⢤⣉⠩⣀⣀⠈⠙⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⣤⠚⠑⠒⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣷⡄⠈⠙⢦⡈⠓⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠩⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⡶⣄⠀⢀⣀⡠⠖⠲⠤⡤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢱⠀⠀⠀⠉⠲⠰⣽⠀⠀⠀⠀⢀⡠⠞⠙⢺⢧⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⢳⣏⡅⠀⠀⠀⠀⠁⠀⠀⠛⠳⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣷⡀⠀⢀⡞⠀⠀⠀⠈⠃⠑⣄⠀⢱⠀⠀⠀⠀⠀⡆⠀⢠⠎⠀⡀⠀⣸⣟⠾⣄⠀⠀⠀⠀⠀⢀⣄⡼⠃⣩⠳⢤⡀⠀
⠀⠀⠀⣿⠀⢧⠑⡄⠀⠀⢀⡴⠃⢠⠎⠁⠀⠀⠀⠀⠀⠢⡈⠁⠀⠁⠀⠀⠀⢰⠃⠰⠃⢰⣋⣀⡐⠿⣿⣧⠘⣦⠀⠀⠀⠀⢲⠋⢠⠞⠁⠀⠀⢿⡆
⠀⠀⠀⢳⡀⠌⡆⢘⣴⢞⡍⠀⠀⢸⠀⠀⢄⣀⠀⠠⠀⠀⠘⢦⡀⠠⡀⠀⠀⡋⣠⣶⠟⠛⠒⠒⠒⠒⠲⠛⠀⢻⡆⠀⠀⡴⠃⠐⠁⠀⠀⢀⡀⠄⡇
⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⣻⠀⠀⠀⠙⠢⠤⠒⠛⠻⠷⠶⣖⡦⢵⡀⢱⠀⣼⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⠞⠁⣀⣀⠀⠒⠉⠁⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⣮⣰⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡼⠚⠉⠁⠉⠻⡳⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⢀⡴⠲⢤⡀⠀⠉⠒⠒⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡼⣶⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⡞⠀⠀⢀⠿⣶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢻⣧⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⢠⡇⠀⡰⠋⠀⠀⠉⠳⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢦⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠸⡿⡄⠀⠀⠀⠀⢠⣿⡿⠁⢀⣠⢟⡇⠘⠁⠀⠀⠀⠀⠈⠹⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠉⠲⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⠓⠦⣤⣀⣴⣿⣿⡴⠚⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⣿⠀⢀⡴⢋⣼⡿⠁⠀⠀⠀⢀⣿⡶⠶⣦⠴⠚⠉⠁⠀⠀⠘⡇⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⢤⣀⣀⣀⡀⠀⠀⠀⠀⣿⡇⣿⢆⣨⢦⣼⡟⠀⠀⠀⣀⣤⣿⣟⡀⣀⢹⣄⠀⠀⠀⠀⢀⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠙⠓⢶⡶⠶⣾⣽⣲⣄⠀⣿⣇⣿⠈⣷⣾⣟⣀⣀⣤⡾⠟⣛⣿⡉⠁⠈⢹⡟⠀⠀⠀⠀⠉⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⡼⢷⣦⡇⠸⠿⣾⣦⣹⣿⡟⣼⣿⣿⣷⣶⡾⠋⠀⠀⠀⣻⠃⠀⢠⡟⠁⠠⣄⠀⠀⡾⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢰⡇⢰⠙⣷⡄⠀⣿⣷⣻⣿⡧⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⢦⡴⢫⡀⢀⠀⠈⠑⣰⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡦⠴⡞⠉⠀⠀⠀⠀⠀⣸⠀⠘⡄⠈⣿⢿⣷⣾⣹⡿⣷⣿⣿⣿⢁⣀⠀⠀⣼⠹⠛⠉⠀⠘⣄⠹⡄⢙⣶⠖⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠳⢤⡤⣀⣀⣀⠀⠇⣀⣠⠿⠚⠁⢀⣽⣿⣿⣶⣿⣿⣽⣇⠈⠘⢿⣦⠳⢄⣀⣄⣀⣀⣛⣤⠵⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠏⠈⠻⠶⣾⡋⠔⠊⠁⠀⢀⠀⠘⠛⠒⠛⠛⠋⠀⠀⠀⠀⠀
❀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀❀