Buny Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱⠋⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡜⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠜⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡾⠁⠈⠀⠀⠄⢚⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠞⠁⠀⠀⡴⠒⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠂⠀⢂
⠀⠀⠀⠀⠀⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠀⢀⣀⢀⡀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡄⠀⠀⠀⡩⠶⠦⠤⠤⠄⠀⠐⠀⠧⣄⣀⠀⠀⠀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠙⣿⣄⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠈⠿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⢶⡶⠀⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⠀⣸⠿⠿⠻⡇⢀⣠⣆⣀⣨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠁⡀⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠠⠬⣌⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠻⡇⠡⠀⠀⠀⠀⠀⢀⠌⣾⠀⡆⠀⣾⡇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡙⠄⠀⠀⠀⡃⠀⣣⠀⠀⠀⠀⠆⣾⡇⢰⡃⢸⣿⡃
⠀⠀⠐⠀⠂⠒⠂⠀⠐⠀⠒⠀⠁⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⡈⢢⠀⠀⢠⡁⠀⢻⡄⠀⠀⡒⣰⡋⠀⢰⣥⠟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⣣⣄⣴⠇⠀⣾⣷⠀⢠⣷⣿⡇⠀⢸⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣿⢀⡼⠟⠋⠀⠘⠉⠛⠸⢦⠈⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠺⢣⠎⠀⠀⡀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡿⢿⣿⣧⡀⠀⣠⠀⢁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠋⠄⣄⡿⠟⠙⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣉⠔⠃⠀⠀⡄⠀⣸⣿⡇⠀⠀⣊⣄⣄⠀⠀⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢠⡾⠁⠀⠀⠀⣴⠁⠀⠀⡈⠀⠀⠠⠶⠟⠛⢧⡄⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠈⠀⠀⠀⠀⢐⡧⠀⠀⢠⠏⠀⢀⠐⠂⠀⠁⠈⠣⡄⠸⣧⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⣿⠃⠀⡄⠀⠀⠀⠀⠘⢿⣴⡀⡊⣠⠀⠀⠀⠑⢦⣥⠖⠀⣤⠀⣯⣴⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠉⠀⣈⠁⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⣠⡇⠀⠐⠁⣰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣷⡖⠀⠀⠀⠈⠁⠀⢀⡸⠏⠙⢚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⡽⣿⠿⡙⢿⠏⠃⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣦⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠖⠂⠠⠶⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⣴⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⣤⣆⣴⣿⡄⠀⠀⠀⢰⣿⡅⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣾⠟⠿⣿⣿⣶⡀⠄⠀⢸⣿⣷⣤⡄⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⠟⢿⡛⠀⠀⠀⠀⠈⢿⠀⠀⠿⠿⣧⠐⣄⢀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠚⢦⡿⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠈⠉⠻⢦⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⠛⣦⣻⣆⣀⢳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⣮⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣶⣤⣼⡿⠿⠋⠉⠛⢷⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⣧⠀⣆⣽⡛⡆⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠒⠒⠒⠲⠤⢄⣀⣀⣤⢀⣿⣿⡷⠀⠀⠙⠛⠛⠇⢻⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣟⣹⡃⠉⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣀⣀⣀⡀⢀⣴⠤⠄⡀⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⢿⣿⣿⡟⠓⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢔⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⣻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣟⡀⠰⣀⣀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣯⢄⠀⠀⠙⣶⡽⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⣾⡾⡀⠀⠰⠋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣵⣀⠀⠀⣿⣷⣦⡗⣨⠋⠀⠀⠀⠀⣠⣾⣭⣸⣟⣤⣶⣿⡇
⠀⠀⠀⠀⠀⢠⣤⡠⠀⢿⣿⣟⡥⠀⢀⣷⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠚⣣⢠⠵⠋⠀⠶⠟⠛⠛⢿⣿⣿⣧⠀⠀⠀⢸⣿⡿⠟⠉⠻⣿⣿⡟⠂
⠀⠀⠀⠀⠨⣄⠀⠃⠀⠄⢀⠀⠀⣀⡀⢰⠜⠞⠻⠿⠟⠃⠀⠀⠻⡐⠄⠀⠀⠀⡈⠣⡀⠀⠠⡴⣤⠀⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠁⠁⠀⡄⠈⠁⠉⠒⠁⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⡄⠲⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢹⡗⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡈⣷⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣹⣿⣿⣷⣶⣤⠴⠶⠲⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⠋⣻⣿⡿⠿⠇⠀⠀⠙⢿⣿⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢀⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣼⣇⡀⣀⡀⠀⠀⠀⣿⣿⣍⠋⠉⠙⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡿⠋⠉⠙⠃⠀⠀⠀⠲⢦⠀⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡏⠀⠀⠀⠘⢷⠔⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⣀⢀⣸⣆⠀⢀⢀⠀⣾⣶⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⣭⣿⣿⣟⣿⣿⣿⣥⣴⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⢻⣿⠟⢻⡟⠛⠻⠻⠏⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⡄⢶⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡇⠠⠀⠀⠀⠀⠘⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡆⢀⡀⢠⣴⠤⠀⠈⠀⠀⠀⠀⠀⢰⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣯⣅⣾⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⡄⠀⣸⣿⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣽⣷⣼⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣇⡀⢀⠀⢀⡸⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠻⠤⠦⠄⠐⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠴⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⡀⠀⢠⣿⠋⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢻⠀⠀⢿⠇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⡄⡆⢸⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⡀⠰⣇⠘⠀⠀⠀⢠⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⣿⢠⠀⠀⠀⠋⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣠⡄⠻⠀⢳⣶⠀⡾⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠙⠁⠸⡄⠀⠻⢠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⢀⡤⠦⢀⠹⣧⣀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠞⣻⣶⣶⣆⣴⡈⢿⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣾⠀⣿⣿⠿⢃⠽⢓⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢪⣷⠿⠿⠶⣴⡿⠋⠁⠠⠟⠛⣾⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣈⠀⠀⠁⡀⠈⣷⣄⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⣴⣭⡾⢛⣂⡐⠀⡹⠛⠛⠛⠛⠛⠓⠉⣁⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣷⣿⣿⣋⠀⣁⣴⡿⣦⣀⠠⠄⠚⠉⠡⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣉⣀⠀⠽⠿⠛⠉⠀⠀⢀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠟⠐⢖⠚⠀⢠⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⠀⠰⠺⣮⠁⠀⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠃⠀⠀⠀⠏⠀⠀⣀⠀⢀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⠐⢇⠀⠁⠀⠖⠀⠈⠁⠘⠃⠀⠀⢠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢠⣿⡀⡈⠀⠀⠀⠀⢾⡀⠀⠀⠀⠐⠂⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣿⡇⠃⠀⠀⠐⠀⢨⣧⠀⠀⠀⡀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣥⠈⢿⣿⠀⠀⠀⠀⠀⢨⣿⣶⠆⠀⠁⠀⠀⢰⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠱⡎⠹⣧⠘⣿⡀⢀⠈⠀⠀⠸⣿⣿⣶⣦⠄⠀⠀⠀⠁⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡀⠸⡆⠀⠀⠘⢦⠘⡇⠋⠀⠀⢀⠘⣿⣿⣏⠀⠀⢠⠀⠈⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢀⣹⣿⡀⠀⠀⠀⠸⣶⠖⠃⠀⢘⣿⡿⠻⡆⣶⠎⠀⠀⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻⡄⠀⠀⠀⢻⡃⠀⠀⢸⠇⠀⠀⢹⡀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠛⠀⠀⢀⠘⠁⠀⠀⠘⠃⠀⠀⠘⠀⠀⠀⡾⢂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣰⠀⠀⠀⣐⡿⡟⢁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢊⡄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠦⣶⣽⣟⠘⣒⠞⠉⠁⢰⠸⠀⠠⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠾⠛⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡇⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⡼⢸⠁⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⠈⡆⠀⠀⠀⠀⠀⣰⠃⡎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢸⡀⢳⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠈⡇⠸⡄⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢇⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡗⠀⠀⡇⠀⠀⠀⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡀⠀⠀⠀⠀⡇⢧⠀⠀⠀⣇⠀⠂⡇⠀⠀⡸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⢀⠀⢀⣇⣿⠀⠀⠀⣿⢧⣀⡇⢠⣰⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⢹⡻⣙⡉⠲⠷⢾⣛⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⡋⢝⠛⠫⠄⠀⠉⠁⢳⡍⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠱⠉⠀⢀⠱⠀⠀⠀⠀⠀⠀⢀⣶⣄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣿⣿⡏⣢⠀⠀⠐⠀⠀⠀⠀⢠⡻⣿⣇⡧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢣⡙⠛⠋⠀⠈⠀⠀⠉⠀⠀⠀⠀⠈⠙⠛⠁⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⠁⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣐⡀⠀⢀⠆⠀⠠⣖⠤⠤⠄⣠⠄⠀⠑⡀⠀⠀⠀⠆⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣇⣌⡤⠤⣸⡅⢀⡀⠈⠙⢶⠞⠁⠀⠀⠀⡗⠶⢀⣊⣃⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠤⠻⣿⣿⣿⣿⣧⠁⠈⠀⣀⠬⢄⣀⠀⢀⠈⣉⡈⢐⢐⡼⠓⠀⠄⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣕⣊⠁⠀⢀⣈⢉⣡⣼⡷⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⢀
⠀⠀⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀⢀⣀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠋⠁⣾⣿⣿⣆⠀⠈⣀⠀⡀⣠⣄⡀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⣬⣤⣴⣽⣿⣿⣿⣷⣷⣿⣷⣾⣿⣿⣿⣿⡎⠀⠀⠀⢀⠀⢆⢠
⠀⣢⠀⠀⠀⠀⢀⠰⡼⠀⠀⠀⣀⣱⣾⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣄⡆⡈⡄⢰⣿⣏⡀
⠀⢿⠀⡀⠄⠀⠀⣦⣽⣷⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣷⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⠀⠈⠉⠉⠋⠈⠁⠈⠈⠀⠉⠉⠈⠋⠉⠛⠉⠁⠹⠋⠉⠋⠉⠈⠁⠉⠉⠁⠈⠉⠁⠀⠈⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡇⢠⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣧⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⢃⣾⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡘⣦⣾⣧⣶⣶⣶⣼⣿⣧⣦⣦⡄⢊⣿⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠹⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡿⠃⠀⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠉⢻⣿⣿⡁⠌⢳⢠⣿⣿⣿⡟⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣻⢶⣄⡿⢟⣿⣿⣷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣷⣯⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⠀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣷⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⣿⡿⠿⠿⠻⠏⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠏⠉⠀⠉⠹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠛⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈



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

⣤⣄⣀⡀
⣽⡻⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣤⣶⣲⣆⣤⣦⣤⣄⣀⣀
⠻⢟⡿⣿⣏⣻⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⣀⣠⣤⣶⣞⣛⡻⢯⡟⣽⣷⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀
⣿⢲⣿⣌⣿⡇⠡⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣫⣿⣟⣿⣿⣟⣿⣷⠿⠿⠿⠿⣿⣿⣿⣿⣦⣄⡀
⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢿⣿⣿⣿⢛⣭⣌⠛⡋⢠⣤⣤⣶⣦⣤⣤⣈⣿⣿⣿⣿⣿⣦⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⣬⣭⠉⠅⠓⠴⠶⣬⣀⣿⡿⣿⣿⣿⣿⠻⣿⣿⣿⣷⠙⡿⣿⣿⣿⣿⣶⣤⡀
⣦⣬⣝⣉⣻⣟⣷⡛⢩⣛⣹⣿⣿⣿⣿⣿⣿⡧⣚⡛⠯⢤⣵⡾⠅⣶⣚⣞⡛⠙⢛⣛⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣁⠡⠞⢿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣽⢏⣿⣿⣿⢫⣿⣄⠙⠩⢥⢏⡝⡫⢂⡿⣿⡦⣾⣶⡌⠻⣿⣮⣝⠿⠿⣭⠾⢋⡉⠙⣣⣤⣦⣿⣿⣿⣿⣿⣿⣿⣻⣦⣄
⠿⠙⠛⣉⣷⣪⣭⡽⣛⣘⣃⣽⣿⣾⣿⣿⣶⣰⣾⣿⡵⣲⣿⡿⣿⣿⡿⢿⣿⣿⣿⠠⣈⠛⠛⢿⡖⣖⠉⠀⣠⡆⣦⣶⣿⣿⣽⣻⣟⣿⣿⣿⣿⣿⣿⣷⡄
⠞⠛⠛⠉⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠶⣿⣶⣿⣿⣦⣿⣯⣿⣿⣿⣿⣾⣷⡶⣫⣖⣥⣶⣷⣮⣾⣿⣾⣿⣿⣿⣶⣷⣞⡚⠻⠥⣾⣿⣉⣴⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣻⣫⢿⠿⢺⣿⣿⣿⣽⠿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡻⠀⡜⠈⠙⢿⣿⡿⠁
⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢡⡞⢀⠀⣢⠀⠀⠀⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣲⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠳⠶⠟⠛⠱⢱⣿⣟⣿⣫⠟⣽⠏⢀⠃⢠⠃⡌⠀⠵⠱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣭⡽⡟⠛⢿⣿⢿⣿⣵⠿⠁⠀⣀⣤⠄⣰⡖⣻⣃⣿⣿⣿⢦⣿⢢⡟⢶⢃⣮⣵⠗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⢯⢍⣶⡋⠐⠀⠀⢀⠈⠙⠻⡖⠋⣙⣃⢪⠏⠙⠃⠻⢋⡿⣿⣿⣿⣿⣿⡿⣿⣿⠇⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣭⣤⢶⣆⣄⡀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡼⠋⢹⠋⢉⠋⡙⠘⠀⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⢿⣿⣿⣾⣧⣉⣹⡎⣀⡊⣀⣀⠀⣀⠀⣀⣤⣤⣺⡿⠃⡆⠀⡌⠀⠸⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣏⣳⣿⣿⣿⣿⣿⣽⣿⣯⣟⣵⢫⣿⡿⢷⣿⣿⣿⡟⠿⠁⠘⠀⢠⠁⠀⠇⠀⠀⠀⠆
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢆⠙⡿⣽⣿⣿⢿⡽⣯⡟⣀⡼⠟⠳⡿⣏⠙⡟⠠⠐⠀⠇⠀⡄
⣻⣿⣷⣟⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣛⠴⠄⣮⠻⢹⣯⠙⠣⣌⣈⣭⡄⠰⠊⠀⠘⣤⡗
⣿⣿⣿⣞⠟⣻⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣜⣷⣶⣦⣛⡄⠀⢄⠈⠒⠀⠀⠰⣦⢰⡶⠀⠀⠘⠀⠀⠀⢀⠀⠀⠐
⣶⣞⣿⣿⡾⣷⣾⣿⡷⣽⣿⢿⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⡞⣹⣿⠷⢀⠀⠀⠵⠖⠀⠠⣀⣥⣿⠁
⣿⣿⣟⣿⡿⠷⢿⣭⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⡄⠬⢧⠈⠀⠀⠀⠀⠐⠠⡀⢿⡛
⣿⣿⣛⡿⢿⣿⣽⢻⢿⣿⣿⣷⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣧⣈⡲⡀⠀⠀⠀⠀⢀⣮⣭⣾⠁
⣿⣿⣿⡿⠠⣽⣍⣺⡹⣃⣊⡍⣚⢙⠿⠹⢦⡛⡻⢿⣿⣿⣷⣍⠛⢷⠍⢶⠀⠀⠀⣨⣽⡟⠁
⣿⣿⣿⣍⣝⡃⣩⠿⢳⡤⣤⣤⣀⣤⠑⢄⣼⣥⠙⠾⣿⣿⣿⣿⣂⠀⡶⡤⠀⠅⣶⣿⣿
⣿⣿⣿⣿⡿⡏⠧⣦⡠⢁⡉⡤⠈⠷⣰⣌⠸⠺⡄⠈⣾⣿⣿⣿⠷⣷⠦⠁⠀⢀⣿⣿⠁
⣿⣿⣿⣿⢸⠧⣗⣹⡟⣪⡇⡇⠠⣾⣤⡿⡄⢀⠁⠀⢹⣿⣿⣿⠰⠀⢰⣀⣾⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠘⣿⣿⣿⢇⠀⠀⠀⠀⢀⣴⣿⠏⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠂⣼⣿⡟⢸⡀⠀⠀⣠⣿⣿⠏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⢹⣿⡇⢸⡄⠀⢰⣿⣿⣟⢰⠂⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⣿⢃⣿⡇⠀⣾⣿⣿⡏⠎⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣼⡿⠿⠶⠟⣛⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠳⠖⠻⣿⣿⣷⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⣳⠊⠛⣻⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃⠟⠁⣀⣿⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣷⣴⡿⢿⣿⣿⢻⡶⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⣾⠄⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠁⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⣿⣁⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣀⢀⣴⣿⣿⠂⠹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠏⠛⠉⠙⠙⠉⠁⣀⠀⠀⢀
⠀⠀⠀⠀⠈⠛⣿⣿⣿⠁⠀⠀⠘⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈
⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⢿⣷⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣢⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⡼⣃⣶⣖⣰⣷⣦⣦⣤⣤⣄⣤⠁
⠀⠀⠀⠀⠈⣁⣺⣿⣿⣯⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⠟⡈⣻⣄⣂⣤⣞⠀⢀⡀
⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠈⢿⣿⣿⣿⣟⣉⡀⢰⣿⣿⣿⣿⣿⣾⡿⡵
⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⡿⣉⢉⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⣿⣿⣿⣆⡀⢿⣿⣿⣿⣿⣟⣡⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠿⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠇⠀⠳⢠⣿⡟⣿⢿⣿⣿⡿⠿⠻⣿⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠈⠁⠀⠀⠀⠁⠀⠀⠀⠃⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠑⡄⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⠀⡀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⣷⣶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡉⢟⠟⣷⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣷⡦⠀⣀⡀
⠀⠀⠀⠀⢂⠀⡄⠀⠀⠀⡆⠀⠀⢠⢎⣠⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣯⣤⣀⡸⠃
⠀⠀⠈⠀⠀⠀⠄⠀⡄⠀⠑⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⢿⡟⠛⠛⠿⢿⣿⣿⣿⠟⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⣠⣢⣴⠶⣶⣿⣿⣿⣿⠟⣫⣏⣁⠂⠙⣏⣿⣿⣶⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠁⠰⡀⠀⢰⠁⠀⠀⣼⣿⣿⣿⣟⣯⣍⠁⢹⡿⠀⠀⢸⠛⠟⣿⡷⢸⠃⠀⡐⠸⢁⠄⠀⡀⠀⠀⣀⠥⣌⣉⡉
⠀⠀⠀⠀⠁⠨⠀⢣⡀⠸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⡎⢀⡤⢺⣷⣼⢻⢃⡎⢀⠔⠁⠘⢁⣠⡠⠈⠙⠀⠃⢀⡠⢀⡠⠄
⠀⠀⠀⠀⠐⢤⠀⠀⢡⠀⢣⠀⣾⣿⣿⣿⠟⠋⣁⣀⠉⠻⣿⣿⠃⠓⠝⠿⠁⣸⡷⠃⠠⠂⠠⢉⠄⠀⢀⠔⠁⠀⡴⠀⠉
⠀⠀⠀⠀⠀⠀⠙⣀⣨⢀⠈⢠⣿⣿⢟⣡⣶⣾⣿⣿⣷⠀⣿⣷⣷⠞⠀⠀⢰⡏⠀⠰⢁⠴⢈⡡⠖⠋⠀⠀⠀⠀⠀⠶⠶⣄
⠀⠀⠀⠀⠈⠁⠈⠁⠸⣹⣿⣼⣿⢷⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡧⠀⠀⣾⡇⠀⠰⠀⠠⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠉⢀⠀⢫⣿⠇⣼⣿⣿⡿⢳⠀⠀⣿⡇⠀⠀⡀⠠⣜⢁⡁⠈⠁⢌⡉⠒⢁⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠔⠀⠀⠒⠀⢰⣿⣿⠏⠀⠸⡀⠀⢛⠀⠀⠀⠀⠀⠙⠣⠙⠂⠤⠀⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢛⢃⡰⣾⣤⣶⣾⠁⠀⢠⣿⣿⣵⠿⠷⠓⢷⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠾⠿⠿⠿⠟⠓⠛⠉⢦⠀⠀⢁⢣⣼⣾⣷⣦⣾⣿⣄⡄⣀
⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣏⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠴⠛⠖⠊⠉⠛⠛⠋⠛⠋⠉⠈⠈⠙⠉⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⡀⠀⠀⡄⠐⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣷⣴⠀⠀⣼⣷⣶⣶⣯⣀⣄⣴⣦⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⡖⠋⠀⠀⠀⢈⡁⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠠⡎⠀⠀⠀⠀⣵⠄⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣷⠀⠀⠀⠀⠀⠃⣿⠀⢇⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠉⠀⠈⠀⠀⠃⠀⠉⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⡰⠀⠀⠀⢼⡧⠀⠀⠀⡄⠀⣿⡂⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣽⡄⢂⠀⢀⡐⣼⡷⣂⡀⢀⠃⣰⣿⣷⠀⠀⠀⠖⠀⠀⠀⠘⡉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠝⡶⢆⣀⡀⠉⠛⠛⠉⢀⣄⡴⣿⣿⡿⠀⠀⠀⠆⠀⠀⠀⠀⢣⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⡇⠀⠀⠀⠣⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⡃⠀⢀⣰⣴⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠁⠀⣾⣿⣷⡧⠄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠿⣄⡀⠀⣀⣀⣠⠶⠟⢋⣶⣩⣧⣾⣿⡯⠬⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠀⣼⡿⢻⠏⠉⠁⠀⣰⡿⠿⠿⠿⢏⠏⣰⠂⠰⢆⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠴⠤⠴⠋⠀⠦⠴⠤⠼⠴⠋⠀⠀⠀⠀⠛⠒⠛⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⡿⡇⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣾⣧⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢸⣿⣿⣿⣇⢀⣄⢀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣞⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠉⠉⠛⠋⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⢴⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⢻⡦⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣨⡿⠋⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣃⢾⣿⣼⠏⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⣾⠏⠀⠀⢀⣾⠁
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⣿⡔⡈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣼⠟⠁⠀⠀⠀⣾⠃
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⢧⡙⠌⢢⡙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠳⣄⠀⢹⣄⠙⢿⣿⣦⡀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⣧⠘⣿⡀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡈⢳⡀⣿⡀⠘⢿⣿⣿⣦⡀⠀⠀⣼⣿⣏⠀⠀⠀⠀⠀⢀⡟⢀⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⢹⡇⠀⢘⣿⣿⣿⣧⠀⢠⣿⣿⡿⠀⠀⠀⠀⢠⠞⢁⣼⣿⠇
⠀⠀⠀⠺⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢸⡇⠀⢸⣿⣿⣿⣿⡆⣼⣿⣿⡇⠀⠀⠀⠀⢁⡴⠟⣹⡟
⠀⠀⠀⠀⠀⠈⠙⠛⠃⠘⣿⣇⠻⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇⢠⠞⠹⠟⠛⠛⢿⣾⣿⣿⣧⠀⠀⢀⡴⠋⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢸⠀⠸⣷⡷⠚⠁⠀⠀⠀⠘⠛⠿⢿⣿⡀⠀⠊⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠟⠛⠛⠛⠻⠿⢷⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⣼⠇⠀⠀⠀⠀⠐⠉⠻⠂⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⠉⠉⠛⠿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢠⣶⠿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠠⠁⠀⠀⠀⠀⠀⢠⣿⣻⣶⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⣯⡐⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢸⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡏⢷⡀
⠀⠀⠀⠀⢘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠳⣶⡶⠊⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⣠⠞⠁⢸⣧
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢀⣨⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⣙⢶⣤⣤⣤⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⣿
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢾⣆⡄⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠸⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⢷⣿⣄⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣠⣶⡀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⠛⣻⡟⠁⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⣴⣏⣀⠀⠀⢰⣿⢶⡶⠆⡠⠶⢿⣿⣿⣿⣶⣤⣤⣤⣬⣷⣄⠀⠙⢻⣿⡿⣷⣦⣤⣤⣤⣤⣤⣴⡶⠾⠛⠉⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣏⠙⠿⣿⣿⣦⡀⠈⠁⠀⠈⠛⠉⠀⠁⠘⣿⠄⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠉⠉⣻⡆⠀⠀⠀⠀⠀⣶⠀⠀⣿⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⢄⠀⠀⡀⠀⠀⢀⡇⠀⠀⠈⢩⣿⡀⠀⠀⠀⠀⠛⠀⠀⣿⣧⡄⠀⠸⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠖⠛⠋⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢶⠀⠀⣿⠉⠉⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡘⠃⠀⡄⠀⠘⠳⠤⠼⠦⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡆⠀⣷⢀⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣄⡀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠈⠉⠙⢦⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣂⠀⠀⠀⠀⠙⢷⣿⣧⣠⡰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣿⣷⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⣤⣼⣿⠿⠟⠉⠛⠿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⣴⣩⣟⢦⢈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠒⠒⠒⠤⢤⣀⣀⣤⣄⣿⣿⣿⠃⠀⠙⠻⠟⠻⠘⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⢿⣿⣛⡓⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣆⣁⠀⡀⠀⣰⡦⠔⢀⠌⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠛⠒⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢔⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠈⢻⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡁⠢⣀⣀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣟⡅⠀⠀⠉⣶⣥⠃⠀⠀⢀⡴⠃⠀⠀⠀⠀⣰⣾⡄⠀⠀⠟⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⢹⢷⣶⡞⢺⠋⠀⠀⠀⠀⢀⣼⣭⣐⣟⣡⣴⣾⡇
⠀⠀⠀⠀⠀⢠⢴⡀⠀⠻⣿⡿⣡⠀⢀⣼⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⠒⣁⣠⠵⠛⠀⠴⠾⠛⠛⢿⣿⣿⣷⡀⠀⠀⠠⣿⡿⠿⠋⠙⢿⣿⡿⠣
⠀⠀⠀⠀⠀⢅⠀⠃⠀⠄⠀⡀⢀⣀⡀⢰⡄⠦⠛⠿⠛⠃⠀⠀⠘⡄⢆⠀⠀⠀⠀⠉⡁⠀⡀⡴⣦⡀⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠈⠈⠉⠁⠠⠠⠀⠁⠊⠑⠊⠀⠀⠀⣀



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣆⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢻⣷⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⡀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠋⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢻⠁⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡟⠀⠈⣿⣿⢿⡇⠀⣠⡀⠀⡂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣀⡀⠀⢠⣄⠀⢠⣤⠀⠀⣠⣠⡄⠀⠀⠀⢴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠄⠲⣶⠄
⠀⠀⣰⣓⣲⠀⢻⠈⢧⣼⣿⠀⢸⣏⠀⣻⠂⣴⡖⠚⠛⣿⠟⠳⢶⣶⡀⠀⢸⢿⣿⡅⠀⠀⠂⢀⣴⢭⣲⡚⠛⢛⣶
⠀⡘⣿⠈⠀⠀⠈⢧⣼⠿⢿⣤⡈⠉⠛⠉⠀⠀⠉⠉⠙⡿⢸⣿⠯⠟⢋⠀⠈⠙⠂⠀⠀⡟⢂⠺⠿⠧⠇⡟⠉⠉⣁⣄
⠸⠎⢛⣾⠀⠀⠀⠸⢳⣿⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣀⣀⣠⣬⣶⡆⠀⠀⠀⠀⠈⠀⢀⠀⠀⢔⠛⢟⠋⠙⠏⠄
⠀⠀⠈⠁⡶⣢⣤⣤⡀⠈⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⠸⠈⠻⠟⠋⠈⡿⢻⡶⠀⠀⠀⠀⣀⠀⠀⡀⠀⠘⠃⣇⢰⣿⡟
⠀⠀⠀⠸⣼⣿⡟⢿⣍⠛⠻⠇⠀⠀⠀⣴⢶⠀⣀⡀⢠⣀⡀⠀⣀⣀⣇⣸⠇⠀⠀⠀⠀⢿⣷⣔⠁⠺⠍⠶⠥⠭⠽⠁
⠀⠀⠀⠀⢻⣿⠇⢾⡿⢀⡀⢄⠀⠀⢸⠃⣸⣿⡿⠁⠘⠛⠋⠉⠛⠋⠙⠛⠀⣀⡀⠀⠀⢈⣹⣿⢦⣤⡶⠚⢋⣻⠃
⠀⠀⠀⠀⠈⠁⠈⠉⠁⠉⠁⠁⠀⢀⣦⣭⣍⠉⢀⠀⠀⣰⡾⣏⠷⣄⠀⢰⢤⡿⠁⡀⢀⣾⣿⢱⣶⡘⢿⠋⠉
⠀⠀⣠⡲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣫⢇⡀⠀⠀⢿⣭⢻⣹⡇⠀⠈⠡⣭⠆⠀⠈⢏⠩⠈⠉⢀⣐⣀⡀⢤
⠀⠘⠟⠋⢁⠀⠀⠀⠀⠀⢸⣷⡆⠔⣄⣀⣀⣘⠿⠋⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣞⢋⣿⢿⣿⣎⡀
⠀⠀⠀⠐⢫⣤⣺⡄⠀⠀⢶⣾⠑⣶⠈⠙⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣦⢄⠀⠀⠀⠀⠀⠀⢣⠀⠛⣿⣧⢸⣿⡿
⠀⠀⠀⠸⠯⢀⡀⠀⠀⠀⠘⡷⠿⡛⣤⠔⣿⠟⡄⠀⠀⠀⡨⢭⡆⠀⠛⠿⡷⠀⠀⡀⠀⠀⠓⠘⠓⠘⠓⠂⠘⠃
⠀⢠⢶⠀⢐⣓⣺⡀⢫⣇⣤⠀⠀⠉⠁⠈⠁⠀⠀⠀⡴⣬⠙⠟⠉⣤⡄⠀⠀⠀⢈⣷⡄⣀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠢⡄
⠀⣤⡾⢦⣤⠈⠁⠀⣜⡍⠛⠀⠀⢰⣶⣄⡀⠀⠸⡷⣾⠀⠀⣆⠄⢑⣧⣲⡄⠀⢠⣛⣻⠻⣾⡟⠁⠀⠀⠑⠔⣿⣿⢌
⠀⠈⠁⠈⠁⠀⠀⠀⠈⠀⠀⢿⣉⠉⢓⡦⠘⠄⠀⠀⠛⠃⠠⠂⠀⠺⠷⠀⢠⣶⡄⠀⠀⠘⠇⠀⢀⣾⡆⠀⠐⠄⠄⠁
⠀⠀⠀⠀⣀⠀⠀⣴⡾⣿⠟⠀⠈⠙⠣⣟⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡴⠛⡟⠀⠀⢸⣿⡇⢀⡤⠶⣦
⠀⣠⣾⣿⣿⡿⣛⡛⣿⣤⠀⠀⠀⠀⡀⠈⠉⠩⢄⡨⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⣿⡤⠞⠁⢀⠄⣾⠿⢿⣯⡤⠖⠁
⠀⠀⠉⠁⢘⠉⠿⠧⠼⢿⡇⠀⠀⠀⠻⣷⣶⣶⢆⠀⠀⠀⠀⠀⠀⡾⠻⠧⣿⣇⠽⡆⠀⠀⡌⣼⣿⣿⡶⠛⠂
⠀⠸⣷⣶⣶⡦⣀⣀⣀⠐⠁⠀⠀⢸⣤⡙⡟⣡⣴⠆⠀⠀⢀⢿⣦⣼⣍⣀⠀⣀⣠⠁⠀⠀⠱⠄⡂⢀⣀⣴⣤⣤⣻⠂
⠀⢲⣿⣿⠹⣷⡄⠉⠉⠄⠀⠀⠀⡐⡙⠛⠗⠛⠋⣆⠀⠀⠸⣾⠛⡏⠀⠙⠛⠿⢿⡄⠀⠀⠀⢸⠛⠉⢡⣾⢫⣿⣿⡜
⠀⠈⡿⠛⣘⣿⢓⣤⢘⠄⠀⠀⠀⣧⣅⢀⣀⢀⣠⣏⠀⠀⠀⢻⣀⣇⣀⡀⠀⢀⣠⠃⠀⠀⠀⢠⠢⣤⢸⣿⡘⠿⡿
⣀⣀⣠⣀⣄⣀⢀⡀⣀⠀⢀⡀⢀⡉⢉⡀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠉⠛⠋⠉⠛⠛⠀⠀⠀⠀⠀⢀⣠⣄⣀⡁⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠞⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢻⣇⣤⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢿⠷⣤⣴⡞⢿⣿⣿⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡿⢁⠀⣼⣿⣄⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡿⢿⣿⣟⣿⠃⠁⣀⠙⣿⣿⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠙⠉⠁⠈⢹⣿⡏⢀⣾⣿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠸⣿⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠺⣿⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⣝⡈⠋⣾⣷⡆⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢶⡈⠻⠟⣁⣼⣿⡟⠶⢤⣤⣤⡁⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⢿⣿⣿⡿⠿⠓⠀⠀⠀⠺⡿⠟⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠍⠥⠀⠀⠂⠀⢀⣀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠲⣆⣽⣿⣿⣿⣿⣧⠠⠈⠁⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠹⠛⢛⣙⣽⣧⣿⡽⣻⠿⠟⠂⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠿⠻⣿⠛⠏⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⣿⣮⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⢻⡏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠿⠃⢻⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⠀⠀⠀⢀⡎⣧⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠃⠀⠀⢸⡇⣿⡄⠀⠀⠀⢀⠔⠻⢡⡏⣤⠔⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⢄⢀⢸⠀⣿⡇⠀⠀⣴⠟⠀⢀⣾⢡⡏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠻⣿⠏⢠⣿⡇⠀⣼⣿⠂⠄⣸⣿⠟⢱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠴⠇⠰⠻⠿⠧⠼⠿⣶⣿⠀⠿⢣⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠐⠋⠀⠄⠲⠄⠀⠀⠉⢶⣡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢡⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠠⡁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡿⢿⠀⡀⠀⢀⡡⠀⠠⠀⡁⢀⠀⣆⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠓⠺⡷⠋⢠⡁⠰⣿⠋⢀⡼⠇⢁⣴⡄⠈⠂⠈⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠅⠀⠀⠤⠄⠀⣷⣤⣹⡀⠈⠀⠀⠀⡏⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠁⠀⠀⠀⠉⠋⠙⠛⠲⣤⣶⣜⣃⣤⣴⠞⡽⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠄⠀⠀⠀⠀⢿⡶⠀⠀⢀⠀⠀⠐⠋⠋⠉⠉⠄⠀⢁⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢢⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡘⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡟⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠂⣴⣿⣧⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡏⠀⣀⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠋⠈⠛⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⠀⣿⡟⠐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠁⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡄⢰⣿⠀⠀⢿⠠⡀⠼⠀⠀⢀⠀⠀⠀⢀⠈⠃⠠⢀⣾⠃⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⠀⠀⠀⠀⠁⣤⣤⠾⣿⣀⠀⠀⠁⠀⠀⠀⣿⡧⠀⠀⠀⠀⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⠡⠀⠀⠀⣸⣿⢏⣵⣿⣿⡇⠀⠀⠀⠀⢰⣿⠃⠀⣀⣀⡀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡭⠉⢻⡿⠀⠀⢀⠀⣿⣯⣈⡙⢉⡻⣿⠃⠀⠠⢠⣿⣿⡃⠀⢉⣉⠙⠛⠒⣄
⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣁⣼⣶⡔⣿⣷⠶⡤⠀⢀⣾⡿⠿⠿⢿⣷⣾⡄⢀⡄⢄⣿⣿⣷⣾⡟⠉⢧⠀⢀⢸⢆
⠢⠁⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⣺⣿⣤⣠⣤⣠⣾⠃⠀⠀⠀⠀⠀⠹⣷⣤⣥⠈⠫⠿⠄⠈⠛⠛⠛⠓⠛⠓⠛⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⢢⢀⡀⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢷⣝⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣫⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠙⢾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡵⠋⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠉⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⢀⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⢿⣿⣿⣇⣀⣴⣯⡀⣼⣿⣿⡟⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣼⣿⣿⡿⠟⠿⣿⡿⣿⣿⣿⣷⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⠿⣿⡇⠀⠀⠁⠀⢸⣿⠿⣻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡸⣿⡀⠀⠀⢠⣿⢣⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣿⣿⡇⠀⠀⢹⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠅⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠋⠀⣤⣀⣀⡤⠀⠙⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⢙⠋⠀⠀⣰⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠿⠿⠶⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣄⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⠆⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣷⡀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡴⠋⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⠀⠈⢿⡄⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣴⠋⡠⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠐⢾⣷⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣾⣟⡮⠑⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠲⣿⣇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⣾⣿⡫⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠐⢻⣿⣧⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣸⣿⡿⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠈⠻⢿⡆⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠿⠃⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠘⣻⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠐⠁⡾⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠻⣿⡆⠸⣿⣀⣀⣀⣤⣤⣾⡿⠃⠀⠴⠃⣰⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⢿⣦⠀⠀⣸⡇⠀⣿⡏⠉⠉⠉⢹⣿⠐⠀⢀⡴⣿⣇⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⣿⣿⣿⡀⢘⣧⠀⠹⡇⠀⠀⠀⠾⠃⠀⠀⡏⠠⣿⣇⡀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⣿⣿⠀⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠔⠛⢿⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠄⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠀⠀⠀⢻⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠠⡖⢶⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⣜⢳⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢠⣝⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⠃⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⢬⡻⢿⣇⡠⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣯⡁⠄⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢹⣿⠃⠀⠀⠀⠀⠉⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⣿⡇⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⣿⡇⠀⠹⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢻⣿⡇⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢰⣿⣧⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡄⠀⠀⢀⣬⣿⣿⣶⡖⢒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠈⢻⣿⣿⣏⣉⣡⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⣿⣁⠀⠈⠁⣠⡼⠿⠻⣿⣿⣿⣇⡀⠀⠀⠘⠷⣦⣠⡾⠟⠀⠀⠀⣰⣿⣽⣿⡿⠻⠧⠞⠩⣤⠞⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢸⣿⠀⠒⠉⠀⣠⡴⠋⣡⠔⠋⠻⣿⣧⣤⣤⣀⣀⣿⣄⣀⣠⣴⡾⢿⡿⠟⠉⠈⠁⠒⢌⠑⠄⠈⠁⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⣀⡄⠈⠃⠀⢠⠞⢁⣤⠞⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠟⠋⠉⠁⠀⡀⠀⠐⢆⠈⢦⠀⠀⠈⠂⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣆⠿⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡷⠅⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠀⠀⠀⠀⠀⠀⢰⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠘⢇⣿⣇⢰⡄⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠃⠀⠀⠀⠀⠀⠀⣠⣾⡇⢠⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢶⠏⠀⠀⠀⠀⠀⣠⣷⣿⠋⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠈⢿⣿⣿⡐⣦⠀⠀⠀⠀⠀⠀⠙⢿⡷⣀⠀⠀⠀⠀⠀⠀⢀⣰⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢻⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⣧⣄⣠⣦⣴⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠁⠀⠀⠠⠀⠀⠀⠀⠀⢠⣿⡾⠃⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣠⣆⠀⠀⠀⢙⣿⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⢻⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣠⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣶⢿⣿⣿⣿⣿⢠⣶⠄⠀⠀⠠⠠⠆⢸⣿⣿⡟⠁⠀⣤⠄⠀⠀⣤⠄⣠⣿⣉⠀⢉⡾⠟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠀⠁⣾⣿⠃⠀⠁⠀⠀⠀⣀⠀⠀⠈⣿⡿⠀⠀⠀⡀⠀⠀⠀⠁⠀⠉⣿⡏⠀⠈⠀⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢾⢻⣿⠀⠀⠀⣗⠀⠀⠙⠀⠀⠀⢿⡇⠀⠀⢰⠃⠀⠀⡾⠀⠀⢠⣿⢁⣎⣀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠿⠿⠿⠿⠶⠾⠿⠿⠷⠿⠿⠶⠶⠿⠿⠿⠿⠿⠷⠶⠿⠿⠶⠾⠿⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠄⠂⠀⢂⠀⠀⡥⠐⠂⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠊⠀⠀⠀⢸⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠃⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠄⣀⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁
⠀⠂⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠁
⣬⣤⡀⠀⠀⠀⠀⠸⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠒⠂⠤⣀
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢄⡀
⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠉⠒⠠⠤⠄⠀⠀⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠁⢣⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠊⠀⡠⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠂⠐⠉
⠀⠀⠀⠀⠀⠀⢆⠀⡁⠀⠀⠀⠀⠀⠀⡠⠋⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣂⣤⣤⣤⣤⣊⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣂⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣶⣶⣦⣤⣀⣤⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣌⣉⣉⠙⠓⠂⣀⣉⣉⣽⣿⣿⣿⣿⣿⣾⣷⣾⣿⠋⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠃⠐⡻⠿⠶
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⡏
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣯⣿⣽⢀⣽⡞⣿⣿⠿⠙⣻⡟⣿⣿⣿⣿⣿⣿⣿⣟⠀⣰⠃
⠀⠀⠀⢀⣿⣿⣿⣿⡟⠩⣷⣾⣿⢿⣳⣾⣿⣿⣿⡏⠒⠣⠀⠁⣿⣿⣷⣭⣠⣜⢹⡗⣠⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣡⣹⣷⣷⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⢸⣿⣿⣿⣟⡿⣾⣿⠃
⣀⠛⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣘⣧⠿⠻⣿⣿⡿⠋
⢹⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣠⠤⠞⠛⠻⣿⣿⣶⣍⣻⣧
⠀⢷⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣾⡶⣾⣷⣦⣤⣀⠀⠈⢿⣷⣀⣿⣿⣷⣄⣀⣀
⠀⠀⠿⠿⠿⠿⠿⠏⠻⠿⠿⠿⠿⠿⠿⠶⠶⠾⠞⠛⠛⠛⠛⠿⠿⠿⠶⠿⢿⠿⢭⡷⠯⣭⣽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⠂⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⠔⡡⠋⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣰⠃⢠⠃⠀⠂⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⠐⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡸⠃⠀⢈⠀⠈⠀⠜
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢀⠀⠀⠂⠀⠈⠀⠀⠊
⠀⠀⠀⠀⠀⡔⠉⠀⠠⢒⣒⠃⢀⠐⠀⠀⠰
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠙⠶⠂⠠⠀⠀⢙⠄⠐⣂⣀⡀⠀⠀⠤⠀⠀⠒⠂⠤⠤⠄⠄⢀⡀
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⢻⠒⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠈⠤⡒⠤⣄⣀⣼⡀⡀⠠⠐⠁⠀⡠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠈⠉⠉⠉⠉⠁⠢⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠐⠐⡄⢄⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣀⠀⠈⢀⠀⠀⠄⢀⠖⠂⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣡⠖⠒⠲⢄⠀⠀⠀⡸⠶⠖⠶⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣫⢭⠀⢀⠀⠀⠔⠲⠃⠀⠀⢠⠄⠑⢄⡎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠠⢤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠀⠑⠲⠜⠃⠤⠤⠖⠀⠒⠒⠒⠈⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⢀⣀⣀⣀⣀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠔⠚⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠲⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠳⣄
⢳⡀⠀⠀⠀⠀⠀⣠⠴⠋⢸⠀⠀⠀⠀⠀⢠⡾⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⣆⠀⠀⠀⠀⠀⣿⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀
⠀⠙⠒⠲⠒⠒⠋⠁⠀⠀⡏⠀⠀⠀⠀⢀⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠉⠛⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁⠁⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡇⠀⠠⡇⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡠⠖⠒⠲⢬⡓⠦⣄⣀⡴⠃⠀⠀⠳⣀⣀⡤⠔⣫⠴⠒⠒⢤⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡞⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠙⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⠀⢀⣀⣤⢧⣤⣤⣤⣤⣤⣤⢧⣀⠀⠀⠀⠀⢀⣠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠠⠂⠐⠄⠀⢈⡤⠐⠈⠉⠉⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠊⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⠃⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠐⠐⠦⠄⡆⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⣶⣶⠆⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠑⠤⠀⡀
⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⣀
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠑⡄⠀⠀⠀⠀⠄⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⡠⠒⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢈⠀⠀⠀⠀⠀⠀⢀⠊⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣀⣀⣀⣀⣂⣁⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⣀⡀⠀⠀⠀⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣀⠀⠀⣠⡄
⠀⠀⠀⠀⠱⠕⠃⠀⠀⠀⢆⡼⠁⠃⠀⠀⠀⠠⠡⠁⠐⢀⣀⠤⡠⠀⠀⢬⡳⣀⢇⠇⠀⠀⣖⢆⣸⣿
⠀⠀⠠⠤⡄⠠⠒⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠙⠟⠂⠈⠀⡈⠜⠀⠈⠙⠄⠀⢀⠜⠛⠓⠇
⠀⠀⠈⠲⣈⡶⡤⡁⠀⠀⡀⢸⢓⠀⠀⠀⠀⠀⠔⠀⠠⡄⠀⠀⠀⠀⢀⠆⠀⠀⠠⡂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠤⠀⢸⣄⠀⠀⠂⠶⠄⠁⠀⠀⠀⠀⠸⢄⣀⠀⠘⠀⠀⠘⡀⠀⠀⠎
⠀⠀⠀⠈⠀⠀⠖⠀⡀⠀⠀⠀⠘⣧⠀⣟⠀⠀⠀⡀⢤⢀⢠⡀⣀⡄⢀⠀⢀⠀⠀⠀⠀⠀⠢⠤⠦⠞
⠀⠀⠀⠈⠂⠀⠰⠀⠈⠀⠀⠀⠀⣿⠀⠀⣷⠿⠷⠁⡸⠈⠸⠏⠡⡇⠘⠚⠿⠃⠀⡀⠀⠀⢠⣄⠀⡔⡢
⠀⠐⣄⡀⡤⠀⡀⠀⠀⠀⠀⠀⠀⣿⣄⣰⠟⣼⠃⢸⠁⠀⢠⡐⠘⠁⠀⣼⠀⠀⠀⠌⠔⠀⠹⡨⠷⠤⡅
⠀⢠⢎⣹⠀⠀⠐⠂⠀⠀⠀⢤⡄⠀⠈⡁⠀⢿⠀⢿⡘⠗⡗⠃⠿⢆⡆⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠈⣴⣂⣴⢛⡞⠀⠈⠁⠀⠀⠀⠁⠄⠀⠀⠁⠈⠀⢦⠲⣼⣩⠀⠐⢤⡶⠄⢲⡀
⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠰⠁⠁⠈⠫⠠⢶⠀⠀⢀⠀⠀⢀⡔⢅⠀⠀⠀⠀⠀⠕⠋⠋⢂⠀⠘⠀⠂⠀⠁
⠀⠀⠀⡎⠲⣲⠀⠀⠀⠀⡥⠀⠀⠀⢠⠀⠀⠀⠀⠛⠿⠂⠙⠰⠁⡀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠁⠸⠴⠀⠀⠀⢔⣁⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠁⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠈⠀⠀⠀⠀⠈⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠤⣤⠤⢤⣞⠋⢈⠋⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣿⠍⣿⢿⣿⡋⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⣥⣿⣿⡯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠿⠛⠉⠉⠉⠉⠉⢻⣿⣷⢺⠏⡟⠛⢏⠛⠆⣴⡿⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⢂⣒⣻⣴⡶⣷⣶⣲⣶⣄⠀⠠⡿⠐⣿⠀⠀⠀⠀⢀⢘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣀⣼⣿⣿⢣⣴⣿⣿⣿⣿⣿⠀⢰⣹⡆⠟⠀⠀⢠⣞⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⣤⣯⣿⠿⣿⣴⣿⣿⣿⣿⣿⣿⣤⣼⣿⡇⠀⢀⣴⡏⠃
⠀⠀⠀⠀⠀⠚⢿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⠃⠀⠘⣿
⠀⠀⠀⠀⠀⠄⠈⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⠀⠈⢻⣦⣀⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡏⣍⣽⣿⣿⡯⠁⠀⠀⠉⠈⠀⠀⠘⢧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⣤⡀⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⢀⡀⠀⢀⣤⡀
⠀⠀⠀⠀⠐⢬⠔⠁⠀⠀⠈⣄⣼⣃⡞⠀⠀⠀⠐⢔⡹⠀⠆⢀⢁⣀⡤⡀⠀⢵⡻⣄⣸⣻⠃⠀⢠⡲⣄⣰⢷⠀⠈⠔
⠀⠀⠀⣠⣀⠀⡠⣤⠀⠀⢀⠋⠀⠀⠐⡄⠀⠀⠀⢀⠔⠁⠀⠻⡮⠴⠓⠀⠐⠠⠋⠈⠙⢋⠀⠀⠀⡻⠿⠯⡏
⠀⠀⠀⢦⡘⢦⣅⢸⠀⠀⠈⡄⢰⢶⠀⠇⠀⠀⠀⢐⣄⠀⢀⠔⠀⠀⠀⠀⠁⣃⠀⠀⠀⢠⠀⠀⡎⠀⠀⠀⠈⡄
⠀⠀⠀⢀⠏⠋⠉⠉⢀⠀⠀⡅⠈⢜⠀⢸⠆⠀⠀⢈⢀⣄⢈⠆⠀⠀⠀⠀⢈⡆⠀⠀⠀⡜⠀⠀⢣⠀⠀⠀⠴⠁
⠀⠀⠀⠐⡄⠀⢀⡀⠨⠀⠀⠈⠁⠩⣄⠐⢿⠆⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠉⠒⠒⠊⠀⠀⠀⠘⡀⠀⡀⣱
⠀⠀⠀⠀⣅⠀⠈⢁⠀⠆⠀⠀⠀⠀⣿⡄⠚⢤⣠⣠⣰⠎⡇⠶⢸⡶⠆⡧⢰⣿⣦⣶⠀⠀⠀⠀⠀⠙⠋⠉⢉⣀
⠀⠀⢀⡀⠈⠉⠀⠁⠀⠀⢀⠤⠄⠀⣿⡇⠀⣼⡟⣫⠅⣠⠇⠀⠈⢁⢈⡇⠀⢉⡍⠋⠀⠠⢄⡀⠀⣞⢳⣀⠏⣹
⠀⠈⢬⣤⠞⠂⠀⢀⠀⠀⠀⠈⠀⠀⠿⢹⣴⠟⢸⡇⠀⡟⢠⠀⡰⡌⣈⡀⣀⢸⠁⠀⠀⠘⠂⠁⠀⢘⠖⠋⠊⠢
⠀⠰⠯⠤⠃⠀⠀⡉⠣⢀⠀⢠⢶⣆⠀⢀⢤⡀⠸⣇⡀⠧⠘⢻⡟⠁⠛⠃⡏⢿⡔⠀⡀⠀⣠⣄⠀⠈⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠢⢀⠀⠀⢀⠅⠀⠘⣾⣫⣴⢋⡷⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⣎⢳⣷⣸⠀⠐⢲⡞⠆⠘⣄
⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⡔⠁⠀⠈⠙⡀⠾⠆⠀⡠⣀⠀⠀⢠⡦⢍⠀⠀⠀⠀⠀⠨⠋⠉⠉⢆⠀⠚⠒⠒⠐⠁
⠀⠀⠀⢞⠲⢖⡆⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⠘⠻⡗⠒⠙⢾⢁⡀⠀⠀⠀⠀⡇⠀⠀⠀⢘⠀⠀⠀⡠⢄
⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀⠀⢃⠀⠀⠀⢰⡃⠀⠀⠀⠀⢰⠀⠀⠀⠘⠀⠈⣄⠀⠀⠀⡘⠠⢮⢷⠉⠀⠀⢔⢛⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠰⠋⠀⠀⠀⠀⠀⠘⠕⠒⠦⠀⠀⠐⠉⠀⠀⠀⠈⠐⠃⠒⠀⠀⠀⠀⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡂⢀
⠀⠀⠀⠧⠈⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⡇⠈⢀⡟
⠀⠀⠀⠀⠈⢿⢦⡉⠓⢦⡀⠀⠀⠀⠀⣰⠋⢰⡿⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠈⢧⠻⡄⠀⠙⠆⠀⠀⠰⠃⠀⣿⣧⠎⡸⠃
⠀⠀⠀⠀⠀⠀⠈⢷⣹⡆⠀⠀⠙⠂⠀⢀⠀⢋⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣄⢃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠈⢋⡄⠀⠀⠀⠀⣄⠀⣻⠿⠟⠛⠛⠋⠉⠉⠀⠈⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠄⡞⠀⠀⠀⠀⠀⠘⣷⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠸⠇⠀⠀⠳⠌⠋⠀⠘⣐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣀⠄⠀⠀⣀⣀⠀⢰⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠁⠛⠀⠙⠋⠁⠉⠙⠉⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⡈⢧⣤⠀⡀⠀⣤⣾⠈⠀⠀⠀⣀⠀⠈⠉⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣽⣿⡟
⠀⠀⠀⠀⠀⢀⣠⡾⠂⠀⠀⣠⡟⠁⠁⣤⠋⠀⠀⠀⣠⣾⠇⠀⠀⠀⢀⣠⣤⡾⠧⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀
⠀⠀⠀⠀⢠⣾⡁⢀⣀⣤⣾⠏⠀⢀⡴⠿⠄⠀⢀⣼⣿⣷⣶⣶⣤⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣧⣤⣄⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠸⠶⠤⠤⠶⠿⠿⠃⠀⠀⠀⠘⠛⠓⠒⠒⠒⠒⠒⠓⠛⠛⠂⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠿⠿⠿⠿⠶⣶⣶⣶⣶⠶⠶⠶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠿⢿⣶⣶⡿⠛⠉⠀⠀⢠⣶⣷⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⡉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣄⣀⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠛⠉⠙⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⣀⣤⣶⠾⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⣠⣾⠛⠉⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⣠⣿⠟⠀⢀⣼⠟⠀⠀⢀⣴⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⣰⣿⠃⠀⢀⣾⡏⠀⠀⢠⣿⠋⢀⣿⠃⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⣰⡿⠃⠀⠀⣼⡿⠀⠀⢀⣿⠃⠀⣸⡏⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠁
⠀⠀⢠⣿⠃⠀⠀⢠⣿⠃⠀⠀⣼⠇⠀⠀⣿⠁⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣆
⠀⠀⣾⠇⠀⠀⠀⣸⡿⠀⠀⠀⣿⠀⠀⢀⡿⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⣸⡟⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⣿⠃⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⣼⠃⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⢸⡿⠀⠀⠀⠀⢸⣿⠁⠀⠀⣿⠀⠀⢠⡟⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣸⡇⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿⠀⠀⣾⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸⡿⠀⣼⠇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣼⣧⣾⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⣿⡇⠀⠀⠀⠀⢸⡿⠀⢠⣿⠏⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡇
⣿⣇⠀⠀⠀⠀⠸⠃⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⣧
⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢸⣿
⠈⣿⡆⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢸⣿
⠀⠹⣿⣄⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⡄⣼⡇⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⡇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢸⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⣸⣿⣶⠀⠀⠸⣷⡀⠀⣀⠀⢠⡄⣼⡿⣿⣠⡇⠀⢀⡗⢀⣿⠏⠀⠀⠀⠀⠘⣿⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠠⠟⢿⡇⠀⠀⠀⠹⢷⣤⣿⣀⣾⣿⠟⠁⠈⠻⢿⣶⣿⡷⠿⠋⠀⠀⠀⠀⢰⣿⣿⡆⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⣿⢁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣼⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢁⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠷⠶⣶⣾⣆⣀⣀⣠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⣼⣿⢁⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⣿⠟⠛⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣀⣀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⡿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⣸⣿⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣤⣴⣿⣿⣤⣴⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣧⡤⠤⠤⠤⠤⠤⠤⣤⣏⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀
⢧⠀⠀⠀⠀⠀⠀⣠⠞⢹⠀⠀⠀⠀⠀⣠⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣦⠀⠀⠀⠀⠀⡇⠀⠙⢦⣀
⠈⠑⠲⠶⠒⠒⠉⠀⠀⡼⠀⠀⠀⠀⢰⣿⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣾⣧⠀⠀⠀⠀⢻⠀⠀⠀⠈⠙⠒⠶⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠘⠿⠿⠿⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠻⢿⠿⠟⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣹⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠋⠉⠉⠀⠐⠒⠛⠓⠚⠛⠓⠂⠈⠉⠉⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢇⠀⠀⠀⠀⠀⢰⠀⢸⡃⠀⠀⠀⠀⢀⠆⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⠤⠤⢤⡑⠤⣀⠀⣀⠇⠀⠈⢇⠀⢀⣀⠔⣣⠤⠤⢄⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡔⠁⠀⠀⠀⠙⢆⠀⠈⠀⠀⠀⠀⠀⠉⠁⢀⠞⠁⠀⠀⠀⠙⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠁⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣀⣀⣀⡠⠴⠷⠶⠶⠶⠶⠶⠶⠦⠄⣀⣀⣀⡀⠤⠚⠁

⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⣿⣷⣦⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⣧⠀⠀⢸⡟⢹⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣇⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⡆⠀⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣇⢰⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣘⣧⠀⣿⣸⠀⣠⣏
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠰⠶⠿⠇⠀⡀⠀⠀⠐⢿⠶⠶⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣀
⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣿⡟⠀⣀
⠀⠀⠘⣿⡋⢷⡀⠀⠀⠀⠀⢀⡼⠃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣸⣧⢿⣿⢱⡇⣿⣷⣦
⠀⠀⠀⠈⢷⡀⢳⡀⠀⠀⠀⡾⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢸⣿⡆⠀⣿⡇⢀⣠⣾
⠀⠀⠀⠀⠀⠙⣼⠷⠖⠲⠾⢧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣇⢸⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⠘⠄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣴⠀⡀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⢱⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢿⣿⣡⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⠿⣯⣭⣍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣄⠣⣭⡼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⣤⡀
⠀⠀⠀⠀⠈⣀⠀⢦⠀⠀⠀⠀⡢⠀⠀⠀⢠⠏⣁⣤⠀⠀⠠⠀⠀⠀⡀⣀⣀⣀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⡸⠃
⠀⠀⠀⠃⠀⠈⠀⡀⠀⠀⡄⠀⠱⠀⠀⠀⠈⠈⠁⢀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⡁⠀⠀⡠⢃⣤⣤⢄⣬⣽⣿⣿⣿⣿⠿⠿⠗⠪⠌⠛⣶⢲⢶⣶⣬⠙⢿⣟⡏⠀⠩⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⢠⠀⠀⠀⠄⠈⡀⠰⠃⠀⡴⠓⠋⠉⢡⣿⣿⣿⣿⣿⡯⠵⠼⠻⢿⡖⠄⠀⠒⣦⣿⣿⣿⣷⠀⣿⠀⠀⢀⠀⡤⠀⠀⠀⠀⠠⠁⠀⠀⠄⢀⡤⠶⠖
⠀⠀⠀⠀⠀⡀⠰⠀⢣⠀⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣗⣾⣷⣀⠀⡟⡍⠀⠀⠀⡇⡈⣩⣿⡿⠀⡏⠀⠀⡌⠘⣠⠞⠁⠀⢤⣤⡀⠀⡖⠒⠲⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠆⠈⢧⠀⠘⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⡂⣠⣶⢡⢾⣷⣿⡹⠃⡼⢀⡠⠊⠀⠀⠁⣀⣤⠔⠀⠀⢁⠘⠀⠀⠴⢀⡠⠆⠂
⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⢣⠀⠱⡀⢠⣿⣿⣿⣿⡿⠟⠉⣁⣀⠈⠙⢿⣿⣿⠋⠮⠪⠞⠟⠁⣠⣯⠞⠁⡠⠂⠀⠎⣁⠄⠀⢀⡠⠊⠀⢀⡴⠂⠈
⠀⠀⠀⠈⠀⠀⠀⠁⠢⠀⢸⠀⠀⠃⣰⣿⣿⡿⢋⣠⣤⣾⣿⣿⣷⡄⠈⣿⣵⣦⣤⠂⠀⠀⢰⣿⠁⠀⠰⠀⣠⠄⢚⣡⠴⠚⠥⠤⠀⠀⠀⠀⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠆⠠⠚⡋⢹⠺⣶⡄⣿⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣧⠀⠀⠀⣼⣿⠀⠀⢠⠌⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⣼⣿⡿⡟⠛⢻⡿⣿⣿⠃⣼⣿⣿⣿⣿⡀⠀⠀⣿⡿⠀⠠⠁⠀⠈⢁⣤⠀⠈⠢⢄⠀⠤⣦⣠⠆⠤
⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⣿⣿⣿⢿⢻⠁⠀⠀⠆⠀⡸⡻⠏⣸⣿⣿⣿⠟⢸⡇⠀⠀⣿⠟⠀⠆⠠⠄⠒⢶⣐⢦⣤⠀⠀⠑⠤⠀⠄⠠⠤⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠉⠀⡀⠠⠘⠁⠀⠀⠉⠀⢠⣿⣿⡿⠋⠀⠈⢇⠀⠀⢫⢠⠀⠀⠀⠀⠀⠈⠙⠆⠈⠑⠒⠀⠀⠓⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠛⡀⠲⣿⣤⣶⣾⣿⠀⠀⢀⣾⣿⣯⣽⡿⠷⠟⠻⡆⠀⠈⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣷⣷⣽⣶⣿⣿⣿⣿⠯⠐⠀⣼⣿⣿⣿⣶⡶⠦⠶⠟⠫⡀⠀⠈⠐⠐⢂⣸⣶⣾⣶⣦⣶⣶⡀⢀
⠀⠀⠀⠀⠀⠐⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⣤⣠⠷⢸⣿⢿⡿⠿⣿⠟⠛⠃⠋⠺⡷⠖⡴
⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠛⠛⠈⠋⠻⠿⢿⣿⡿⢦⠴⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣦⣤⣀⡀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣭⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣟⠿⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⡽⣿⡿⠛⣫⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦⣤⣤⣤⣤⣄⣈⣉⡉⠉⠉⠛⠒⠒⠂⠂⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠏⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣉⣩⣿⣿⣿⣤⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣠⡞⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⢉⣿⣞⣿⣿⣿⣿⡿⠻⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⣸⠁
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣹⣽⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⢏⣵⡤⠛⢿⡸⣿⣿⣿⣟⡿⣿⣙⢻⢻⣿⣿⠀⣼⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣩⠛⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠷⢟⠈⢻⡀⠀⠱⢿⣿⣿⣿⣿⣿⣾⣷⢸⣿⣧⡶⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠆⠂⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣟⡿⢺⣿⣿⠇
⠀⠴⢶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠈⠄⠀⠀⠸⣿⣹⣿⣿⣿⣿⣷⣿⣿⠏
⢸⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠑⠠⢈⣤⣶⣿⣿⣿⣁⠈⡻⣿⣿⣟⠁
⠸⣇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⢀⣨⡷⠖⠋⠉⠉⠙⢿⣿⣿⡿⣷⢤⣻⣿⣆
⠀⢻⣷⣄⠉⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⣷⣶⣾⣧⣤⣤⣀⣀⠀⠀⠀⢻⣿⣿⡌⠐⣿⣿⣿⣧⡀
⠀⠀⠛⣻⣿⣶⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣤⣭⣍⣭⣍⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣙⣿⣿⣿⡿⠿⢿⣟⡿⠶⠾⢿⣶⡄