⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⡠⠊⠀⠀⠀⠈⠢⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⣒⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⢀⠆⠄⠀⠀⠀⠸⠀⠀⢠⢇⠀⠀⠀⠣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢚⠀⠀⠘⡌⠀⠀⠈⠙⠃⠒⠈⠁⠀⢃⠀⢀⠇⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠢⣀⣀⢠⠑⣠⣴⣄⡀⠀⣠⠤⣤⡃⠔⠉⠀⠀⠘⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠧⠂⠀⢀⡠⢄⣀⣎⣽⣷⣻⣭⣷⣡⠄⢀⣱⣀⣀⠀⢄⡀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⢠⡃⠠⣄⢾⣻⣾⣥⣬⡷⢿⡌⡛⢂⣁⠀⡀⢳⠀⢭⢄⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢐⠎⠁⠓⡴⢊⢎⠹⣤⢿⠾⣟⠮⠴⢯⣉⣌⡳⠀⢤⠃⢨⢈⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢻⠀⠸⣋⢅⡫⠞⠝⡈⠌⠐⠠⢈⡹⠠⡤⢈⡑⢎⣹⠠⠃⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠃⠓⠤⡍⣋⡴⠉⠀⠀⢄⡡⠒⠉⢀⠶⠑⢆⠈⠒⢌⡆⡀⠀⠀⠉⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⡼⠐⣴⠀⢂⡤⠋⠀⣀⡠⠴⠉⠸⡄⠈⢢⡁⠀⠈⢳⡀⠀⠀⠀⠈⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡼⠁⡚⢰⠈⣦⠔⠊⠉⠀⠀⠀⠀⠀⡘⢢⡄⠘⢆⠠⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠒⠒⠒⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⡜⠀⢸⠀⢨⢖⡧⠐⢠⡀⠀⠀⠀⠀⠞⠀⠆⠜⢣⢌⢣⠀⠌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠀⠀⠀⠀⢠⠇⠀⢎⡰⠁⡌⠂⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡆⠐⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠠⠄⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡁⠌⢲⡁⠀⢀⣀⣀⡒⠤⠀⠀⠀⠀⠘⣵⡾⣶⠿⣄⠀⡇⠐⡾⢳⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣧⢠⡹⡄⠐⣲⢯⠟⠛⣷⠀⠀⠀⠀⢈⣿⣀⣠⢿⣹⠤⣃⣼⠁⠀⠓⡌⠙⢲⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡆⢣⡆⠹⣄⡟⢾⢲⣶⢽⠀⠀⠀⠀⠀⢧⠛⡻⡜⠸⢺⡱⣸⢅⠀⠂⠘⡆⠀⢣⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠃⠀⢛⢸⡀⢯⠐⡈⠞⠈⢧⡜⡎⠀⠀⠐⡀⣠⠀⠉⠓⠉⠀⡗⣷⣁⠘⡄⢈⠀⠸⡄⢹⠀⠐⠠⠀⠘⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⣠⢠⠗⠈⡀⠄⢈⠀⢇⢢⡈⢣⠐⡈⢣⠈⠁⠀⢈⡿⢉⡉⠍⣇⠀⠀⠀⢰⢿⡟⠁⡀⢹⠀⠀⠂⢱⡘⠂⢁⠀⠂⠁⡈⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⢃⡔⠋⢀⠀⡀⠂⠀⠄⠂⢠⠘⠤⣈⡄⠀⠀⠀⠑⢆⠀⠀⢧⠂⡜⢐⠎⠀⢀⡴⠋⠀⢀⠐⠀⢼⠀⠈⠄⠰⣝⠠⠀⠂⠁⡐⠀⡭⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠋⠀⡀⠄⠠⠀⠄⠁⢠⠌⠃⠀⠄⢀⡸⠓⣄⠀⠀⠀⠱⢤⣀⠉⠀⢈⣠⣞⡽⣲⢧⢀⣂⢤⡨⢆⡀⢌⡠⢼⠇⠤⠦⢌⠀⠠⣰⠁⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠄⠐⢀⠐⠈⡔⠃⠀⠂⣁⡄⢺⠠⢄⣀⠓⣄⡀⠀⠈⢯⡙⢛⡋⢱⡿⣼⠓⠋⠀⠀⠀⠀⢠⠉⢈⠀⢨⠀⠸⠀⡌⣉⢧⠃⠀⡐⠀⠀⠀⠀
⠑⢄⠀⠀⠀⠀⠀⠀⠱⡄⠈⢀⠠⢸⠀⢠⠜⠃⠁⠀⠀⠀⠀⠀⠈⣞⢰⢢⠀⢣⠽⢡⠙⠧⣻⡗⣦⣀⠀⠀⢀⠔⠚⠀⠀⠂⠀⠀⠘⢀⠏⠀⡼⠀⠐⠀⡈⢀⠀⠀
⠀⠀⠉⠤⠀⠀⠀⠀⠀⠘⢥⠀⠀⢣⢠⠋⠀⠀⠀⠀⢀⠤⠤⠒⠈⠣⠋⠀⠀⠘⠤⢈⠁⠠⠂⢻⡵⣫⢷⡀⡌⠀⠀⠀⠀⠀⣀⠤⠴⠚⠀⡀⣟⠀⢈⠀⠄⡀⠄⠀
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠠⠈⣆⠁⠘⡎⠀⠀⠀⠀⠀⠀⠑⠠⠄⠴⠂⠀⢠⠀⠈⡄⠠⡔⢦⡀⠀⢻⡵⣫⡗⠁⢠⠄⢶⠆⠉⠀⠀⣚⠀⠄⢀⠸⣆⠀⠄⠂⠀⠄⠂
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠄⠸⡄⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⢻⣆⠀⢧⠴⡧⢤⠷⠞⣯⡻⠃⠀⠀⠀⠙⠚⡄⠀⠀⠀⡎⠀⡀⠂⢀⠈⠧⣄⠂⠁⡀⠂
⠀⠀⣀⠄⠊⠀⠀⠀⠀⠀⡐⠠⡇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠈⢁⡿⣌⠟⣮⣤⡧⠔⣦⣶⣋⠀⣀⡴⠀⠀⢤⠀⠘⠄⠀⡜⠁⠀⠄⠐⠀⠠⢀⠈⠓⠲⠤⣤
⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⠀⡤⠓⠉⠂⠀⠀⠀⠀⠀⢀⠏⠀⠀⣸⠳⣬⣿⣻⠝⠳⢤⠛⠹⣟⣯⣵⢫⠀⠀⡎⠑⠠⠌⠟⠰⡀⠁⠄⢈⠀⡁⠠⠀⠂⡀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡰⠃⢰⠁⠀⠀⣀⠂⠀⠀⢀⢦⠌⠀⠀⢀⡯⣽⣟⡞⠁⠆⠀⠻⠀⢨⠀⡿⡍⠀⠓⡌⠇⢠⡀⠀⠀⠀⢃⠠⠈⢀⠠⠀⠐⠀⡁⠀⠄⠈
⡖⠒⠃⢉⠀⠠⣀⢢⠵⠊⠁⡀⠈⠑⣈⠏⠘⡀⠀⢠⠞⠊⠀⠀⠀⡼⠛⠳⡟⢘⠆⢡⠀⢀⠀⠰⠘⡴⠁⠀⠀⠀⡇⢠⠉⠒⠲⣄⠫⣄⠐⠀⠠⠀⡁⠐⠀⡐⠈⡀