Algebra Emojis & Symbols

⠓⠀⠀⠘⠢⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠸⡷
⠹⠀⠀⠀⠀⠔⠠⣶⡀⠀⠠⠀⠀⡴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠰⣇⣀⡔⠄
⠀⡀⠀⢠⠊⠉⠀⠈⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⢨⠉⠁⡀⠐⠂
⠀⠀⢀⠈⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⠀⡴⠆⠻⣿⠔⠋
⡟⠶⡆⠀⢰⣶⣾⠉⠀⠀⠀⠀⠆⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠀⠀⢸⡀⢀
⠀⠈⠁⠀⠰⡄⠁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣤⣤⠀⠁⠈⠀⢀
⠁⠂⠀⣤⡄⠁⠀⠈⠁⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠈⠀⠀⠀⠘⠃⠀⣶⡶
⠂⡠⠀⠈⠰⠶⠆⢀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠄⡀⠈⢀⠀⠊
⣤⡄⠀⠁⠀⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢃⡀⠀⢀⠀⢿⠄⢉
⢞⠹⣞⠀⠈⠁⢩⠾⠶⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠓⠃⠀⣴⢛
⠋⠁⠙⢛⡐⠂⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⣀⡀⠀⠁⠐⠈⠉
⢶⠇⢀⠀⠀⢢⠀⠈⠀⠀⠀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠢⠃⠐⠁⠀⠀⢀
⣥⠇⢀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣳⢀
⢿⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠆⠀⠀⠀⠀⠀⠃⠀⠀⣠
⡌⠃⠀⠠⠇⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣠⣦⠀⢀⣀
⠈⠠⠤⣆⠂⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠄⠀⠀⠀⠀⠉⠘⠂⠈⠉
⠀⠄⠠⠮⠂⠀⠀⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠇⠀⠹⣤⣖
⠀⠀⠀⠀⠔⡄⠀⠀⠀⢁⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢩
⠀⠈⠁⠀⠄⡬⠤⠀⠀⠀⠉⠆⠀⠀⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢸⣿⠟⠀⢺⣭⠧
⠣⠛⠀⠀⠯⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⣒⠀⠀⠀⠀⢄⠀⠀⠀⢀
⢄⠰⠁⠀⢀⡆⠀⢠⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣤⠀⣀⢀⠀⠙⡆⠘
⢚⣰⣳⠄⠈⠀⠀⠀⢙⠀⠀⠘⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡁⠀⠂⠀⢰⣛⡅⠸
⢤⠏⡁⠘⠀⠀⠀⠈⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⢄⠀⠐⠊⠁⠀⡻
⡞⠀⢛⡒⠀⠀⡦⠀⢀⠈⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⢢⠀⠈⠤
⠁⠀⠀⣷⡆⠀⠀⠀⠈⢩⠁⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣲⠀⠈⠠⣞⢳⠀⠀⠈⠁⢀
⠳⠀⡠⣍⠠⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠀⡀⠀⠁⠘
⠇⠀⠁⣰⠋⣸⡋⠀⠀⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠰⠟⠃⠀⢀
⠻⢃⠘⠉⠹⢥⡿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⢀⠀⠀⠀⠠⠄⢀⡈
⠐⠿⡆⠀⠀⠀⣶⠆⠦⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠘⠲⠀⠀⢦⡁
⡆⢠⡀⢹⣻⣇⠀⢠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢖⣙⢤⠲⡅
⣀⣧⠙⠈⢫⡟⠈⠛⠀⠀⠈⠓⠂⠀⠀⠀⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘
⢋⡄⠦⣴⠄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠦⠀⠰⡞⠓⢬⠴⢎⡁⠐
⣋⣠⠀⡀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⡁⢶
⠈⠉⡀⠀⡞⣳⠀⠰⣿⣇⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⡠⠂⠭⣤

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆
⠀⠐⠷⠶⠶⠶⠿⣽⠂⠀⠀⠐⠳⠶⠶⠶⠆⠀⠀⠈⠐⠂⢵⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠂⠀⢀⣄⠀⠀⠀⠀⣄⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠩⠀⠀⠀⡀⠙⠀⠈⠁⠁⡌⠀⡁⠈⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠃⠁⠋⠀⠀⠀⠀⠀⠂⠘⠐⠀⠀⠄⠈⠀⠀⠀⠘⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠘⠒⢚⠒⠒⠀⠀⠀⠀⣰⠉⢀
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠘⠂⠀⠄⠤⠤⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⠝⠁⡀⠀⢀⣜⣄⠀⠀⠀⠀⠄⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣁⡤⣲⡄
⠀⢀⠂⡀⠀⠀⠀⠀⠓⠃⠲⠃⠀⠀⠈⠈⠀⠀⠀⠠⠈⠀⡀⠀⠀⠀⠀⠃⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠉⠈⡉⡀⠘⠁⠈⠈⠀⠀⠀⠙⠘⠀⠻⠻⠿⠚⠉
⠀⠀⠀⢹⡢⠄⣀⡀⠀⠀⠀⠀⢀⢂⠀⠀⠀⢀⠆⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠄⠀⠀⠀⠃⠃⠃⠽⠐⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀
⠀⠀⠀⠈⣅⠜⠉⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠆⠀⡀⡀⠀⠁⠀⠀⠘⠀⠀⠀⣆⠂⠂⠀⠠⠰⠂⠐⠒⠘⠀⠂⠑⠀⠁⠀⠁⠁
⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡉⢂⠀⠓⠀⠉⢀⠃⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠆⠀⠀⠀⠛⠀⠀⠨⠀⠀⠚⠀⠀⠃⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠖⠀⠀⠀⠐⡀⣀⠐⠂⡄⠀⠀⠀⠀⠠⠠⠀⠐⠂⠀⠀⢸⣁⡦⠤⠸⠇
⠀⠀⣀⣀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠁⠠⠃⣀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⢠
⠀⠀⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣄⡀⠀⠀⠀⠈⢀⣀⡀⠀⠀⠀⠐⠐⠂⠙⠂⠁⠠⣿⣛⣿⣷⠰⠈⠐⠀⠡⢚⠇⠜⠈⠀⠘⠀⠀⡀⣠⣄
⠀⠀⣀⠠⠮⠅⠀⠀⠈⠉⠉⡉⠃⠀⠘⠛⠋⠋⠙⠐⠀⠀⢸⣿⢛⣿⠀⠀⡀⢀⣠⠀⡀⠀⠀⠀⠛⠙⠛⠉⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠳⢝⡫⠼⡇
⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⣀⣀⣀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⢈⣁⣈⠁⠀⠀⠀⠀⢀⣯⢠⠤⣤⣄⢦⢰
⠈⠁⠒⢲⡠⠤⢄⡄⠄⠀⢠⠂⠀⢀⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣻⣾⡿⣧⠀⠀⠘⠁⠉⠈⠃⠁⠀⠀⢠⢉⡅⠀⠉⠼
⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠊⢀⠤⠄⠀⠋⠈⠀⠀⠀⠀⠀⠀⠘⠯⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⠀⠀⠈⢠⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⣄
⠀⠀⡌⠀⠀⠀⡐⠀⡄⢀⡀⠂⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⣤⣀⠀⣤⢠⢠⡄⡆⠀⠀⠄⠀⠀⠄⢀⡀⠘⢧⡼⠇⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠛
⠀⠀⠀⠈⠀⠑⠉⡀⠀⠄⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣸⣿⣧⣤⡄⠈⠐⠤⡀⠀⠀⠀⠃⠀⠈⠀⣠⣤⢤⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠾⠰⠂⠇⠔⠀⠌⠀⠀⠀⠀⢼⣯⣭⡽⣷⠀⢸⣿⣿⣾⣿⣿⣷⣶⣆⣶⣦⠀⠙⠀⠀⠀⠀⢸⡷⣾⣻⣽⡇⠀⠈
⠀⠀⠨⠴⢅⣇⣐⠣⠀⠀⠀⠀⠉⠈⠁⠈⢁⠌⣬⠉⠉⠀⠀⠀⠀⠀⠙⢦⣽⣧⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⠀⠀⠀⠀⠘⠿⣭⡯⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⢂⠄⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠂⠀⡁⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠡⡀⠀⠀⠀⠰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠃⠀⡀⠀⠈⠀⠀⠂⠀⠀⠀⠄⡀⠂⠀⠀⠀⠀⠈⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠁⠀⣠⠀⠀⠀⠁⠀⠃⠀⡀⠀⠈⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢐⠦⠀⣀
⠀⠀⠘⠀⠂⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠈⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣎⠁⠀⠁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠈⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡶⠌⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠈
⠀⠀⡆⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠈⠠⠃⠆⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⢌⠂⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢉⠈⠀⠈⡀⠀⠠⠀⠀⣀⠸⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡅⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠄⠀⠀⢀
⠀⠀⠈⠄⠀⠀⢁⠀⠁⠘⠀⠀⢀⠀⠀⠐⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠄⠑⡀⠠⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⡀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡦⠁⠀⢁⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⡀⠀⠈⠇⠀⠃⠈⠂⠀⠈⠆⠀⠀⠀⠈⠂
⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠙⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠴⣀⠀⠠⡀
⠀⠀⠔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠠⠂⡠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⡰⠂⠁
⠀⠘⠀⠀⠀⠆⠀⡥⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠄⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠂⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠁⠂⠠⠀⠄⠀⠀⠀⠊⠀⠀⡡⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠐⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⢀⡁⢀⠢⠀⡄⢁⠘⢀⠀⡠⠊⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠄⠀⠀⠂
⠀⠀⠠⡂⠀⡐⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⡠⠁⠁⠈⠀⠁⠐⢁⠜⠀⠀⡀⠀⠐⠠⠀⢸⠀⣒⡀⠛⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠓⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⠄⠈⠀⠀⠀⡀⠰
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠒⠀⠀⠀⢀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢄⠀⠀⡄⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀

⠀⣤⠀⠂⠀⠀⠀⡴⢦⡈⣇⠀⠀⠀⠀⠒⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⠠⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⣤
⠀⠀⠀⠔⠢⡀⠀⠙⠛⠁⣿⢀⡀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠀⠀⠐⠃⠀⠀⠀⠰⠶⠆⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢸⠃⢠⡏
⠀⠀⠘⠀⠀⢱⠀⠀⠀⠀⣿⠸⣟⡷⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣾⠃
⠀⢸⠀⠀⠀⠀⢃⠔⠁⠀⠛⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡄⠀⠀⠀⡄⠠⡤⠀⠀⡟⢀⡟
⠀⠃⠀⠀⠀⢀⠛⠀⠀⠠⠀⢠⠀⠀⠁⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠄⠀⢂⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⣈⡉
⠀⠠⠀⠀⠀⠊⠀⠁⠙⠀⠀⠀⠀⢀⢀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠆⠼⠀⠀⢎⠧⠀⠁⠈⠃⠉⠀⠀⠀⠠⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⢀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⡀⢀⡞⣧⠀⠀⠦⠍⠉⢀⣀⠁⠀⠀⢠⣼⣶⣦⣤⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠹⡀⠂⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠀⠀⡖⠀⠀⣿⠃⡄⢸⣎⠀⢸⠃⠹⠀⢀⠀⢒⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠁
⠃⠀⠀⠀⠄⠈⠀⠁⠐⢖⠒⠈⠁⠀⠀⠀⠀⠀⡜⠃⠀⡏⠀⢸⡇⢠⠀⠏⠀⠀⠛⠈⠀⠈⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠀⠀⡀⠀⠀⣼
⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⡱⠀⠀⠀⠈⠄⠀⢰⠃⠉⠐⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠃⠄⠁
⠀⠀⡀⡄⠀⡀⠈⠀⠀⠴⠥⠤⠤⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠅⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⠈
⡁⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⠀⠀⠁⠀⠀⠘⠍⢁⠀⠀⠀⠀⠀⡠⠋⢀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⣀⠀⠀⠤⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⢀⠄⠰⠔⠚⠉⠁⠀⠀⠀⠄⠀⠀⠐⠀⠁⠈⠀⠀⠀⠋⡽⢩⠖⠃⢰⠀⠀⠀⠀⠀⠀⣀
⠀⣀⣀⣠⢤⡀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠃⠀⠀⠀⢠⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⣣⠄⠀⠀⡄⠀⠀⠀⡆⠀⠂⠬
⠸⠃⠈⡏⠐⠃⠈⠒⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⠀⠀⢠⠤⢤⣄⡀⠀⠁⠀⠀⠴⠀⠀⡰⠃⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠀⠀⢛⠒
⠀⠀⢠⡇⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⡄⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣀⠄⠀⠀⠈⠒
⠘⠧⠞⠛⠴⠃⠀⠀⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⢠⠾⢧⣀⢰⡄⠀⠐⠃⠁⠀⠀⠃⢸⠀⢹⠀⠇⠸⠀⣦⠀⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⡠⠖⠀⠀⠀⢠
⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠃⠀⠀⠀⠋⠁⠀⠈⠀⠀⠀⡰⠃⢀⣈⠀⢀
⠀⠁⢀⢀⡀⢠⡶⣤⢹⡆⠰⠒⢨⢀⢁⢡⡂⠦⣤⣤⢀⡂⠢⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡼⠀⣾
⠀⠀⠎⠀⠱⡀⠙⠋⢸⡇⣀⡁⠀⠀⠀⠀⠀⠀⠉⠈⠈⠁⠀⠀⠄⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡣⢴⠇
⠀⡆⠀⠀⠀⢇⡠⠂⢸⡇⢿⣿⠀⡀⠈⠀⠀⠀⢀⠀⢰⡁⠀⢠⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠸⣁⡜
⠐⡃⠀⠀⠀⠞⠄⠀⠈⠃⠀⠠⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⡈⠤⠀⠀⠠
⠀⠆⠀⠀⠘⠀⠑⠘⠀⠰⠂⠰⠀⠰⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠠⠀⠀⠀⠀⠈⠀⠐⢠⠐⠃⠰⢍⣁⠀⠒⠈
⠀⠄⠀⠂⡀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠐⠀⠀⠀⠀⠙⠛⠟⠛⠛⢁⠀⠀⠠⡄⠆⠀⠀⣀⠒⠀⢌⢀⠒⠠⠀⠁
⠀⠀⠀⠀⠣⠄⠀⠀⠄⠉⠀⠀⣀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⣠⠀⠠⠄⡁⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠄⠀⠀⠀⠠⠀⠀⢀⠀⢰⠋⡆⡿⠀⣼⠉⠧⡏⠙⢲⣶⡄⢸⢻⠀⣸⢻⡆⣀⠄⠠⠂⠀⠐⠃
⢀⡈⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⣼⡇⡇⠀⡇⢲⡆⡧⠄⢨⡿⣅⢸⣏⠀⡿⠶⡇⠠⠆⠀⠴⠀⠐⡁⠄
⠘⠁⠀⠐⠇⠐⠀⠀⢀⠁⢸⡇⢸⠇⠧⠤⢻⡼⢹⣇⣀⢸⡇⣸⢸⠈⣧⡇⠀⠷⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠
⠀⣐⣀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⢉⣀⣉⣅⠈⠀⠀⠀⠀⠀⠀⠂⠀⠃⠂⠀⠀⠁⠀⣤⠤
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡏⠘⠁⠀⠀⠀⡀⠒⠀⠀⠀⢠⠀⠇⠈⠀⠀⣈⡉
⠀⠀⠀⠀⠀⠞⠆⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠒⠂⣄⣰⣇⡠⠀⡀⠐⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣈⡉
⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⡀⣈⡁
⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠃⠀⣠⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠖⡳⢶⣤⡤⠁⠀⠀⠀⠀⣄⣀
⠀⠑⠄⠀⠀⠀⡄⣀⠄⡈⠁⠀⠈⠀⠀⢠⠀⠁⠈⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⡼⠁⡎⡀⠀⢡⠀⠀⠸⠀⠤⣅
⠀⡄⠀⠀⡀⠀⠘⠄⠚⠀⢀⠀⠀⠀⠀⠁⠈⠀⢀⠤⠤⣬⠀⠀⠎⠀⠔⠈⠉⠀⠘⠛⠁⠀⠀⢆⢀⠂⠀⠢⢄
⠀⠀⠀⠰⠀⠀⠆⠈⢄⠀⡈⠀⠈⠀⠀⠀⠀⠄⠀⣠⠞⠁⠀⠀⠀⠀⠐⠃⠐⢀⠔⠂⠀⠀⠀⠀⠁⠀⠀⠠
⣀⣀⣈⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣂⣀⣀⣈⣀⣊⣙⣲⣛⣀⣀⣃⣀⣐⣃⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣦⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⠀⠉⣻⡏
⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢨⣿⠻⣶⡟
⠀⠀⠀⣀⣀⣤⣿⠀⢸⣧⣤⣤⣤⣤⣤⣿⠁⢸⣧⣤⣤⣤⣤⣤⣼⡇⠀⣿⣤⣤⣤⣤⣤⣼⡏⠀⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⣼⠏⢠⣾⠃⣰⡟
⠀⣴⡾⠋⠉⠉⣿⠀⢸⡏⠉⠉⠉⠉⠉⣿⠀⢸⡯⠉⠉⠉⠉⠉⢹⡇⠀⣿⠉⠉⠉⠉⠉⢹⡇⠀⣿⡋⠉⠙⠿⣦⠀⠀⠀⣼⠏⢠⣾⠃⣰⡟
⣼⡏⠀⠀⠀⠀⣿⡀⣸⡇⠀⠀⠀⠀⠀⣿⣀⣸⡏⠀⠀⠀⠀⠀⢸⣇⢀⣿⠀⠀⠀⠀⠀⢸⣇⢀⣿⠇⠀⠀⠀⠹⣷⠀⣼⠏⢠⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⣿⣼⠟⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⢠⣾⠃⣰⡟
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠏⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣾⠃⣰⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣾⠃⣰⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣾⠃⣰⡿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠛⣿⡟⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⠇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢋⣿⠆⠀⠀⠀⠀⠀⠀⢠⣥⣀⣠⡾⠋⠀⠀⣿
⣿⠀⠀⠀⠀⠀⣠⣤⣄⠀⣿⣧⡄⠀⠀⢠⡄⠀⠀⢸⣿⣤⣤⡀⠰⣿⣧⠄⠀⣀⣀⣀⡀⠀⣾⣣⣿⠋⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢀⣥⣤⣿⠆⠀⠀⠀⠠⠶⣾⡷⠦⠀⢸⣿⠁⠈⣿⠀⠀⠀⠀⠈⠋⠉⠉⠉⢠⣿⠟⠁⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠸⣧⣤⣿⠇⠀⠀⠀⠀⠀⠸⠃⠀⠀⠸⣿⣤⣴⠟⠀⠀⠀⠀⠐⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏
⣀⣈⣙⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠠⠀⠀⢀⣀⢰⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠀⢀⠄⡆⡆⡄⡀⣀⢀⢀⠀⠀⠀⠰⢲⠀⡖
⠀⠀⢀⠤⡀⠘⠾⠛⡇⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢀⡀⠀⢋⠁⠀⠀⠺⠀⠈⠀⣠⠁⠀⠁⠁⠘⠈⠈⠁⠀⠀⢇⣼⠃
⠀⢀⠀⠀⢸⠀⢀⠀⡇⠻⡷⠀⠀⠗⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠀⠁⠀⠠⠄⠀⠒⠈⠀⠀⠀⡈⠀⠂⠀⠀⠀⠰⣇⠎
⠀⠞⠀⠀⢀⡗⠁⠀⠉⠠⠂⠀⠀⡀⠄⠊⠀⠀⠀⠄⢀⠄⡎⠁⠔⠈⢰⠀⠀⠀⠀⠁⠀⠐⠄⠀⠀⠀⠂⠀⠀⡀⠀⠀⢠
⠀⠂⠐⠀⠚⠐⠰⠂⠀⠀⠀⠀⠃⠀⠀⡘⠀⠁⠁⠀⠀⠀⠱⡄⠀⡠⠊⠀⠀⠐⠈⠀⠔⠀⠀⠂⠐⠒⠀⠀⠀⠩⠄⠐
⠀⠄⠀⠀⠀⠀⠀⢇⠐⠀⠀⠀⠄⠈⠀⢀⣤⢠⠀⢀⣤⢀⣀⡈⡊⠀⣀⠀⢀⣤⠀⠘⢁⠀⠀⠀⠁⠀⠀⠀⠄⠂⠈
⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⡼⢸⢸⠀⣾⣀⢹⡀⢹⣿⠀⣯⠇⣾⣸⠀⠁⠀⢴⣷⣶⣶⡶⠂⠀⠀⠀⠀⡁
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⡀⢀⡏⢹⢸⣀⢧⡸⢻⠉⢸⡏⣷⡟⣆⡏⢸⡆⠀⠀⠈⠁⠁⠀⠀⠀⢠⡘⠀⠀⠁
⠀⢐⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠈⠉⠉⠛⠁⠁⠈⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠐⠈⠀⠀⠠⠀⠲⠆
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠰⠥⠤⠄⠀⠠⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢀⠀⠈⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⡠⠂⠀⠀⠈⠂⠉⠉⠀⠀⠂⠀⠐⠀⠀⠀⠈⡼⡩⠓⠀⠀⠀⠀⠀⠀⣈⡁
⠀⠋⢹⠙⠀⡀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠗⠀⠀⢠⠀⢀⠀⠀⠦⠄
⠀⣄⡾⡠⠀⠐⠅⢪⡂⡠⠀⠀⠀⠀⠀⠁⠀⠀⠐⢒⠖⠀⠀⠀⠀⠘⠀⠀⢊⠐⠀⠂⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠂⠈⢄⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠧⣰⠆⠀⠀⠎⠀⢰⠄⠀⢆⡆⣂⢴⢰⢠⡀⡆⠀⠂

⠀⠆⠘⠀⠀⠀⡖⣦⢹⡀⠀⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡐⠒⠀⠀⠀⠀⡴⢱⢇⡎⣠⠂⡴⢠⠄⣀⠀⡴⡄⢀⡄
⠀⠀⡀⠈⢆⠀⠈⠉⢸⡇⣤⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠈⠈⠁⠉⠐⠃⠀⢰⠁⢸⠇
⠀⡠⠀⠀⠘⡆⢀⠀⢸⡇⠻⠋⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠆⠀⠀⠀⠀⠀⡉⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣨⡉⡿
⢀⠇⠀⠀⠀⢼⠁⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠁⠀⠁⡄⠐⠃⠐⠀⠀⠘⠁⠀⠙⠴⠃
⠀⠀⠀⠀⠘⠀⠂⠒⠀⠀⠁⠀⡀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠂⠀⠀⠼⠀⠀⠘⠀⠀⣠⠂⠀⠀⠀⠀⡀⠰⠀⠀⠈⠉⠉⠁⠀⠂
⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠮⠀⠀⣀⠂⠀⠀⢠⣶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠸⡀⠂⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⢠⠀⠀⠀⠁⠀⠀⢄⠀⠉⠀⠠⠁⠂⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠁⠀⢂⠀⠀⡠⠄⠈⠫⡁⠈⠀⠀⠀⠀⣀⡀⠀⠀⠐⠈⣀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⣋⡀⢠⠁⠀⠀⠀⠀⠀⠂⠂⠁⠀⢠⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠆⠀⣠⠃⠀⣀⠀⠠⠀⠜⠣⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠈⠀⠐⠀⠀⠀⠘⠀⠁⠀⢀
⡀⠈⠨⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠡
⠂⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⢸⢀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠇⠈⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⠀⠐⠛⠀⠀⠠⠀⠀⠐⠃⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠌⠈⠀⠀⠀⠄⠁⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠀⠀⡴⠈⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢡⢋⠟⠋⠰⠀⠀⠀⠰⠀⠠⢁
⢠⡴⢤⠖⡆⠠⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠂⠀⡞⠀⠀⡀⠀⠀⡠⠀⠀⠀⠒⠁⠸⠒⠀⠀⡀⠀⠀⡄⠀⣁⡀
⠈⠀⢸⠀⠁⠀⠀⠢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠋⢉⡶⠂⠀⠀⠀⠈⠁⠀⠘⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⢠⠀⠀⢠⡀
⢠⣆⡿⣄⠔⠀⠀⣀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⡉⢠⡀⠀⠬⠰⠀⠀⡄⡤⠠⡄⡄⢠⢀⡄⢠⠀⠈⠀⠀⠑⠁⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⡇⢹⡃⣸⢿⡇⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣹⡇⠉⠁⣿⣼⣧⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠶⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⢸⣿⣛⠃⢦⡆⣾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⡛⢹⡇⠞⠇⣿⢻⣧⢨⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠿⠾⠃⠀⠀⠻⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡗⠀⠀⣴⢶⡄⢀⡀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣬⡅⣸⡇⣿⣧⣭⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⣿⣼⡇⠀⠀⢿⣧⣿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣺⣿⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⠘⠓⠒⠚⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠺⠿⠿⠷⠶⠾⠿⠿⠷⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⣠⡤⠖⠛⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠛⣷⡀⢰⠏⠀⠀⠀⠀⢹⣀⡼⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣠⡶⠦⣤⣀⡀
⠀⠀⢀⣀⡤⣄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣀⡼⢳⣼⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠀⠀⠐⣟⡆⠀⠀⠀⠀⣿⢁⡇⠀⠀⠈⠉⢹⡆⢀⣤⣀⡀
⣶⠚⠉⠀⠀⢋⠓⢦⣄⠀⠀⢻⠀⠀⠀⠀⠏⠀⠀⠀⢻⠀⠀⢰⢦⠀⠀⠈⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢸⠃⠀⠀⠀⠀⠘⣇⡏⠀⠀⠉
⠘⡆⠀⠀⠀⠘⡄⠀⠈⠳⣄⡸⡆⠀⠀⠀⠘⠲⡄⠀⢸⠀⠀⠈⠉⠀⠀⠀⢸⡄⡏⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⠰⡀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢰⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢷⠀⠀⠀⠀⠳⠴⠀⠂⠉⢹⡆⠀⠀⠀⠀⠉⠉⢿⠀⠀⠀⢀⣦⠀⢀⣀⡀⢿⠀⠀⠀⡟⢆⠀⠀⠘⡆⢸⠇⠀⠀⢠⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡸⠈⡶⠁⠠⠌⢿⠤⠤⠤⠇⠀⠲⠤⠤⢽⣾⠀⠀⠀⡇⠱⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⣀⠸⠷⠤⠤⠒⠒⠒⢉⡉⠁⠀⢀⣤⣧⡘⠠⢊⣼⠦⣤⣤⣀⡶⣄⣀⣀⣤⠀⠈⠉⠚⢀⠀⢦⣀⠀⢀⡏
⠀⠀⠀⠀⢳⡀⢀⡠⠤⠒⠋⠉⠀⠀⣐⣶⠤⠶⠶⠶⠚⠙⠛⠋⠉⠁⠈⣯⠀⠸⡇⠀⠀⠀⠈⠀⠀⠈⠉⠉⠛⠛⠓⠶⠟⠳⣄⣈⣉⡿⠃
⠀⠀⠀⠀⠈⠻⢥⣀⣠⡤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠈⠷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠰⠂⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡖⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⢷⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡞⠈⣇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠇⠀⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡸⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⠒⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⣌⣙⠒⠦⠤⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠸⡤⠴⠖⢋⣁⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⡄⠀⠀⢘⡛⠛⠛⠛⢋⢙⡀⠀⠀⢢⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⢣⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠃

⠀⢀⠔⠀⠐⡄⠀⠀⠀⠀⠀⢀⠔⢉⢉⠑⡄
⢠⡡⠊⠉⡆⡀⠀⠀⡎⠃⠀⠈⠒⠁⢠⢃⠇⢀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡖⠛⡄
⠀⠀⠀⡜⡰⠁⣖⣂⠃⢘⣒⡆⠀⡠⢃⠎⠀⢈⣉⣁⣈⡩⠖⢊⡩⠟⠋⠉⠉⠉⠉⠳⣄⠀⠀⠀⠸⡀⢱
⠀⣠⠊⡴⠁⠀⠀⠀⡁⡏⠉⠁⡰⢁⠎⠀⠀⠘⠒⠒⢺⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⢷⡈⡟⠓⠲⡄
⢴⣁⠚⠀⠤⢤⠀⠀⠉⠁⠀⠴⣀⣉⣐⠒⠀⡄⠀⠀⢸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠱⠇⠀⠀⠉⠳⡆
⠀⠀⠈⠉⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠤⠀⣠⡼⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠶⠚⠛⠋⠉⠙⠛⠛⠿⢤⣀⠀⢰⠇⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡴⠚⠁⣰⠉⠉⠋⠉⠉⠉⠉⠋⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠠⡀⢀⣀⠠⠤⢤⣀⡴⠀⠀⠀⠀⠸⡏⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠀⢠⡇
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⣇⠀⠀⠲⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠽⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⡏⢀⡠⠄⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⣷⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢿⠀⠀⠀⠀⠀⠀⡠⠊⠙⠒⠒⠒⠉⠁⠈⠂⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠛⠶⣦⣀⡀⠀⠀⣀⣀⣤⠶⠋⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⢹⠋⠉⠉⠉⡇⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠤⣴⣄⣀⣴⣤⠼⠇⠀⠀⠸⠧⢤⣦⣤⣤⠼⠦⠼⠃

⠀⢀⣀⣀⣠⣀⠀⠀⣀⡀⢀⡀⠀⠠⢄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠈⠉⠉⠉⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠓⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠇⠀⠒⢀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢠⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣄
⠀⠠⡀⠀⠀⠘⠛⠻⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠒⠀⠀⠀⠁⠙⠘⢁⠐⠀⠐⠀⠀⠓⠃⠺⠿⠛⠋
⠀⠀⠹⢒⠤⠄⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⡀⣈⠁⠃⡀⢀⢀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠁⠀⠈⠀⡢⠀⠆⠐⠐⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠈⠀⠈⢡⠀⠀⢠⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣠⡀⠀⠙⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠄⠀⠐⠂⠰⠀⠀⠀⠈⣀⠀⠀⠀⠈⡊⠉⠉
⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⢠⣷⣄⠀⠀⠀⣠⣄⠀⠀⠀⠐⠘⠂⠀⣾⣻⡷⠀⠀⠀⠐⠆⠀⠀⠂⠀⠀⣤
⢀⠐⠈⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠐⠀⠊⠀⠀⠀⠈⠉⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠈⠐⢢⠀⢀⠀⠀⠤⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠈⠘⠀⠀⠀⠀⠀⠀⠅⠀⠠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠈⠛⠛⢁⠀⠀⠀⠀⠀⠀⢠⠲⡄⠀⠐⠀⠀⠀⠀⠀⢀⠒⢲
⠀⠀⠐⠀⠐⠈⡈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⣉⣈⠉⠀⣀⣴⣆⣀⠀⠀⠉⠀⠀⠂⠐⠂⣀⣤⡀⠀⢀
⠀⠀⢀⢀⢀⡀⠀⠀⢀⠠⠸⠐⠐⠀⠀⠀⠀⠀⢸⠯⡟⡧⠀⣿⣿⣿⣿⣿⣶⣶⠀⠁⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠒⠚⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠈⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⣿
⠀⠀⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣤⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠴⠧⠤⠶⠀⠀⠀⠀⠻⠤⠤⠤⠴⠶⠶⣦
⣠⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⠞⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡆⠀⠀⠀⣏⠀⠸⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⢸⡆⠀⠧⠤⠤⠤⠴⠖⠒⠒⠒⠒⠒⠚⠛⠛⣿⠃⠀⠀⠀⢹⡀⠀⠉⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡏⠉⠉⠉⠉⣩⠟⠁
⠀⢷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⠧⠤⠤⠤⠤⠴⢦⠀⠀⢸⠀⠀⠀⠀⢷⠖⠒⠒⠛⠁
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠓⠚⠛⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⠳⣤⡀⠀⠀⠀⠀⢀⡞⠁⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠈⢙⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⠲⣄⠀⣠⠏⠀⠀⠀⣠⢾⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣙⣶⣾⣯⣤⡤⠤⠴⠶⠶⠶⠶⠶⣆⠀⠀⠀⠀⠀⠀⡼⠉⠓⠦⣀⠀⠀⠀⠈⠙⠃⠀⠀⢀⡜⠁⣼
⠀⠀⣾⡏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⢰⣋⡠⠞⠁
⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡴⠃⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀
⢸⡁⠀⠹⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠚⠋⠉⠉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢠⠞⠲⢤⣀⠐⠀⠀⠀⠉⢹
⠈⣧⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⡰⠃⣀⡀⠀⠈⠑⠦⣀⠀⡠⣿
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣤⠞⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠢⡀⢀⡜⠁⡼⠋⠙⠲⣤⡀⠀⠈⣹⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠢⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠋⢀⡞⠁⠀⠀⠀⠀⠉⠓⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄⠀⠀⠀⠀⠀⠀⡠⠊⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣶⣌⠃⠀⠀⠀⣠⢎⣴⣿⣧⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣿⣿⡿⢟⡛⠂⠘⣛⠛⠛⠿⢿⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⡜⢡⠝⡆⣞⢡⢽⡆⠀⢤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠂⠀⠙⠲⢒⣁⣈⠓⠊⠀⠀⠀⢤⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣀⣀⣀⣿⣿⠛⠓⠀⣠⡄⠀⠻⣿⠟⠁⠀⠶⣄⣀⡤⠴⠖⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠙⢿⡇⠀⠹⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠘⣏⠉⢉⣉⣿⣉⣀⡀⠀⣿⠀⠀⣨⠭⠭⣧⠴⠶⠚⢻⠟⠒⠈⠂⠀⠀⠀⠀⠀⠀⠀⣴⡋⠙⣻⡶⠚⠋⠛⠛⠿⣿⣿⠇
⠀⠀⠋⠉⠉⠉⢿⡉⠉⢉⣯⣩⠄⠀⠀⣿⠀⠀⠀⠒⣺⠟⠉⠉⣩⣿⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣾⠋
⠀⠀⠀⠀⠀⠤⠐⠻⢏⡁⠀⠑⠶⠶⢶⡉⣹⠛⠛⠋⠁⣀⣤⠾⣿⣿⠋⣿⣿⡟⣷⣦⣄⠀⠀⠀⣸⣷⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⣶⣶⠿⠷⠶⠶⠛⠋⠉⠀⢸⣿⡟⠀⣿⡿⠁⢻⣿⠏⠱⣤⣾⣇⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢰⣿⠃⠀⢸⡟⠀⠀⢀⣀⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⠁⠀⢠⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣟⠿⠌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣂⠈⠻⣀⡴⢋⣼⣧⡀⢀⣠⣀⣀⣀⣀⠀⣀⣀⣠⣤⣤⣶⡟⣠⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠛⠉⡴⠿⣷⡈⠉⡜⠀⠀⠀⠈⠉⠉⣿⣿⠆⢹⡌⢿⣿⢋⡰⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡴⢀⠀⢁⡼⠁⠀⠀⠀⠀⠀⢰⠟⠛⠛⢸⡇⠀⠙⠲⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠘⠾⣵⠧⠞

⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐
⠀⠀⠀⠀⡶⠒⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠐⠒⠦⠖⢀⣤⠇⠀⠀⠀⠀⣀⣠⡖⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢁⠀⠛⡁
⠀⠀⠀⡀⠙⠀⠀⠸⠀⠀⠠⠃⠀⠀⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡾
⠀⠀⠀⠈⠉⠉⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠄⠀⠀⢀⣀⠈⠳⡄⠀⠑⠂⠤⠚⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⠀⣀⣠⡁⠀⠀⢀⠀⠀⠐⠦⠾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠐⠚⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠞⠂⢈⠛
⠀⠀⠀⠀⠤⠤⠤⠀⠀⡤⠇⠀⠀⠀⠀⠀⣀⡤⠾⠀⠀⡀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠠⠤⠴⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠀⠀⢀⣉⡀⠀⡀⠀⠈⠉⠉⠉⡉⠁⠀⡀⠀⠀⢠⡂⠐⠂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⢁⠀⠀⡀⠘⠅⠉⠀⡽⠀⠀⠀⠀⠲⠁⠂⢀⡇⠀⠀⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⢸⠀⠀⠙⠢⠤⠴⠐⠁⠀⠀⠀⠀⢀⢀⡀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠢⠄⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠔⠂

⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⡂⠀⠀⠀⢰⠀⠀⠆⠀⠆⠀⠀⠀⢐⡀⡀⠀⠈⠠⠀⠠⠀⠀⠄⠀⠄⡃⠀⠀⢀⡑⢄⠐⠂⠐⠀⡇
⠀⠠⣀⣆⣆⣠⡠⠀⠀⠠⠀⠂⠀⠀⠐⡀⢀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⢑⡝⠀⠑⢄⠈⠀⡇
⠀⠐⠭⡯⡯⢽⢹⠀⠀⠲⣐⠆⠀⠀⠀⠿⠛⠀⠀⠠⡄⠀⠀⢠⡄⠠⠀⢠⠅⢰⣃⡎⠀⣀⡀⡀⠑⢄⡁
⠀⠐⠀⠁⠉⠉⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢢⡃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⠔⢁⠄⠠⠈⠂⡀⠁
⠀⡾⠭⠭⠬⠭⠷⠀⠠⠊⠀⢽⡖⡽⣆⠀⠀⢀⢳⡞⡀⠀⠀⢀⠂⠈⠄⠀⠀⠀⠘⠀⠃⠀⠀⠘⠀⠃⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡋⠀⠀⢂⠁⠈⠐⠀⠀⠂⢀⡀⡈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠈⠛⠛⠛⠛⠃⠀⠀⠀⠒⠐⠀⠃⠐⠂
⠀⠣⠀⠀⠀⡀⠔⠀⠀⠀⠀⠒⠒⡂⠀⠰⠂⠂⠰⠀⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⡀⠠⣴⠤⣄
⠀⢠⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠐⡂⠀⠀⡀⠤⠒⠢⠄⡀⠀⠀⠀⡈⣀⢀⢀⡀⡀⠀⡌⠀⠀⣿⣊⣸⡆
⠀⡷⠎⠱⠈⠎⠁⢺⠀⠀⢀⠀⡂⡇⠀⡘⢀⠂⠀⠀⠄⠱⠀⠀⠀⢜⣿⣻⣻⠟⠀⠀⢃⠀⠀⠀⠀⢨
⠀⡧⠄⢰⠀⠆⡢⢼⠀⠀⠈⠀⢁⠁⠈⠁⠀⠉⠉⠉⠁⠀⠩⠀⠀⠁⠛⠘⠘⠃⠠⠀⠀⠐⠀⠀⠐⠁
⠀⢂⠒⠒⠒⠒⠒⠘⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⡒⣂⣄⠀⠠⠤⢄
⠀⠀⠐⢄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⢢⠃⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠀⡍
⠀⠀⠀⡄⠑⢄⠀⠀⡘⡈⠉⠔⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠁⠀⠠⡳⡛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡃
⠀⠀⠀⠄⠠⠀⠑⢄⠀⢸⡺⠀⠀⠀⠀⣐⢂⠀⡀⢀⣒⠂⠄⠀⠨⠁⠉⠁⠀⠰⠀⠀⠀⠀⠜⠀⠈⠿⠋
⠀⠀⠒⠒⣒⣖⡒⠒⠓⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠊⠀⢸⣷⣿⡆⠀⠐⠂⠒⠘⠀⠐⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢈⠐⠂⠁⠀⠀⠁⠀⠐⡀
⠀⠀⠀⠀⠈⠉⡩⠀⠀⠠⡞⡃⠀⠐⠈⠁⡄⠀⢈⠐⠐⠐⠂⠀⠀⠀⢈⠀⠀⠀⡦⣴⠀⠀⣦⣤⣆⣤⡴
⠀⠀⠀⠐⠒⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⣀⠤⠄⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂
⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣰⣶⡆⢰⣿⡄⢰⣶⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣵⣶⣶⣶⡦⣤⣄⣀⠀⣀⡀⠉⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡽⣻⡏⢸⠹⣿⣷⣳⡈⠛⠮⠳⡻⠏⠀⠛⠛⢜⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⣇⢀⠈⠀⢈⠀⠳⡓⠄⣄⢀⠈⢀⠳⡄⢰⣾⣧⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡆⠘⠙⢾⣇⢵⣄⡳⣄⣙⣌⣿⣎⣯⣦⣷⣿⣦⣁⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⠀⠀⠉⠦⠽⠿⣿⠿⠛⣛⡉⠻⠿⠿⠿⣯⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⣀⡉⠃⠀⣀⣤⢶⣞⣷⡒⠨⣍⣠⣀⠀⢀⠀⠈⠄⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠋⣩⠻⣿⣿⢿⡟⠀⠾⡹⠿⠏⢀⣿⠋⠉⠁⣤⡀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣿⠀⣈⠇⠀⠻⣦⣀⣀⣀⣤⡾⠃⠀⠀⠀⣿⣿⠈⠀⠁⠀⠀⠇
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠙⠀⠒⠀⢠⠉⠛⠉⠉⠀⠀⠀⠀⢠⡿⠁⠀⠀⠂⠀⠀⢳
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⢂⠀⠀⠀⡀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⣧⣿⡆⣦⠸⣿⣿⣿⣦⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠒⠢⠤⠤⠤⠖⠊⠁⠀⠀⢿⣿⡇⡹⣷⣸⣿⣿⣿⠃⠀⠀⠀⢀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⢱⠀⠻⢿⣝⣿⣿⠛⠛⠉⠀⠀⠀⠀⢾⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠻⣝⣻⣧⣄⣀⠀⠠⡀⠀⠘⢿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⣤⣤⣤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⠉⣁⡀⠠⠵⠀⠀⠀⠀⠈⠛⠻⠇⠀⠀⠀⠀⠀⠀⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⣹⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣿⣅⠀⣥⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠿⣿⣿⡿⢷⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣴⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⡟⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠶⠶⠶⠤⢴⡷⠀⠀⠀⠀⠸⠾⠷⠶⠶⠶⢶⣄
⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⢋⣰⡇
⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠚⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⠶⢶⡇⠀⠀⠀⠀⢸⠀⣾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣧⣤⣀⣠⣤⣤⣤⣤⣤⣶⣶⡶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠶⠶⠶⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⣤⡀⠀⠀⣠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠙⢶⡴⠋⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣞⣡⡾⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠿⠛⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢙⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢀⡾⢁⣙⠳⢤⡀⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⢻⣶⣛⣛⣋⣩⣭⣭⣭⣥⣤⣤⣤⣤⣶⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⣰⠏⣴⠟⠛⠷⣦⡉⠳⠶⢋⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⢦⣤⠞⢁⣾⠋⠀⠀⠀⠈⠻⢶⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠒⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠁⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⡠⠒⣶⠀⠘⡄⠀⠀⢀⠄⠊⠢⡀⣠⡶⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠉⢉⢤⠾⠋⠄⡰⠁⠀⠀⢿⣦⡀⠀⢈⠁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⢠⡤⠤⠛⠃⠀⠀⠀⠈⠈⠩⠍⡇⠀⠀⠀⢺⡇⠀⠀⢂⣀⠀⠤⠄⠠⠇⠀⠀⠀⠀⣰⣕⠁⢀⡴⠊⠀⠀⠀⠀⠀⣨⡟⢀⠀⠀⠀⢪⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⡇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢙⣣⠤⠌⠀⠀⠀⠀⠀⠠⢾⡁⠀⢀⠤⣦⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠹⣧⡠⠤⣶⡆⠀⠁⢸⠉⠉⠁⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⡀⠈⠀⠜⠀⠀⠀⠀⠻⣁⡂⠆⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠈⠛⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠈⢣
⠀⠀⠀⠀⠀⢰⡟⠹⢑⡄⣴⣻⠋⠐⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣸⡇⠀⣶⠶⠒⡄⠀⠀⠀⠀⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠑⠒⢋⣴⡷⠁⠰⢀⠜⠀⠀⠀⠀⠀⠀⢀⣄⡤⢤⠴⠶⠒⠚⠛⠛⠛⠓⡄⠀⠸⢇⣀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⢸⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⢎⠞⠀⠀⢠⠊⢀⡀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣼⠟⠀⣠⡐⠑⡄⠀⠀⠀⠀⠀⠈⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡴⡳⠋⠀⠁⡔⠁⠠⡟⠭⠳⡄⠀⠀⠀⠀⠙⠒⠒⠒⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠲⠊⠈⠻⠒⠁⠀⠀⠀⠀⠀⠀⠙⣒⣒⠁
⠀⠀⠀⠀⠀⠀⠻⡁⠀⢤⠎⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁
⠀⠀⠀⢀⣠⣤⠤⢀⠀⠀⠀⠀⠀⠀⡴⡒⠀⠀⢠⣴⡂⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⢆⠀⠀⠀⣾⡏⠁⠂⠤⢀
⠀⠀⢠⢛⠋⠀⣠⡀⠙⡆⠀⠀⠀⢳⡇⠀⡁⠀⠀⠉⢹⡆⢸⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠄⣠⠖⠁⠀⠀⠀⠈⠁⠒⠤⢔⡀⠀⠑⢐⠄
⠀⠀⣇⡎⠀⠌⣸⣿⠀⢸⠀⠀⢀⢾⠋⢐⠁⠀⠀⠀⢅⡄⠸⢄⠀⠀⠀⠀⢠⣾⠟⠁⠀⢠⣋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⡮⠟⢁⡴⠋
⠀⠀⣿⡇⠸⣴⡿⠃⢀⡎⠀⠀⠀⢀⣣⠘⡆⠀⠀⠀⠜⠟⠀⡎⠀⠀⠀⠀⠀⠉⠓⠦⢅⣀⠈⢉⠓⠶⢤⠀⠠⣴⡿⠛⠙⢀⡴⠋
⠀⠀⠈⠳⣄⣀⣀⡤⠊⠀⠀⠀⠀⢸⡟⠰⠇⠀⠀⣤⣤⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣤⠞⠀⠀⠘⢆⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠤⠃⠀⠙⠃⠥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⣠⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡄⠀⠀⠀⢀⡴⠖⠒⠒⠛⠒⠃⠀⠀⠀⠳⠒⠒⠒⠒⢲⡄
⠀⠀⠀⡞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢳⠀⢇⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⢤⡇⠀⠀⠘⡆⠀⠓⠂⠉⠉⠉⠙⠀⠀⠀⢠⠖⠒⠒⠒⣲⠏
⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠎⠀⠀⠀⠀⠳⠤⠤⠤⠤⢤⠀⠀⡇⠀⠀⠈⡶⠶⠒⠚⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢃⠀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣈⣉⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⡀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠲⣄⠀⠀⠀⢠⠞⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠽⠋⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡧⣀⠀⠀⠈⠙⠦⣴⠋⠀⠀⡠⢺⠁
⠀⠀⠀⠀⢠⡴⠖⠒⠒⠒⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⡇⠀⠀⠀⠀⢼⡀⠀⠑⠢⣄⠀⠀⠀⠀⢀⠞⣡⠞
⠀⠀⠀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠲⣄⣠⠎⠀⠀⠀⠀⠈⠛⠧⣄⡀
⠀⠀⠀⢾⠀⠘⠦⠤⠤⠤⠒⠒⠒⠒⠒⠒⠚⠉⢉⡽⠋⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⡰⠒⠢⢄⡀⠀⠀⠉⣹
⠀⠀⠀⠘⣦⠤⠤⠤⠤⠤⠤⠶⠖⢒⣶⡚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⢀⠞⣠⢤⣀⠀⠉⠲⢤⣔⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢏⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠙⠦⠊⡰⠃⠀⠈⠓⠦⣄⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⠀⠀⢰⣷⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠈⠑⣄⠔⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠄⢸⠀⠀⠀⠦⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢆⠀⠀⠀⣠⠎⠣⣄⣀⡤⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢦⡀⠉⠓⠋⠁⠀⠀⠀⠀⢀⠴⠂⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠈⠑⠒⠂⠤⠄⠒⠒⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⣠⡶⠟⢻⡆⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡾⠋⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠁⠀⠈⠁⠢⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢀⡨⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠓⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣠⣴⡶⠀⠀⠀⣠⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⣀⣤⣶⣾⠿⠋⠁⢹⠀⠀⠀⠛⡻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠦⢤⣀
⠈⠉⠁⠀⠀⠀⠀⠈⣇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⢿⣷⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣤⠀⣀⣀⠀⠀⢠⡄⠀⠀⠀⠀⡞⣩⣭⣭⣍⡍⠆⠀⠀⠀⠀⢠⠶⠶⠶⠶⡄⣚⡇⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⢰⢫⣩⢩⢩⢳
⠀⠀⣿⢉⣛⣛⣉⣉⢹⡇⠀⠀⠀⠀⡇⣉⣉⢉⢉⡁⠀⠀⠀⠀⠀⢸⠀⣒⣒⠀⡇⢹⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠘⢸⢸⢸
⠀⠀⣿⣨⣭⣉⣩⣭⣸⡇⠀⠀⠀⠀⡇⠒⢲⢰⢸⡇⠀⠀⠀⠀⠀⢸⢀⣂⣀⡀⡇⡼⡇⠀⠀⠀⠀⣸⢻⠛⠛⡟⡏⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠙⠀⠁⠀⠀⠉⠘⠃⠀⠀⠀⠀⠳⠭⠬⠬⠬⠥⠆⠀⠀⠀⠀⠸⠦⠤⠤⠤⠇⠘⠀⠀⠀⠀⠀⠿⠿⠧⠤⠼⠿⠿⠀⠀⠀⠀⠀⠘⠦⠤⠥⠤⠞


⠀⠀⠀⣠⠖⠛⠓⢦⡄⠀⠀⠀⠀⠀⢀⡴⠚⠛⠳⣤⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⡴⠞⢛⠓⢦⡀⠀⠀⠀⠀⠀⢠⡴⠚⠛⠲⣄
⠀⠀⢸⡇⢤⣤⣤⡄⢻⠀⠀⠀⠀⠀⣾⠀⣤⣿⣤⠈⡇⠀⠀⠀⠀⢠⡏⠀⣷⣞⠀⢹⡄⠀⠀⠀⠀⢸⠁⣤⣭⣤⠀⣷⠀⠀⠀⠀⠀⡟⠐⠒⠒⠒⢸⡆
⠀⠀⠈⢧⣀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠹⣆⡀⠛⢀⡼⠃⠀⠀⠀⠀⠀⢳⣌⠁⠈⣠⡞⠀⠀⠀⠀⠀⠘⢦⡀⠚⢀⣰⠏⠀⠀⠀⠀⠀⠻⣌⠉⠉⣉⡼⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡂⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡆
⠀⠀⢸⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⣙⣿⣧⠀⠀⠀⠀⠀⠀⠀⢴⠟⣧⠀⠀⠀⠀⠀⠀⢰⡇⢀⡶⠳⣆⠀⡇
⠀⠀⢸⣿⣤⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠠⡌⠈⠹⣧⠀⠀⠀⠀⠀⠸⣇⣀⣻⣞⣃⣀⡇
⠀⠀⠀⠁⠁⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⡤⢤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢰⢋⠓⢸⠐⢉⢳⠀⠀⠀⠀⠀⠰⣦⡖⠐⣆⢠⠆⠀⠀⠀⠀⠀⢀⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣡⠟⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠁
⠀⠀⢸⠀⣱⣸⣰⠃⢘⠀⠀⠀⠀⠀⠰⠛⠧⠀⢹⡞⠀⠀⠀⠀⠀⠀⠀⣿⠀⢄⣠⠄⠀⠀⠀⠀⠀⠀⢹⣶⠋⠀⠉⠁⠀⠀⠀⠀⠀⠉⢳⣼⠁
⠀⠀⠈⠣⣃⢸⠐⡲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⢳⡀⠀⠀⠀⠀⠀⢠⡾⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⡂
⠀⠠⣤⠤⠠⠴⠖⠀⠄⠰⠆⠀⠈⠂⠀⠀⠀⢠⠅⠀⠀⠈⠀⠀⠀⠂
⢀⡁⠀⠈⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⢈⠌⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠈⠄⠀⠀⠀⠀⠘⠂⠀⡀
⠘⠒⠇⠀⠂⠀⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡄⠀⠀⠀⠅⠀⠀⠨⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠊⠁⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⣀⠀⠁⡀⣀⠀⠀⠀⣤
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠲⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀
⠀⠁⠀⠀⡀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⠂⡁⠠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⢷⠄⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠀⠀⢰⠰⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠐⠲⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄⣤⠄
⠀⡄⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣾⣿⢿⣿⣿⣷⣶⣷⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⣿⣾⣿⣯⣿⣿⣟⣿⣿⣿⡿⢿⣶⣶⣶⣦⣤
⠢⠑⢀⡀⢀⠀⠀⠠⢤⠃⠀⠈⠁⠀⠀⢀⢀⠀⠀⠀⠀⠐⢿⡿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣿⣼⣿⠿⠿⠟⠁
⢰⡄⠀⠀⠈⠀⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣄⠉⠉⠋⠁⠉⠁⠆
⠀⡄⠀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠑⠦⠄
⠀⠃⠀⠀⠁⠀⠀⠁⠀⠈⠀⠠⠂⠀⠀⢀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⣀⢀⠀⣄⡐⠀⢀⢀⢀⠢⡐⠂⠀⠙⠙⠉⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠚⠀⠁⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠠⡀⠀⠐⠁⠢⠀⠀⠀⠁⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠠⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⢈⠂⢀⠀⠀⠂⠐⠈⠀⠀⠀⠀⡀⠀⠀⡆⢀⠢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⢸⡇⡀⠀⠈⣤
⠀⠀⠀⠀⡀⠸⠮⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠠⠊⡀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠄⢸⡇⢰⣶⠀⣿
⠀⠁⠀⠀⠁⠃⠀⠀⣀⣤⠄⠀⠑⢄⡴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⠉⠉⠈⠉⡉⠉⢩⠉⢩⡍⠉⡏⠉⠃⠐
⠀⢠⣂⡀⠀⠀⠀⠀⠛⠁⠀⠀⡰⠋⡠⠒⡀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠉⠠⣉⠕⠊⠝⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠊⠀⢈⠁⠥⠐⠂⠃⠀⠀⢀⡡⠤⠔⠒⠓⠋⠀⣀⠀⠀⢀⠀⠰⠢⠀⠒⠀⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢁⢊⡀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠰⠉⠀⠀⡀⠀⠐⠀⠆⠀⠀⠠⠀⡀
⠀⠀⡠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠘⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠦⣀⠘⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣷⡄
⠀⠀⠃⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠁⠈⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠈⠻⣿⠄
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠻⠶⣲⠴⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠆⠑⠒⣀⣤⣧⡄
⠀⠀⠀⡀⠀⠀⠂⣀⠀⠃⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠐⠫⡨⠆⠀⠀⠀⠀⠀⠸⠄⠨⠜⠉⠛⠛⠁
⠀⠀⠰⠀⠐⠚⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⠀⠈⠃⠀⠀⠀⠀⠀⠰⠱⠀⠀⠀⠀⢀⡀⠀⢠⠀⣀⠀⠀⡀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠄⡒⠇⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠘⠀⠙⠃⠐⠂⠇⠘⠘⠃
⠀⠀⢠⠂⠀⠀⠀⠀⢸⠀⠀⠃⡀⠀⡜⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡰⢢⠕⠂⠀⠀⠀⠀⠀⠀⢀⡈⠀⡈⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠈⠒⠀⠀⠀⠀⠈⢸⠀⣦⠆⠀⡏⠀⠑⠀⣴⣁⣀⣩⠆⠀⡠⢊⠔⠁⠀⢀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⡂⠀⠀⠀⠐⠀⢀⣠⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠛⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⣀⠀⡰⠁⠀⠀⢠⢠⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠘⡀⡄⠀⠀⠀⠀⠀⣮⣤⣼⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⢀⠀⡠⡀⢠⡄⡄⠀⡄⢠⡄⠀⠀⠀⠀⠈⠱⠃⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⢀⡡⠶⠂⡀⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⢄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠀⡠⠔⠁⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠠⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠸
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⠐⠀⠀⠀⠈⢀⠈⡄⠀⠀⠀⠀⠀⠠⠈⠀⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄⠀⠀⠀⠀⢠⣄⠀⡗⣄⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⡦⠀⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣤⣿⡖⣦⣸⢙⡏⡈⠛⣿⣿⣴⣃⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⣙⣾⣿⣻⣷⣿⠖⢹⠀⡖⢢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⣒⢷⣼⠂⡜⠳⣧⣛⠿⣧⣱⣇⢾⣉⣉⣠⡇⠀⠀⠀⠀⠀⠀⣎⠻⣸⣧⣫⢧⣸⣄⡰⣯⣻⣡⣆⣰⣿⣿⣟⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣇⠘⡝⡉⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⢹⣿⡤⠵⠋⠀⠀⠀⠀⠀⣀⣣⡬⢿⡵⠋⠉⠉⠉⠉⠉⠉⠉⢻⡹⣍⠳⡅⠈⠉
⠀⠀⠀⠀⠀⡦⠶⠤⡀⠀⢧⡮⣻⣧⠧⢧⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⣶⣀⠀⠀⢀⣀⢤⣽⣭⣓⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣺⢓⢤⣀⡿
⠀⠀⠀⠀⠀⠙⢄⣶⡟⢩⠭⢽⠋⢚⣽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⡺⠏⠋⠀⠛⢻⣆⠀⣱⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣶⠿⣛⣰⠍⡩
⠀⠀⠀⣀⣠⠴⠪⠭⠭⡖⣻⡽⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠃⢠⡔⠒⣒⣲⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡻⠿⣓⠋
⣤⡒⢉⣰⣿⢷⣦⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣙⣮⠽⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⣶⡶⣞⣉⣄⡀
⠀⠉⠉⢸⠑⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣏⣃⣱⡈⣹⡅⢀
⠀⠀⠀⢘⡶⣻⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢻⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⠎⠉⢠⠟⠛⣏
⠀⠀⣀⣯⣴⣧⡇⠀⠀⠀⣀⣤⠖⣋⠣⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣻⠄⠀⠀⠀⣀⡤⢶⣿⠹⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠤⡀⠓⠻⠞⣼
⠀⠈⠳⣏⣿⣹⣧⣶⡾⣏⢟⡧⢘⢿⣠⣶⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣽⢤⡶⢾⡟⡽⢛⡵⢻⣠⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣣⡥⣆⣀
⠀⠀⠀⢠⢫⣿⣗⠤⠙⡼⠊⠓⠁⠀⣯⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⠛⢲⣿⠷⢗⠋⠀⠈⣥⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⡥⣠⠿⣾⣇
⠀⠀⠀⠸⡄⣽⠈⠙⠒⠛⠀⠀⠀⠀⡮⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠻⣎⣱⣋⣳⠞⠀⠀⠀⣈⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠾⣅⢇⡟⣾
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢰⢲⣷⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⣩⣀⡴⠀⠀⢀⣠⣒⣋⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⠋⢻⡟⡻
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⢺⢞⣟⡉⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣧⢿⠳⣦⣜⠃⠈⢣⡀⢸⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⣕⢾⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣅⠀⠦⢦⠴⡏⠠⣼⢟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⡬⠦⠘⢿⢳⠓⠀⠀⢙⣶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠆⣾⢻⡗⣛
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣤⣧⡤⠿⣎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⡔⠒⢆⠀⠙⠃⠀⡰⢋⣫⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⠈⡻⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠘⣃⣧⣀⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⢷⡤⠊⠀⠀⠀⠐⠛⠉⡰⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡋⠧⠤⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠺⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣸⣀⡠⡄⠀⢠⠤⢤⣳⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠗⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⣆⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⣽⣒⡴⠃⠀⠈⢧⣀⠮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣤⣾⣷⣒⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢉⣿⣩⢋⡽⣻⢻⣙⢿⣙⠛⠿⣋⡿⠫⣻⣷⣆⣈⡷⠄⠀⠀⠀⠀⢈⠟⣻⡿⢩⠿⣯⣛⣛⣽⣟⣹⣻⢻⣶⣦⠌⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⣰⣁⣹⠴⠋⠢⣉⠉⣿⠉⡝⠉⡷⠚⢃⡓⢳⠀⠀⠀⠀⠀⠀⠀⣏⣨⠟⠱⢄⣀⣁⢟⢀⣣⣸⢾⡵⢿⣯⣫⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠈⠣⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠙⠋⠂⠀⠀⠀⠀⠈⠰⢄⠀⠐⠄⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠲⣤⣐⣀⣀⣀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⠀⠀⠀⠄
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠢⡊⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠒⠈⡁⠀⠀⠈
⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⢄⠀⠀⠀⣀⡀⡀⠀⠠⠤⠠⠤
⠀⠈⠀⠈⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠂⠤⠄⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⡀
⠀⠐⠀⠒⠃⠈⠁⠀⡀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠉⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠂⠈⠓⠒⠉⠉⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠲⣤⠀⢠⡄⠈⠢
⠂⠀⠀⡀⢀⡀⠀⠀⠀⠀⠈⠁⠁⠈⠑⠋⠂⠊⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠳⠀⠀⠜⡀⢀⠳⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠲⠦⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⠀⠂⠀⠀⠀⠀⡂⠘⠀⠀⠀⠀⠈
⠕⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠠
⠀⠐⢆⠀⠀⠀⠀⠀⠐⠂⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢊
⠀⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠄⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⡠⠃⠀⠀⠀⡐⠀⠀⢀⡀⠀⠉⠉⠙⠀⠀⠘⠀⠈⠆
⠀⠄⠀⠀⢀⠀⠀⢠⢀⡀⠀⠀⠈⠰⢤⡀⠈⠀⠀⠐⠀⠀⠀⢀⠉⠈⠓⠒⠛⠢⠤⢌⠀⠀⠀⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠂⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠁⠀⠈⠙⠦⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡆⠀⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⠉⠉⠛⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢷⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡰⠋⠁⠀⠀⠉⠲⡀⣠⠊⠁⠀⠈⠹⣄⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⡀⠀⢹⠃⢀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠛⠀⢸⡆⠈⠋⠀⠀⠀⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⢦⡀⠀⠀⠀⠀⣠⠏⠙⢦⣄⣀⣠⠞⠁⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢠⡄⢀⣙⡲⠶⠖⠋⠁⠀⠀⠀⠀⡀⢄⠀⣠⠦⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠙⠾⣤⣨⡂⠀⠀⠀⠀⠀⠀⣘⣤⠴⠛⠁⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⢀⣴⡿⠋⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣾⠋⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⡐⠂⠢⠀⠀⠀⠀⠀⣠⣾⣟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠳⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠟⠋⠁⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣀⣤⣤⣤⣀⠀⠀⡰⠟⠉⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⡿⠿⠛⠻⣿⣧⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⢠⣿⣿⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡟⠁⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠁⠁⠁
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⢉⡼⡇
⠀⠀⠀⠀⠀⠀⣿⠑⡤⠶⠶⠒⠚⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⡇
⠀⠀⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠔⢳⠄⠀⠠⠤⠄⠀⢉⣼⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⢸⠇⣿⠀⠀⠀⠀⠀⠐⡏⠀⠀⠚⠟⠁⣀⣴⣋⠀⠀⠚⠉⠀⢠⣠⠞⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠶⠓⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠁
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⣩⣇⠀⠠⠖⠒⠀⠀⡠⠋⠀⠀⠬⠤⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠠⠤⠊⠀⠀⠀⠀⠐⠋⠙⠋⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣸⠀⣾
⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⢠⡇
⠀⠀⠀⠀⢸⣠⠞⠒⠒⠒⠂⠉⠉⠁⠉⠉⠉⠉⠉⣉⣉⣀⣀⣀⣠⣶⣶⣶⣶⣶⣶⠀⣀⣀⣀⣈⡩⠤⢼⡅
⠀⠀⡠⠖⠋⢩⠭⠭⠭⠭⠭⠭⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⣀⣠⡾⠁
⠀⠘⠓⠲⠦⠬⠭⠭⠭⠭⠭⠭⠭⠤⠴⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢱⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡇⢆⠀⠀⠀⠀⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡾⠃⢸⠀⢠⠀⠀⠸⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠈⠀⢸⡆⠀⠀⡇⠳⣄⣰⢄⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⣆⠐⠊⠉⠒⠈⣀⣀⣍⣁⠀⠙⠢⡈⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⣿⣿⣦⣼⣷⡶⠟⠋⠉⠉⠉⠉⠁⠀⠚⠺⠧⣀⢢⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢗⠒⠋⠀⣹⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣜⣧
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠑⢄⠘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⢏⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⢘⡆⠛⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠙⣡⡇⠀⠊⠀⠀⠙⡆⣳⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⡀⠀⠘⢀⠀⢀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡙⢿⠀⠀⠀⠀⠀⠸⠀⠈⠻⣿⣿⣿⣿⣷⠞⢋⠀⡈⢲⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠎⠂⡀⠀⠀⠀⣠⢀⠀⠀⠈⠉⠉⠉⠁⠀⣠⣾⣿⡀⠟⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠘⢷⣅⣉⣛⣀⣀⠀⢀⣀⣠⡄⠀⣼⣿⣿⣿⣇⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢑⡀⡿⢛⣭⣄⠈⢻⣿⠋⠀⠀⠀⠈⠉⠹⠋⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈⠀⠀⠘⢎⠝⣄⣀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣠⠇⡟⢀⡟⢰⡶⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠁⠀⠙⠻⠇

⠶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠰⠆⠴⠀⠤



⠀⠀⠀⣠⡶⣆⠀⠀⠠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⡄⠀⠀⠀⠐
⠀⠀⠀⠻⠧⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠄⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠄⠀⠀⠠⠀⠠
⠀⠀⠀⢻⣍⣿⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡇⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⠀⠀⠣
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢼⣟⣷⠀⠀⠀⠀⠀⢰⣿⣹⡇⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠃⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠶
⢠⣿⣿⡆⢰⣟⣿⡆⢰⡯⣷⠀⣾⡏⣷⠀⣾⣛⣷⠀⣾⣻⡆⢰⣟⣻⡆⢰⡿⣵⡆⣾⣟⣷⠀⣾⣛⣷⠀⣾⢻⡧⢰⣿⣿⡆⠀⠀⠐⠂⠀⠂⠀⠆⠀⠒
⠀⢙⡋⠁⠈⣋⡋⠀⠈⣉⡉⠀⢈⣙⠉⠀⢉⣛⠁⠀⢉⣛⠁⠀⢙⣉⠁⠈⣙⡋⠀⠈⣋⠋⠀⢉⣙⠁⠀⢙⣛⠁⠀⢙⣋⠁⠀⠀⠀⠀⡄⠀⠀⠀⣤
⠰⣿⣿⡇⢸⣿⣿⡆⢸⣿⣿⠄⣾⣿⣿⠀⣾⣟⣷⠀⣿⣽⡗⠰⣿⣻⡇⢸⣿⣿⡆⢾⣿⣿⠀⣿⣿⣷⠠⣿⣿⡇⢰⣿⣹⡇⠀⠀⠠⠄⠠⠄⠀⠤⠀⠠
⣀⣈⣉⣀⣀⣉⣁⣀⣀⣉⣁⣀⣀⣉⣁⣀⣈⣉⣁⣀⣈⣉⣀⣀⣉⣉⣀⣀⣉⣁⣀⣀⣉⣁⣀⣈⣉⣁⣀⣈⣉⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡡⠤⣟⣋⡛⢛⣛⣛⡙⢋⣙⣛⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⠀⠉⠐
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠃⢀⠀⠀⡂⠁⠀⠈⡀⠅⠀⠀⠀⠀⠀⠛
⠀⠀⠉⢀⠈⠉⡁⠀⢉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠆⠀⠀⠐⠀⠈⠤⠀⠀⠊⠀⠀⠀⠀⠀⡀⡅
⠐⡘⠄⠀⠀⠀⠙⡀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠶⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠻⡁⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠂⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢠⠦⢸⡀⠀⠀⠀⠋
⠀⠘⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⣀⠈⠁
⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠓⣾⠎⠀⠀⠀⠠⠈⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⡄⢠⡆
⡌⠀⡀⠀⠀⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠠
⠀⠀⠈⠀⠀⠈⠀⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⡆⠀⠀⢀⡄⠠⠀⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⣂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠉⠀⠀⢀⠒
⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠀⢄⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⢀⣀⠈⠁⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⡀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⢤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠎⠐⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠄⢈⢤⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⠀⠀⠀⠂⠂⠂
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠠⡆⠀⠀⠀⠈⠈⠉⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡆⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⡀
⠀⠀⠈⡁⠀⢀⠀⠀⠠⠄⠐⠀⣠⠀⡀⠀⠞⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢄
⠐⠀⠁⠢⣤⠋⠀⠀⠀⢠⠸⠈⠉⠀⠩⠄⠀⠐⠐⠚⠀⠀⠒⠀⡀⠀⢀⠘⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀⢀⠀⠀⠑⡄
⠀⠀⢀⢀⡄⡀⠀⠀⠀⢰⡀⠀⠄⢃⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠄⠠⠀⠀⠈
⠰⠀⠃⠀⠀⠀⠄⠠⠂⠀⠁⠀⠀⠀⢃⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠂⠀⠃⠀⣠⠄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⢡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⡀
⠀⠶⢤⣦⠂⠀⠀⠀⡈⠐⠲⠒⠂⢸⠀⠀⠀⠀⠁⠀⡠⠀⢀⡄⡀⢀⠉⠀⠠⠄⠀⠀⠀⠀⠒⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠂⠀⠀⠄⠀⠉⠐⠀⠀⠓⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀
⡠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠐⠀⣠⠀⣀⠀⠀⠀⠀⠩⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠔⠒⠒⠊⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠐⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⣿⢢⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣿⢸⣼⣿⡇
⠀⠀⠀⠀⠀⢸⠃⡟⠀⠀⠰⠄⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠃⠀⠀⠀⣿⠸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠐⠀⠀⠇⠰⠂⠀⠁⠀⠀⡀⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⣿⢀⣼⣿⡇
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠛⠀⠀⠀⢀⠀⡀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣿⡇
⠀⠀⠀⠀⠀⡟⠸⠇⠀⠠⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⡠⢀⠀⠀⠀⠀⠀⣿⢀⠀⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠠⠂⡐⢀⠂⠀⣄⢀⠀⢠⡟⢸⢠⣿⡇
⠀⠀⠀⠀⠀⡇⢀⠀⠀⣠⡤⠀⠀⠀⢰⡿⠀⡖⢰⠀⠀⠀⢠⠄⠀⠈⠁⠀⠘⠁⠀⠀⢸⡇⣼⢘⣿⡇
⠀⠀⠀⠀⠀⡇⢸⠀⠈⠁⠂⠀⠀⢠⡿⠀⠀⢷⠈⣹⠀⠀⠨⠀⠀⠈⠐⠠⠀⠀⠀⠀⢸⡇⡋⣼⣿
⠀⠀⠀⠀⠀⡇⢸⠀⡀⠀⣄⠀⠀⣼⠁⠀⠀⠸⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠆⠀⢸⡇⡇⣿⣿
⠀⠀⠀⠀⠀⡇⣾⠀⠁⣀⠂⠐⠻⠃⠀⣀⠀⠀⢰⠋⠉⡆⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⡇⡇⣿⣿
⠀⠀⠀⠀⠀⡇⠛⠀⠀⠀⠀⣸⠏⠀⠿⠷⠀⠀⠈⠂⠀⠁⠇⠀⠀⢀⠔⠩⡇⡠⣁⠀⢸⡇⡇⣿⣿
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⡎⠀⠀⢀⢀⣤⡆⣴⢠⢤⡰⠤⣀⠰⠁⠀⠀⠔⠁⠾⠀⢸⡇⡇⣿⣿
⠀⠀⠀⠀⢸⠇⢠⠀⠀⢘⡟⠀⣴⣷⢻⣾⣿⡇⡏⣿⢸⢃⡠⠊⠀⠀⠀⣀⣀⡠⠂⠀⢸⡇⡇⢸⣿
⠀⠀⠀⠀⢸⠀⣾⠀⢤⡾⠁⡸⠟⣛⣸⣿⣿⠇⢿⣿⢸⣨⣶⠀⠀⠐⢻⠀⢸⠀⠀⠀⣸⡇⡇⢸⡇
⠀⠀⠀⠀⢸⠀⡏⠀⢀⠤⡀⠃⠀⠀⣠⢄⣹⣿⢘⡩⠮⣬⠒⡆⠀⠀⡾⠀⢬⠀⠀⠀⣿⡇⣇⣼⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡄⠀⠐⢸⣿⣾⢡⣿⠜⡬⠿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠰⠐⠁⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⠶⢿⠁⣿⣿⡇
⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠻⡿⠿⡟⣞⠿⠯⠽⣦⣾⣶⡘⢦⣿⣿⡇
⠀⠀⠀⠀⠘⣴⣖⡺⢿⣿⣿⣻⣻⣝⣯⡧⠽⠦⠤⣄⣻⣿⠶⠤⠤⠐⠒⣊⣉⣩⡿⠥⠴⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠪⡻⣾⡉⠡⠤⠄⠒⢒⣂⣉⣉⣁⣭⣄⣀⣀⣤⣤⣼⣷⣾⠷⠶⠟⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⣴⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣦
⠀⠀⠀⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸
⠀⠀⠀⡇⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⡇⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⡇⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠙⣦⠀⠀⢠⡞⠉⠉⠉⠉⠉⠉⢻⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⣦⠀⠀⡴⠒⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠁

⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠈⣉⣴⣷⣾⢿⣿⣷⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣱⣿⣿⡿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡼⣿⣿⡘⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⢻⣿⣿⠟⠟⣿⣿⢎⣿⣿⢃⠜⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠁⠈⢻⣿⣶⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣽⣿⡿⣿⣿⣿⣷⣮⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⠋⣼⠟⢉⣉⣭⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⢸⡇⠀⠃⠀⠉⠀⢤⣈⠙⣿⣿⣠
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿⣿⡀⠳⡀⠀⠀⠀⠀⠀⠈⢷⣬⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠷⣤⣀⡀⠀⠀⠀⢀⡇⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣷⣤⣤⣤⡤⠆⢀⣼⣇⣼⡿⢋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢿⣾⣿⣴⣶⣿⣷⣿⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠩⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠉⣉⡉⠉⠉⠁⣈⡀⠀⠀⢉⣉⣁⠉⣉⡉⢉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠭⠥⡤⠄⢼⣿⢿⣿⡆⣿⡇⠀⠀⢠⣿⣿⠀⢰⣿⠿⣿⣆⣿⣧⣾⡿⠃⠀⢤⠬⠽⣿⣿⣿⣿
⣿⠿⠶⢶⠒⠀⠂⠀⢸⣿⠿⣿⡆⣿⣇⠀⠀⣼⣿⣿⡇⢺⣿⠀⣨⡅⣿⣿⣿⣧⠀⠀⠀⠀⠐⡾⠿⣿⣿
⣿⡟⠁⠉⠀⠀⠀⠀⢸⣿⣿⣿⠇⣿⣿⣿⣷⣿⠟⢻⣿⠘⢿⣿⡿⠃⣿⡇⠹⣿⡆⠀⠀⠀⠀⠉⠉⢻⣿
⣉⡉⠀⠉⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠁⢈⣉⣩
⠼⠦⠀⠀⠀⠀⠀⢸⠀⠛⠛⢻⠀⠛⠃⡠⠄⠀⠠⠀⠟⠆⠠⠀⠀⡆⠀⠸⡄⠁⡸⠁⠀⠀⠀⠀⠠⠬⢧
⢶⡖⠀⠒⠀⠀⠀⠰⠀⠒⠚⢰⠀⠖⠆⢠⡤⣀⠀⠀⠂⠀⡰⠀⢈⣁⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⢲⡾
⣟⣃⣀⢐⠀⠀⠀⠈⠓⠃⠀⠘⠒⠃⢳⡟⠑⠚⠘⠒⢒⡟⠁⠒⠋⠉⠓⠃⠘⠚⠃⠀⠀⠀⠀⣂⣘⣛⣿
⣿⣯⣭⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⡀⣸⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣉⣩⣽⣿
⣿⣿⣿⣾⡦⠤⣤⠀⠀⠀⠀⠀⠀⠀⣴⠎⢷⡴⢻⢧⡏⣾⣿⡀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣿⣶⢲⡆⠀⠀⠀⠀⢿⣶⠿⣷⣿⣾⡾⢿⡿⠃⠀⠀⠀⠐⠀⢲⡶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣁⣀⣰⣇⣀⣈⣀⣀⣇⣀⣈⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣰⠀⠀⣿⣿⣿⠀⣿⡟⢻⣿⢸⣿⡟⠛⠃⣿⡟⣿⠀⠀⠀⣿⣿⠛⠋⠙⢻⣿
⠀⠀⠀⠀⠀⣿⠀⢀⣿⣿⣿⡀⣿⣧⣾⣿⢸⣿⡿⠇⠀⣿⣇⣿⡇⠀⠀⠿⠿⣿⣷⠀⢸⣿⠀⣤
⠀⠀⠀⠀⠀⢻⠀⢸⣿⠛⣿⡇⣿⡏⣿⡏⢸⣿⣧⣤⣠⣿⡟⣿⡇⠀⠀⣤⣤⣼⣿⠀⣸⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠁⠈⠉⠈⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⠀⠁⠛⠛⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠐⠒⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠋⠁

⠉⠰⠣⢋⡀⠑⠃⠔⠁⠐⢋⣥⡤⠂⠀⠹⢛⣃⡀
⠰⢃⠕⠿⣁⠀⠈⣴⢡⣾⡿⠋⠀⣐⡨⠥⠤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠃⢀⡀⡄⠉⠀⡸⢃⠾⠟⡡⠀⢸⠏⠀⣀⡀⠈⡇
⠠⣸⣧⣙⡁⠀⠇⣿⡀⠀⠷⣒⠌⡇⣼⣿⣧⠀⡇
⡡⠘⢗⠉⠀⠀⢠⠘⠳⡰⣤⠐⠆⢰⢹⠈⢿⡀⣇
⠠⡋⠠⠍⠀⢴⣊⣁⠀⢈⢎⠀⠄⠸⡿⠀⠈⡇⠘
⠜⣁⡣⢲⢪⡐⡆⢩⠄⣰⠘⠫⢘⢽⠇⠀⠀⠙
⠸⡁⣴⢣⡞⢠⠇⠸⠀⢉⡥⠂⠈⢀⣼⡿
⠑⢤⡈⠥⣄⠀⠛⠓⠀⠉⢀⠀⣰⠟⠉
⠀⠀⠉⠀⠛⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠈
⠀⠀⠀⠀⡀⣀⠀⣀⢀⠀⡀
⠀⠀⠀⢨⡇⣿⢷⣿⢹⢿⡁⢀
⠀⠀⠀⢀⣥⣩⡄⣥⣬⡤⣩⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢶⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡀⢀⡷⠊⠀⠀⠀⢠⣴⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⢃⡞⠁⠀⠀⠀⠀⢾⣇⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⣒⠀⠀⠀⢀⣴⠋⠀⢠⣤⣤⡄⠀⠈⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⠀⠀⠐⠛⠀⠀⠀⠸⣏⠀⠀⠘⢻⣦⡄⠀⠀⠀⠀⢠⣶⡤
⠀⠀⠀⠀⠀⢀⣾⣀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣤⡄
⠀⢠⣴⣶⠀⠈⠉⠉⠛⠻⢷⣤⡀⠀⠀⠀⠀⠘⢦⡀⠀⢠⣿⠉⠉⠻⣦⡀⠀⣤⠶⣤⡀⠀⠀⠀⠀⠀⠰⠶⠆
⠀⠀⢾⡏⠀⠰⢦⡶⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠙⣦⣼⠏⠀⠀⠀⢸⡇⠈⢷⣤⡿⠃
⠀⠀⠀⠀⠀⠐⠟⠑⠂⠀⠀⠀⠀⠻⣷⣦⣄⡀⠀⣰⡟⠁⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⣄⣈⠙⠻⣶⡟⠀⠶⠀⣀⣼⡿⠖⠀⠀⠀⠀⠀⣰⠃⢠⣼⠿⠃
⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠰⣿⣧⠀⠀⠉⠙⠲⣿⣧⢀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⢠⡇⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣾⠛⢁⣀⣀⠀⢀⣾⡿⠓⠶⠌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠘⠓⢲⡒⢺⢧⡀⠀⠀⠀⢀⣶⢠⣿⡇⠀⣨⣿⣇⠀⢸⣿⠁⢀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯
⠀⢀⣤⣄⠀⠈⠐⠒⠈⠉⠉⠻⣛⣛⣷⣶⣿⠃⢸⣿⠁⠀⠀⠀⠀⢰⣿⣿⡾⠛⠁⠀⠀⠀⠀⠀⡀⢊⡠⠀⠂⣀⣀⡀⠈
⠀⢀⣺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠻⣷⣄⠨⣿⡇⠐⠦⣤⣴⣿⣟⣡⠶⢤⢤⣔⣒⠛⢈⣉⣁⠤⠛⠉⠉⠁⠀⠙⠁
⠀⠈⠉⠁⠀⠀⣰⣤⣴⡄⠀⠀⠀⣀⡀⠀⠉⠻⣷⣿⣿⣄⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠉⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⢼⡷⣿⠇⠀⠀⣰⡟⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠸⣿⣳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡔⠁⠀⠀⡀⠀⠀⢀
⠀⠀⢠⠆⡕⣳⣄⣄⣰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀
⠀⣰⠋⣠⡿⠀⠀⠐⠻⠀⠀⣮⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⠀⢁⣠⣠⡀
⠘⠱⣁⠴⠀⠀⠀⠐⡄⢀⠀⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⢂⠛⠁⠀⣌⡇
⠀⠘⠁⣠⡖⢤⡔⠸⠁⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢪⡆⠀⡀⠐⠢⠂⠄⣠⠺⡀
⠀⠀⠠⢻⣦⠛⠬⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡛⠙⣠⠴⣦⣬⣉⠀⢉
⠀⠀⠀⠻⢦⠐⠀⠀⠀⠱⡐⡀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠛⠀⠀⠀⠀⠀⠈⢱⣾⠃⢸⡏⢨⢿⡍⢀⡤⠞
⠀⠀⠀⠀⠈⠀⠈⢀⠠⠀⠀⠁⠐⠀⠀⠀⣀⡀⠀⠀⡰⢐⡆⠄⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠠⢭⣿⣦⣿⢁⠀⣾⢃⡞
⠀⠀⠀⠀⢀⠀⢤⣎⣄⣀⣴⠃⡀⠑⠀⠀⠻⠇⠀⠀⠰⡊⠒⠐⠀⠀⠀⠀⠀⢸⡄⠀⠠⠀⠠⢰⠆⠈⡋⠩⠞⢙⡿⣻⠁⠀⠉
⢀⣤⡖⢑⡞⠶⣇⣠⣾⣿⣵⣷⣰⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⢲⣶⣾⣷⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⢈⣿⡇
⣾⣿⣹⣏⣵⡄⣵⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⣀⡀⠀⠀⠀⡀⠴⠃⠈⢠⠄⠙⠿⢿⠃⠀⠣⣀⡈⠔⠀⠔⠖⠀⣸⡿⠗⠘⠀⠈
⣿⣿⣿⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡷⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡟⠁⠐⠒⠃⠀⠀⠀⢀⣰⠄⠀⠈
⣯⣿⣿⣿⣾⣿⣿⣿⣿⠟⠛⠻⠋⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⠄⠀⠐⠿⣏⣀⣠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠈⠀⠀⠀⠀⣼⣿⣿⣯
⣿⣿⣿⢿⢫⡉⠉⡉⡋⢟⠞⢸⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢤⡄⠀⣰⣿⣿⣷⣷
⢯⠔⠃⢈⠀⢉⡟⢁⠀⢠⣤⣄⢸⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠄⡄⠁⠀⠀⠀⠀⠀⠀⢀⣴⣶⣯⣵⣿⣿⣿⣿⣿⣿
⠈⠒⠄⠘⢅⡼⠈⡈⠤⠀⢀⠀⠄⢠⠼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡏⠀⠀⠉⢻
⠀⠄⠘⠑⠀⠞⠀⠀⣥⠀⠀⠀⢀⠺⣠⠹⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣿⡇⠀⢷
⢁⠘⠠⠀⠀⡘⢷⠀⠁⡔⢈⠈⠁⢤⡔⡐⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⣀⡿⠟⠛⢛⡻⢧⣀⡀⠈⡀
⠘⢣⠐⠠⢾⡋⠀⠠⠁⠐⢚⠈⠈⠀⠙⢸⣧⣤⣴⣾⣇⠀⠀⢠⣆⠀⠀⠀⡀⠀⠀⢸⣿⣯⡀⠀⠀⠀⠏⡀⠠⠤⠂⠚⠁⠀⠐
⠣⣴⠀⠑⠠⠰⠀⡐⠛⠀⠄⣀⠖⠁⢠⡿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣄⠀⣰⣟⢶⣤⣾⣿⣿⣿⣴⣦⡄⠈⠀⠀⠀⠀⠀⠀⠀⡀
⣷⡿⢆⠄⠀⢀⡈⠲⡌⠹⠉⢈⢑⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠉⡻⠋⠁⠈⠛⣼⠋⠀⠀⠖⠀⠃⢀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠄
⠀⠀⣠⣤⣤⢶⣶⣀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠻⠋⠀⠀⠈⠙⠻⢶⣴⡄⠐⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠢⠖⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠰⠆⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠰⠂
⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⢀⠐⡘⠂⠀⠀⢀⣀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢄
⠀⠀⠀⠀⠁⠤⠄⢀⣀⣀⣤⠇⠀⠀⠀⠈⠯⠿⠿⡿⠿⠟⠃⡀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠉⠀⠒⠒⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠊⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠐⠗⠒⠒⠲⠤⠤⠧⠤⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠉⠛⠙⠇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠇⠈⠢⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠐⠟⠁⠐⠠⡀⠀⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⡈⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠛⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠛⠛⢻⣿⣿⣿⡀⣠⣾⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠀⡼⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣿⣷⣿⡿⠃⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⢰⣿⠿⠿⣻⣻⣿⣷⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣴⣿⣿⣿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣁⣀⣀⡀⠀⠀⠀⠈⠙⠛⠟⠛⠉⠀⢀⣾⣿⣿⣿⣏⣀⣀⣄⣿⣿⡛⠛⠛⠛⢻⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⣿⣽⣿⣽⣿⣯⣽⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⢿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠈⢻⣿⡌⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣞⢷⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⣀⠀⢹⣿⣄⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡘⣧⣸⡇
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣄⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡝⢿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⢿⣶⣄⠀⠀⠀⠀⠀⢻⣿⡌⣿⡄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠻⣿⣶⣄⠀⠀⢀⢹⣿⣿⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⡄⠀⠀⠈⠙⠻⣧⠀⠸⣧⣽⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣇⢸⣿⣿⣿⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉⣹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⢻⣿⣿⣿⣿⣿⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠸⠃⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⣤⣤⡀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠂⠀⢠⣿⣿⣄⣻⣿⡿⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⠀⢀⣤⠶⣿⡿⠋⣉⣴⣿⡿⢛⣧⣿⣿⡆⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⠻⣶⣝⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣋⠁⠀⠀⣴⠟⠡⠞⣉⠁⣴⣿⣿⣿⣖⢿⡿⢛⠻⠇⠀⠄⠀⣿⣿⣿⣷⡈⢿⣿⣧⣄⣹⣦⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⣴⡇⠀⠀⣾⠃⠀⠀⣴⠃⣼⣿⣿⡿⣿⣿⣆⡸⢿⣷⢀⣀⠀⡀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣸⣿⠁⢰⣿⡀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣿⣿⣷⡜⢿⣿⠇⠈⠻⢏⣿⠀⠁⠈⣻⡙⢿⣿⣿⣿⣿⣿⣟⢿⣿⡿⢿⡄
⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⣼⡇⢸⣿⣷⣘⢿⣿⣦⡉⠀⠀⠀⡼⠃⠀⠀⣸⣿⣏⡛⠻⢟⣘⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠾⠃⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡿⣿⣦⣙⠿⡇⠀⠀⠀⠁⠀⠀⠛⠛⢿⣿⣿⣶⣾⣟⣴⣏⡻⣿⣿⣿⢻⣬⣿⣦⣾⡇
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⣧⣜⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⣿⠿⣿⣿⣿⣷⣌⡙⢿⣿⣿⣯⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⠀⣿⣿⣿⣷⣮⣙⠻⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠁⢠⣿⣿⣿⣿⣿⣿⣧⠙⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡌⣿⣧⠘⣿⣷⣉⡻⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢸⡟⠙⠏⠀⣿⢿⣿⡿⣿⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⣠⡜⢿⣧⠈⢿⣿⣿⣶⣬⣙⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢰⠏⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣷⡌⢿⣷⣄⠹⣿⣏⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡟⠁⠀⠻⣿⣷⣄⠙⢷⣶⣬⣍⡛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠈⠻⢿⣿⣦⣈⠛⢿⣿⣿⣶⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⠙⠻⣿⣷⣦⣤⣉⠛⠷⣦⣄⡈⠉⠙⠛⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣷⣦⣄⡉⠛⠿⣿⣿⣶⣦⣌⣉⠓⠤⠀⠀⠀⠉⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠛⠻⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣄⡀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⡀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃

⠀⠀⠀⡠⠤⠤⠄⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠒⠒⠒⠒⠂⠠⢤⡀
⠀⠀⢀⠁⠀⠔⠒⠒⠒⠒⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠐⠒⠲⡄⠈⣵⡄
⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡧⡇
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢰⢭
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⢸
⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⡠⠤⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠸
⠀⠀⢸⠀⠀⡇⠀⠀⡔⠁⣠⠤⢆⡀⠐⡃⠀⠀⠀⠀⠀⢀⠊⢀⠴⠒⠢⡀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠲⡀
⠀⠀⢸⠀⠀⡇⠀⡜⠀⡜⠁⠀⣰⠀⢸⠃⠀⠀⠀⠀⠀⠱⢄⠊⠀⠀⢀⠇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⡇
⠀⠀⢸⠀⠀⡇⠀⠓⠚⠁⠀⡰⠁⡰⠃⡠⢢⡀⡠⠢⡀⠀⠀⠀⠀⡠⠃⢠⠋⠀⠀⣋⠙⡁⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠞⠁⡴⠁⠀⠑⡄⠈⠀⡔⠋⠀⠀⡠⠊⢀⠔⠁⠀⠀⠀⡭⢉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠸⠀⠀⠇⠀⠀⡰⠃⢀⡜⠀⠀⠀⢼⢁⠤⢄⣹⠆⣠⠊⠀⡴⠁⠀⠀⠀⠀⠀⢦⣀⣤⡨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡄⠀⡰⠀⢀⠜⠀⠀⠀⠀⠀⠁⠀⠀⠁⠰⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⡇
⠀⠀⠀⡇⠀⡇⠀⡇⠀⠈⠀⠊⠀⠙⠁⠐⠆⠀⠀⠀⡇⠀⠈⠉⠉⠙⠂⠀⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⠀⡇⠀⡇⠀⠙⠀⠈⠁⠀⠁⠀⠈⠁⠉⠀⠀⠀⠘⠃⠀⠂⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⠀⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⡇
⠀⠀⠀⠶⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠇⢀⠣⡇
⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠑
⠀⠀⠀⠀⠈⠓⠛⠩⠯⠥⠴⠰⠆⠀⠖⣲⣀⣂⣀⣂⣐⣂⣐⣂⣐⣂⣐⣂⣀⣂⣐⣂⣀⣒⣒⢒⠀⠲⠀⠴⠨⠯⠭⠭⠭⠥⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⡌⢠⣤⢠⣵⡐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃
⠀⢠⠀⠈⠑⠀⠀⠀⠀⡀⢀⠀⠄⡗⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠁⠉⠈⠈⠂⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇⠀⠷
⠀⠀⠀⠉⠏⠀⠀⠀⠀⠄⠀⠀⠄⠠⢄⣤⡄⢀⠀⠀⠀⠀⢠⠀⢰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠦⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢄⠀⠀⠀⠀⠠⠀⠀⠠⡀⠈⠀⠀⢀⠁⠀⠈⠀⠁⠀⠀⠈⠀⠈⠠⠄⠼⠠⠄⣤⢤⠤⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⢹⡀⠀⠁⠈⠀⠀⢰⠀⠀⠀⠈⠁⠀⠀⠀⢰⡇⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⠀⠣⢀⣀⡄
⠀⠀⠰⠊⠁⠀⢠⡄⠀⠀⠀⠀⠋⠀⠀⡸⣀⡀⠀⠈⠈⠀⠀⠀⠀⠠⠄⠀⠠⡀⠀⠒⠂⠀⠈⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⣷⡄⠀⠀⠀⠲⠄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠉⠀⠀⠀⡇⠁⡱⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠃⠀⠜⠓⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠞⠂⠀⠀⠲⡄⠀⠀⠀⠀⠀⠷⡀⠀⠀⠈⢉⡅⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⡠⠖⠋⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠁⣸⢠⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠉⠀⠀⡟⢨⡀⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⡀⠀⠉⠐⠀⠀⢀⡔⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠄⣦⡄⠀⠀⠀⠀⠀⠀⠠⡀⠁⠃⠥⠀⠉
⠉⠉⠀⠀⠀⠁⠀⠀⠘⡆⠀⠂⠀⠸⢋⢃⠀⠀⠀⠀⢀⠀⠁⠀⢀⣀⣀⡀⠠⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣴⠀⠛⠀⠀⠈⠀⠀⠉⠈⠑⠒⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡤⠀⠀⠀⠀⠀⢄⡁⣨⢠⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⣻
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⢐⡼⠁⠀⠤⠀⠀⠀⠈⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿
⠐⠋⠉⠀⠀⠀⠀⠀⠈⠙⠒⡗⠒⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠐⠂⠀⠀⢈⣀⠀⠹⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠳⠂⠀⠀⠀⡀⡷⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠃⠀⠈
⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠓⠊⠙⠂⠀⠀⠀⠠⠀⠀⠀⡄⠉⠁⠀⡸⠀⠀⠀⠇⣠⠂⠀⠘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠘⠓⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠚⠀⠒⠙⠃⠀⠀⢀⡈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⡀⠈⠀⠀⠀⠉⠑⠄⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠈⠀⠀⠀⠀⠐⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠀⠈⠛⠁⠂⣠⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠁
⢀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡀⡿⠰⠄⠀⠀⠀⠀⢐⠆⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⡆⢀⠀⢰⠀⣀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠠
⠀⠅⠀⠀⠀⡀⠠⠀⢀⡣⠀⠀⠀⠀⠀⠠⠀⠀⠘⠂⠀⠀⠀⠐⠀⠀⠀⠃⠈⠐⠧⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⢀
⠌⣶⠀⡀⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠙⠀⠄⠛⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀⠄⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⡄⠀⠰⠄⠀⠀⠠⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠓⠀⠀⠀⠘⠢⠀⠀⠀⠠⠄⠀⠀⢠⡆⢇⠀⠿⠘⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠼⠼⠭⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠿⠟⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⢿⠿⠿⠿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣿⣧⡀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠰⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠐⡀⢄⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣲⢀⠀⠘⠁⠀⠀⡆⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⠁⠀⠀⠀⠀⠀⠱⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠀⠤⠄⠀⠀⢀⠀⠀⢸⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠒⠂⠀⡀⠠⠄⠀⠘⡼⠀⠀⠀⣀⡠⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢄⣀⡀⣇⠀⠀⠠⡤⠄⠀⠀⢠⣴⡡⢖⡌⣱⡂⠶⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣓⢙⣬⣯⣬⢻⣦⡠⠛⣟⠀⠀⡠⠊⠑⠮⡟⣘⢃⡳⠚⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⢌⣐⠛⡞⠉⡔⠀⠀⠁⠿⠀⠀⠀⠀⠀⠈⢪⠛⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣨⡙⣾⠀⡐⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⢹⢡⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣻⡧⠊⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠎⢀⣀⡀⠠⠑⠀⠀⠣⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⠉⠓⠛⠛⠢⠤⢒⡅⠒⠒⠂⢤⡀⠀⠀⢀⣀⡑⣄⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠉⢣⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⢢⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠀⠀⣧⡀⠀⠀⢀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠄⠠⠧⠈⠉⠅⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢄⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣾⠀⠀⠀⠀⠀⢀⡤⠐⠉⠀⠀⣀⡀⣤⡀⣤⣤⡀⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠉⠢⢀⠀⠀⠀⠀⠀⡀⠀⢹⣇⠀⠀⡠⠊⠁⣀⢰⡄⠀⠀⣿⠷⣄⢻⣌⢿⠻⣆⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠒⠒⠶⠞⠓⠂⠀⠊⠉⠈⠉⠉⠁⠙⠓⠸⢿⡶⠋⠀⢠⡈⣽⡀⡟⠦⠀⠛⠀⠈⠈⠀⠀⠀⠀⣀⣀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⡟⢯⡇⠴⠃⠁⠀⣀⣤⠴⠶⠛⣿⠟⢻⠟⠿⣿⡏
⠀⠀⠀⠀⠀⠀⡸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣻⠈⠁⢀⣠⠔⠿⠓⠂⠀⣀⡀⣀⣂⠀⣒⡀⠁⠙⣆
⠀⠀⠀⠀⠀⣰⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⠇⠀⠶⠶⠀⣒⣒⡂⣘⣒⠀⠰⠩⠄⠠⠨⢧
⠀⠀⠀⠀⣰⣧⠔⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⢠⡀⡆⣰⣊⠀⠀⣀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠓⢠⡳⡀
⠀⠀⠀⠀⠷⠿⠾⠷⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠛⠚⠛⠛⠛⠛⠳⠴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⢠⣶⣿⠿⣿⣦⡀
⠘⠛⠀⠀⢸⣿⡇
⠀⠀⢀⣴⣿⠟
⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠴⡴⢤⢠⣄⢠⢠⠴⢤
⠾⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠇⠈⠿⠸⠇⠹⢤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡠⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢨⡄⠀⠰⠘⠀⠰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠉⠀⠀⠀⠈⠑⠒⠈⠓⠤⠄⠊⠉⠢⣄⠀⠀⠀⠀⠀⠀⡄⢐⡁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⢂⠀⠀⠀⠀⠀⠠⠴⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢂⠀⠀⠀⠈⠰⣖⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⡇⠀⠀⠈⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠤⠐⠂⠀⠀⠒⢄⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⡅⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠰⠂⠀⠀⠀⠀⠀⠃⡀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⡃⢀⠀⢉⠦⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠮⠔⠉⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⠤⠤⠀⠤⠤⠤⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢢⡀⠀⠀⠴⣿⣧⡀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣦⣤⣄⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢡⣸⣷⣀⣀⠀⢀⡰⢢⠔⠀⠀⠀⠛⠋⠀⢿⢿⡂⣠⡭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠁⠸⣟⣂⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⠶⣡⣖⡛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡏⢠⡶⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⢷⣿⣿⣿⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⡇⠁⢸⡇⢸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠚⠋⣩⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⡿⠀⠈⡷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠶⠦⠀⢠⣿⠇⠸⣤⡤⠤⠄⠒⠒⠒⠒⠒⠂⠀⠀⠀⡖⠒⠀⠀⠔⠚⠀⡔⠿⢤⡴⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⣠⡤⠼⠛⠀⠀⠀⠀⠀⠀⠀⠠⠔⠶⠋⠁⠀⠀⣀⡛⠋⠙⢳⣖⣦⣤⢷⢰⡞⠉⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠟⠋⠁⠀⠀⠀⠀⣠⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣡⣴⣾⣿⣿⣿⢿⣿⡏⠀⠠⣴⣺⡇
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⢀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣽⣿⣿⣟⣿⣿⣷⣿⣿⣿⡇⠀⢀⠛⢸⡇
⠀⠀⠀⠀⢀⣤⡴⠟⢃⡠⠠⠾⡶⠷⠴⠶⡤⣾⠀⠀⠀⠀⠀⠀⢰⣷⣤⣾⣿⣯⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⣶⣿⣼⣿⡇
⠀⠀⢀⡾⠋⠁⠀⢠⣿⣷⣶⣶⣷⠾⠷⡷⠷⢶⣶⣶⣶⣿⣦⣶⣿⣿⡿⠛⠋⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣼⢿⣿⣿⣇
⠀⠀⣿⣡⣀⡀⢀⣀⠈⠙⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠈⣿⠋⠁⣤⣴⣶⣶⣶⣦⡀⠀⢀⠀⣠⡄⣨⣇⠏⣿⣿⡿⢿
⠀⠸⣿⡿⠟⠿⢿⣿⣷⣆⣄⣶⡀⣄⣶⡀⠀⠀⠀⠀⢀⡀⣀⣠⣧⣨⣥⣬⣧⣤⣼⣧⣤⣷⣤⣿⣴⣿⣿⣿⠷⣴⣿⡟⠀⢸
⠀⢸⣿⡿⠒⡐⡷⣹⠙⠉⢹⠟⠛⠿⢿⡿⣾⣿⡿⠿⣿⣿⣿⠟⠙⣿⡿⢿⣿⣧⣤⡀⣭⢻⣿⣿⣿⣿⣿⣿⣇⣿⡿⣧⣴⡿
⠀⠀⣿⡇⢉⣡⣷⣿⣿⣆⠘⢦⣤⣤⣌⣠⣤⣿⣤⣬⣁⣐⠛⠀⠀⣿⡁⠘⣿⡷⠶⡧⣿⣷⣿⡛⠻⣿⣿⣿⣿⣿⡇⣿⣿⠃
⠀⠀⣾⣿⣿⣿⣿⠿⠟⢻⣶⠾⠿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣷⡌⢡⣿⣿⣯⣁⣀⣘⣼⣿⣿⣧⣴⣿⣿⣿⠃⣿⣷⣿⠋
⠀⢸⡟⠿⣿⣿⣤⣤⣤⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠙⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣟⢾⣿⣿⣹⠂⣿⣿⡟
⠀⠸⣇⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠶⠶⣤⣤⣤⣄⣼⣤⣤⣄⣠⣤⣀⣀⣀⣀⡐⠉⢉⣽⢹⣿⣿⣶⣿⣿⣿⣁⢿⣿⠇
⠀⠀⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠶⠸⠿⠿⠟⠻⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣀⣠⣄⠀⠀⠀⠀⢀⣠⣤⣿⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠶⠏⠀⠀⣠⣼⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢿⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣄⠀⠀⠀⠈⢙⡧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠿⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠷⠶⠶⣶⡄⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣼⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⠀⠀⠀⣼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⣠⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⡄⠠⢤⣼⣿⣶⣄⢸⣆⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣟⡛⢛⡉⠁⠀⠈⢛⣻⣿⣿⡟⠋⠉⠛⠛⢻⡿⠿⢿⡿⢿⣶⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣏⢻⣿⣿⣿⣿⣿⣿⣷⣦⣥⣤⣀⣀⣩⣿⣿⣟⣁⣀⣀⣀⣀⣉⣉⣽⣶⣶⣶⣿⣿⠟⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣽⣿⣷⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠺⢻⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣻⣿⣷⣿⣯⣿⣿⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣼⣧⢸⡟⡉⠙⢿⣿⡟⢛⠉⠝⢻⣿⠟⠉⠉⠉⠻⣿⣇⢀⠀⣹⣾⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⣿⣿⣿⣷⡽⣦⣾⣿⡐⡿⣤⡆⣻⣿⡄⢳⣴⠀⢠⣿⣿⣦⣴⣿⠟⢯⠁⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⡄⠈⢹⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣶⣷⣶⣿⣿⣿⠿⠿⣧⠀⠈⣷⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣏⣶⣾⣿⣄⡀⠀⢸⣏⢻⡟⠛⠉⠀⠈⢹⡋⠁⠀⣿⡁⠀⠀⣸⣷⢾⡿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣤⣤⣴⣿⣷⣶⣿⣿⣿⣾⣷⡿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⠛⠟⠻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⣾⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢴⠄⠀⢀⡇⠀⠀⢨⠇⠀⠘⡉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠳⠜⠀⠀⢸⠃⡀⠈⣼⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠽⠂⠀⠀⢀⡀⠄⣾⠀⢀⣀⠾⣀⠀⠀⢀⠀⠀⣀⠤⢤
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢰⠃⠀⠀⠀⠱⡎⠀⠀⠀⢣⠀⢯⡓⠜⠁⣂⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⡆⠀⠀⠀⠀⠐⡖⢲⠄
⠀⠀⠀⣠⢊⢴⡖⠈⡴⠬⠵⠀⠀⣸⠀⠀⠀⠃⢠⢇⠉⠀⢀⡼⣤⡀⠈⠑⠬⣉⡭⠽⠃⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠈⠁⢸⠐⡰⠃⠀⢀⡴⠋⡀⠓⠤⠤⠔⠁⠀⠙⠒⠉⢠⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢄⠀⠀⠀⠀⠀⠀⢀⣠⢄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⡴⠋⠀⠀⠉⠲⠤⢀⣀⢀⣀⠠⠴⠊⠁⠀⠀⢹⡆⠀⢴⣙⡄⠀⢀⡤⢒⡒⠢⠒⠢⢄⠀⠐⠗⠊⠁⠀⠀⢎⠳⠴⠋⠖⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠀⠀⠀⠀⠀⣀⡴⠶⣦⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠫⠜⣹⢡⢀⠏⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣛⣒⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⣀⡾⠋⠀⣰⠃⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠊⠀⠀⠀⠀⡤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡞⠁⠀⠀⠀⠀⠀⢀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠉⠓⠦⣀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⢣⡀⠀⠀⠀⠀⢠⡏⠀⠉⠙⢳⢄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠱⣄⠀⠀⠀⡞⠀⠀⠀⠀⡞⣸⠁⠀⠀⠀⣼⠛⠲⣄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡾⢫⡇⠀⠀⠀⠀⠀⠀⠘⢦⠀⣸⠁⠀⠀⠀⣸⢁⡇⠀⠀⠀⢰⠇⠀⠀⠈⣷⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⠇⠀⠀⠀⢠⠇⡼⠀⠀⠀⠀⡾⠀⠀⠀⢀⡏⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⢀⡏⠀⠀⠀⢰⠟⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠇⠀⠀⠀⢰⠇⠀⢀⡤⠊⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⣸⠁⠀⠀⠀⡾⠀⠈⠳⡄⠀⠀⠀⠀⠀⣼⠁⡾⠀⠀⠀⠀⠿⠒⠊⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡏⠀⠀⠀⢠⡇⠀⠀⠀⠙⣆⠀⠀⠀⢰⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠲⠶⠦⡼⠀⠀⠀⠀⠀⠈⢷⡀⢀⡟⠀⡟⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣾⣁⣀⣙⣛⣛⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠒⠂⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠛⠛⠉⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⢠⡄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⢂⢂⢠⣀⠈⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⡄⡟⠀⣼⣿⣿⣓⣢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡀⣿⡇⠀⢻⣿⣿⣏⣛⠧⠝
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠐⢲⣶⣤⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠂⢿⡠⠀⠀⣨⡏
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣷⣄⠀⠀⣀⠤⠼⠤⢀⣀⠀⠀⠀⠀⠑⢎⠫⢟⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢳⠊⠀⠑⢄⠀⠀⢣⠉⠙⠒⠠⢄⡀⠉⠈⠉⡢
⠀⠀⠀⠀⠀⠀⠛⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠁⠈⡄⠀⠀⠈⢢⠀⢸⠀⠀⠀⠀⠀⠈⠁⠂⠉
⠀⠀⠀⠀⠀⢠⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⢀⣼⡄⢸⠔⠒⠒⢷⡄
⠀⠀⠀⠀⠀⠘⡇⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠥⠴⣃⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⢃⠀⠀⢫⡣⠤⣀⣀⣀⣀⠠⠤⠶⢂⣀⡴⠒⣲⠄⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠒⠠⠠⠤⠤⠤⣤⣶⡿⠟⣠⠊⠀⠁⠀⠈⠁⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⢀⣈⠡⠒⠈⠈⠢⠀⠄⠂⠈⠁⠀⠉⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠰⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠈⠐⡀⢄⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣲⢀⠀⠘⠁⠀⠀⡆⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⠁⠀⠀⠀⠀⠀⠱⡄⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠀⠠⠄⠀⠀⢀⡀⠀⢸⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠒⠂⠀⡀⠠⠄⠀⠘⡼⠀⠀⠀⣀⡠⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢄⣀⡀⣇⠀⠀⢠⡤⠄⠀⠀⢠⣴⡡⢔⡈⣱⡂⠶⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣓⢙⣨⣯⣬⢻⣦⡠⠛⣟⠀⠀⡠⠊⠑⠮⡟⣘⢃⡳⢚⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⢌⣰⠛⡞⠉⡔⠀⠀⠁⢿⠀⠀⠀⠀⠀⠈⢪⠛⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣨⡹⣾⠀⡐⠁⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⢹⢡⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣻⡧⠊⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠎⢀⣀⡀⠤⠑⠀⠀⠣⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⠉⠓⠛⠛⠢⠤⢒⠅⠒⠒⠀⢤⡀⠀⠀⢀⣀⡑⣄⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠉⢣⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠑⢢⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠀⠀⣧⡀⠀⠀⢀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠄⠠⠧⠈⠉⡅⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢄⠀⠀⠀⠀⠀⠠⢀⠀⢀⣠⣶⠀⠀⠀⠀⠀⢀⡤⠐⠉⠀⠀⣀⡀⣤⡀⣤⣤⡀⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠉⠢⢀⠀⠀⠀⠀⠀⡀⠀⢹⣇⠀⠀⡠⠊⠁⣀⢰⡄⠀⠀⣿⠷⣄⢻⣌⢿⠻⣆⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠒⠒⠶⠞⠓⠂⠀⠊⠉⠀⠉⠉⠁⠙⠓⠸⢿⡶⠋⠀⢠⡈⣽⡀⡟⠦⠀⠛⠀⠈⠈⠀⠀⠀⠀⣀⣀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⡟⢯⡇⠴⠃⠁⠀⣀⣤⠴⠶⠛⢿⠛⢻⠟⠿⣿⡏
⠀⠀⠀⠀⠀⠀⡸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣻⠈⠁⢀⣠⠔⠟⠓⠀⢀⢀⡀⢀⣂⠀⣒⡀⠁⠙⣆
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⠇⠀⠶⠖⠀⣒⣒⡂⣘⣒⠀⠀⠩⠄⠠⠈⢧
⠀⠀⠀⠀⣰⣧⠔⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠒⢠⡀⡆⣴⡊⠀⠀⡀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠓⢠⡳⡀
⠀⠀⠀⠀⠷⠿⠾⠷⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠓⠚⠛⠛⠛⠛⠳⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠰⢍⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣊⠥⠔⢒⣒⡓⠒⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢉⠔⢉⡑⢊⣄⠙⣧⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠙⠁⠈⠉⠀⣸⠀⠀⠀⠀⠀⠀⠀⢻⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⢳⣶⠖⠙⠲⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⢳⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢀⡠⢤⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⠎⡰⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣌⡰⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⠤⠤⠯⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⣀⠠⠤⣔⣒⣒⡲⠦⠤⠴⢖⣒⣤⡤⠞⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣤⣒⡊⠭⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠒⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣄⣤⡄⠀⠀⠀⣶⣶⠶⠆⠀⣴⣿⡇⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣧⠀⢸⣷⠀⢰⣦⢸⣿⠉⠉⠀⢸⣿⢻⣧⠀⠀⠀⣿⣇⠀⠀⠀⠀⢿⣇⠀⢹⣇
⠀⠀⠀⠀⠀⣸⡇⠀⢀⣿⠋⣿⡄⢸⣿⢀⣸⡿⠸⣿⣦⣶⠀⢸⣿⠘⣿⡄⠀⠀⠙⠛⠛⢻⣦⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡀⢻⣧⠸⣿⡏⢻⣷⡄⣿⡇⠀⠀⣾⣿⣶⢿⣧⠀⠀⢰⣶⣀⢸⡿⠀⢸⣿⠀⠸⠏
⠀⠀⠀⠀⠀⢻⣇⠀⢸⣿⠟⠛⣿⡄⣿⠀⠀⢿⡇⣿⡧⣶⡦⠿⠏⠀⠘⠿⠀⠀⠈⠛⠛⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠛⠀⠘⠛⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⢤⡤⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠶⠒⠒⠒⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣤⠶⠶⠦⣄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⣠⢴⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⣦⠀⠀⣰⣯⠗⠲⢄⠸⡆⠀⠙⠋⠉⠳⡌⢧⠀⠀⠀⠈⣧
⠀⠀⠀⣰⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⡆⢹⠀⠀⢧⠿⠀⠀⢸⢠⡇⠀⢠⣄⣀⡴⠃⡼⠀⠀⠀⠀⠸⡆
⠀⠀⢰⡇⢠⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⡇⢸⠀⠀⠀⠀⠀⢀⡜⣼⠁⠀⠈⠙⠓⣦⠸⡅⠀⠀⠀⠀⠀⢻
⠀⠀⡾⢠⠂⠱⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣏⣘⣆⠀⠀⣶⠚⢉⣚⣋⣻⠀⢸⣗⣚⣁⡴⠃⠀⠀⠀⠀⠀⠈⣇
⠀⠀⣇⡇⠀⣠⠔⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢹⡗⠊⠀⡜⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢧⠀⡸⠀⢱⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢸⡄⠉⠐⠒⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢰⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢵⣲⣇⡾⢸⢀⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢹⡀⠀⠀⠰⡏⢻⠀⣀⣄⠀⠀⠀⠀⠀⠀⠘⠒⠒⢁⡇⡇⠸⣜⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⣇⠀⢀⣤⠟⠈⢋⣡⡽⠀⢰⠶⠦⠤⣄⣀⠀⠀⠸⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⡄⠈⢧⠴⢶⠈⣇⠀⠀⠸⠦⢤⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⢤⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢳⠀⠀⠀⠘⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠴⠶⠒⠒⠛⠋⠉⠉⠀⠀⠀⣀⣀⣀⡀⠤⠤⠤⠶⠖⠒⠒⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⡤⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠴⠖⠒⠒⠉⠉⢉⣀⣀⡠⠤⠤⠤⠶⢒⣒⣺⣭⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢰⠃⠀⡤⠴⠖⠒⠒⠒⣋⣉⣉⣉⣀⣠⠤⠤⠴⠒⠒⣒⣉⣩⣭⠤⠴⠶⠖⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣾⠀⠀⠀⠀⠀⠀⢉⣉⣁⣀⣤⡤⠤⠴⠶⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠒⠛⠛⠙⠉⠉⠉⠉