⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⡂⠀⠀⠒⠢⢀⠈⠢⠀⠴⠉⠀⢀⡠⢆⡒⠐⠀⠂⠀⠀⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢁⠌⠐⡠⠉⡉⡁⠄⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⣈⠂⠄⠀⠀⢕⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⠂⠠⠃⡤⠊⡠⠊⠀⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡔⡀⠀⠀⢇⢀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠞⡠⠀⠀⠀⠄⡠⠂⠔⠀⠀⠀⢀⠜⣀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠠⡀⠠⠈⠀⠢⠘⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⡴⠡⡐⢀⠀⠀⠨⡊⢀⠂⠀⠀⠀⠀⡠⠰⠈⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⡀⠀⠀⢓⠀⠄⡃⠀⠠⠘⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡸⠁⢠⠀⠊⠀⠠⡁⠠⠀⠀⠀⠀⢀⠈⠁⠂⠁⠀⠀⠀⡀⠀⠆⠀⢰⢠⠡⠡⣄⠀⠠⡀⠀⡀⡠⡘⠀⠀⠀⢁⠘⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡰⠁⠀⠂⠰⢀⢀⠎⠐⡁⠀⠀⠀⡐⠆⡘⠀⠂⡆⢀⠀⠀⠁⠀⠀⠀⠀⣂⠫⠐⠃⡀⠀⡠⡀⠀⣠⠀⠀⠀⢀⠌⠦⠘⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢰⠁⠄⠁⠀⠃⠀⠼⠀⡰⠀⢠⠀⠠⡌⠀⠁⢠⠀⠀⠨⠄⠀⠀⠀⠐⠀⠀⠜⠀⢢⠉⣩⠄⠐⠁⠀⢹⠀⠈⠀⠀⠆⠢⠀⢼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠠⠃⠈⠐⠀⠠⡜⠀⠆⢀⡁⠈⢀⠃⠰⠁⢾⠀⢸⠀⡀⠀⠀⠀⠘⠀⠀⠀⡄⡄⠁⡀⢁⠀⢆⠈⡄⢂⠀⡀⠀⠀⠀⠀⠠⠀⠀⠧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡴⠁⠀⠀⠀⠀⠁⡈⠄⠀⠀⠀⠈⠀⢃⡌⠈⢠⠀⠀⠃⠀⠀⠀⢠⠀⠀⡄⢡⡆⠁⠀⠄⢂⠘⡆⢁⠄⠀⠰⡀⠌⠀⠀⠄⠀⠀⠘⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢘⡄⠀⠀⠀⠰⠀⠀⠀⢀⠂⠰⡐⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠃⡄⠄⠐⠀⠰⠠⠘⣈⢡⢀⠀⠄⠀⠀⠀⡆⠀⠀⢇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠂⠀⠐⠂⠀⠀⠸⡄⢀⠠⠄⣄⡂⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢂⡀⢃⡗⠀⠀⠐⠀⢱⠀⠁⡂⠘⢰⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⡀⠀⠀⠀⡆⠀⠀⡇⢂⡁⢀⡎⡀⠁⠈⠀⠀⠀⢇⠁⡄⠀⠀⠀⠀⠀⠐⡀⠰⢜⡸⠀⠀⠀⠀⢀⢀⣀⢢⠐⡂⠃⠀⠀⢰⠀⠇⠀⢂⠨⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⡜⠀⠀⠀⣠⢀⠾⠐⠗⠁⡖⡑⠴⠀⠇⡆⠀⠀⠀⠈⠇⢆⠀⡀⠀⠀⠐⠀⠡⠃⠇⠳⡉⠛⠉⠉⠀⠀⡾⠄⢶⠉⠂⠀⠀⢸⠀⡆⢄⢀⢨⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠇⢤⡪⢥⠊⢁⡠⠠⢦⠊⠀⣸⠀⠀⣃⣇⣠⣄⣄⣠⠜⡔⢆⢀⠀⠀⠀⢆⠀⢆⡰⠀⠙⢄⣀⣠⣤⣤⣧⠀⡞⢰⠀⠀⠀⠸⠀⠠⠐⡪⢸⠀⠀
⠀⠀⠀⢀⣀⢀⠂⠌⢰⠈⠁⡀⠠⠚⠁⢀⣴⠈⡇⢀⣁⣧⣿⣿⢿⡿⢿⣿⣿⣯⣥⠀⠹⢠⠀⠀⠘⡀⠀⠇⣠⡿⣿⢿⠿⣿⣟⠿⣿⡇⡆⠀⠀⠀⠐⠀⢸⡀⠱⠇⠀
⠀⡀⠀⠁⠘⠣⡀⠠⠘⢑⡁⠀⡀⠔⠈⠁⠫⠄⢃⠸⣼⣿⡇⠠⣾⣷⢿⠝⢿⡞⠈⠆⠀⡾⢀⠀⠀⠕⡀⠈⡀⠀⣿⠧⠿⠚⣿⠐⣨⢁⠀⠀⠀⠀⠈⠀⠘⠡⡘⡀⠀
⠀⠀⠀⠀⠀⠠⠈⠢⢀⣀⡖⠈⠐⠀⠀⠀⠀⢎⠀⣒⠀⠉⠃⠀⠹⣇⣂⣀⡸⠀⠀⠈⠂⠁⠀⠈⠀⠚⠐⠀⠾⠄⠑⣅⣀⣰⠃⠐⢰⠸⠀⠀⠀⠀⠀⠀⠀⢰⢣⠧⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⡕⠀⢀⢨⠀⠀⠀⡡⠈⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢆⠀⠀⠀⠀⠀⠀⢸⠊⢠⡰⠀⠀
⠀⠀⠀⠀⢀⠔⠁⡡⡜⠒⠉⠘⠄⡨⠀⠖⠀⠀⠈⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠀⠀⠀⠀⠀⠀⠈⡶⠑⠀⠆⠀
⠀⢀⠀⡔⢡⠄⠊⠁⢏⠢⢄⠀⡰⣹⠄⠎⢊⣄⠀⠘⠄⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢸⠀⠀⠀⠆⣄⠀⠀⢧⠀⠀⢰⠀
⢠⣀⠁⠔⠉⠀⠀⠀⠈⠀⠀⠐⠡⡗⠈⠌⡀⠀⡏⢀⠙⡖⠚⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠈⠀⠀⢠⠀⠸⣠⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠡⣰⢃⢿⠵⠠⢄⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⠀⢦⠀⠀⠸⠀⡆⠏⠀⡌⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⠀⣡⠇⡘⢠⠂⠞⠀⢨⣢⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⡌⠀⠰⠀⠀⠀⠀⡇⢠⠇⠁⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠡⠀⠀⠳⢀⡆⠞⠀⠀⠇⣜⠠⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠈⠀⠀⠀⠀⠀⠀⣠⠞⠑⡈⠇⢀⡀⠀⠀⠃⢰⠁⠸⠀⢈⠀⢂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⢀⠎⠛⢸⢠⠆⡘⠀⢰⠏⠣⣐⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣎⠌⢀⠔⢓⠀⡄⡇⠀⠀⠀⢼⠀⠀⡇⠄⡀⠀⡜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠁⠄⢨⠀⡘⠉⢰⡇⠀⢸⠀⠀⠈⠑⢦⣼⢈⢁⠢⢄⡀⠀⠀⠀⠀⣀⠠⠊⠁⢠⣗⠀⠁⠘⣏⠀⠇⠁⠀⠀⡄⡎⠀⠀⠇⡆⠃⠀⠃⠀
⢀⠤⠒⠒⠒⠲⣄⠀⠀⠄⠀⠘⡈⠀⡆⢀⠃⡄⠀⡆⠁⠸⠀⠀⠀⣴⣿⣿⡀⠀⠄⠀⠈⠁⠐⠒⠈⠀⠀⠀⠀⢸⣿⣷⡀⢀⢸⠀⠀⠀⠀⠀⢂⠃⠀⠀⢠⡇⠀⠀⠸⠀
⠁⠀⠀⡀⠀⠀⠀⠙⠣⣀⠀⡏⠀⢠⠇⢈⠀⢃⠀⠆⠈⠄⡆⢀⣾⣿⡿⣁⡥⢡⢀⠈⠀⠈⠄⠂⠀⠀⠀⠀⠀⢸⡜⣿⣿⡼⢸⢀⠠⠀⠀⠀⡟⠀⠀⠀⢰⢁⠀⢀⡄⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⢰⠀⠁⠀⠘⡀⡁⠀⠐⣀⣾⣿⡿⠁⢫⠣⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢸⣿⣿⢺⡄⠀⠀⠀⠀⡅⠀⠀⠀⡜⠘⠀⢸⠇⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡂⠀⠀⢸⠢⢤⡀⠀⢆⡄⠀⠀⢸⡿⠋⡐⠀⠀⠑⢤⠉⠓⢄⠀⠀⠀⠀⡠⢄⠊⠄⠀⠀⢸⣿⣿⡸⣷⠈⠀⠠⠁⡆⠀⠀⢀⠇⡆⠀⡇⠂⠀