⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠹⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣠⣤⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⠀⠀⠀⠀⣿⡏⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠉⠉⠟⠀⠀⠀⠀⠉⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⣠⣄⠀⠀⠀⠀⠀⢀⣾⠁⢹⣧⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀
⣿⠛⢷⣤⣤⡴⠶⠾⠃⠀⠀⣿⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀⠀
⢻⡆⣀⡀⠀⠀⠀⠀⣀⣀⠀⣿⡟⠁⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠋⠁⠀⠀⠀
⠸⣿⡿⠟⣿⣄⡾⠟⡛⢓⣿⠋⠀⠀⠀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣷⣼⣁⣽⣧⣽⠿⠋⢁⣠⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡿⠛⠉⠁⠀⠀⠰⣯⣁⣠⠴⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣾⠋⢀⣄⠀⠀⠀⣀⠀⢿⡷⠦⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡏⢠⣿⢹⣧⠀⣾⠻⣧⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢷⠟⠁⢸⡏⠀⣿⠀⠻⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⢸⡟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠲⠚⠓⠚⠓⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡀⠠⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡴⡋⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡀⠀⠀⢠⠀⢷⡀⠀⡀⠻⢝⠲⢄⡀⠻⣷⡄⠀⠀⠀⠀⠀
⠀⠀⢀⣞⡜⡏⠀⡰⢻⠀⠀⠀⡾⢀⡴⠋⡇⠀⣠⢻⠀⣾⣿⣾⡏⠑⠮⣷⣄⠙⠢⣭⢻⣄⠀⠀⠀⠀
⠀⢀⣾⡞⠀⡇⡴⠁⠸⡆⠀⣸⡷⠋⠀⢰⣧⠞⠁⢸⡼⠁⠈⢿⣿⠐⠀⠀⠙⠆⠘⡆⠁⢻⡄⠀⠀⠀
⠀⣾⡿⠀⠀⡿⠁⠀⠀⢧⠖⢫⠀⠀⡰⠘⠃⠀⠀⣾⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢹⡀⠀⢻⡄⠀⠀
⢸⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠓⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⣇⠀⠈⣧⠀⠀
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠧⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠷⣄⠀⢹⠀⠀⢹⡆⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⢀⡤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣈⣳⡜⠃⠀⠘⣷⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡠⠋⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣖⣭⣴⣶⡶⣿⠀⠀⠀⣿⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⣯⣭⣽⣶⣶⣭⡂⠀⠀⠀⠀⠀⠸⢿⠹⣿⠀⡇⢸⠀⠀⠀⢻⠄
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠉⠉⡇⠀⣷⡏⢹⠙⠀⠀⠀⠀⠀⠀⠘⠦⣅⣠⠇⢸⡆⠀⠀⢸⡇
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠳⣤⣄⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⠒⠛⣇⠀⠀⢸⠇
⠀⠀⢿⡸⡀⠀⠠⠀⠀⠀⠀⢀⢧⠳⢶⡤⠤⠭⠕⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⣽⠃
⠀⠀⠈⢷⢳⡀⠀⢃⠀⠀⠀⠈⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⡠⠧⠀⢠⡿⠀
⠀⠀⠀⠘⣧⢳⡀⠈⢢⠀⠀⠀⠑⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢀⣠⣴⣾⢧⡆⢀⡾⠁⠀
⠀⠀⠀⠀⠘⢷⡑⢄⠀⠳⡀⠀⠀⠈⣦⣄⣀⣀⣀⢀⣀⣀⣀⣤⣤⣴⣶⣿⡟⠋⠀⠀⠈⠳⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢮⣷⣤⣈⣶⣤⣀⣈⣿⣿⣿⡇⠈⡆⠞⠀⣾⣿⣿⣿⠋⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⢿⣿⣿⣿⣿⣧⠰⣿⡇⣹⡟⠁⣿⣿⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣟⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⡽⠋⠉⠉⠛⣿⣿⠟⠉⠉⠉⠻⡅⠀⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣸⣇⠀⢀⣄⣀⣸⣯⣤⣀⡀⠀⣀⡇⠀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠉⠉⠀⠀⠈⡇⠀⠀⠈⠉⠉⠙⠻⣷⠿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣀⣸⣀⣀⣀⡀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀