⠄⣂⠆⢆⢆⢆⠆⢆⠢⢂⢂⢂⠆⠆⢆⢆⠂⡀⠄⡀⠄⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⢀⠀⡀⠠⡀⠀⠀⠄
⡐⡐⡐⡐⠄⠄⢂⢂⢂⢂⢂⠢⢂⢂⢂⠢⡂⡀⠄⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⡀⡀⡀⠀⢀⠠
⡐⡐⠔⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠄⢂⢂⠆⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⢀⠄⠀⢀⠄
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠔⠰⡐⠔⠔⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀⢀⠀⢀⠄
⡐⡐⠔⠰⠰⡰⠰⡰⠰⡰⠰⠰⠰⡐⡔⠔⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠄⠀⠀⡀
⠢⠢⠢⠢⡂⠆⠢⡂⠆⠢⢂⠢⢂⢂⢂⢂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⡀⠀⠀⡀
⠰⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⠀⠀⠠
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠄⢀⢯⡳⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⡀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠄⢯⣻⣻⣻⣻⢶⣔⢤⢤⢢⢦⣞⣾⣿⡿⡽⣞⡜⣆⢆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⡀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠄⢂⢂⢂⢣⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⢯⢫⢎⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡐⠄⢂⢂⢂⢂⢂⢂⢂⢂⢂⢂⢂⢂⢜⢎⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢯⢫⢫⢣⢣⢣⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⠄⡐⠄⢂⢂⠠⠹⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⡹⣣⢣⢣⢣⢣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⢀⠀⠀⠀⡝⡝⡽⡽⡹⡽⣫⡻⣻⣻⣻⣻⢯⢫⠳⡱⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⠄⢂⢂⢂⢂⢂⠢⢢⡀⠄⠠⢀⢯⣎⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⢣⢣⢣⠱⢢⠢⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⣭⣳⢦⢦⢢⣿⣿⠧⢢⠠⡀⠀⠀⢀⠂⠂⠀⡀⢀⠌⠢⡂⠆⣂⠐⠄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⠄⢂⢂⠐⠄⢂⡝⡝⡝⢧⣿⣿⡝⡜⡜⡜⡜⡔⡄⢂⠆⡂⠄⠠⠠⡠⢂⠆⢂⠐⠄⠄⠀⠀⠀⢀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡱⡱⢥⣿⣿⢯⢣⢣⢣⢫⣻⣿⣿⣿⣿⣳⢧⣫⣫⢎⢆⠆⢂⠄⠄⡀⠀⠀⠀⠀⠀⠐⠔⠄⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠄⢂⠐⡐⡐⡐⡐⡐⡐⡐⡐⡐⡌⢎⣿⣿⣏⢆⠂⠀⠠⡹⡹⡽⡽⣻⣻⣻⡝⡝⡭⢎⠎⢂⠄⠄⠀⠀⠀⡀⡐⡔⠀⠀⡀⠰⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠄⢂⢂⢂⢂⢂⢂⢂⢂⢂⢂⢂⢣⡘⡝⡝⢣⠡⠣⡑⠐⠰⡱⣍⠞⡜⡜⡜⡜⡌⠆⢂⠄⠀⠀⠀⠀⠀⠀⠠⠠⢰⡳⡙⠉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⠄⢂⠐⠄⢂⠐⡐⡐⡐⠔⠔⡔⠄⠀⠠⢢⢢⢎⢎⢎⠜⡜⡌⢆⠆⢂⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐⠔⡰⠰⡐⠄⠀⠀⠂⠓⠳⡱⡡⠢⢂⠆⢆⠆⠆⢂⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠰⡰⠰⠰⡐⡐⡐⠄⠀⠀⠀⠀⠠⡘⡐⠄⠠⡐⠔⠆⠤⠤⡀⠀⡐⡐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠂⠀⠀⠀⠀⡀⠄⢆⢎⢒⠔⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⢢⢦⢘⡜⢆⢂⠄⡄⡄⢢⢢⠢⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠄⠄⠄⠀⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⡐⡽⡽⣻⡿⣻⢧⠱⠱⡱⢭⢫⢎⠎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⢿⣻⢯⣏⣏⢎⢎⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⢰⡽⣟⣟⣿⣻⣻⣻⡽⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢯⢯⣚⢧⢣⢂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢢⣻⢿⢿⣻⣟⣟⢯⢯⠃⢆⡒⡐⡀⠄⢀⢀⠀⣤⣾⣿⢿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⡝⠧⠩⠊⠈⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢰⣻⣻⡿⣻⣻⡽⣯⠏⠠⣚⢞⢧⢣⢂⢀⣠⣾⢯⣿⡿⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢁⢲⡱⡱⡱⡰⡀⠀⠀⠀⠀⠀⠀⠀
⠀⢼⢯⣻⣻⣻⡽⡹⡍⠀⡜⡞⡼⣹⡹⣽⢯⣿⢯⣿⣻⡟⠛⠉⠀⠀⠀⠀⡀⠄⠠⠠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⡜⡜⡜⣜⣝⡽⡽⡞⡧⣣⡀⠀⠀⠀⠀⠀
⢰⣻⡿⡿⣻⢯⠃⠀⡰⡱⡝⡜⣾⣿⢿⣻⠏⠉⢀⠄⠄⠀⠀⠀⠀⠀⠀⡐⡜⡜⡜⡜⡜⡜⡌⢿⣿⣿⣿⣿⢋⢆⢆⠱⡱⣹⡽⣻⣻⡿⡿⣻⣻⣹⢞⢆⠀⠀⠀⠀