⢀⣒⠒⠆⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡛⠛⠻⣷⣶⣦⣬⣕⡒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣳⠖⢋⣩⣭⣿⣶⡤⠶⠶⢶⣒⣲⢶⣉⣐⣒⣒⣒⢤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠉⣩⣭⣽⣶⣾⣿⢿⡏⢁⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⢭⣯⣟⡿⣷⣘⠢⡀⠀⠀⠀⠀⠀
⠹⣷⣿⣿⣿⣿⣿⢟⣵⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣦⣾⣢⠀⠀⠀⠀
⠀⠹⣿⣿⣿⡿⣳⣿⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣵⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣯⡇⠛⣽⣦⣿⠀⠀⠀⠀⢀⠔⠙⣄⠀⠀⠀⠀⠀⠀⣠⠳⡀⠀⠀⠀⠀⢿⡵⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⠿⢿⠟⠀⠀⠀⢀⡏⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃⠀⠹⡄⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⠒⠤⢤⣀⣘⣆⠀⠀⠀⡏⢀⣀⡠⢷⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠸⣿⣿⠟⢹⣥⠀⠀⠀⠀⠀⣸⣀⣀⣤⣀⣀⠈⠳⢤⡀⡇⣀⣠⣄⣸⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠁⠀⢸⢟⡄⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⠁⠀⠈⠙⠙⣯⣿⣿⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⢨⢞⢆⠀⠀⠀⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⡇⠀⣠⢟⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠀⢈⡏⢎⠳⣄⠀⡇⠙⠛⠟⠛⠀⠀⠀⠀⠀⠀⠘⠻⠛⢱⢃⡜⡝⠈⠚⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣅⠁⢸⣋⠈⢣⡈⢷⠇⠀⠀⠀⠀⠀⣄⠀⠀⢀⡄⠀⠀⣠⣼⢯⣴⠇⣀⡀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⡌⠛⣶⣆⣷⣿⣦⣄⣀⠀⠀⠀⠈⠉⠉⢉⣀⣤⡞⢛⣄⡀⢀⡨⢗⡦⠎⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣿⠁⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⢸⠀⠀⠀⠄⠙⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡉⢳⡄⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣠⣧⣤⣄⣀⡀⡰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⢀⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣠⠖⠒⠒⠛⢿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠤⠴⠞⢋⣵⣿⢿⣿⣿⣿⣿⣿⣿⠗⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡼⣶⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⢛⣿⠀⠙⠲⠽⠛⠛⠵⠞⠉⠙⠳⢦⣀⣀⡞⠀⠀⠀⠀⡠⠋⠐⠣⠮⡁⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣎⡀⢀⣾⠇⢀⣠⡶⢶⠞⠋⠉⠉⠒⢄⡀⠉⠈⠉⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠘⢁⡴⢟⣯⣞⢉⠀⠀⠀⠀⠀⠀⢹⠶⠤⠤⡤⢖⣿⡋⢇⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⠗⠺⠟⠖⢈⡣⡄⠀⠀⠀⠀⢀⣼⡤⣬⣽⠾⠋⠉⠑⠺⠧⣀⣤⣤⡠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀i