⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⢠⠟⣁⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣽⣿⣿⣿⢿⡿⣿⣤⣞⣿⣾⣷⣦⣀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢟⣁⣴⣿⡿⣝⣮⢯⣽⣳⣻⣿⣿⣿⣝⣻⣿⣷⣄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣿⣷⣿⣯⣿⣷⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣧⣹⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⢩⣿⣿⣿⣿⠚⣿⣿⣯⣿⣿⣿⡿⣟⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡹⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⢿⣿⠂⠉⠻⣷⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⠁⠀⠀⠀⠙⠋⠁⠿⣿⠷⢻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀
⠀
⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠀⠀⠉⠋⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⢻⣿⣿⣧⠀⠀⠀⠀⠀
⢀⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡛⢷⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢘⣿⣿⣿⡆⠀⠀⠀⠀
⠐⣿⣿⡇⢿⢻⣷⠹⣿⣿⣿⡿⢿⡿⣿⣿⣿⢻⣿⣜⠢⡜⢩⠿⣿⣿⣿⣿⣿⢏⣿⠟⣼⠃⢰⡏⢹⣿⠇⠀⠀⠀⠀
⠀⠘⠻⢷⡸⣆⠼⠛⠹⣇⠻⣿⠚⠛⠙⠻⢿⣷⣽⡻⣦⠉⠓⡈⠽⢯⣋⣚⡉⠼⠧⠔⠃⠒⠾⡀⢾⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⠋⠀⠀⠀⠻⡄⠘⠷⣄⠀⠀⠈⠉⠓⠾⠼⣟⠳⢼⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣌⢫⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠘⣆⢧⠀⠀⠀⠀⠀
⠀⠀

⠀⠀⠀
⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡟⠁⢀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣌⠳⡀⠀
⠀⠀⠀⠀⠘⡇⠀⠀⢀⡿⠀⠀⣿⣿⣿⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠀⢹⡄
⠀⠀⠀⠀⠀⢿⠀⠀⣼⡇⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⢸⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⣧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣆⠰⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣤⡞⠁⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠴⣋⡴⠃⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⡱⢌⡛⣦⣤⣀⣀⣀⣀⣦⣥⢶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣟⠶⣶⣶⡏⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡌⠲⣄⠫⢿⠶⡑⢊⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⡱⢌⢣⡛⣧⢣⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢷⡹⢬⠳⣜⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢎⢿⣭⢳⢯⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢈⠦⡙⣭⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡎⢲⡽⢋⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠈⢿⣾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠯⡿⢡⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡞⢡⠃⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠂⠌⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣯⠀⠀
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴