░██╗░░░░░░░██╗███████╗██╗░░░░░░█████╗░░█████╗░███╗░░░███╗███████╗
░██║░░██╗░░██║██╔════╝██║░░░░░██╔══██╗██╔══██╗████╗░████║██╔════╝
░╚██╗████╗██╔╝█████╗░░██║░░░░░██║░░╚═╝██║░░██║██╔████╔██║█████╗░░
░░████╔═████║░██╔══╝░░██║░░░░░██║░░██╗██║░░██║██║╚██╔╝██║██╔══╝░░
░░╚██╔╝░╚██╔╝░███████╗███████╗╚█████╔╝╚█████╔╝██║░╚═╝░██║███████╗
░░░╚═╝░░░╚═╝░░╚══════╝╚══════╝░╚════╝░░╚════╝░╚═╝░░░░░╚═╝╚══════╝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠈⢳⣼⡟⢷⡦⠤⢿⣂⣄⡒⣤⣉⠙⠢⣜⡿⣬⢹⣱⣻⡿⠛⠒⠒⠒⠒⠢⠤⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⡙⠒⠽⠟⣦⣙⣢⣄⠀⡠⢀⣀⡠⠽⠛⠳⠿⣿⡾⢱⡿⣀⠀⠉⣉⠛⢶⣮⣉⡒⠛⠛⠶⢤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣲⣶⠉⠉⠀⠀⢀⣬⠭⠟⢛⣩⠤⢒⡦⠖⠀⣠⠙⠢⡄⠤⣤⣀⠈⠑⢶⣿⣿⣷⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠤⢍⣉⣩⣿⠟⣡⡶⠚⡡⢒⣴⡏⠀⣠⠎⣀⣠⣀⡈⢢⡀⠙⢿⠦⣀⠈⢹⣯⣻⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠑⣾⠿⠛⢃⣼⢟⣤⢎⣴⣿⣉⡙⠺⣅⠀⠀⢈⣁⣉⣐⠃⠀⠀⢳⣄⠀⠀⠿⣯⣿⣿⣷⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢶⠀⠘⣤⣠⢾⣡⣿⣣⣿⣿⣿⢿⣿⣶⣄⡽⣾⣿⠇⢌⣭⡟⠛⡉⠂⣿⣷⣄⢐⠦⣝⢿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠸⠂⠀⠙⠀⡀⠻⣿⣿⣿⣾⣯⣀⡼⢻⣿⣿⡉⠳⡤⠞⣡⡴⠋⠀⠀⣿⡄⢿⡏⢝⠿⣻⣿⣿⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣿⡶⠊⠀⠀⠀⠱⣄⠙⣿⢿⡟⢿⠙⣿⢿⡛⢿⣷⡞⣠⢞⠁⠀⡴⢱⣾⣿⣷⢸⢳⡈⢣⡈⠻⣿⣧
⠀⠀⠀⢀⣾⣿⣿⠛⠻⢿⣿⣿⣦⡀⠀⠀⠀⠈⠉⠉⠈⠃⠘⣦⡻⣦⣹⣧⣠⡴⠋⠁⡠⠊⡴⢋⡟⣹⠁⢸⢸⣷⡀⢹⣦⡘⢿
⠀⠀⢀⣾⡿⠛⠛⠿⣦⣄⠀⠀⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣠⠞⣁⠤⢒⣩⣿⢟⣴⡿⢁⠋⠀⢸⠈⢧⡑⣆⠉⣿⡄
⢀⣴⠟⠁⠀⠀⠀⠀⠈⠙⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠓⢀⡠⠚⢡⣿⣿⡿⠃⣠⡟⠀⢀⡇⠠⣿⠹⣜⢦⠈⢧
⣿⡋⠂⠠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢛⣿⣇⣴⡟⣾⢿⠁⣰⡇⡘⠀⢸⣧⠀⢹⠀⠈⠀⢳⠀
⠹⣿⣦⣀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠁⢀⣾⠟⠁⣿⣹⢧⣆⣼⣿⣷⣿⡠⣿⣿⡄⠿⢄⠀⠀⠀⠑
⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠺⢭⣼⡿⠋⣽⣿⣿⣷⡟⣿⠇⠀⠀⠑⠠⢄⠐
⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⢀⣘⣻⠥⠛⣩⢞⡽⠃⠈⠙⠀⠓⢦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄⠀⢠⡀⠁⠀⠀⠉⠉⠒⠒⠢⣤⣀⣤⣴⣧⣤⣤⣤⡤⠤⠤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⢳⣔⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣝⠒⠀⠀⠀⣀⣠⠴⠚⠋⠈⠉⠀⣀⡒⠉⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⠉⠉⠀⠀⠐⠛⠁⢁⣴⠂⠀⠀⠀⢀⣀⣤⣶⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⣧⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣷⡏⢁⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⡀⠀⣀⠀⣆⠸⣧⣿⡇⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⡦⣟⠱⣿⠙⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠻⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶