Breadstuff Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠤⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⣀⣀⣀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠁⠀⢀⣀⣀⣀⠠⠤⠤⢅⣠⣄⣈⡓⢦⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠢⣄
⠀⠀⠀⠀⣷⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠈⠉⠉⠉⢀⡀⠀⠀⠀⠀⣉⣁⡒⠠⢀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⣀⠠⠄⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠤⠀⠀⠀⠒⠒⢲⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠐⣂⡈⠄⠂⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠒⠠⠤⠤⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠂⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⣀⣀⣀
⠀⠀⠀⠀⠺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠈⠙⠲⢦⣀⠀⠰⠦⢀⡤⠒⠉⠀⠀⠀⠀⠀⠠⠁⠀⠧⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠴⠒⠚⠋⠉⠉⠀⠐⠉⠀⠉⠉⠒⢄⠀⠀⠀⠂⠀⠀⡀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠂
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⠁
⠀⠀⠀⢸⠀⠀⠈⠉⠛⠛⠒⠒⠂⠀⠈⠹⠀⠀⠈⡄⠀⠀⠀⠀⠀⠉⠙⠲⢄⣀⠀⠀⠀⢀⠀⠀⠀⠚⠁⠀⢀⡀⠄⣀⠴⠁⠀⠀⠰
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠺⠅⠢⠰⠄⠿⠥⡤⠖⠛⠉⠁⢀⣀⣀⠠⠂
⠀⠀⠀⢻⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢤⡀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⡤⠴⠖⡂⢲⣆⣲⣖⠲⠄⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⢰⠈⠁⠈⡁⡂⠐⠂⠀⢖⠐⠂⠀⠆⠀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⢀⣘⣛⣁⣉⣓⣀⣸⣤⣀⣀⡀⡇⠀⠀⠀⠀⢁⠈⠰⠀⠠⠀⡀⠄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⢸⠀⠀⢀⠸⠄⠤⠤⠄⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠠⠈⠀⠤⣩⠡⠀⠤⣀⠁⢬⠤⠈⡄⠤⠄⢀⠀⠀⢀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢐⠀⠀⠁⠀⠀⠀⠅⠐⠀⠁⠀⠀⢰
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠛⠀⠛⠌⠛⠂⠒⠐⠃⠀⠋⠀⠑⠤⠤
⠀⠀⠀⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠂⠐⠂⠒⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⡤⡀⣤⡄⡄⣽⢳⣀⡖⣆⢰⠏⣤⡄⢸⡇⠰⡀⣎⢢⣿⡇⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⢺⣦⠿⡽⠿⠷⠟⠛⠟⠛⠉⠙⠋⠃⠙⠋⠀⠈⠙⠷⣧⣨⠞⣼⣾⣜⡁⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡵⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠛⠶⠾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⢀⣤⣀⣤⣾⣿⣤⣤⣤⣤⣤⣆⣀⡀⣀⡠⠤⣤⣀⡄⠀⠀⠀⢀⣤⣄⣄⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⠉⠇⠈⠒⢼⠷⠌⠐⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠁⠀⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠯⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠋⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠘⣏⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠩⠘⠏⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⢢⡀⠆⣨⡏⣾⣦⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣾⣿⣾⣿⣦⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢀⢻⣿⠃
⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠉⠿⠛⠟⠛⠛⠋⠻⣿⡀⢀⣠⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠄
⠀⠀⠀⠀⣿⣿⣅⡄⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⢿⣿⣯⠁⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⡅
⠀⠀⠀⠀⢸⣿⣂⠀⠀⠀⠀⠀⠀⠀⢀⠗⠂⠀⡄⠀⠀⠛⡿⠉⠲⠀⠀⠠⠐⠀⣴⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡇
⠀⠀⠀⠀⢸⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠐⠶⡆⠀⠀⠀⠈⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠆⠀⢀⣶⡆⠸⣷⡾⠁⠀⠀⠀⠀⠀⠞⠋⠉⠀⠈⠉⠛⠋
⠀⠀⠀⠀⠀⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⢶⡀⠘⢿⣿⣷⠖⠀⠀⠀⠐⠋⠉⠀⣠⣿⣷⣄⣀⠄
⠀⠀⠀⠀⠘⣿⣿⣇⡄⠀⠀⠀⠀⠀⠄⠀⠳⠘⢿⣯⠤⠀⠀⠀⠀⠀⠀⠐⠃⠠⠈⠀⠈⠈⠀⢤⡁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠈⣀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢈⣶⣄⢀⢀⠀⢀⢀⣽
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡾⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣽⣿⣟⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣞⢵⡘⣥⡀⣤⡄⠈⠀⠀⠀⠀⠈⢓⣀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣸⠋⠴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣿⢿⣿⣿⣿⣿⣿⣾⣯⣽⢶⠤⠦⣄⡀⣀⣢⣀⣀⣿⣤⣀⠀⣀⣠⣦⣰⢆⣴⣏⡶⢚⣵⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⣤⣤⣴⡤⠄⠐⠒⠚⠋⠭⠭⠿⠿⠿⠿⠶⠶⣦⣤⣄⡂
⠀⠀⠀⠀⢠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠙⠷⠦⣤⣄⡉⠉⠙⠛⠛⠃⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⣀⠠⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠠⠤⠄⠀⠀⠒⠐⠒⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡾⠷⠶⢶⣶⣄⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠐⠢⠀⠈⠸⡄
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⢀⠙⠙⠻⣦⠀⠰⠃⠀⠀⠀⠀⠀⠓⠁⠀⠙⠄⣠⠐⠀⠀⠢⠀⠘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣁⠄⠀⠀⠀⠀⣰⠀⠀⠣⣀⡀⠀⢀⢄⠀⠀⠀⠁⠀⢠
⠀⠀⠠⠁⣀⣤⣤⣴⣦⣤⣀⣀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠁⠀⡡
⠀⠀⡀⠙⠻⠿⢍⣉⠉⠉⠈⢙⡛⠷⠰⡾⠟⠀⠀⠀⠀⠀⠀⠰⡀⣸⠻⣀⠀⠈⠀⠄⠂⠀⠐⡄⠀⢀⠀⠁
⠀⠀⠇⠀⠀⠀⠀⠈⢉⣈⣩⣽⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠆⢀⠌
⠀⠈⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠼⠁⠉⠗⠆⠒⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠈⠉⠉⠻⣿⠄⠀⠀⠀⠀⠀⣧⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⣣⠈⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠢⠄⢀⠀⠀⠸⡇⢀⡹⠀⠀⠀⠀⠀⠀⠀⠸⣹⡀⠀⠀⠀⠀⠀⢰⣗⣙⡆⢀⣀⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠗⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠒⠊⠁⠠⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢲⠁⣘⠀⠀⣀⣀⣠⡇⢉⣭⡄⠸⡄
⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠜⠀⠀⢀⠀⠀⣀⢈⣤⡖⡦⢖⡞⠀⠇⠀⣾⠙⢯⠏⣿⣯⠽⠁⢠⣷
⠀⠈⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⡐⠁⠀⡰⠁⢰⠏⣽⠀⣽⣛⣿⢈⠃⠘⠀⠀⣧⣤⣄⣈⣀⣀⣠⠴⠫⠃
⠀⠀⠀⠀⠈⠐⠀⠂⠠⠂⠄⠀⠠⠂⠒⠀⠀⠀⢰⠁⣰⣏⡓⠯⠿⢼⡿⠐⠁⢠⠂⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣷⣂⡃⠴⠔⠋⢀⡠⠒⠁
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⡝⠓⠢⢀⠀⠀⠀⡜⠀⠜⠉⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠠⡤⠆⠀⠀⠠
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢰⡃⠀⠀⠈⠀⢌⢠⠇⡐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⢠⣀⡆⠀⠀⠹⠅⠀⠀⠉⠀⠀⠁
⢰⣁⠀⣀⠀⠀⠀⠀⢈⡸⢻⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠑⠀⠀⠀⠀⡀⠠⠄⠂
⠙⠀⠀⠀⣱⠤⠔⠊⠁⠀⢊⠀⠐⠁⠀⠀⠀⠀⢀⠄⠒⢖⡃⠀⠀⠀⠈⠀⠀⣀
⠰⡄⠀⠀⠉⠉⠁⠲⠀⠀⠀⠀⠀⡀⣀⠆⠀⠙⠽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠⢐⣦⡴⠊⠀⡈⣯⠝⠉⠀⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢸⠟⠁⠀⢸⠟⠁⠀⠀⢠⣟⠭⠛⠳
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⠀⠀⠀⢀⠠⠀⢒⣀⢀⡐⠒⠀⠄⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀
⠀⠀⡠⠔⢁⣄⣈⣉⠙⠻⠦⣹⠀⡔⠁⢰⢚⣋⣸⣁⠋⣛⣻⢦⠈⠂⠈⡓⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⡏
⣠⡊⣐⡶⠦⢤⣌⠉⣳⠔⠋⠁⠀⠀⠀⠀⠀⠿⠠⣤⡤⠭⠓⠁⠀⠀⠀⢠⡁⠀⠀⠩⠉⠉⠉⠉⠉⠁⠄⠀⢀⡼
⢇⠶⠶⢶⡏⢢⡴⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠊⣀⠔⠁⠀⠀⠳⢮⣀⣀⠀⠀⠀⠀⠐⠀⣐⣨⠞⠁

⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⢰⣟⡺⢭⣍⡙⠿⣍⣉⡛⠶⣍⣉⡛⠣⣝⢛⠓⢬⣍⠛⠯⣽⣷⠀⠀⣀⠴⡦⠞⠋⡷⣄⠽⢷⣶⣆⣤⡀
⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠘⢿⣶⣶⣤⣶⣦⣤⣤⣶⣾⣿⣿⣿
⠀⢀⣴⡒⡂⠀⠈⠴⠀⢐⣲⡄⢀⡄⢀⠀⠀⢠⣴⡄⠀⠀⣤⢶⣄⠀⠀⠀⠀⠈⢁⠉⠉⠭⠩⣉⡉⠁
⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⣧⣼⡇⠀⡗⠨⣷⠀⠀⠉⢀⣹⣆⠀⠀⡠⠊⠀⠀⡀⠀⠐⠀⢉⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡇⢸⡥⠀⣿⠀⢀⡔⠁⠈⣿⠀⢀⠁⠀⣀⢀⠜⠁⢄⡴⡈⠀⠉⠄
⠀⠀⠈⠒⠒⢀⣁⣀⠀⠚⠃⠀⠀⢹⢻⠃⢸⠀⠀⣿⠀⠈⢀⠴⡊⣿⠀⠏⠀⠀⣨⠁⢦⡠⠃⠈⠣⡀⠀⠠
⠀⠰⠈⠠⠴⠿⣿⢁⣭⠟⢳⣶⣄⠀⢠⠄⢸⡞⠀⣻⠀⠰⠃⢀⡠⢿⠀⢠⡄⠸⠃⠀⡴⡀⠢⣄⠀⠈⢸⠏
⠀⠀⠀⠀⠐⠠⡇⡌⠺⢋⠟⣟⡿⠟⠀⠀⠀⣇⠀⣿⠀⠀⡔⠁⢐⡿⠀⠀⠻⣷⣦⠞⠀⠀⠀⠈⣗⣵⠟
⠀⠀⠠⢀⣤⣤⣬⣧⣧⡟⠛⣛⣇⣒⠐⠶⠀⠸⣄⠏⠀⠀⠦⢐⠽⠃⠀⠀⠀⠈⠛⠿⠶⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠶⠟⠛⠋⠉⠉⠉⠉⠉⣉⡭⠟⠉⠉⠉⠉⠉⠛⠛⠛⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠁⣀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡁⠀⠀⠀⠀⠠⠤⠤⠤⣀⡴⠞⠉⠀⠀⠉⠙⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⢀⡴⠊⣁⣀⡠⠤⠐⠂⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⣀⣠⡴⠟⠊⠉⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠾⠷⣄
⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⢀⣠⠴⠒⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⢀⡴⠋⠀⠀⡴⠞⠉⠀⠀⢠⠞⠀⠀⠀⣀⣀⣠⣤⣤⠴⠥⠤⠴⠶⠒⠒⠒⠒⠒⠒⡶⠚⠀⠤⠤⠤⠤⠤⠀⠀⠀⣠⡾⠋⠀⢀⢤⡀⠀⠀⠲⠀⠀⠀⣿
⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠒⠛⠉⠉⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⢀⣾⠃
⠀⣿⠀⠀⠀⢀⣠⣤⣤⣤⣤⡿⠤⠤⠤⠤⠤⠤⣤⣬⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠐⠊⡗⠀⠀⠀⠀⣠⡞⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢾⠀⠀⠀⠀⠀⠠⠄⠀⣠⠟⠁
⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠷⣤⡀⠀⢸⡇⠀⠀⠀⠓⠂⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠙⠦⠀⠀⠀⠀⠰⣒⠀⠀⠀⠈⣿⣦⠘⣧⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡟⣧⣙⣷⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠚⠀⣸⠃⢸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡤⠀⠀⠀⠀⣠⡾⠁⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⡾⠡⠤⠤⠤⠤⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠲⠖⠒⠒⠒⢲⠋⠁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⢷⡤⠤⢤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⠛⠛⠶⠶⠶⠦⠤⢤⣄⣀⣀⣿⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢊⢉⣭⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢸⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢻⠉⠩⢿⣿⣿⣧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⡇⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠛⠛⠉⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠡⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡄⠀⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣬⠠⠆⠤⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣸⠦⠤⠄⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠍⠁⠒⠲⠂⠠⠤⠤⠀⠀⠀⠀⠀⠤⠄⠄⢐⣂⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣾⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣷⣿⡏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣖⣿⣟⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢷⣿⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣜⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⡷⡑⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢿⣝⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣿⣿⣿⣿⡓⠁⣴⢠⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣤⡄⠀⠤⠀⠀⠄⠀⢀⠀⠀⠀⠀⠘⡵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣦⠘⡿⡟⣿⣿⡄⠀⡷⢸⡟
⠀⠀⠀⠀⠀⢦⢁⣠⣥⣤⣿⣿⣿⣿⡿⠿⠶⣶⣬⣀⠈⠢⡀⠀⠀⢱⢬⣷⡀⠀⠀⠀⠀⠀⠀⠴⣬⢣⡘⣴⣇⡏⠐⠀⠀⣷⣿⠇
⠀⢀⢔⠁⢠⣶⣿⠿⠛⠋⠉⠈⠙⣿⣧⠀⠀⠀⠂⠀⠀⠀⠈⠢⠀⠘⡇⢿⣥⣤⡀⣄⡀⣤⣰⢿⣿⣿⡝⣦⣻⣷⡀⢀⣀⡿⠟⣠⣶⣽⡿⠛⢁
⠀⠀⠀⢀⡟⠋⠀⡀⠀⠀⠀⠰⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣗⠺⡷⠿⣿⣿⣝⣿⣿⢾⣿⣿⣿⡿⢹⠟⠋⠉⢈⡩⣿⠛⠛⠺⠯⡉
⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠉⠙⠒⠶⠥⠬⠭⣽⣮⣭⣿⣟⡂⣿⣶⣶⣾⣿⣿⣿⣿⣷⣤⣤⣬⡆
⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣟⡇⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡋⠈⠛⠻⠿⠿⠝⠷
⠸⣏⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡠⢴⣺⡿⠁
⠀⠘⢿⣿⡍⠑⠤⢀⣀⠄⠀⠀⠀⠀⠘⠛⠛⠀⠀⢐⣾⣿⡯⠟⠁⠀⠁
⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⣤⠤⠤⠔⠒⠒⠒⠂⣙⣉⣉⡓
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣐⠻⠿⣿⡏⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⠛⠻⠍⠉⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠯⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡷⠟⠋⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡭⠍⠙⣇
⠀⠀⠀⠀⠀⣠⣀⣀⣀⠉⠉⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢠⣾⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠴⡿⣿⠟⢻⣿⣷⣆⠖⢶⣶⣦⣄
⠀⠀⠀⣾⣿⣿⣿⣤⣠⣤⡬⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣚⠙⠟⠿⣿⣶⣄⠙⢧⠀⠈⠛⠛⠢⠀⠹⠋⠉⠉⢆
⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠉⠻⢦⡀⠁⠉⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢿⠿⢿⡿⢿⢿⣶⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠈⠹⡃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣂⣼⠟⠉⠀⠉⠛⢧⣄⣠⠽⠓⠀⠠⣄⣀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⣠⠶⠋⢉⣹⠿⣿⣶⢤⣀⣠⡴⠟⠛⢻⡦⣀⠀⠀⠙⣿⡱⢆
⠀⠀⠀⡀⠃⠀⠀⠊⠁⠀⠀⠘⣻⣿⣏⠀⠀⠀⠀⢻⡌⣷⠖⠋⠉⠉⠈⣧
⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠈⢳⣷⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⢳⡕⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠂⠀⠀⠀⠀⠀⠀⠠⣌⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠠⢴⡦⠶⠤⠀⠀⡦⠀⠀⠀⡀
⠀⠀⠀⠙⠿⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠉⠀⠀⠀⡀⠀⣴⣿⣴⣶⣶⠶⠒⠒⠀⢪⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢄⣄⣄⣠⣀⠀⠀⠙⠛⡇⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⣻⣄⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⢋⠩⠉⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⣸⣿⣧⣤⣠⣄⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠀⠀⣠⣳⣳⠀⠀⠀⠀⠀⢠⣿⣄⣄⡀⠀⢰⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⣧⣀⡀⣠⠀⣿⣿⣿⣿⣿⠽⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠻⠿⠿⠿⠖⠀⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠈⠁⠀⠀⠒⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣀⣀⣀⣠⡦⠾⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣀⣀⣀⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⠉⠝⢻⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⠛⢦⣄⠀⠀⠈⠑⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⡇⠀⠀⠰⠙⠿⠷⢶⣄⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠶⠃⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⣶⣶⡶⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠁⢸⣿
⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠤⡆
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣖⣤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠆⠀⠀⠀⡄⠀⠀⢀⡎⠀⠁⢀⡖⠀⠀⠀⠀⢸⠃
⠀⠀⢸⣶⣤⣀⠀⠀⠀⠀⠀⠉⠛⠒⠻⠶⢲⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⠀⠉⠀⠀⠀⣀⡤⠖⠉⠀⢀⣤⢸⡀⠀⠀⠘⠋⠀⠀⠀⠐⣿
⠀⢠⠉⠉⠛⠛⠽⠆⣶⣶⠀⢸⡗⠒⠛⡿⠟⠁⠀⠀⠀⢀⣀⣀⠈⠉⠑⠂⠀⠀⠀⢀⣀⠦⠚⠉⠀⠀⠀⠀⢰⠋⠉⠀⠳⢣⡞⠁⠀⠀⠀⢀⠘⠁
⠀⠈⠻⢿⣶⣤⡀⣀⣀⠀⠁⣾⠂⠀⠀⠀⠀⠀⠠⠤⠄⡀⠀⠈⠉⠀⠀⣀⡠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⢁⡌⠁⠀⠀⠀⢶⣾
⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠀⠁⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⢀⠠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣇⡄⣴⡉⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣤⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣿⣤⠍⠀⠀⢀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⠄⠂⠈⠀⠉⠁⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⡾⣿⡁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⡄⡀⠀⠀⠀⠻⣿⣿⣿⣷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠤⢧⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠉⠛⠿⣿⣾⣭⡙⠳⣦⣤⠔⠒⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠠⠶⠋⠉⠙⠉⠓⣆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣷⣀⣠⡤⠔⠋⠉⠀⠀⠀⠀⠠⠞⠉⠐⢦⣄⣀⢀⠀⠀⣸⠷⣦
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠠⠚⠹⢸⣟⢛⣏⠀⠀⠈⡇
⠀⠀⠀⠑⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⣰⠀⠀⠀⠀⠈⣿⠁⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠙⠻⠿⣿⣏⣀⣛⢛⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠁⢿⡀⠀⠀⠀⡀⠑⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠒⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤⠤⠤⢄
⠀⠀⠀⠀⢀⠠⣔⠊⠉⣷⠒⠂⠙⣆⠡⡈⢻⠳⡄⠀⠀⠐⡟⡡⠒⣉⣭⣷⣆⠀⠀⡰⠁⢀⠠⠔⠁⠰⢄⡀⠑⡄
⠀⠀⡠⢊⡔⢄⠹⡌⢢⠘⣧⠀⠀⠘⡆⠃⠈⣧⡇⠀⢸⠀⠉⠠⠈⠉⢁⣀⣈⡄⠀⣇⠐⠁⠀⢰⢀⠂⠀⠘⠄⣱
⠀⡘⠀⠀⢧⠀⠀⠱⡄⢧⠘⣇⠀⠀⢳⣸⡶⠟⠀⠀⠈⠳⣄⠐⠂⠉⠈⠀⣸⠇⠀⣿⣦⣀⠀⠈⠎⠀⢀⣠⣴⠇
⠀⠳⣄⣀⠀⠑⣠⣦⣘⣾⣦⣬⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⠶⠚⠁⠀⠀⠈⠻⣿⣿⣷⣿⣿⡿⠿⠋
⠀⠀⠈⠉⣉⠉⡉⣉⡉⠉⠉⠀⠀⠔⠊⠁⠀⠀⠑⢄⠀⠀⠀⠀⠠⣤⣤⣤⡀⠀⠀⠀⠀⣀⠤⠒⠘⠙⠲⠤⢤⢄⡀
⠀⢀⡴⠉⢑⢆⠀⠀⢹⡗⢆⠀⢸⠠⠀⠀⠀⠀⠀⢈⠀⢠⡃⠀⠀⢈⡇⠀⠱⠀⠀⢀⡴⠣⡁⡀⠀⠀⠀⠆⢠⠤⠚
⠰⠭⠭⢄⡊⣷⡄⣠⣾⢁⡎⠳⠸⡀⠀⠀⠀⠀⠀⡼⠀⡼⠛⠛⢦⡎⠀⠀⣠⡇⠠⠓⣄⡀⠘⣎⣄⣀⡼⠃
⢰⠀⣀⣰⠿⠟⠛⠋⠉⠉⠙⠃⠀⠙⠲⠤⠤⠖⠋⠀⠀⢃⠀⠀⠀⠆⠀⠉⡹⠃⠐⠐⠙⢛⣚⡭⠍⠭⠤⢄⡀
⠈⠉⢁⠤⠐⠂⠀⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠦⠤⠽⠖⠀⠀⠀⢀⡄⠀⠉⠉⠉⠓⠦⣄⠀⠈⠳⡀
⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠉⠋⠙⠻⠿⣗⠒⠠⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠈⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢺⡟⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸
⠀⠀⠀⠧⣀⣀⣀⣀⣀⠤⠼⠃⠀⠀⠀⠉⠀⠐⠂⠀⠀⠄⢀⣀⠴⠟⠁⠀⠀⠀⠧⣄⣀⡀⡀⠀⠀⠀⢰⣧⠴⠋
⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣥⣬⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠀⠉⣢⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⡀
⠀⠀⠀⠀⠀⠀⣀⣠⠄⠒⠈⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠂⠒⠖⠊⠀⠀⣨⠁⠀⠀⢀⡄⠀⢱⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠑⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⢸⠃⠀⠀⠀⡜⠁⠔⠃⠀⠀⠀⠀⡜⠁⠀⠀⠀⠑⠀⠀⠀⣀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠀⠀⠂⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⢀⡀⠀⠀⠀⠰⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠆⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠤⠤⢴⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠀⠁⠀⠀⠁⠀⠐⠐⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠁⠰⠂⢈⢠⠀⠒⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⠀⠀⠀⢐⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢨⠁⠐⠂⠄⡀⠹⠇⠀⠀⡖⠰⡂⣴⡂⢠⠀⢰⢰⠀⠀⢰⠂⢰⠂⢴⠀⠀⡆⢰⢠⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⡂⠀⠀⠐⠂⠀⠀⠀⠀⡟⠁⡛⣾⡋⢈⠳⣜⢸⠀⠀⢸⡛⣼⠛⣼⠃⠠⢥⣸⢸⠀⠀⠀⠀⢸
⠀⠀⠐⢦⣀⣀⣀⠤⠀⠐⠈⠁⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⢁⣁⢈⠀⢈⠀⠀⡀⡀⠁⠀⠀⣈⡀⠀⠈⠈⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⠀⠐⠒⠒⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡠⠖⠈⠒⢀⣀⠁⢀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠆⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠉⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠨⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣲⠂⠀⠈⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠁⠀⠄⡀⠀⡀⢀⣀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠱⢏⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠉⢁⡈⢡⡀⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠒⠶⠦⠀⠒⠂
⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⣀⣴⠖⠛⠁⠀⠉⠀⢀⡀⠀⠀⠀⠀⠁⣀⡤⠙⠀⠈⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢀⣀⡀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠀⠈⠁

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⠦⠀⠀⠀⠀⠀⡀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠀⠀⠀⠀⠀⠀⠁⣤⠀⠄
⠀⠀⠀⠀⢀⣠⣶⣾⠿⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢈⠁⠠⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢰⡾⠿⢿⠻⢸⣀⣧⠾⠀⠠⡒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⠀⡀
⠀⠀⠘⡇⣰⣦⠼⠛⠉⠀⠀⠀⠀⢀⡠⠀⠂⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀
⠀⠀⠀⠟⠉⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⡄⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠿⠿⠾⠇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⢂⡀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡌⢈⠤⠉⢩⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⣀⠖⠂⡠⠚⠂⡀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠠⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡤⡈⢙⣤⡋⠉⠀⠀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠄⠀⠀⠐⠃⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠤⠰⠀⠈⠡
⠀⠘⠂⠀⡀⠀⠄⠂⠀⠀⡀⠀⠀⠀⠀⠀⢀⣄⣤⡀⢀⡀⠀⢠⢤⡀⢀⣀⠠⠀⣬⠄⠀⢨⣴⣦⣤⣅⣤⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⠈⠢⠀⠀⠀⠈⠂⠀⠁⠀⠉⠀⠈⠉⠀⣞⣎⣭⣝⢎⠆⠀⠸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢈⠆⠊⠀⠀⠀⠱⠆⠉⠃⠉⠑⠌⠀⠀⠀⠉⠈⠁⠟⡹⠄⠀⠀⠀⠉⠉⠙⠛⠁
⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠃⠈⣉⠘⠊⠀⠀⠈⠘⠉⠙⠓⠈⠀⠀⠐⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣲⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣿⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⣷⣤⣄⣀⠀⠀⣾⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⢀⡴⡡⠀⣀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠻⣆⠀⠀⠀⠀⠀⠈⢻⡓⢤⡀
⠀⠀⠀⢀⡴⢋⡼⢁⡴⢉⡴⠂⠀⣠⠟⠉⡿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠉⠳⢿⣷⣄
⠀⠀⣴⠋⣠⠞⡴⠋⣠⠎⠀⣴⠞⠁⢀⡞⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠶⣦⣤⣤⣤⡀⠀⠻⣿⣷⣄
⠀⢰⠇⣠⡇⡼⢡⠞⠁⢠⠞⠁⠀⠀⣾⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢿⣿⣿⣦⣀⣀⢙⡝⣦
⣰⣋⠞⢹⢸⡇⡟⠀⣰⡇⠀⠀⠀⠀⠙⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⢹⣿⣿⡏⠀⢿
⠉⠁⠀⣾⣾⡼⠁⣠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠂⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣶⣶⣶⣴⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⡏⢻⡀⢸
⠀⠀⠀⠿⣿⣁⠔⢩⣿⣿⣿⣷⣄⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠋⠛⠿⣿⣷⣦⡄⠀⠀⠀⢀⡼⠃⣿⣿⢸⡇⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡟⠻⠿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣦⣤⡴⠋⠀⠀⣾⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⠙⠻⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠟⠉⠀⠀⠀⠀⣿⠌⣧⣻⣴
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣴⢷⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠳⢿⣿⢿⣿⣿⣿⣿⣶⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢶⣶⡶⣞⡯⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠛⠿⢭⣟⣛⡿⣿⣿⣶⣶⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠛⠷⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠲⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢃⢉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠘⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡤⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠠⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠉⠔⠂⠐⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⢀⣀
⠀⠀⠀⠀⠀⡀⠀⣠⡾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⢺⣟⢿⣿⣞⣶⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⣰⣿⣏⢠⠀⢠
⠀⠀⠀⣔⢾⣏⠍⠉⠣⣀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣗⡻⢿⣽⣧⢟⡿⣯⣟⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⠸⣇
⠀⠀⠀⢸⡆⠻⣧⣾⣄⣐⡦⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢻⣿⣯⣾⣿⣭⣳⣿⣯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣇⢻⡄
⠀⠀⠀⠀⠛⠿⠧⣥⣤⣽⣷⣤⡽⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣾⣷⣤⡤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⣀⣀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣲⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣼⣿⡷⠾⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢋⠘⠛⣉⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠟⠃
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢒⢦⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⣦⣄
⠀⠀⠀⠐⠤⣙⢮⣵⣲⣤⣤⣶⣿⣯⣿⣷⡦⠀⠀⠀⠀⠀⠀⡤⣦⣼⣇⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⢣⢿⢏⡦⣄⢀⡀
⠀⠀⠀⠀⠀⢀⣩⣷⣮⣼⣿⡻⣽⢻⡷⣏⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣆⢸⣏⣞⣴⡿⣷⡵
⠀⠀⠀⡠⠶⣿⣿⠗⠋⣡⣾⢿⡿⠓⠿⢷⣈⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣔⡫⣟⠻⣷⣜⡿⣼⣗⣽⣷⡀
⠀⠀⠀⠙⠛⠉⠀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣽⣿⠿⣀⡀⠀⠀⠀⠀⢀⡿⡯⣽⡿⢿⣶⡿⠗⢾⣇⣟⣿⡷
⠀⠀⠀⠀⠀⠀⠸⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠟⣩⡿⣷⣴⡶⠟⠛⠀⠀⠀⠀⠀⠙⠒⠒⠛⠋⠁⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣡⣿⣾⣭⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⢛⣽⣶⣶⣶⣾⠗
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣟⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣛⣻⡟⠲⣦⡀
⠀⠀⠀⠸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣹⣿⡿⣽⣯⣿⡿⠦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣥⣾⣿⣿⣿⣿⣿⣿⣯⣷⣄
⠀⠀⠀⠀⢿⣽⣹⣟⣿⢿⣿⣿⠳⣿⣽⣧⡇⠀⠀⠀⠀⠀⢸⡫⡽⠯⠿⢿⠋⣩⣦⣤⣤⠇⠀⠀⠀⠀⠀⠙⢾⠿⠟⢿⡿⣿⠇⠀⠈⠻⢿⣝⣻
⠀⠀⠀⠘⠲⠦⣬⣍⣛⡛⠻⠿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠻⢿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣍⣃⣻⣦⣤⣤⣀⣂⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣀⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⢀⣾⡿⠁⠀⠀⠺⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠗⠀⠀⠈⢿⣷⡀
⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠏⠀⠀⢀⣤⣤⡀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢻⣿⣆⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⢻⣿⡆⠀⣿
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣸⣿⡇⢀⣿
⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠙⠿⣿⣿⠿⠋⠀⣸⣿
⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⣡⣤⣾⣿⣿⣿⣿⣿⣿⣶⣤⣄⠈⠉⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠀⠉⠉⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣴⣾⠟⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣤⣶⣿⠟⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣄⣀⡀⠈⠙⠛⠛⠋⠁⢀⣀⣠⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⢀⣠⠖⠋⠉⣹⣶⡶⠒⠒⠦⣤⣠⡴⠚⠛⢛⣶⡦⣄⡀
⠀⠀⠀⢠⠞⠁⠀⠀⠛⠋⠁⠀⠀⠀⠾⠟⠁⠀⢀⡴⢋⠀⡀⠃⠉⠳⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡄⠀⢀⠀⠁⠠⠘⡆
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠀⠠⠀⠀⠀⠀⠀⠄⢹⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠠⠄⠀⠂⠀⠁⠀⠠⠸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⢠⠀⠠⠀⠄⠀⠂⠀⢂⡇⠀⣀⣤⠴⠖⠛⠉⠹⡆
⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠠⠀⡄⠀⢀⠂⠀⣁⡼⠗⠋⠁⠀⠀⢀⣠⡤⢾⣥⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠲⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣳⣄⣀⣐⣀⣠⡤⠖⠋⠁⠀⢀⣀⣤⠶⠚⠏⢁⠑⠀⠠⠈⡈⢍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⢯⣀⣠⣤⡶⠾⠯⠥⢭⣤⣥⣤⣬⣥⣤⣥⣤⣥⠤⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢻⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⢻⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⣠⣾⣿⣿⡿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣴⣶⣶⣶⣶⣶⣦⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠻⣿⣿⠿⠛⠉⠉⠙⠻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣩⣬⡉⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠛⠿⠿⠟⢁⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣰⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠏⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⣧⠀⠘⠋⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣤⣤⣤⣤⣤⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢉⢉⣿⣷⠀⠀⠀⢸⣾⣿⣿⠀⠀⣿⣿⣿⣄⣸⣿⣿⣿⣇⣀⣀⡀⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⣾⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢻⡀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣶⡀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠛⠙⠛⠋⠋⠉⠉⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⡿⠈⠉⠉⠈⣿⣿⣿⣷⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⢀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⠀⢸⡟⠻⣿⣿⠇⠀⠀⠀⠀⣀⣿⢹⣿⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣻⣿⣿⠀⠀⣠⣄⣀⡀⠀⢻⠧⠀⠈⠹⣆⠀⠀⠀⠀⠀⢠⣤⣶⠀⠀⠈⠀⠀⠈⠛⠀⠀⠀⠀⠀⠛⢿⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠟⣿⣶⣶⣶⣾⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⡄⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠘⡅⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣥⣤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠃⠀⠈⢁⠀⠀⠀⠀⠀⠸⣦⣾⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⢿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⡀⠀⠀⣿⠀⡆⠀⠀⠀⢠⣾⢻⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣶⠀⠀⠀⠀⣤⣼⠉⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠻⢽⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣿⡄⠀⠀⠀⠉⠙⠁⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣧⠀⠀⠀⣈⠀⠀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⡀⣀⣴⠃⢰⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⡋⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠻⣿⣿⣿⣷⠀⠰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⡇⠈⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠮⢭⣉⠁⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡖⠯⠤⠤⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠠⠙⠲⢤⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣕⡀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣠⠀⠀⠀⠀⠈⠳⠄⢊⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣠⡺⠓⠘⠉⠉⠉⠙⠛⠛⠓⡛⠃⠶⢤⡄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⣠⡀
⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠠⠀⠀⠠⠙⢦⡁⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⢀⡿⠍⠓⠄
⠀⠀⣠⠴⠶⠟⠉⠿⠳⠖⠶⠄⣤⣄⣀⣀⠀⠲⠀⠀⠀⠀⠠⠀⠀⠀⠈⠈⢻⡄⠠⠊⠀⠀⠀⠀⠀⠀⠀⣤⠞⠀⠀⠀⠈⠑⠂
⢀⡚⠁⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠉⠙⠛⠰⠶⢦⣄⠀⠀⠀⡀⠁⠐⠀⢸⡇⢀⠀⠂⢀⠀⢀⣠⡤⠞⠀⠀⠀⠀⠀⠄
⢺⡉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⢦⣈⠁⠀⢀⣠⠟⠁⠀⣀⣠⠔⠛⠉⠁⠈⠀⠁
⠀⠉⠐⠢⠤⣈⠉⠒⠤⣄⣀⠀⠄⠀⠀⠐⠒⠀⠀⡀⠀⠀⡿⡟⡻⠻⢿⣷⡒⠋⢉⠓⠒⠤⠍⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠆⣤⣈⡁⠢⠤⣄⣀⡀⢈⣀⠀⣤⡶⢺⠇⡂⠀⠀⠀⠀⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⡤⣌⣤⣠⣵⣩⡷⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⠿⠿⠿⠿⠿⢷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⣸⡿⠀⠀⠀⠰⠏⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠷⣦⡀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠰⣿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣤⣀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠄⠀⢰⣿⣿⣿⣿⣿⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠞⠛⠉⠀⠀⠀⠀⠀⠻⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣶⣶⣶⣶⣶⣶⡿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠁⠀⠈⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣷⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠉⠉⠉⠉⠛⠷⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠙⠛⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⣛⣻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠛⠛⠻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⠀⠀⣀⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠷⣄⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠈⠁⠢⡀
⠀⡠⠂⠁⠀⠀⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠈⡐⠠⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠐⡀⠀⠉⠐⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⣶⣶⣶⣶⣶⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⠶⢦⣤⣄⣀⠀⠀⢀⣤⣴⠏⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠛⢶⣄⡀⠀⠀⣠⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⢀⡘⠋⠛⠀⠀⠀⠀⠀⠘⠛⠉⠀⣀⣀⣀⣀⡈⠻⢦⡼⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣴⠏⣠⠶⠛⠋⢉⣛⠳⣦⡀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠛⢷⣄⠻⣦⠀⠀⣠⡴⠶⠾⠃
⠀⠀⠀⠀⢀⡾⢁⡾⠃⠀⠀⢸⣿⣿⣷⠈⢻⡄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢷⡀⠋
⠀⠀⠀⢠⡿⠁⢸⡇⠀⠀⠀⠈⠛⠛⠋⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣠⣶⣶⡄⠀⠀⣿⠀⠈⣷
⠀⠀⠀⣾⠇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣧⠀⠀⠀⢿⣿⣿⠇⠀⢠⡟⠀⠀⠸⡇
⠀⠀⢸⣿⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠈⠙⠷⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠛⠋⠁⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⡴⠦⣤⡀⠀⠙⣧⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠸⣧⣀⠀⠰⣏⠉⠉⠉⠉⠷⠀⠀⠀⠈⣷⢀⣠⡿⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠙⠛⠶⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣼⠃⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣤⣀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⣀⣤⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⠉⠉⠉⢒⣒⣲⣦⣤⣀
⠀⠀⠀⠀⢠⠖⠉⠀⠀⣀⡤⠖⠚⠉⢁⣀⠠⠤⠖⠒⠛⠁⠈⣑⣒⣤⣄⡀
⠀⠀⠀⢠⡏⠀⠀⣠⣊⡡⠤⠒⠊⠉⠁⠀⣀⡤⠔⠒⠊⠉⢉⣀⡤⠤⠤⠟⠓⠢⠤⢄⡀
⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⠤⠤⠒⠊⠉⠀⢀⣀⡤⠤⠤⠖⠒⠶⠬⢵⣤⡀
⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠐⠓⠂⠉⠁⠀⠀⠀⢀⣠⠔⠊⠉⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠽⠦⢄⡀
⠀⠀⠀⠀⠀⠙⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⡁⠤⠤⠔⠒⠒⠉⠉⠁⠀⠀⠀⠀⢀⡀⣀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⣄⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠉⠉⣉⣉⣉⣉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣵⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠥⠤⠔⠒⠒⠋⠉⠉⠁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⢴⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠺⠶⢤⣤⣤⣀⣀⣀⣠⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠙⠋⠉⠉⠛⠛⠛⠿⠻⢿⠉⠛⠛⠉⠉⠙⠛⠛⠛⢛⡟⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠃⠀⠀⣾
⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⡇
⣿
⣿⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠑⠄⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡅
⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡿⠁
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠠⠀⠠
⣿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⢀⡀⣀⢀⣀⣠⣤⣶⣦⣠⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⢻⣿⡿⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⣾⣿⣷⡄⣾⣿⡟⣿⣿⣶⣿⣷⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢰⣿⣿⣿⣷⡽⣿⣟⢻⣿⣧⠸⣿⣿⣹⣿⣷⣸⣿⡿⢹⣿⡆⢸⡿⠇
⠀⠀⠀⠀⢀⣤⣴⣆⠹⠏⠀⣀⣤⣤⣶⣦⡰⣿⣿⣿⣿⣷⡈⣡⣶⣿⣿⣿⣻⣿⡀⣿⣿⡆⢿⣿⡏⠻⣿⣿⡿⠃⠘⠋⠁⠀⠀⠀⠀⣿⣿⣄⣤⣤⡀
⠀⠀⠀⢠⣿⣿⠟⠋⠐⣾⣯⢻⣿⣿⢻⣿⣿⣿⣿⡆⢿⣿⡇⣿⣿⣹⣿⣿⣟⣿⡧⢸⠿⠇⠘⠋⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣶⣿⢹⣿⣿⢿⣿⣷
⠀⠀⠀⢸⣿⣿⠀⠀⠀⢿⣿⡽⣿⣿⡄⣿⣿⣯⣿⣷⠘⣿⣷⠻⢿⡿⠛⢛⣉⣉⠀⠀⠀⢀⢀⣀⡀⣤⣤⡰⣿⣿⣿⣿⣿⣄⣿⣿⠁⠈⣿⣿⡆⢿⣿⡇
⠀⠀⠀⠈⣿⣿⣧⣀⣀⣸⣿⣧⢻⣿⣧⢹⣿⠿⠻⠛⠀⠉⠁⠀⠀⠀⣰⣿⡿⠟⢰⣶⣿⣿⣎⣿⡇⢹⣿⡗⣿⣿⣇⢹⣿⣿⣻⣿⣄⣀⣸⣿⣷⢸⣿⡿⠠
⠀⠀⠀⠀⠘⢿⣿⣿⣿⠇⠛⠛⠈⠉⠉⠀⠀⠀⠀⢀⣺⣿⣶⡄⠀⢠⣿⣿⠀⠀⠈⣿⣿⡇⠸⣿⣿⠈⢿⣿⣜⣿⣿⡈⣿⣿⡍⠻⠿⠟⠛⠛⠉
⠀⠀⠀⣀⣀⡄⠀⠁⠀⠀⠀⢀⣤⣤⣤⡄⢠⣾⡿⠏⠟⣿⣿⠀⠀⠀⣿⣿⣆⠀⠀⢹⣿⣿⠀⢽⣿⣷⣿⣿⡇⠻⠟⠃⠉⠉
⠀⢿⣿⣿⣿⠛⣠⣶⣿⣶⡄⠘⠛⣻⣿⣿⡾⣿⣿⣶⣄⢽⣿⡆⠀⠀⠹⣿⣿⣷⣾⣯⢿⠿⠇⠀⠉⠉
⠀⠀⠘⣿⣿⡄⣿⣿⡙⣿⣿⣤⣾⡿⢻⣿⣷⣈⣉⣿⣿⠩⣿⣿⡇⠀⠀⠀⠙⠛⠉
⠀⠀⠀⢹⣿⣷⢻⣿⣧⣹⣿⡿⣿⣿⣾⣿⣿⠿⠟⠛⠁⠀⠈⠁
⠀⠀⠀⠈⣿⣿⡄⠻⠿⠿⠟⠁⠈⠉⠁
⠀⠀⠀⠀⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⠋⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣹⡷⠴⣠⣄⠱⣿⣶⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣚⠋⠶⣦⣝⣿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠉⠐⢿⣦⣈⣿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⠙⡿⣮⣿⠛⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠦⡀⣊⣢⠟⡫⠃⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠭⠁⠜⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣤⠀⠤⠤⠤⠤⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣂⣉⣀⣲⡤⢶⠤⠃⢀⠰⣶⠦⠴⠄⠀⣀⣀⡀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠴⢏⣙⣇⣸⡠⡧⠼⣦⠀⠈⠐⢦⣤⠤⠤⠤⢤⣄⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣶⢮⣉⣉⠭⠄⣀⠀⠠⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣽⣂⠈⣉⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⡄⠐⣁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣝⡻⣟⠀⣴⡂⠀⠀⠀⢠⣶⡄⢰⡯⢦⡀⢂⡀⣇⢈⣀⡥⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢈⢀⡇⠁⠈⠋⢮⡇⠀⠀⠂⢨⠟⡻⢿⠺⠾⠟⠛⠋⠙⠁⠃⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠀⠀⠀⠀⢀⠀⠀⢀⠓⢸⡃⢌⢂⢃⠀⡀⠠⠠⠀⠀⡘⢰⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⣠⣆⠀⠤⠅⣼⡷⠶⠶⢄⠀⠀⠁⠆⡀⠀⠃⡈⠀⠁⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⣠⡾⠃⠈⠳⠶⠞⣦⣀⠀⡀⢋⣆⠀⠀⠠⠀⡘⢀⠃⠃⠠⢸⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠀⣔⠝⢁⡀⠠⠠⠤⠤⣴⣿⣤⡟⢀⠄⠘⣧⡀⠀⠈⠁⠸⢰⡖⠓⠮⡈⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠠⢄⠀⣠⣶⣯⢁⣿⠃⠀⠀⣀⠘⢟⡄⠀⠀⠃⣼⠀⠀⠀⠡⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠨⡥⣀⡠⢶⣦⣙⡿⣿⠀⢀⡄⠀⠀⡜⡌⠀⠀⢀⠻⠀⣄⠀⠀⠀⠠⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣁⠀⠔⢸⠷⣶⣝⣿⢷⠻⡃⠈⣠⠂⡘⡘⠀⠀⢨⡘⢀⠶⣈⡁⠾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠴⠐⠀⠀⠀⠀⠰⠘⢆⠶⠻⠷⠼⢋⢾⡈⠤⠁⠐⠁⣲⠌⠀⠀⠀⠀⠃⡈⡀⢁⠁⠆⠀⢠⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⢦⡀⠋⠀⠀⠀⠖⢠⡳⠁⠀⠠⢀⠂⠈⠰⢡⠁⠄⡘⠰⠀⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠚⠭⠴⠶⠖⣂⣀⣀⣰⠏⠀⠀⢀⠂⠌⡀⢀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠐⡐⡀⢀⠎⠎⡰⢁⠎⣀⠎
⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠊⠑⣠⣉⠂⠑⢊⠔⡠⠂⠂⠐⠀⠁⡠⢁⠌⠔⠜⠀⠀⠎⠈⠀⣤⠞⣣⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠠⠀⠄⢉⡰⠛⡰⠦⣤⢀⣀⣀⢀⢀⡀⣀⡀⢀⡤⠀⠄⣐⢞⠕⢁⠈⡡⢊⠐⢁⠔⡡⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠡⠒⢁⠔⢉⠔⢊⠤⠂⠠⠀⠀⠀⡁⠀⡠⠂⠔⠠⠂⡠⢁⠄⡡⠊⡄⠁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠊⠐⠀⠐⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣶⣦⣄⣀⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠙⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⣿⠏⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⣀⣀⢠⣤⣄⣒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠾⣟⣋⣉⠉⠉⠁⠀⠀⠈⣀⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠨⣗⡲⠦⢭⣍⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣊⢻⣿⣿⣶⡖⠒⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠶⠋⠀⣤⡀⠉⢿⣿⣍⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠰⠶⠶⣾⡋⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⡉⠁⠀⡄⠀⠀⠝⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⢤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⢀⡀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⡛⠻⠿⠿⠿⠯⠷⠢⢒⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⠽⠛⠓⠒⠶⠖⠚⠛⠉⠁⠀⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⡜⢆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢧⢹⣾⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⠿⠿⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣲⣶⣒⣒⣲⣶⣶⣶⣶⣦⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⠿⠿⠿⠿⠛⡛⠿⡭⠩⠿⠭⣭⣩⠭⣤⣄⠬⣭⣉⡙⠻⢽⣓⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⣒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣖⣒⣫⡭⠭⣭⣛⣓⢶⣤⣌⣙⡒⠮⣍⣓⠦⡌⠙⠶⢭⣝⣢⢄⡺⠿⡷⢶⣦⣄
⠀⢀⣠⣞⣫⡭⠥⠤⠤⠤⠬⠥⣭⣍⣉⣉⡛⠛⠳⠿⢿⣯⣿⣛⡻⠷⡶⢮⣤⣶⣤⣭⡉⠛⠒⠿⢓⣤⣒⠤⣐⠨⣙⠷⣮⣗⠮⣳⢌⠻⣷
⢀⣾⣿⠏⠁⣴⢢⠀⠀⠀⠁⠀⡀⠀⠈⠉⡉⠛⠛⠿⢶⣦⠬⣉⠛⠻⠭⣓⢶⠄⠀⠈⠉⠀⠀⠉⠲⠈⠛⠏⠂⠙⠂⠀⡈⡙⠳⠈⠙⣱⢟
⢸⣿⣿⠀⠀⠈⠁⠀⠛⠀⠀⠀⠁⠀⢴⣶⠀⠐⠒⠀⠀⠈⠻⢮⢝⣦⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⣠⠀⠀⠀⡇⢹⠀⠇⣼⣏⡼
⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠱⡄⠙⣯⠢⡄⡄⢸⢰⠆⣾⢸⠀⠇⠘⢀⣈⣠⠤⠤⠗⠚⠒⠀⣿⡟
⠀⠀⠈⣿⠢⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⡇⠅⠇⠘⢘⣤⠛⡶⢒⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⣿⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⣠⡏⡠⠖⣋⢿⠿⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢻⡿⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⣸⡤⡪⠒⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⣟⡕⡠⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣷⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡾⡻⠏⠀⢀⠖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢠⣿⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⢱⣯⢊⠆⡰⠁⡰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄
⠀⠀⠀⠘⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⢠⣹⠸⣣⠃⡜⠀⡜⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣵⠟⠁
⠀⠀⠀⠀⠉⠒⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠀⠠⠀⠁⠀⠀⠀⢈⣿⣷⢃⠎⠀⠜⠀⠀⠀⢀⠀⣀⠤⣐⣂⣭⣶⡾⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠶⣶⣤⣄⣂⣤⣒⠲⠶⣎⣸⠸⡇⠈⠀⣠⡤⣶⣿⣿⡿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⣄⡉⢰⣯⡵⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠩⠭⠤⢓⣒⡒⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⣉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⢻⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣼⠟⠋⠀⡀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣼⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠁⠀⡠⠊⠀⠀⠀⠀⠑⣀⠖⠁⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡁⠀⠀⣀⣀⣀⣀⣰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢺⡁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⠯⠿⠀⠀⡘⠉⠉⢹⣿⠇⠀⠺⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⣀⠔⠙⢄⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢻⠐⠛⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠂⠈⠐⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢦⣄⠈⠲⡀
⠀⠀⡀⠀⠤⢄⡴⢁⠔⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠑⢦⠘⢆⡀⡄⠄⡀
⠀⢊⡀⠤⠀⠀⠀⠞⠠⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⢀⠠⠱⠈⠀⠀⢀⣀⠑
⡼⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢇⠀⢀⣴⠛⠀⢂⠀⠘⢄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⡠⠃⠀⠰⠀⠿⣦
⠈⠁⠈⠁⠊⠀⠈⠓⠤⠊⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠚⠀⠀⠣⠤⠔⠁⠀⠑⠚⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⠶⠢⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠄⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣾⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣉⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣁⠈⠙⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠷⣶⣤⣈⣉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣦⣄⡉⠙⠳⠦⡤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⠀⢀⡞⢉⡼⠛⣫⣷⠆⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣀⡟⢁⡞⢁⡴⠋⣺⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣾⡄⣼⡁⣼⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡴⢆⢀⣀⠀⠀⠀⠀⠀⠀⠉⡛⠿⣿⣷⡿⡿⢃⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠢⣼⡈⣻⡇⣸⠃⣸⠤⠄⣀⡴⠖⣋⣩⣥⡷⢤⡉⠧⠆⡼⠀⣉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠚⠢⣼⣿⣿⣿⣿⣿⡇⢠⠞⣡⣶⣟⣭⠵⠶⣒⣚⣗⣛⣒⡇⠀⠀⠀⠀⠀⣄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠒⣿⣿⣿⣾⣧⣿⢧⡏⣼⣿⣿⣽⢶⣛⣋⣭⡭⣯⠭⢽⠃⠀⠀⠀⢈⡲⢤⡙⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡬⣝⠛⡿⢿⢿⣻⢸⡇⡜⢿⣿⣿⣻⣭⡷⠶⠖⡟⠲⢺⣷⣶⣤⣄⣲⣽⣶⡝⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣞⣾⠉⢻⣧⡼⣾⡟⣼⣷⣜⠦⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⢛⣩⣾⣿⣿⣆
⠀⠀⠀⠀⢠⠖⠦⣄⣇⠀⠘⣇⠀⣸⡏⠀⠸⣼⣿⣿⣿⡷⣤⣉⠀⠀⠀⠉⢉⣉⣉⣩⣭⣥⣴⣶⣾⣿⣿⣿⣿⡿⢿⡆⠀⠀⢀⡀⠀⡀
⠀⠀⠀⣀⣈⣣⣀⠀⢽⣾⣶⣿⣾⣿⣾⣤⢶⣿⣟⠷⣬⡛⠲⢭⣙⠛⠶⠶⠶⠶⠶⠶⠶⠶⢛⣛⣯⣿⣿⣿⣿⡿⣻⣿⠐⢦⡏⠱⡾⢹⣤⢤⡀
⠀⠀⠸⣅⠀⠈⢽⣿⣿⣿⡿⣛⣛⣻⣿⣯⢸⣿⣝⠷⣄⠉⠓⠂⠀⠈⠀⠀⠀⠀⠐⠒⠛⢛⣋⣩⣥⡾⣿⣿⣿⡿⣫⣿⠰⣴⣿⣶⣿⣟⣅⡼⠶⣄
⠀⠀⡴⠚⠛⠓⠺⣿⣿⣯⣾⣿⣿⣿⣿⣿⡞⣿⣟⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣩⣥⣶⡾⣿⣿⣿⣿⣫⡿⢬⣿⣿⣽⣯⣿⣿⠦⠶⣅
⠀⠀⢙⡶⠖⠶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣉⠳⢻⣿⣿⢶⣍⡑⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣥⣤⠶⢾⣿⣿⣿⣿⣿⣃⡤⠾⣿⣿⣿⣿⣿⠣⣴⠚
⠀⠀⠘⠲⣦⠶⠒⠚⢛⡿⠋⢹⡏⠙⡄⠈⣳⣿⣿⣿⣷⣦⣍⣙⠒⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⢶⣿⣿⣿⣿⢿⣿⣿⣯⣤⡞⠁⡾⢻⡟⢱⡦⠼⠃
⠀⠀⠀⠀⠿⠶⠴⣖⣉⠀⣠⣿⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⣦⣭⣙⡓⠒⠶⠤⠤⠤⢤⡶⠶⠶⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣷⣾⣧⣸⣓⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣯⣝⣛⠳⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⡤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠈⠁⠒⠒⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡦⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠛⠓⠾⠷⠶⠷⠶⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣀⣀⠀⢀⣀⣀⡤⠖⠀⠀⠀⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠿⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠠⠅⢀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠑⠀⢄⡀⠀⢾⣧⡤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡀⠀⢠⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⣰⣞⣋⣙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⡄⠀⠀⠀⠀⣠⡤⠶⠴⠢⢤⣤⠤⠤⠬⢧⣤⡉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠶⠶⠖⠒⠒⠛⠻⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠢⣹⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠒⠒⠀⠀⠀⠘⠒⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡍⠳⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠁⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡤⠤⠀⠹⣇
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄⠀⡤⠀⢠⠲⡀⠀⠁⠈⠁⠘⠒⠄⠀⠀⢿⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠃⡅⡌⠉⢠⠋⠀⢱⠸⠙⢦⡃⢰⠖⠑⡞⢀⡱⠞⡔⠢⣀⠔⡆⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠐⠃⠀⠈⠈⠙⢸⡗⢠⣄⠑⢪⡄⠀⡇⠡⢄⠀⠘⢆⢠⠊⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡀⠔⡆⢠⢰⠈⠂⠘⠃⠀⡀⠑⡄⠀⠀⠇⠏⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠳⠤⠡⢠⠀⠢⠤⠌⠘⠒⠀⠀⠘⠢⠃⠣⠤⠤⠇⠀⢧⠃⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⣨⠆
⠀⠀⠘⢀⠀⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣂⡈⠁⠀⠀⠀⠀⣀⣀⣄⣀⣀⣠⠜⠉
⠀⠀⠘⠄⠀⠀⠠⢀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣶⠿⢿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠈⠐⠠⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠶⠔⡶⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠶⠶⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⣴⣾⡿⠟⠛⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠛⠻⢿⣷⣄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⢠⣾⡿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣾⠛⠉⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⡆⢰⡟⠋⠉⢹⣶⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠘⣧⡀⠀⠀⠻⢿⣿⣿⣿⠿⣫⡟⠀⠀⢻⣄⠀⠀⠙⠿⣿⣿⣿⡿⢋⣼⠃⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⣐⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠖⠀⠠⠐⠆⠀⠀⠀⠀⠒⠒⠒⠂⠀⠐⠀⠀⠤⠄
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢈⣉⠉⣀⠉⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠉⠙⡄⠉⠳⡄⠀⠀⠘⡶⠶⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠘⢃⡀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠘⠃⢹⠆⠀⠛⠀⠘⠃⠠⠀⠷⠀⠀⠀⠀⠂⠀⠐⠘⠓⠒⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠤⣤⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠀⠀⠀⡆⠀⠀⠀⢒⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣴⠛⠀⠀⠀⠘⣁⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂⠐⠂⣴⠀⠀⠀⡅⠀⠀⠄⠈⠁⠤⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⠉⠉⢉⡿⢀⡀⠀⠀⠀⠁⣀⠿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣿⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⣠⠴⠋⠀⠀⠀⡄⠀⠀⠐⡉⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠒⠉⠛⠋
⠀⠀⠠⠀⠠⠤⠤⠤⠄⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠒⠒
⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠄
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠄
⠀⠀⠈⠀⠈⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘⠀⠚⠀⠓⠐⠂⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠘⠛⢶⡶⣤⠀⠈⠃⠀⠀⠀⠢⠀⠀⠀⠀⠞⠀⠀⠀⠈⢡⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣾⠿⠻⠿⣷⡀⠀⠾⠀⠀⢀⣀⣀⣠⣄⡀⠀⠀⠠⠄⠀⠇⠈⣆⠀⠈⠐⠂⠤⣤⣀⢀⢀⡀⠀⠹⠀⣇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠿⠞⠋⣰⡿⠁⢰⡆⠀⠀⠀⠛⠛⠟⠋⣄⠀⠀⣰⠀⡠⠂⠈⠀⡉⢀⢸⠉⠁⠀⠈⢢⡄⢩⣜⠁⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣠⣾⠿⠧⠀⢸⡇⠠⠈⢀⡀⠀⠀⢀⡀⠀⠀⢹⡀⠁⢀⠀⠀⢩⡀⢠⡂⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠾⠛⠉⠀⠀⠀⠀⡼⠀⠀⠉⠀⠀⠀⠀⠘⠃⠀⠀⠘⡇⠀⠘⠉⠹⡉⢃⠐⡅⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⠀⠤⠶⠀⠀⠀⠀⠹⣀⠃⠎⠀⠀⠉⣠⠇⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⡀⠃
⠀⠠⢤⡄⠠⠤⠤⠀⠤⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠈⠐⠀⠀⠀⠈⠀⠐⠒⠂⠀⠀⠈

⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⡀⡀⢀⣀⣠⣤⠄
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠎⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠆⠰⠏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠞⠿⠳⠆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠠⠀⠀⠀⢸⠁⣔⠐⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢘⣃⡉⠘⠁⠐⠆⣠⠆⠀⠀⠀⢦⣿⣹⣦⡁
⠀⠀⠀⠀⠀⠈⠉⠑⢀⠖⠚⠒⠙⠀⠈⠀⠀⠘⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⡠
⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠲⠂⠀⠀⠀⠀⠀⠰⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠢⢀⠀⡁⠀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⢷⡤⣀⠀⠀⠀⠀⠀⠐⢄⡀⢠⣹⣥⣔⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡶⣦⢳⣱⣿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠁⠀⠀⠏⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣿⣮⡷⠉⠁⠐⢆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡃⣿⢿⣿⡿⣃⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢀⡜⠀⡄⠐⢇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⣄⠀⣭⡈⠀⣰⡈⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠛⠃
⠀⠀⠀⢀⣀⠀⢈⣀⠁⢉⡀⠉⣁⡉⢉⣩⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠉⠁
⠀⠀⢠⡋⠉⠁⠁⢉⡀⠉⣹⠚⠉⢓⠋⢉⡋⠁⠀⠀⠀⣠⣼⠾⣏⠙⣧⠈⣧⢈⣠⠤⠔⠚⠉⠉
⠀⠀⠈⠇⠙⠈⡃⠉⠛⠐⠊⠑⠘⠛⠃⢘⠋⠀⠀⠀⠀⡏⢹⡆⢹⣆⢽⣶⣾⡿⠃
⠀⠀⠀⠘⠃⡈⠛⠆⠛⠛⠀⠞⠛⢆⠘⠀⠶⠀⠀⠀⠀⠸⣿⣿⣷⣿⣾⣿⠛⠁
⠀⠀⠀⠈⠳⠶⡄⠜⠶⠤⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⠨⡝⠃⠀⣚⠠⠌⢹⡻⠦⣥⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡀⠈⢘⠷⢤⣀⣈⣵⡒⠜⢃⡴⠋⣛⣻⣿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠀⠀⠈⠐⠯⢁⠵⠔⣩⡿⠙⠈⠉⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢶⣴⠀⢳⢉⣶⢻⡇⢠⡴⠖⠚⠩
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⣀⠀⠀⠐⢀⣺⣖⢂⣸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣦⡙⠛⠟⠀⢸⡏⠀⠀⣠⢤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢉⠛⠳⠛⠛⢻⡯⡹⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡤⡼⠧⠤⠞⠛⠉⡇
⠀⠀⠀⠀⠀⠤⠀⠐⣷⠀⠁⠀⠒⢄⢚⡄⣿⡝⠯⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣄⠠⢀⡀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠝⠻⣦⡵⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡛⠊⠿⢶⣥⠴⡧⠤⠆⠂⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠓⠀⠀⡠⠀⠳⡟⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠅⠀⠀⠈⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣦⡇⢀⢓⣶⣾⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⡤⠀⡶⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠋⠉⠩⠛⣒⠦⣤⣶⡞⠛⠛⠶⢤⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣖⣤⣄⡀⠀⠀⠈⠳⣌⢻⣿⣄⠀⠀⠠⡝⡆
⠀⠀⢀⣴⡾⠛⠉⠉⠀⠀⠉⠺⡿⣆⠀⠀⠀⣀⣼⡿⠇⠀⠀⠀⣗⣿⠀⠀⠀⠀⢀⣀⣤⣤⠤⠴⠶⠶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⣸⠭⠀⠀⠀⠀⡠⢟⣡⠴⠚⠲⢲⠻⠻⠻⠉⠀⠀⠀⠀⢀⡏⣿⢀⣠⡴⠟⠋⠥⠴⠒⠲⠿⠀⠀⠀⠉⡀⠀⠉⠉⠦⠀⠀⠉⠙⠗⣦⡀
⠀⠀⢸⡾⣆⠀⠀⠠⢀⡞⡀⠐⠀⢠⡀⠀⠀⠐⠀⠀⠀⢀⣄⣾⣾⠿⠟⠛⠛⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡄
⠀⠀⠀⠻⣬⣃⣐⣀⣘⣧⠣⢄⣀⣀⠀⢀⢀⣤⣤⣶⣾⣿⢟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢶⡀⠀⠀⡀⠀⠀⡀⢀⠀⡀⠑⡠⠀⡀⣤⡇
⠀⠀⠀⠀⠘⣿⣟⠿⠋⠉⠛⠶⠤⠭⠼⠿⠿⠛⠛⠭⣗⠊⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠄⡶⡄⢀⢃⣴⣷⡅⣆⣆⣰⣷⡿⠃
⠀⠀⠀⠀⠀⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡍⢰⣿⣿⣠⣥⣤⣤⣤⣄⡀⢀⠀⢀⠀⠀⠀⣿⣇⣤⣧⣶⣾⣿⣿⣿⠿⠿⠟⠛⢹⡇
⠀⠀⠀⠀⠀⢸⣶⠈⡄⠀⠀⠀⠀⠀⢀⣀⣠⣤⣥⣾⣷⣮⡾⠋⠀⠀⠀⠄⠉⠻⣿⣷⣌⠁⠂⠀⣼⡿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣸⣿⣤⡇⠠⢤⠀⣠⣀⡜⠁⠀⠀⠀⡢⠌⠙⠿⣶⣭⡁⠀⠀⠀⠀⠈⢻⣿⡆⢘⣾⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣈⣭⣽⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡄⠉⠠⠄⡠⣸⠻⠇⠘⠻⠴⡖⠆⠀⠀⠀⠀⠀⢀⠰⠀⢀⣤⣴⡆⣿⡀
⠀⠀⣰⡾⠿⣿⣿⣿⣟⣛⣛⣛⣻⣿⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠋⡇⠀⢀⣠⣴⣿⡶⠀⢰⠆⠰⣷⢦⠀⡀⢰⣄⣠⣾⣴⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠉⠙⠋⠭⢭⣉⣉⡛⠟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠞⠁⠀⡟⠻⡿⠋⠀⠀⠈⣿⣿⣷⢸⣤⣿⣿⣯⣿⣿⡿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⡼⠻⡟⠁⠀⢀⢒⣥⣾⣁⠀⠀⠀⢰⢹⣿⣿⣿⣿⣿⣿⠿⠫⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠤⠀⠀⠀⢰⣧⣼⣅⣀⣐⣣⣾⣿⣿⣛⠛⠛⠒⠒⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⢀⣀⣵⣿⣿⡟⠋⠙⠛⠛⠛⠋⠂

⠀⠀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢃⠀⢠⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⣠⠖⠂⢉⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠄⠀⣴
⠀⠀⠈⡄⠀⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⡀⡎⠀⠀⠠⢴⠋⠀⣀⠴⠟⠀⠀⠀⢀⡀⠱⠶⠄⠀⣒⡲⠔⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠴⠀⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡇⠀⠶⢅⡀⠀⣱⠛⠁⠀⢰⠃⠀⠈⠠⠀⠈⠀⢀⠂⠁⠀⠈⠀⠀⢀⠂
⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠄⠐⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠀⠀⠀⠀⠀⠈⠀⠀⠡
⠀⠀⠀⠀⢀⠷⠊⠉⠭⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠄⠀⢠⡶⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢦⠂⢀⠤⠒⠒⠚⢆⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠸⠎⢀⠄⠐⠀⠉⠙⡄⠀⠀⠀⢀⠀⠀⠘⠀⡄⠀⠀⢠⠀⠀⢸⠀⠀⠆⠀⢀⡇⠀⡤⠀⠀⠀⡓⠀⢼⣷⡆⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠻⠁⡠⠒⠊⠉⠁⣇⠀⠀⠀⢸⠀⠀⡇⠀⣇⠀⠀⢸⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠂
⠀⠀⠀⠀⠀⠀⠙⢤⢀⠀⡠⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢀⡀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⡀⠐⠋⠁
⠀⠀⢀⠀⣀⠙⠀⠀⡇⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⢈⢺⡇⠀⠀⠀⠄⠂⠀⠀⡀⠀⠠⣌⠀⢉⢢⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠜⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⣄⣉⣉⠉⠉⠉⣩⡝⢛⢛⠉⠋⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡐⠐⠉⠀⠈⠀⠘⠀⢄⠉⠀⢌⠀⠈⠁⠀⠀⣁
⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠜⠀⠀⠀⠠⠜⠉⠉⠀⠉⢷⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢁⠈⠠⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠆⠀⠀⡀
⠀⣁⠰⠀⣅⠀⠀⡁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠙⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡁⠂⠠⠌⠙⠁⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⠀⢄⠀⠀⡀⢠⠄⠁⠀⠀⠲⠀⢠⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠂⠀⠀⠐⠔⠀⠈⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠑⠈⠒⠘⠂⠀⠀⠠⠀⠠⠈⠀⠈⠀⠀⠀⠀⠀⠛⠥⣴⣀⣀⣀⡩⠔⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣙⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣠⠀⠀⠸⣻⠉⣿⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⡶⠂⠀⠀⠀⠀⢠⣼⣿⣿⣿⠀⠀⢸⣿⣿⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠿⠛⠉⠛⠀⠀⠀⣀⣀⠀⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣸⣿⣧⣤⣀⣭⣧⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⣀⣤⣀⣀⣀⣀⣀⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠲⠖⠀⠰⠆⠀⣐⣂⠀⣤⣤⠐⣿⣿⠇⠀⣿⠿⠿⠿⠿⠛⢛⣿⣿⣿⣿⣿
⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣦⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣭⣙⡻⠶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠛⢻⠿⣿⣛⠟⢻⣭⡉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣷⣶⣼⣿⣍⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣦⠋⣿⣄⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣽⣿⣿⡿⢿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣯⡿⣻⣿⡞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⡿⣿⣎⣾⣿⣿⡞⣿⢂⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣷⣿⣿⣿⣌⢻⣿⣼⡇
⠀⠀⠀⠀⠀⠀⢰⡿⣟⣿⣷⡾⣿⡿⠛⣿⣼⡝⣾⠇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⣻⣿⣿⡟⠿⣿⣭⣸⣧
⠀⠀⠀⠀⠀⠀⢸⡿⣭⣈⣿⣧⡽⣷⣏⣼⣿⣧⣿⠀⠀⠀⣴⢻⢏⣛⣛⣛⣟⢻⣿⣟⣛⢋⠻⣦⠀⢀⣿⣿⡿⣿⣿⣿⣿⣿⣦⣤⣿⣫⡟
⠀⠀⠀⠀⠀⠀⠈⠷⠿⠿⣿⣿⣷⣿⣿⣿⣷⣲⡟⠀⠀⠀⣿⡙⣛⠛⠛⠿⢿⣦⡴⢿⣿⣶⢰⡟⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⡏⣿⡿⣿⣿⣶⣭⣿⣯⣦⠿⣾⠇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⡼⣿⣿⣟⣹⣿⣝⣫⡏⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠶⣽⣟⠶⣦⣤⣀⣀⠀⠀⠀⠀⣿⣤⣽⢿⣯⡿⣿⣏⡡⢟⣛⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣟⣿⣶⣬⡝⣿⡛⣦⠀⠀⣿⣳⣿⣾⣿⣿⣷⣿⣿⣿⣿⣟⣸⡇⠀⠀⣴⠛⣛⢛⣻⡶⠶⢶⠶⠖⢛⣻⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣯⠻⣷⣅⣿⣿⡶⢿⣧⡿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⣿⠺⣾⣿⣟⣿⣧⣾⣿⣌⢹⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣷⣧⣸⣿⣆⣹⣿⢻⢿⣷⠎⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢮⣿⣿⣯⣿⣿⣙⣿⣾⣿⡇
⠀⠀⠀⠀⠀⣼⣿⡋⣿⡋⢿⣿⣷⣿⣞⢺⢿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣷⣿⣻⣿⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣟⠿⣿⢿⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣷⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⣿⣿⣭⡟⠿⣿⣿⣿⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠶⠶⢤⣶⣶⣾⠿⡟⠉⠳⣄⠹⣶⢢⡹⡌⢷⣦⡐⠲⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠙⢯⠻⡀⠘⡆⠀⠘⡄⠘⡄⠁⢻⢸⠉⡇⠀⠈⣿⣷⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢡⠀⡇⠀⢀⡇⡀⡇⠀⣸⡾⢀⡗⠀⠀⡟⢹⠂⠀⠀⡇⢹⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣯⣴⠇⢁⣼⡞⣼⡗⢠⢿⡇⣼⠃⢀⡜⢃⡞⠀⠀⡸⡁⣸⠁⠀⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⢠⠞⢋⠞⢹⠏⠀⣼⠁⢸⠉⠀⢫⡎⡰⢡⡶⢫⡴⠏⢀⠤⡞⢁⣸⠃⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡄⣴⠀⠀⡇⠀⢸⠁⠆⢯⡅⠙⠈⡿⣿⠀⠀⣧⡤⡴⠛⠁⠀⠀⠀⠀⣀⡠⠾⣿⣀⠔⠋⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄⢾⡇⢻⡀⠀⢇⠀⠘⡆⠀⢸⡇⠀⣇⡏⢻⡆⡼⢹⣿⠁⠀⠀⠀⠀⡰⠉⣿⠦⠖⠉⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠈⡇⠀⢸⠀⠀⡇⠀⠘⣇⠀⣹⠄⢰⣱⠁⢀⡇⠀⠀⠀⣠⢞⣀⠞⠁⠀⠀⢀⣀⡤⢒⡒⠋⣻⠇
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢱⠀⢸⠀⠀⡇⢠⡷⢻⡄⣿⣤⣼⡏⠀⡾⠀⣀⡴⠋⣡⣟⣥⠴⠒⠚⠉⠩⠅⣠⠿⠖⠚⠁
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣇⠄⡼⢀⣸⠇⢸⡇⣈⣯⣏⡴⠿⠗⠿⠤⠶⠗⠾⠿⠞⠻⠿⠬⠿⠶⠖⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣧⠽⠓⠖⠓⠒⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁



⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣠⣤⣄⣀⣤⡴⠶⠶⠶⣤⡴⠞⠛⠛⠓⠶⠶⠶⠛⠛⠛⠓⠲⠶⢤⡤⠶⠒⠲⢶⣤⣄⡀
⠀⢀⡴⠞⣉⠥⠴⠞⠛⠓⠲⠦⠤⠴⠒⠛⠛⠓⠒⠛⠛⠋⠉⠉⠉⠙⠓⠒⠒⠒⠚⠛⠲⣄⠀⢳⡈⠙⣦
⢀⡾⢡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣧⠀⢸
⢸⡇⢸⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⠀⡟⠀⢸
⠘⣧⠘⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠇⠀⣼
⠀⠈⠳⣦⣄⡉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠟⣋⣉⡴⠋⠀⣴⠏
⠀⠀⠀⠀⢨⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣶⠞⠛⠁
⠀⠀⠀⠀⢸⠇⣾⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣿
⠀⠀⠀⠀⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⣷⠀⣿
⠀⠀⠀⢰⠇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⢿⠀⣿
⠀⠀⠀⣼⠀⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣿
⠀⠀⢀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡆⢸⡄
⠀⠀⢸⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⡀⢸⡇⢸⡇
⠀⠀⡿⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢸⡇⢸⡇⠈⣇
⠀⢰⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⣿
⠀⢸⢃⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢻
⠀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⢸⡆
⢠⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇
⢸⠇⡟⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇
⣾⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇
⣿⢸⡇⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⢸⡇
⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⢸⠇
⢻⡄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣸⢀⣴⠟
⠀⠻⢦⣌⡙⠒⠲⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⠤⠤⠶⠚⠁⣀⡴⠟⠋⠁
⣀⣀⣀⣈⣉⣛⣛⣛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣚⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⣋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠋⢉⣉⣉⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠈⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢀⡴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⠃⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⠛⠉⠁⢀⣀⣠⣴⠾⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⡶⠶⠾⠛⠛⠉⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠾⠛⠋⠉⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠀⢹⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⡴⠛⠛⠳⡄⠀⠀⠀⠀⠘⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣀⣤⣤⣀⠀⣼⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠠⣴⡏⠀⢀⣿⣿⡿⠓⠦⣾⡃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣤⣼⣿⣿⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⣫⠟⠻⣧⣀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠠⡇⠀⠀⢀⡿⠙⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠙⠶⠶⠋⠀⣴⠛⠛⠲⢤⠀⠀⠀⠀⢀⣼⠃⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⣿⠀⠀⢨⡿⠶⣤⣀⣠⠞⠁⠀⠀⠀⢸⡇⣀⣤⠾⠋⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⣿⠀⢠⡟⠀⠀⠀⠈⣿⠀⠀⣀⣤⡴⠾⠛⠉⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿⠀⢹⠀⠀⠀⣀⣤⡿⠶⠛⠉⠁⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠂⠴⠞⠁⠀⠀⡇⠀⠀⢿⣤⣼⠶⠞⠛⠉⠀⢀⣠⣤⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⣿⣿⣶⣶⣶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒