⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠃⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡰⠏⠀⠀⢀⣀⡤⢤⡶⡶⡶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡏⣀⠴⣺⣿⠟⠛⠉⠉⠉⠉⠉⠙⡒⣭⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠊⣷⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣿⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣄⣀⡀⠀⠀⠀⠀⣠⣷⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⢩⢿⢊⢡⣇⠛⢿⡣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⢿⠉⠁⠀⠀⢀⣴⣿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠂⠀⠀⡌⠉⠋⠉⠙⠮⠦⠷⠀⠙⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠃⠀⠀⠞⠀⠀⠀⠀⠡⠀⠂⠂⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡰⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡴⣱⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣤⠀⠀⠀⡰⢡⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡄⡹⣦⠀⢠⢋⣯⠼⣒⣲⡯⣷⡫⠖⠒⠒⠒⠢⢄⡀⠈⠓⠦⠤⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠁⠱⡙⡆⣇⣿⡿⢫⣿⣯⢷⠏⠀⠐⠀⢄⠀⠀⠀⠙⣄⠀⠀⠀⠈⠳⣆⡀⠄⢀⣀⣴⠃⠀⠀⠀⠊⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⡇⣻⣸⡟⠀⠀⡟⠁⡇⠀⠀⠀⠀⠀⠁⠢⡀⠀⠘⢆⠐⣀⠀⠀⠀⠉⠉⠉⠀⠈⠙⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣹⡼⡿⠀⠀⢸⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠉⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡑⡇⠀⠀⢿⢾⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⣳⡠⠠⡼⠉⠀⣠⣄⡠⠴⠒⠒⠦⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⠸⡾⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⣗⠒⠁⠀⡖⠟⠉⠁⠀⠀⠀⠀⠈⠙⠚⠒⠒⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠷⣖⠦⢤⣀⠀⠀⠀⠀⠀⠀⠨⡇⡇⠀⠀⠀⠙⢾⣆⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⠏⠀⠀⢸⠛⠀⠀⠠⠶⠶⣦⡄⠀⠀⠀⢀⣀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀
⠀⠀⠀⠀⠈⠳⡀⠈⠙⠦⡀⠀⠀⠀⠈⡇⡇⠀⠀⠀⠀⠀⠙⢳⣤⠀⠀⠈⡗⡒⠒⠚⠉⠀⠀⠀⠸⣆⠀⠀⠀⠐⠀⠃⠀⠀⠀⢠⡈⠓⠈⠉⢉⠒⠤⣀⠈⠓⢄⠀
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠙⢦⠀⠀⠀⢧⢳⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡴⠃⠀⠀⠀⣠⡆⠀⠀⠀⠛⢴⣄⠀⠀⠀⠀⠀⠀⠀⢀⣟⠲⠤⣀⡀⠀⠀⠀⠉⠂⠈⢷
⠀⠀⠀⠀⠀⠀⢸⠈⠀⠘⣆⠈⢣⡀⠀⠸⡜⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠖⢱⠁⠀⠀⠀⣐⠾⠉⠀⠀⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠉⠉⠒⠒⢖⠶⠝⠚
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠘⡆⠀⠘⠲⣄⣣⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠠⡏⠄⠀⠀⢰⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠑⠢⢄⣀⣀⣀⣀⡷⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⡀⠀⠀⠈⠻⣾⣧⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠐⢷⠀⠀⢀⣾⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢠⠖⠋⠁⢠⠆⠀⠀⢸⠄⢠⠎⢸⡄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢳⡀⠠⠀⠀⠹⣿⡄⠀⠀⢰⠃⠀⠀⢰⠃⠀⠀⠀⣼⢠⡧⡄⠀⢙⣎⠄⠂⠀⢀⣠⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠠⠀⠀⠀⠈⠲⢤⡀⠀⢻⣼⡄⠀⣿⠀⠀⠀⡏⠀⠀⠀⢀⣇⠌⠳⠯⣔⠁⠻⣼⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡢⣄⣀⣀⡀⠀⠀⠈⠙⢦⣻⣽⣆⣿⠀⠀⠀⣇⠠⠀⢠⣟⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣀⡀⠛⢧⣀⡀⢀⠀⣧⣿⣿⣿⡀⠀⠀⢸⡀⠀⠀⢻⢀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡋⠉⡉⢉⠓⠧⣌⢿⣷⣄⠀⠘⡇⠀⢀⣾⡸⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠠⠂⠤⣀⠑⠿⣾⣳⣼⠗⠀⣾⠇⠀⢠⢶⣋⠳⡤⠀⠀⣠⢶⣞⡻⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⢰⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣀⣵⣶⣬⣟⣿⣷⣔⣯⡀⠀⠸⣞⣸⣁⣙⣮⣀⣧⡋⢾⠁⠀⠀⠀⢀⣀⣠⠴⣏⠀⢐⣱⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀