⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡃⢰⣸⢰⣿⣥⡄⢿⠠⠀⠠⠏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣥⣿⣼⢈⣿⡇⣇⢸⠈⣆⠀⢲⠉⠽⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠀⠀⠀⠀⠀⠀⠀⢠⢰⠂⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⢸⣿⡟⢹⠈⡆⠈⡆⠈⠀⠈⢗⠔⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠃⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⢸⡻⡟⢽⣸⠟⡇⠃⡀⠀⠀⢐⡀⡀⠀⠀⠘⠤⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠘⠃⠀⠁⠈⠁⠀⠀⠀⢖⠐⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿
⡘⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⠀⠁⠃⠈⠀⠀⠂⠀⠀⠀⠅⠐⠄⠀⠀⠀⠀⠈⠀⠙⢦⡄⠀⠘⣵⠵⡀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠋⣴⣿
⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠧⠣⠀⠀⠀⠀⠀⠀⠀⢸⣧⡠⠀⠀⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠃⠀⠀⠐⠔⠄⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢸⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠄⠀⠀⢁⡂⠀⠐⢀⠀⠀⠀⠀⠲⠨⡀⠀⠀⠀⡦⡐⡀⠒⠒⢔⡶⢔⡂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠩⠄⠀⢸⣿⣿
⠃⢰⡃⠨⠀⠀⠀⠀⠈⠀⠃⠉⠁⠉⠀⠀⠀⠀⠈⠉⠩⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢣⠀⠀⠀⢸⣿⣿
⡄⠈⠁⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣂⣶⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⢸⣿⣿
⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢥⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠒⣢⠀⠄⠀⠨⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⠛⠛⠻⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⢿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⣾⣷⢄⣤⠉⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠻⠫⠉⠉⡑⠉⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣶⣿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠅⠁⠉⠐⠚⠰⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⢰⣿⣿⣿⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⢸⣿⣿⣿⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠈⠧⢀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣷⣶⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠟⠉⠹⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠣⠀⠀⠀⠛⠷⣤⣀⠀⠀⠀⠈⠹⠿⠿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠁⠀⠀⠀⠀⠈⠻⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⢸⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⣄⡀⠀⠀⠀⠀⠀⢀⣤⣴⡿⠟⠋⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⢨⠃⠈⠀⠀⠀⠈⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣾⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢸⡇⢘⠀⠀⠀⠀⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡇⠀⠀⠀⠀⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢘⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⢸⡏⡿⣿
⠿⠑⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢷⡀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⢇⠃⠀
⠀⠀⠀⠀⠀⢘⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡻⠀⠀⡽⠿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⣄⠀⣠⣥⡅⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠞⡇⠀⠀