⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠂⠀⠀⠀⠀⢀⣀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢧⡀⠀⢀⣤⡶⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣀⠤⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⢼⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⢀⠔⣺⣦⡀⣀⠀⠀⠀⠀⠨⣉⡵⠋⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠴⠁⢀⡟⠹⡝⢦⣀⠀⠀⠀⢠⡎⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⣦⣄⠘⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠂⠐⠂⠘⠀⢠⠊⠀⡠⢺⢣⠤⠽⣦⠈⠳⢦⣞⣹⡀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢈⡿⠳⢯⠉⠑⠢⡄⠀
⠀⠀⠀⠓⠤⢄⡀⠀⠀⠈⡆⡜⠀⣼⡈⣶⠄⠈⠳⣄⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡞⠁⡔⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠸⠀⢀⠀⠈⡜⠀⡼⠉⣿⣥⣀⣀⠀⣈⠷⢤⣀⢿⢦⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⡀⡻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠰⡇⡜⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠃⠀⠁⠀⠘⣦⠀⠙⠊⠁⡠⠖⡛⠈⢮⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⢟⡿⠿⠛⠋⠉⢷⠀⠀⠹⣇⠀⠀⠀⠀⣠⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⢠⠟⠢⠤⠖⠉⠀⣸⠁⠀⠀⠳⣿⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠸⡆⠀⠀⠈⠙⠒⠒⠛⠁⠀⠀
⠀⠀⠀⠀⠀⡄⠀⢰⠀⠀⠳⡀⠱⡄⠘⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡼⠈⠑⠮⡑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢡⠀⠀⠣⡀⠀⠙⢤⣈⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⣸⠀⠀⠴⠒⣻⢟⣿⡿⣷⣶⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣤⢞⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠢⣀⡀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠀⡏⠀⠀⣠⣞⣁⠘⠋⠀⠀⢸⠑⠒⡼⢢⢞⣠⣤⣽⣦⡒⠛⣦⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⡧⠀⠀⠀⠀⢸⠀⠀⠀⢰⡧⠖⠛⡟⠛⠻⠿⣿⣷⠀⡞⣠⣾⠗⠹⡿⠛⠛⢏⠈⣧⢠⠇⣷⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡴⣸⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⢰⠀⠰⠛⠁⠁⠀⠀⠃⠀⠀⠈⠀⡟⣿⠀⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠜⢡⡏⣠⠖⠀⠀⠀⢸⠀⠀⠀⠀⢷⠀⠸⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠈⠱⡌⠀⣧⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡞⠋⠀⠀⠀⠀⣼⡀⠀⠘⢦⡈⣧⠀⠱⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠑⠤⠴⠋⠀⠀⡥⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⡆⠀⢰⠃⡇⡄⠀⢸⠙⠾⣧⡀⠀⠀⠀⠀⡔⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⢀⡴⠁⣆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⡇⢠⡇⡸⢹⣳⡀⠘⣇⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠏⢀⣠⠤⣶⠉⠀⡀⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡿⣇⣼⣧⡷⣰⢿⣷⣄⢻⡛⠯⢥⣒⣒⡒⠲⣞⠒⠒⢒⣚⣿⡉⣭⠀⠀⡏⠀⢰⢃⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⠈⢿⠹⣇⠉⣠⠋⠈⠳⣿⡽⢗⣒⣲⡦⠭⠽⠭⣭⡥⣶⠺⣿⢿⣀⣶⢁⡴⢻⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠀⠀⠈⠀⢇⡀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠉⡏⡇⢹⣣⠈⢧⢹⣿⠋⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠉⠉⠉⠓⠲⢄⣀⠀⠀⠀⠀⠈⢩⡷⠶⣶⣤⣤⣀⣀⣀⣀⣀⡇⡇⣀⣿⡆⠈⢻⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⡴⢺⠿⠀⠀⠀⠀⠉⢯⠉⠉⠛⣇⠉⠉⠛⢻⡗⣦⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣜⣀⣀⡀⠀⠄⢀⣈⡆⠀⠀⢹⠀⠀⠀⠈⢿⣦⡴⠋⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢻⡟⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠸⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⡇⠀⣀⣠⣤⣴⣦⡤⣀⣸⡄⣠⠀⠀⠀⠀⠀⢻⣁⣀⣀⡠⠤⠴⠚⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠋⣟⠙⢎⠈⠉⠓⠀⠈⠻⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀
⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⠷⣄⣹⣤⠼⠳⢤⣀⢁⡶⠤⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀
⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠟⠀⠀⠠⠄⠀⠀⠀⠀⢹⣀⣀⣤⡤⠤⢤⣤⣤⡤⠄⠀⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠲⠥⠤⠤⠤⠤⠤⠤⠤⠶⠶⠞⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀