⡛⣛⢻⣿⣿⠛⠛⠛⠿⠿⠟⢻⠛⠛⠻⣿
⣿⣷⣿⣶⣶⣷⣾⣶⣾⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⣾⠏⣀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠞⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣄⣀⣀⠀⢻⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣿⣀⣿⣤⡟⠿⠁⢼⡟⠛⠛⣧⣀⣿⣆⠀⠀⠀⠀⢵
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣃⣼⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡂⢠⠟⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⠄⠀⢸⠃
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⡄⢀⡎
⠀⠀⠀⠀⠀⢹⣸⣇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠆⣸⠃
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋
⠀⠀⠀⠀⠀⠀⢹⣆⠹⣦⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣠⡾⠃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠼⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣦⣤⣄⣀⡀⠀⠀⢀⣀⣠⣤⠞⠛⣿⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠙⢿⣄⠈⠉⠙⠛⠚⠉⠉⠁⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠛⠿⠶⢶⣤⣀⣀⣀⣤⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣠⡛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠶⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠶⣦⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢾⡷⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣧⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⡀⢠⣴⠀⢶⣾⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣦⣾⡿⠿⠛⠉⠁⣿⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⢻⡃⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠄⢦⣤⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠶⠶⠶⢶⣤⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⣤⠚⠛⠛⠛⠛⢳⣄⣼⠋⠁⠀⠀⠀⠀⠈⠙⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢾⣧⣄⠀⠀⠀⠀⠀⠀⣨⣿⣤⣤⣀⣤⣤⣤⡤⠶⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣿⣶⣶⣾⡛⠾⠉⠈⠙⠛⠋⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⢦
⠀⠀⠀⠀⢀⣴⢲⡴⠲⡀
⠀⠀⠀⠠⢧⡴⠋⢀⢆⠡
⡀⢿⠀⢸⢄⠉⢻⣙⠂⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠂
⢇⠈⢆⠈⠶⠑⠚⠤⡾⠁⡸⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣯⣭⣭⣶⣷⣶
⠈⢦⡀⠑⠆⠀⠀⠀⠙⠶⠳⢄⠑⢄⠀⠀⠀⠀⠀⣠⣼⣏⠉⡹⢮⡉⠉⠻⣅⡀
⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠑⢌⠳⢄⠀⣶⠎⠀⠥⠾⠀⠔⠛⢠⡄⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⡏⠀⠀⠐⠮⠤⠀⢀⠞⣷⡀⠀⡷⠈⠀⢱⠂⠀⡀⠀⠀⢀⠀⠀⠀⢀⠰⠋⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠤⢶⢋⣸⠏⡇⢠⣧⡂⠀⠘⠶⠒⠉⠑⠲⢤⣀⠈⠁⠀⠀⢀⡰⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⢯⣡⡴⣡⠟⠱⡎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠉⠀⣠⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡴⠚⠁⠑⠀⡇⠈⠻⣅⣂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢘⠃⠑⠢⣌⠀⢷⠀⠀⠙⢆⠉⠚⢕⡢⡶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣄⡙⠹⡀⠀⠀⠈⢳⡀⠀⠈⣇⣘⢉⡉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⣹⢄⠀⠀⠉⢧⣱⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡞⠃⠀⣕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠉⠩⠴⠈⠀⠉⠀⠀⠪⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⠬⣽⡀⢴⠈⠓⢅⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢱⠀⠈⠳⣌⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠂⠀⠢⡈⠛⢄⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠢⠀⠙⢦⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⡄⠠⡀⣀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢐⠃⠇⠁⡇⠀⡇⠀⣼⠏⠀⠁⠀⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⢉⣥⡁⠀⠒⠀⢰⠻⠀⠀⠀⡐⡝⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡟⠉⠙⢡⠣⢀⠁⠀⠐⣸⠁⠀⠀⠀⡌⠀⠀⠀⠀⠠⠀⠀⠀⠰⡀⠀⠀⠆⠀⠀⢀⠄⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠁⠄⠄⣈⢐⠍⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠁⠀⠘⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⢧⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⠙⠋⠀⠀⢸⠀⠀⠀⠀⠔⠁⣠⠑⠄⠀⢠⠀⡇⠀⢀⠄⣠⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠓⠚⠆⠀⠀⡀⠀⢀⠌⢀⠜⠀⠑⠌⠢⠈⠀⡇⠠⢂⠔⠀⠑⢄⠈⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣧⡤⢤⣤⣀⠀⠁⠀⠌⡠⠂⠀⠀⠀⠈⠢⡘⡀⡱⠡⠂⠀⠀⠀⠈⠢⡈⠆⢀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠨⡀⡜⠐⠁⠀⠀⠀⠀⠀⠀⢱⡜⣰⠁⠀⠀⠀⠀⠀⠀⠐⠌⡌
⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠃⠀⠀⠀⠀⠀⠀⢀⠏⡸⡉⢇⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠈⠄⠀⠀⠀⠀⠔⢡⠎⠀⠈⢢⠑⠄⠀⠀⠀⠀⡐⠠
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣠⣤⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠠⠓⠐⠒⠒⠀⠤⠀⠀⡇⠀⠀⠀⠘⠊⠀⠀⠀⠀⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠍⣐⣂⣒⣛⣛⣛⣛⣛⣛⣛⣓⣒⣀⠨⡁⠢⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡘⣐⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⠸⡀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⡇⡟⡈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠑⠀⠠⠤⠤⢌⢧⣀⠀⠀⣀⢎⣔⣀⣢⡡⣀⠀⡀⣀⡼⣰⠇⠧⢀⡀⠀⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠉⠩⠐⠀⠀⠀⠀⠈⠂⠽⡟⢋⡊⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂

⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣷⣦⣄⡀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣶⣦⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡙⠿⠿⣿⣿⣿⡿⠿⠋⠙⠻⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠈⠓⠂⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣭⣿⠁⠀⠀⣀⣀⣀⣉⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣄⣠⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠈⢳⡤⣀⠀⠀⡞⢹⣷⣶⣄⣀⠀⠀⠀⠀⠈⢳⣄⠀⣩⣽⣿⣿⣿⣿⣿⣟⣋⣉⣤⣤⣴⣦⡀⠸⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡑⡼⠃⠀⠛⢿⣿⣿⣶⣄⢀⣰⣶⣶⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⢻⣷⣤⣬⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡆⠀⢀⣠⣬⠿⠿⠿⠻⠟⠉⠛⣿⣿⣿⣿⣿⣿⣿⡿⢻⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣮⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡟⠻⠛⠋⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣋⡁⣀⣠⣤⣶⣾⠶⠿⢿⡯⣁⣀⣀⡁⡀⢀⣠⣤⡄⣀⣀⣠⣆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⣸⣿⡿⠟⠉⠁⠀⠀⠀⠀⠙⠋⠉⣹⢛⣟⠛⠣⡈⢑⣄⠀⠈⢮⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠷⠁⢠⡿⣾⣨⣦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠁

⠀⠀⠀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣉⣀⠀⠀⠈⠳⡄⠀⠀⠠⠂⠀⠠⠀⠀⠐⢁⡀⠁⢀⠀⠀⠂
⠀⡐⠀⢀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠋⠀⠀⠀⠑⡆⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠀⠘⠀⣶⠾⠛⠛⢛⠒⠦⣄
⠰⠀⠀⠀⠢⡔⠁⠀⠀⡅⠀⠀⠀⡄⠀⠀⠀⠀⣸⠀⠀⢸⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠀⠀⠹⣄⣀⠔⠛⡆⠀⠀⣷
⠀⠑⠒⠒⠉⠈⠑⠒⠚⠀⠀⠀⠀⠐⣄⠀⢀⡴⠃⠀⢀⠜⠀⠀⠀⢰⠄⠀⠰⠀⢠⠀⠀⣠⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠙⠶⠚⠉
⠀⣏⠐⠒⠀⠀⠒⠂⢈⠇⠀⠀⠀⠀⠈⠉⠃⠒⠐⠊⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⢢⠴⠁
⠀⠀⠠⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⡙⠀⠀⠀⠠
⠀⠀⠀⠐⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠈⠑⠢⢀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠓⢦⠀⠀⠀⠀⠀⠈⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠰⠒⠀⠀⠠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⣄⠐⡦⡌⢀⢴⠀⡀
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠤⡴⡼⠋⠁⠉⠙⢤⢠⠄
⠀⠙⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⠏⠀⠀⠀⠈⠢⡀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠙⡖⠒⢊⠒⣺⠉⠁⠀⠀⠠⠆⣹⠀⠀⠀⠀⠀⢸⡉⠤
⠀⠀⠙⠿⠿⠟⠁⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠘⢦⣀⠇⠀⠀⠀⠀⠀⠀⠀⢻⢀⠠⢐⡇⠀⠀⠀⠀⠀⠚⠰⠣⣀⠀⢀⣠⠺⠔⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠈⣇⠀⡽⠀⠀⠀⠀⠀⠀⠀⠋⠸⡞⢃⠝⠮⠀⠃
⠀⠀⠀⠈⡄⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠃⢀⡤⠀⠀⠀⠀⠀⠘⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⢶⠿⠀⠁⠰⡀⠅⠀⠀⠀⢴⠿⠿⣿⣿⣿⠿⢗⡆⠀⠈⠀⠀⠏⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉
⠀⠀⠀⠈⡄⠀⠀⣴⠁⠀⠀⠀⠀⠈⣖⠒⠂⠒⠒⠂⡉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣄⢸⣷⣄⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠠⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⡷⢌⢄⠀⠀⠠⠂⠀⠀⠀⠠⢀⠀⢰⣿⠿⠛⠉⠉⠀⣶⠀⠈⠂⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠒⢰⠀⠀⠰⢐⠪⠜⠀⠘⠁⠀⠀⠀⠀⣼⣿⣧⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠈⠂⠩⡭⠐⠁⠀⠀⠀⠀⠀⠈⠂⠤⠠⠄⣊⣀⠀⡐⠁⠀⠀⠀⠀⠂⠀⠀⢀⣼⣿⣿⣿⡔⠀⠀⣀⣂⣴⣿⣀⣀⣀⠴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠒⠺⠿⠟⠛⠁⠀⠀⠀⠈⢙⡙⠛⢋⡋⠛⠋⣙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣠⠖⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠻⠟⠋⠉⠈⢉⣉⣩⣬⣿⣿⣶⣶⣶⡶⠞⢋⡡⠛⠱⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣦⣾⣾⣷⣿⣿⡿⠿⢛⠛⣽⠾⠋⢀⡴⠋⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡌⣉⣉⠉⣙⠉⡉⣉⣩⡄⣴⡖⠚⠋⠁⠀⣠⡞⠁⠀⢀⡿⡿⢿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢿⣫⣾⣟⣾⣟⣻⣿⣅⣋⠁⣀⣠⢴⣾⠁⠂⠀⠘⣩⣿⣿⢠⣝⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⣿⣿⣿⣿⠿⠟⢟⣻⣿⡿⢁⡞⠁⠀⠀⠀⠸⣿⣿⣷⠐⢿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠈⠁⠈⠈⠀⠀⢠⣠⣽⣿⣿⠟⢁⡜⠁⠐⠒⠳⣤⠀⠙⢿⣯⠰⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣄⣀⣢⣤⣶⣶⣾⣿⣿⠻⠋⠀⡼⠁⠀⠀⠀⠀⠙⢧⡀⠀⠉⠺⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⢿⣽⣿⡿⠟⠋⠁⠀⠀⡴⠁⠀⠀⡄⠀⠀⠀⠀⠙⠢⡀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⢲⣶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⢀⡄⠀⠀⣆⢰⡀⠀⡀⢸⣿⣿⣼⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⡀⠀⠀⢀⣠⠴⠋⣀⠀⠀⠀⠀⠉⠀⠈⣧⠘⢶⣿⡶⠶⠞⠋⣩⠇⠀⠁
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠄⠈⠁⠀⡴⠎⠁⡴⠉⠉⢷⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢰⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⢀⣤⠐⠀⠀⢰⠁⠀⠀⢸⡂⢸⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠈⠀⠀⠀⢸⣧⣸⠇⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠀⠀⠠⣿⡀⠀⠀⢠⡀⠀⠀⣧⠀⢀⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⠀⠀⣿⣿⣷⣀⠠⢀⣳⣦⣤⣯⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⢀⣸⡟⠛⠉⠿⢿⡿⠋⠈⠻⡟⠛⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⡼⠿⠁⠀⠀⠀⡉⠀⠀⠀⠀⢠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠲⠙⠓⠉⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠉⡻⠛⠲⢤⡀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⡎⠀⢀⣀⣀⣀⠤⣤⣤⠤⢂⣁⣀⡀⠀⠹⡄⢠⠦⠀⠀⠠⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⢉⣉⠀⣤⣤⡄⠀⠀⠀⣤⡀⠀⣉⡑⠂⡗⠀⠋⠀⡀⠀⠑⠨⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡚⢡⣿⣿⣿⣷⣶⣤⡄⢠⣤⣶⣾⣿⣿⣿⡆⠙⡄⠀⠞⣡⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠻⣿⣿⣽⣿⡿⠀⠀⢿⣿⣯⣿⣿⠟⠠⢚⣷⠀⠀⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡐⣚⠁⠈⠛⠛⠛⠑⠛⠚⠊⠛⠛⠋⠁⠀⣐⠃⡼⢂⡠⠀⠀⠀⠀⠀⠮⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢧⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠⠏⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⠞⢉⠉⠒⠤⡙⢦⣄⣀⣀⠀⠀⠀⣀⣀⣤⠞⠁⠀⠀⠀⠊⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⡍⠀⡀⠀⠀⠀⠈⣦⠤⠽⢿⣉⣉⣹⠿⠷⠦⢤⠀⡀⠤⢄⠄⡀⠀⠀⠀⢀⠀⠤⠤⠒⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⠤⠄⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⠉⠉⠁⠀⠀⠀⡞⠘⠀⠠⠀⢀⠈⠆⠀⠀⠀⠳⣤⡀⠀⠀⠐⠴⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠐⠁⠠⠒⢄⠀⠀⣸⡀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠠⢹⣦⣌⠛⠿⠶⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠰⠀⠀⠀⠁⠐⠙⡇⠀⠀⢀⠘⠄⠀⠀⢠⡇⢀⠀⠀⠀⠂⠀⠀⠀⠁⠌⢉⡙⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣄⠤⢤⣿⣄⣀⡴⠛⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠀⠀⢀⠢⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠘⠁⠀⠀⠀⠀⠉⠑⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⣿⠃⠉⠁⠀⢬⠀⠀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠊⣾⠁⠈⠉⠉⠉⠉⠀⠀⠘⣿⣿⣉⠀⠀⠀⢀⡴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡷⠀⠀⠀⢠⣴⠀⠀⠀⠀⢿⠈⠻⢃⠂⠤⠞⠁⠀⠀⠤⠀⠴
⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢸⢹⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡂⠀⠀⠄⡀⠀⠈
⠀⠀⠀⠀⢸⠀⢀⠀⠈⠐⠄⣸⡆⠀⠀⠀⠀⠀⢀⣠⠊⣿⠀⠀⠀⠀⣾⠘⡆⠀⠀⠀⠀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢄⣸⣀⣀⣨⠉⠑⠉⠉⠀⠀⠉⡇⠀⠀⠖⠋⠀⢧⣤⡀⠤⠄⡞⠅⠀⠀⠀⠁⠘⠁⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠈⠻⠤⣄⣠⠶⣹⠋⠉⣹⠉⡁⠀⠰⠀⠀⣠⣖⣠⠀⡄⠀⠀⠀⠀⠀⠀⠄⣴⡒⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠈⠠⠴⠃⠠⠁⠀⠀⢀⣴⢋⡽⠁⠀⠀⠀⠀⠀⠀⡲⠘⠻⠶⠻⢦⣄⠀⠀⠃⠉⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣷⡏⠀⠀⠀⠀⡀⠀⡜⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⡆⠀⠀⠀⠐⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠣⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠂⡠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡟⠁⠢⠤⣀⢀⡒⠀⢤⡀⠀⢸⣿⠀⢀⡎⣰⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⡇⠀⠀⠀⠀⡀⠁⠐⠃⠀⢠⣿⡿⠁⣾⠀⣿⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣇⠀⠀⠀⠀⡇⢰⣂⠴⠀⠀⠈⠸⠆⢹⡄⢿⡀⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⠀⠀⠀⢀⡳⡀⠀⠀⠀⠠⠃⠀⠀⠘⡇⢸⡇⠀⣾⣿⡿
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠓⠒⠈⠉⠦⣼⡄⢀⠤⠓⢤⣄⡀⠀⣷⠸⡇⢰⣿⣿⡇
⠀⠀⠀⡆⣿⢰⢶⣄⠀⠀⠀⠀⡄⠲⣤⠤⠼⠄⡀⢴⡀⠀⠀⡤⠀⢠⡴⠇⠈⠁⢠⠀⠀⠀⠉⠓⢿⢀⡇⣾⣿⣿
⠀⠀⠀⣷⣿⣼⡀⣿⠀⣀⡀⠀⠻⠀⠹⡆⠀⠠⡁⢀⠇⠀⡸⢀⣴⠏⠀⢀⡤⠀⠐⣶⢤⣄⡀⠀⣸⣸⢣⣿⣿⡏
⠀⠀⠀⣿⣿⡇⣃⣿⣎⠳⣄⠉⠙⠒⠒⠒⠒⠰⠤⠠⠴⠒⠂⠈⢠⡀⠀⠾⠀⠀⠀⠟⣀⣠⣭⣼⡏⠁⣼⣿⣿⠃
⢀⠀⠀⠉⠉⠁⠻⠿⠛⠁⠘⠧⢤⡄⠶⢤⣀⣀⣠⣄⠀⠀⠀⢠⡎⢠⠂⣤⣶⠷⠿⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠒⠒⠒⠂⠀⢲⡀⠉⠉⠉⠓⠒⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠳⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠸⠃⠙⠓⠒⠒⠂⠘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⡇⡎⠀⢘⠰⠀⠈⡔⠋⠈⠉⢍⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁
⠀⢠⠠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆⢧⠠⣀⣀⣀⡀⠀⠀⠀⢿⢸⡇⠀⠀⠀⢀⣀⣀⣠⡤⠴⠶⠚⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⡇
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⠿⠆⣀
⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣦⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣶⣶⣬⣭⣛⡻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠴⠚⠉⠻⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠈⠉⠙⢦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⡑⣤⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠈⢛⢳⣿⣶⣿⣾⡾⣾⣷⣴
⣿⣿⡿⣠⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠐⢯⣑⣸⣧⣽⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣵⣿⡫⢈⣠⣂⠤⠀⣀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿
⣿⣿⣿⣿⣿⣿⣿⡷⢺⣿⣿⣿⣿⣿⣿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠩⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠃⠘⠀⠀⢀⣾⣭⡙⠻⣿⣷⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠢⡀⠹⢿⣿⣎⢦⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠝⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡻⡧⠀⠀⠀⠂⠀⠙⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠘⠀⠀⡤⠚⠋⠉⠉⠉⠹⡿⠹⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻
⠈⠈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠄⡀⠀⠀⣠⠄⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⠘⠁⣼⣿⣇⠀⠛⡴⠽⠂⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠋⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⠂⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⣤⠴⠶⠖⠒⢂⠀⠀⠀⠀⠤⠀⠛⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⣀⣀⣀⠌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣯⠷⠿⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠠⠄⠐⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀⠀⠴⠖⣒⣺⠃
⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠉⠀⢐⡀⠈⣭⣤⣿⣉⣄⣀
⠀⠀⠀⠀⠀⡀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠿⠿⢿⡄⠘⠟⠿⠟⠋⠁⠀⠘⢁⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠠⠀⠀⠀⡀⠀⡀⣈⠂⠛⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⣤⠿⡿⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠈⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣷⡀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣴⣿⠛⠟⠛⠁⠒⠀⢀⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠀⠀⠀⠀⠀⠀⣀⡒⣒⠚⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣀⣠⡄⠀⠀⠀⠨⣥⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣤⠀⠀⠁⠈⠀⠀⠒⣂⣿⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠂⠀⠀⠀⠀⢦⣹⣃⠀⠀⠀⠀⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡌⠀⠠⠀⠐⢾⣻⡷⠀⠀⠄⠰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡄⢀⠀⠀⢙⣷⣄⡀⠄⠀⣹⣿⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠙⢄⠀⠶⠻⣿⣿⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠆⠻⢶⣿⣿⣿⠃⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⡀⠈⠉⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⠓⠚⡶⠿⢋⡶⣯⣷⣟⣣
⠒⠒⡾⠿⠿⠻⠿⠻⠿⠻⢟⠳⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⡞⠀⣠⡄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⡠⠄⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢹⡇⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠈⢳⣴⣿⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⠀⠀⠀⢹⣇⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣵⡀⠀⠀⡐⠂⠀⠤⠤⠴⠞⠻⣍⠛⠳⠶⢾⣿⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⠓⠶⠤⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⣒⠉⢀⠄⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢄⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠴⠂⢺⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠈⢧⠘⣿⣿⣿⣿⣦⡀⠀⠈⠀⠀⣸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠻⢽⣿⣿⠆⠀⠀⢰⣿⣿⡿⠛⠀⠀⠀⢺⣆
⠀⠀⢀⠀⢰⡇⠀⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠸⣿⠏⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⡀
⠀⠀⣸⠀⢸⡇⠀⠀⠀⠉⠉⠉⠙⠻⢣⣶⣤⡀⠐⠛⠁⠀⠀⢀⢞⣻⣿⠁⠀⠀⠀⠀⢠⡄⢸⡇
⠀⠀⢹⡀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠀⠀⠀⢄⡛⠿⣿⡇⠀⠀⠀⠀⠀⠀⣷⠸⠇
⠀⠀⠸⣇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠙⠶⡼⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠻⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣀⣀⠀⣀⣤⣤⣤⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢻⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣻⡟⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠤⣙⠂⠱⠄
⠀⠀⠀⠀⠀⠀⠈⠹⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣢⡀⠒⢤⡀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠮⣽⡳⠮⣽⣦⣌⠳⡄⠀⢀⣠⣴⠦⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣧⣀⣤⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⢠⡹⣿⣽⣿⣿⣿⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⣿⣿⣿⣯⣟⡻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠀⣬⣻⣿⣿⣿⡿⠟⠂⠙⢻⣷⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠈⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⣿⣿⠆
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⠀⣀⣤⣤⣶⡚⣿⣿⣿⣿⣿⡿⠎⠀⠘⣿⣿⡄
⠀⠀⠀⠐⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢀⠟⣱⣾⣿⡇⠿⠿⠛⠛⢃⠀⠠⣶⣶⣿⣿⢻
⠀⠀⠀⠀⢀⠀⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠞⡼⠉⠉⠉⠀⠀⠀⠀⠀⢸⡆⢰⣮⣿⣿⣯⠎
⠆⠀⠀⠀⢨⡄⠁⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠟⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠻⢿⣿⠟⣻⣿⣿⠇⠀⠀⠀⠀⠀⠠⠤⠤⣤⣤⢤⠀⠀⠀⣠⣤⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢃⣴⠟⣤⠈⢻⠷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠘⠃⠀⠀⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⡎⠁⠘⢥⣄⠈⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣷⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡔⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⠖⢿⠲⠾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⠋⠀⠀⣀
⠀⠀⠐⠒⡆⢈⠀⡀⢸⡗⡷⠛⠿⣿⣿⣿⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⣹⠂
⢀⠄⠀⠀⣇⣈⣀⡁⠶⡀⡇⢀⣄⠠⠿⣿⡁⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠀⠋
⠈⢉⠁⠁⠁⠀⠀⢀⡀⢂⣠⣤⣽⣤⡿⠋⠀⡀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡀⢟⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⣤⣀⣀⣀⣠⠴⠁
⠀⠀⢀⣠⣼⣧⣻⣿⣿⡿⠟⠛⠛⠟⢸⡀⢀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣅
⣠⣶⣿⣿⣿⡿⠇⠙⠋⠁⠀⠀⢀⣀⠀⢿⣦⠓⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠳⡖⠀⠐
⣿⡿⠟⣋⠁⠺⣇⣴⣤⣤⢠⣾⣿⣿⣷⡸⡏⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡌⡳⣄
⣽⡆⢸⣿⡀⠀⣿⡘⢛⣵⣿⠉⠉⣿⣿⣿⢿⠀⠀⠉⠓⠄⠀⠀⠀⠀⠀⠀⠁⠀⡠⠞⢿⣿⣿⣷⢀⣩⠻⣄⡅
⢹⠇⢸⣿⡇⠀⢹⣷⣿⣿⣿⠀⠀⣹⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠙⠿⣿⡘⢹⣷⢧⣅
⠈⠀⢸⣿⡇⠀⠈⣿⣿⣿⣟⠀⠀⣿⣿⡏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢋⣤⠈⠛⢿
⠀⠀⣾⣿⡇⠀⠰⠏⠸⣻⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢿⣶⣄
⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⣼⣿⡄⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⢰⣿⣿⣗⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⢀⣀⣀⣀⣀⠀⠀⢠⠀⠀⢄⠀⠀⠐⡄⠀⠀⠀⢀⡠⠤⠄⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣄
⠊⠉⡀⠀⠀⠀⠀⠈⠱⠒⠦⡀⠀⠆⢀⠀⠚⠀⠀⣀⠨⠤⠀⢀⠠⠀⠛⠁⢄⡀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠂⠀⠈⠤⠶⢤⣖⡀⠀⠉⠈⠀⠀⠲⡀⠔⠓⢤⠚⠃
⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠈⠢⠚⠀⠀⠀⠄⠀⠀⠐⡖⠂⣠⣤⠀⠀⠀⠀⠙⣤⠤⠀⠒⠂⠀⠉⠁⠀⠀⠀⡀⠐⠀⠀⠀⠉⠢⡀⠀⠀⠴⠦⡁⠀⠀⠀⠡⠶
⠀⠀⠀⠀⢌⠀⠀⠀⢁⢀⣀⠀⠀⡡⠀⣛⡀⠀⠀⠐⠃⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⢄⠀⠀⠀⠀⠀⠂⠁⠀⡠⠠⠀⠀⠄⠀⢈⠳⢄⠀⣀⡕⠄⡠⠔⢥⡀
⠀⠐⠒⠂⣀⠔⠂⠉⠈⠀⢉⠈⡙⣤⢤⠇⠙⢤⠠⠄⢀⡀⠋⠀⠐⢄⠒⠒⠀⢀⠠⠼⠀⠀⠧⠄⣀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠀⠀⠡⡀⠑⢌⠀⠐⠗
⠀⠀⡠⠀⠓⠀⠀⡤⠀⠒⠉⠀⢀⡈⣎⠀⡠⠊⠉⠉⠀⡇⠀⠒⢀⠀⠑⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠡⠁⠀⠀⠀⠧⠀⠀⠀⠐⠄⠀⠑⢄⠀⠀⣀⠄
⢀⠎⠀⡰⠉⠈⠣⣀⠀⠀⠀⣩⣄⡄⠈⣱⣷⡄⠀⢴⠏⢀⣄⣀⠀⠈⠀⠈⠆⠈⠂⢀⣤⠀⠀⠀⠀⠀⠀⠀⠝⠳⠄⠀⢤⣀⠀⠈⡀⠀⠀⠀⠄⠀⠠⡑⢎
⢃⠔⢨⠅⠠⠀⠊⠀⢁⡦⠁⡸⠂⠘⡏⠀⠀⢰⠀⣈⣶⠂⠈⡄⠀⠉⠁⠒⠬⡄⠒⠀⠀⠀⠤⠤⠤⠤⢤⠎⠰⠇⠀⠀⠀⠀⠓⠢⣄⠠⠤⠤⢈⣂⠀⠀⠄⠳⡄
⠠⠄⠚⠀⠀⠀⠀⠈⢣⡀⠀⢠⣴⡈⠉⠑⠲⡗⠻⣄⢈⣶⣍⠈⢑⠶⠀⠀⠀⠀⠒⠢⠀⠐⠒⠒⠒⠒⠚⠒⠓⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠠⠀⠈⢩⠉⠉⠁⠚
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢹⠂⠉⠛⠉⢲⠖⠋⠀⠀⠈⠁⣉⡇⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠆
⠀⢠⠄⠀⠀⠐⠠⠄⠀⠨⠤⢤⠚⠤⣈⡆⠀⣴⣦⠉⠉⣶⡎⠉⠁⣰⠲⡀⠀⢰⠋⠉⠉⠙⢲⣼⠋⠉⠉⠑⢦⢰⡖⣄⠀⢠⢤⡄⠀⠀⠀⠀⡁⠪⠥⠤⠤⠤⠄
⠀⢸⡠⠀⠀⠢⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⣏⣿⢀⣠⡏⡇⠀⢠⠏⣀⢳⠀⢸⡇⠀⠛⠀⣸⢻⠀⠈⠛⠀⣸⠃⠹⣼⢶⣫⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠖⠆
⠀⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⢹⠛⠒⡗⡇⢠⣏⣀⣉⡀⢧⢸⢰⡖⠒⠋⠁⢸⢰⠖⠒⠋⠁⠀⠀⠘⣲⡇⠀⠀⠀⠀⠀⠀⣄
⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⢨⣿⠀⠀⣷⠇⣾⠼⠁⠀⠱⠼⠦⠶⠇⠀⠀⠀⠸⠾⠀⠀⠀⠀⠀⠀⠘⣯⠇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣀⢠⣤⡀⣠⢤⠀⠀⡴⢦⣴⢲⡀⠀⠰⠒⠆⠖⣦⠀⢀⡖⢶⢠⣤⣤⣤⣤⡀⣤⣤⣤⣀⡀⠀⠀⠀⡗
⠀⠀⡆⠀⢀⠠⠀⡀⠀⠀⠾⠀⡇⢠⠏⡴⠒⢦⣿⣜⢺⠀⠀⡏⣿⡿⣀⣇⢠⢷⡀⣆⡆⣸⡄⡸⣧⢸⢾⣰⠒⠚⠚⠃⡆⠀⣤⠀⠙⡆⠀⠀⡇
⠀⠈⣵⠚⠀⠀⠀⠈⠁⠀⢸⠀⡇⠈⠳⢯⣷⠲⣄⢸⣼⠀⠀⡇⣼⣯⣿⣸⡼⣸⠞⢃⣤⣧⣷⡇⣿⢺⢸⢈⣯⣉⣹⠀⡇⡀⢀⣠⠜⠁⠀⠀⡃
⢀⠞⢰⡀⠆⠁⠀⠀⠀⠀⢺⠀⡇⠸⡟⢧⣬⡷⣹⢳⡜⠦⠴⢃⡽⡇⣺⣏⢣⡟⣤⣾⠀⡿⡈⣼⢋⣸⢸⣹⣀⣀⣀⡀⠇⡟⢦⡑⢦⡀⠀⠀⡅⠀⠈
⠊⠀⠀⣇⠰⠀⠀⠄⠀⠀⢸⠀⡇⠀⠉⠓⠒⠛⠁⠀⠙⠓⠒⠚⠁⠻⠏⠙⠚⠀⠛⠛⠿⠇⠓⠋⠘⠛⠸⠾⠶⠚⠺⠋⠛⠃⠀⠉⠉⠁⠀⢠⠄⣀⠤⢄
⠠⡀⠀⢹⠀⢃⠘⠀⠀⠀⠘⠤⠇⡀⣀⠀⢀⢀⡀⠀⠀⡀⡄⠀⠀⣠⢠⡄⠀⠀⠀⠄⠀⠄⠒⠀⠀⠀⠤⠤⠤⠄⠤⠰⠀⠠⠖⠀⠐⠐⠒⠘⠁⠁⠂⠀⠀⠐
⠀⠈⠚⠀⢃⠈⢄⠠⠂⠀⠀⠀⠄⠠⠀⢀⠸⣀⣠⣶⡄⡅⡇⠐⠴⢁⠎⠄⡀⠀⠀⡀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠
⢀⠖⠀⠀⠘⣄⠚⠄⠀⠀⠀⠀⠤⠠⢰⡁⡀⠈⣧⡉⠀⢱⣇⣠⢁⡆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⢠⣔⡂⠁⠀⠀⡤⠓⢌⠑⢤⡀⠀⠀⠀⠈
⠁⣀⠀⠀⠀⠸⡀⠚⠀⠀⠀⠀⠀⠠⡉⠀⠀⠠⠿⢶⠀⠉⠐⡄⠉⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡗⠉⠀⠀⠀⠀⠀⠦⢤⡼⠁⠐⠙⢆
⠙⠛⠛⠁⠀⠀⢱⠀⠀⠀⠀⣶⡀⠐⠉⢢⣰⠁⠀⠀⣣⣠⡾⢔⡊⣡⣷⡆⠀⠀⠀⠀⠀⢀⡠⠒⠒⠆⠀⠀⠀⡎⠀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠱⡈⠆
⠀⠀⠀⠠⠄⠤⠀⢧⠀⠀⠀⠽⡓⠉⠞⠙⠴⢇⢲⡖⣏⠀⠀⠀⠵⠈⠁⠐⢄⠀⠀⠀⢠⠋⢀⠎⣁⠛⡄⠀⢸⡇⠀⠀⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠐
⠀⠀⠀⠀⢀⠠⠀⠀⢣⡀⠈⠓⠿⣶⣀⠀⠀⠘⠷⠎⠁⠀⠈⢳⣤⡆⠀⠰⠦⡀⠀⠀⠘⢆⠈⠎⠾⣰⠃⠀⠘⡇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠃⠒⠊⠁⠀⢣⡀⠀⡰⠋⠛⠄⠀⠀⢴⡰⣀⠀⡠⠊⠙⢃⠐⠀⠀⡘⠴⠆⠱⠀⠙⠒⠊⠁⠀⠀⢀⡐⣆⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡰⠁
⠉⠀⠀⠀⠀⠀⠄⠂⠀⡐⠁⢲⡀⡀⠀⠘⠒⠖⡁⢠⡌⠉⢀⡀⠀⠀⣦⠴⠚⠁⠀⠀⠀⠀⠀⠐⠒⠂⠁⠂⠁⠀⠈⠢⣀⠀⠀⠀⠀⢀⠌⠀⠀⡠⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠤⠘⠉⠑⠠⠤⠤⡼⢀⠄⠈⠉⠣⢈⠁⢀⠁⠀⠀⠀⠀⢀⣠⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠾⠐⠒⠉⢀⡀⠤⠂
⠀⠀⠀⠁⠉⠐⠈⠀⠀⠁⠀⠀⠀⠐⠒⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠘⠓⠒⠒⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣁⠀⠀⡀⣀
⣿⣿⡟⠻⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⣶⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⣿⣎⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣝⡛⣷⡙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣯⣝⣿⣿⣿⣞⣿⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠿⣯⡛⢻⣅
⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⣧⣙⣿⣯⣿⣿⣻⡿⣞⢷⣿⢷⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣍⠻⢧⡈⢙⠎⢻⣆
⠀⠀⠀⠀⠀⣠⣾⣿⣝⣿⣿⣻⢷⣟⢿⣏⡹⣿⣿⣏⢿⡸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⡻⢦⣝⢳⡌⠳⠈⠆⢰⡿⡄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣷⣯⣿⢯⣟⡿⢿⣿⣾⣿⣷⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣯⣿⣦⣙⣆⠙⣦⣬⣵⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⡿⢿⣿⣿⡯⣿⣆⡀⠀⠀⠀⠀⠀⠀⣰⣛⣛⣿⣿⣿⣟⣶⣼⣾⣿⣿⢿⣿⢿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣯⣽⣿⣿⣿⣿⣿⠟⣫⣷⡾⠯⢿⣶⣤⣤⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠉⠹⠉⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣯⡽⣿⡶⢾⣿⠚⣽⣿⣿⣿⣿⣿⣷⣾⣿⣛⡋⠛⠀⢹⣿⢿⣿⣿⣿⠦⠀⠲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣻⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⡷⠯⠆⠁⡠⠄⠲⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣟⢿⡾⣥⣽⠶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣷⣶⣶⣤⣤⣶⣶⣤⣆⡟⡙⠚⣯⣿⠛⢭⡁⣬⣭⣡⡉⢙⠻⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡷⡀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣯⣿⡿⣇⣚⢿⣮⠾⢿⣾⠛⢿⣿⣦⠉⢮⡙⢿⣿⣿⡯⣽⡿⣿⣿⣿⠉⢉⠘⠻⣿⠶⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣮⣿⣷⢏⠀⢈⣿⣟⣦⣿⣤⣀⡆⡀⠘⣿⣿⣿⡿⠟⡊⠉⢂⠀⣀⢀⣀⣤⠀⣾⣷⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡆⠛⠻⣻⣏⢡⣼⠛⠁⠀⠀⠈⡯⠀⠐⢦⣴⣶⠏⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠎⣧⢛⢦⣟⠂⢀⣴⣿⣤⣶⣴⡷⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠛⠒⣶⠄⠀⠐⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⢀⠞⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠁⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠼⢦⣄⠀⠀⠀⠰⠋⠀⠀⢀⣀⣨⡤⠤⠴⠶⠶⢦⡀⣼⡇
⠀⠀⠀⠀⠀⣾⠙⣍⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢈⡤⢒⣛⠫⣄⠀⠀⠀⠀⠀⠀⠀⢹⢸⠁
⠀⠀⠀⠀⠀⠸⠀⠹⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡐⠁⠀⢱⠘⣆⠀⠀⠀⠀⣀⡤⠎⢸
⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⠂⢀⣿⠤⠐⠊⠉⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⡇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠡⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠂⣴⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣯⡒⠢⣤⠤⣀⠀⠀⠀⠀⠴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠙⠷⠊⡬⣹⠲⡁⠀⠀⠀⢠⢀⡇⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣌⡉⠒⠂⠤⠁⠁⠀⠀⠀⡌⡼⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠀⠁⠀⠪⠚⠀⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⠉⠉⠀⠈⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣤⣀⡀⠀⣀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣤⣠⣴⣶⣾⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⣠⣤⣄⣀⣀⡀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⣀⣀⣠⣤⣤⠀⠀⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⡇
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣤⢀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣉⣁⣤⣤⣤⣀⣉⡙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣿⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣼⣿⡿⠿⠛⠉⠈⠛⠻⠿⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⢿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠀⠉⠃⠈⠃⢹⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢋⠅⡀
⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠈⠁⠀⢀
⠀⠀⠀⠀⡕⢢⠙⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢱⠿⠠⠂⠀⢀⠀⠀⠀⠀⢒⡶⢶⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⡗⠚⢾⡔
⠀⠀⠀⠀⠠⢈⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠃⠀⠀⠆⠀⠁⢄⢀⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠁⡙⠿⣷⣦⣤⣄⠀⢀⣴⣶⣾⡿⠟⢉⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠁⠂⣀⠉⠙⠋⠀⠜⠙⠋⠀⢠⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⡐⢂⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢹⣶⡄⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠃⠀⠀⠘⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢡⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⣀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⠀⠥
⠀⠀⠀⠄⡀⠑⠂⠀⠌⠀⠀⠠⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠂⠂
⠀⠀⠈⠁⠜⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡡⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠡⠀⠀⢸⣯⣿⡇
⠀⠀⠀⠿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠶⠷
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠂⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⣿⠛⠛⠛⣿⠀⠄⠁⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⣿⡀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠠⠀⠀⠀⠛⠋⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣨⣠⣤⣍⢥⠀⠐⠐⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡄⠀⠀⡄⠀⠈
⠀⠀⠀⠁⣠⣤⣤⣀⡀⠀⠀⠓⠊⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠇
⠀⠀⠀⠀⠋⠉⢙⣿⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⢀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⡟⡛⣛⡛⣻⠿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣤⡶⠀⠂⠀⣄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣨⡷⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⡀⠀⠀⢹⢡⠙⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡙⢂⡆⠀⠄⠀⠀⠂⠈⠠⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⣾⠃⠄⠀⠀⠀⠂⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣳⣀⣹⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣵⢧⠋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣛⠛⠛⡂⠀⣀⣀⣤⣾⣿⣿⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⣀⠛⠛⠉⠀⠀⠿⡿⣿⡏⢍⡊⠼⢽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⠧⠻⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣄⠰⡱⡑⣕⢮⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣶⠔⠔⣱⢲⢿⢸⢹⠈⢢⣤⢀⡆⠈⠁⠓⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⢪⢦⢃⣇⣎⣄⢤⠖⠉⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡈⠀⢄⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠑⠋⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


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

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣇⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⡐⢲⠆⠿⡿⠁⠘⣿⠇⢶⠖⢠⡤⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⡁⠀⠀⠑⠊⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠐⠀⠀⢻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⣽⡶⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠰⡟⡷⠀⠀⠈⠠⠆⠈⠀⠀⠀⠀⠀⠀⡠⠀⠰⣾⢆⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⠀⠸⣧⠀⢀⠈⢀⠀⠄⠀⠀⠁⠀⠠⠆⠀⠀⠀⠀⠀⠀⠦⠀⠀⠁⠀⠄⠀⢈⡁⠀⠀⢠⡿⢀⠐⣡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠿⣆⠙⣿⡀⡌⠀⢠⡁⠀⠀⠘⠁⠀⠀⠀⠀⢠⣾⣜⠀⠀⠀⠀⡀⠙⠀⠀⠀⠡⠀⠈⡄⣸⡟⠁⣾⠟⣡
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣷⠖⠠⢧⠘⡄⠸⣠⣄⢠⠀⠀⠀⣀⣠⠄⠚⠓⠛⠁⠉⠓⠛⠒⢤⣀⡀⠀⠀⢠⠁⣤⠸⠀⡝⢠⠇⢠⠞⡾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠉⠈⢻⡀⠀⡄⠀⠙⠋⣸⡓⠚⠛⠩⠙⠁⠀⠀⠈⠀⠈⠀⠀⠀⠙⠡⠙⠛⠒⣻⡈⠫⠁⠀⡄⠀⣸⢋⠀⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣶⣷⡖⣴⣊⠁⠙⣾⠗⢶⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⣴⠖⢿⡞⠁⢉⣲⡔⢶⣷⣾⠏⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠄⢻⣅⠈⣥⣾⡙⣠⠂⢼⡀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⣼⠄⣠⡘⣹⣦⠄⢀⣼⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⣿⡃⡤⠘⠏⠙⢧⡘⠓⣮⡁⠙⡀⠀⠀⠀⠀⠀⠀⡘⠁⣩⡞⠓⣠⠟⠉⠏⠰⡄⣻⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⣱⠀⠀⠀⠀⠙⣣⡟⠓⢤⡖⣮⢳⣄⠨⡋⠰⣤⠀⠀⠀⠀⠀⢀⡴⠈⡹⢀⣴⢫⡖⣦⠜⠛⢧⠛⠀⠀⠀⠀⠀⣏⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⢷⣄⠈⠳⠤⣰⡿⢶⠶⠶⠶⢶⠾⣷⡠⠴⠏⢀⣼⢧⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣏⢼⡍⢻⠾⠟⠿⠡⠀⣀⠀⢀⡀⠀⠩⠿⠛⢾⠋⣽⢌⡇⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢷⡄⠀⠀⠀⠀⢤⣽⠈⣿⢦⣼⡅⣴⡇⡰⠉⠛⠋⠡⠀⣷⠄⣭⣤⢾⡏⢨⣥⠄⠀⠀⠀⠀⣠⡾⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣀⣼⠇⠀⠀⠀⠀⠀⠹⠆⠘⢦⡀⠸⣞⢸⣇⠿⣿⡿⠇⣿⢘⡿⠀⢠⡞⠀⠼⠁⠀⠀⠀⠀⠀⢹⣄⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢄⠀⠀⠀⠀⠀⠀⠨⠷⠘⣯⠀⠙⢷⠿⠾⢿⡗⠾⢶⠞⠁⢬⡟⠰⠿⠀⠀⠀⠀⠀⠀⠀⡠⠉⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠤⡀⠀⠀⠀⠀⠈⠉⢿⡂⠀⠈⠀⠀⠁⠈⠀⠀⣺⠏⠙⠀⠀⠀⠀⠀⢀⢤⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠗⡀⠀⠀⠀⠀⠀⡈⢳⢣⠀⠀⠀⠀⠀⢠⡳⠋⡄⠀⠀⠀⠀⢀⠀⠷⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⣀⣸⡄⢍⣢⣄⡶⣞⣤⣪⠍⣸⣀⣀⠠⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠛⠤⠤⠄⣤⠄⠤⠤⠖⠛⠴⠋

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠠⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠄⠁⠀⠀⠂⠀⠀⠠⠀⠀⠀⠠⠖⠒⠓⠒⢄
⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠂⡀⠂⠀⠀⠐⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⡀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⡦⠶⣂⡠⣀⣰⠦⢴⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⡀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣗⣾⠀⠀⠀⠘⠋⠈⠀⠀⠠⠀⠁⠀⠀⠂⠀⠀⠬⣘⠒⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠑⠂⠴⠊⠁⠈⠱⢦⠀⢄⡤⠀⢆⠁⠀⠀⠀⠀⡌⠈⠀⣀⡠⠋⠁
⠀⠀⠀⠀⠀⠅⡀⠘⠀⡀⠊⠁⢠⠀⠃⣀⣾⣒⣛⣋⠉⠉⠉⣙⢂⣋⣛⣺⢄
⠀⠀⠀⠀⠀⣀⠁⠠⠂⠀⠰⠀⠀⠐⠀⠀⠀⠀⠁⠉⠈⠉⠉⠉⠉⠈⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣈⠂⡀⠈⢠⠀⠁⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂
⠀⠀⠀⠀⢀⣐⣄⠐⠂⠤⠌⠠⠤⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⢦⣐⠂
⠀⠀⠀⠈⣞⠐⡼⠆⠐⠆⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⣂⢸⠡
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣦⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⡭⠭⢽⡿
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠙⠛⠚⠳⣮⣽⣿⣯⣭⣿⡭⠽⢭⣭⣉⣉⣙⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠒⠂⠀⠀⠠⠀⠀⠠⡄⡀⠈⠉⡙⠉⢠⠊⠈⠀⠨⠻⣿⡟
⣤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⣈⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣷⣬⣿⣭⢡⣆⣀⣈⣄⣠⣄⣴⣶⣶
⣾⠓⠤⣄⣀⣀⣂⡈⣀⠀⠀⠑⠒⠖⠘⠉⠉⠉⠉⠉⠉⠉⠤⡤⠤⣤⡭⣽⣟⣄⣬⣤⣧⣏⣈⣈⣹⣿⣿
⡉⠉⡒⠀⠐⣦⢤⣬⣾⣿⠟⢻⠇⠚⢛⡟⠛⠛⠙⠉⠉⣽⣿⣿⢻⡉⠻⠉⣯⣌⣁⣉⣘⣩⣭⣿⣿⣿⣿
⣷⣦⣶⡶⠶⠀⠀⠈⠁⢹⠷⡄⢀⣶⡄⠀⠀⠀⠉⠹⣶⣿⣿⡇⢸⣿⡀⢿⣛⣅⣀⣀⣈⣹⣿⣿⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠀⠀⠀⣸⠀⠀⠸⡟⠻⢿⣾⣎⣿⣟⣏⣿⣿⣷⣾⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠉⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠇⠀⠀⠀⢸⣿⣿⣏⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⣸⣷⡀⡰⣾⣦⣲⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⡾⠛⠻⢿⠿⠛⠻⣿⠟⡿⢿⡿⠟⠛⢿⡿⠛⠻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣤⣤⡀⢀⣤⣤⡀⣠⡀⣄⠀⣠⣤⣄⢀⣤⣤⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⢷⣯⣁⠿⣿⣶⣤⡀⠀⣇⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣈⠑⠒⠁⡀⠉⠛⠻⣿⣧⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡼⠛⠿⣾⣝⡻⢿⡿⢟⣫⣴⣮⣭⣛⡿⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⣤⣄⡉⠳⢤⣀⣀⣠⠴⠛⠛⠲⠦⣬⣹⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣾⣥⣤⣤⣤⣭⣿⣷⣾⣿⣯⣥⣤⣭⣽⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠸⠛⠿⠟⠳⠆⠈⠉⠀⠰⠾⠻⠗⠶⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿