⠀⠀⣸⠖⠚⢦⠀⠀⠀⠀⡾⠀⣘⣿⠟⠛⠃⠘⣧⡄⢠⠆⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠃⣴⡶⢼⠒⣦⢠⡞⠷⠾⠉⣁⣲⢹⠶⠆⠁⠁⠀⠀⣴⣄⡴⢖⣻⡋⠉⢈⣙⢺⢻⣍⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠤⠋⠀⠈⠉⠀⠀⠨⠗⠛⠈⠀⠀⠀⠀⠀⠀⣠⢿⠟⠁⠀⠈⠀⠀⠠⡀⠻⣿⡈⢧⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡜⠀⢀⣢⠘⡗⣦⣄⠙⢆⢹⢣⣈⡱⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡜⡇⢰⡾⣳⣽⣼⣾⣿⡹⣮⣿⣀⣟⠝⢦⣱⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢻⢶⡙⣟⠬⠏⠉⢛⠉⣹⢻⡟⢹⣶⢶⣿⣿⡄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢸⠀⠘⡼⢦⣿⣷⣄⣛⣸⣞⣿⣴⠇⠀⠉⠀⠈⠛⢿⣦⣀⠹⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⣸⠂⠀⣩⡈⣽⣷⡿⠉⣾⠍⢘⣷⡗⡄⡀⠀⠀⠑⠉⠧⡈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⠇⢀⠇⠀⡸⢡⡞⡿⣿⢿⡟⣭⣠⢤⣈⣁⣇⠈⠰⢄⡀⠀⠀⡹⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⢸⠀⡎⠀⢰⡩⠋⠀⡞⡦⣶⡇⢻⣅⡞⠀⠈⠉⠉⠉⠑⠒⢲⠒⢳⠝⡄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⢄⡇⣸⠁⢰⠃⡇⠀⣸⢡⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢱⠘⣆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡜⠰⢡⠃⣠⢿⣦⡧⢰⠁⡎⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡇⠘⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠀⡸⠁⠃⡎⡰⠁⠀⢰⢧⠇⢠⢣⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⡀⠘⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡠⠎⣠⠃⠀⣼⡞⠁⠀⢠⢜⣏⡀⡼⠀⠀⠀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠘⡿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠃⢀⠇⠀⣰⠋⠀⣀⠔⠋⡸⠿⢳⠇⠀⠀⠐⠁⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢂⠀⠑⡜⢇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⢾⠃⢀⡜⢀⣼⣽⡷⠋⠁⠀⡸⠁⠀⡜⢸⠀⢠⠀⠀⢞⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⡄⠀⢣⠘⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠡⡞⡜⠀⡜⢠⣿⡿⣩⣇⠀⡴⡺⠃⠀⢀⢇⠘⢄⠜⠀⠀⠀⢱⣽⠆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠀⠀⢸⢱⠀⠘⡤⠙⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⡎⢘⠀⠐⣵⣿⠟⠱⣋⣿⣯⣴⠷⣄⡠⠾⣬⠀⡄⢀⣠⡴⠾⢋⣀⠵⣦⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠃⠀⠀⡈⢸⠀⠀⢱⢇⢣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠃⡄⡸⠀⠀⢀⣻⣟⠋⠀⠀⢸⠣⣼⠳⣄⡖⠀⢰⠉⢿⣷⡟⣟⣆⡤⢚⡿⢻⣧⠀⠀⠀⠀⠀⠀⡇⠀⠀⣎⡄⠀⠀⡇⠸⠀⠀⠘⣬⠎⣆⠀⠀⠀
⠀⠀⠀⠀⡰⠁⡎⢰⠑⣯⣽⣶⣶⡾⣻⣦⣀⢸⠀⠀⠉⢲⣉⣓⠸⡆⠰⠶⣟⣮⣯⣟⠉⠀⠀⣿⠀⠀⠀⠀⠀⢰⠃⠀⢰⣿⠁⠀⢠⠇⢸⠀⠀⠀⡇⢃⠸⡄⠀⠀
⠀⠀⠀⡴⠃⢸⠀⡌⠀⠉⠉⠡⠛⠚⠁⡜⠉⠻⠀⠀⠀⠀⢠⠃⠀⠹⡗⠋⠁⠀⠙⢾⣿⣶⠾⠏⠀⠀⠀⠀⠀⡜⠀⢠⢳⡇⠀⠀⡆⠀⢸⠀⠀⠀⢰⢩⡸⢧⠀⠀
⠀⠀⣰⠁⠀⠘⠀⠁⠀⣠⣲⠁⡌⠀⢠⠃⠀⢸⣤⣀⣀⣀⡎⠀⠀⠀⠹⡀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⢿⣻⠁⠀⡸⠀⠀⢸⠀⠀⠀⠘⠈⣼⠈⡆⠀
⠀⡸⠁⢸⠀⢰⠀⡄⢠⣣⠃⡸⠀⠀⠘⠀⠀⡎⠀⠀⠈⢹⠃⠀⠀⠀⠀⢻⠛⠛⠋⠛⢹⠀⠀⠀⠀⠀⠀⢐⠇⠀⣠⡳⠃⠀⡼⠀⠀⢠⡿⠀⠀⠀⠀⠀⢻⠀⡇⠀
⢠⠃⢠⢾⠀⠘⡆⠘⢿⡃⡸⠁⠀⠀⢰⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⡎⠀⢀⡖⠁⢀⠞⠁⠀⠀⣞⠃⠀⠀⠠⠀⠀⢸⠀⢡⠀
⡇⢀⡎⠈⣇⠀⠀⠀⠀⠈⠛⠒⠤⠤⢼⣆⣰⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢱⠀⠀⠀⢀⡞⣀⡴⠋⢀⡶⠋⠀⠀⢀⡞⡜⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀
⠀⡜⠀⠀⠈⠲⣄⡀⠀⠀⠀⣀⣀⣀⣀⡀⠉⠒⢤⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡇⠀⢠⡾⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⡔⠁⠀⠀⢰⢁⠀⠀⠂⠀⢸⠀
⢰⠁⢠⠀⠀⠀⢄⠈⠉⢏⠉⠀⠀⠀⠀⠈⢩⠓⠤⣈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢹⡋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠜⠀⠀⠀⠀⡼⢈⠀⠀⢰⠀⡸⠀
⡇⠀⢸⠀⠀⠀⠈⢳⣄⠈⠳⣤⠀⠀⠀⠀⠸⠀⠀⠈⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⣠⠞⣁⡞⠋⠀⠀⠀⠀⣠⠃⡜⠀⠀⡜⠀⡇⠀
⡇⠀⠸⠀⠀⠀⠀⠀⢸⠱⠦⣀⣁⠲⢄⡀⢸⠈⠲⢶⠋⢳⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⠘⣆⠀⠀⢀⡴⠊⣁⠞⠁⠀⠀⠀⠀⠀⢠⠇⣸⠃⠀⣸⠀⡜⠀⠀
⠇⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠑⠐⠢⡆⠀⠀⢸⠀⢸⡿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠙⣄⡾⠃⣠⡚⠁⠀⠀⠀⠀⠀⠀⣰⠏⣨⠃⠀⢠⠇⢰⠁⠀⠀
⠈⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢍⣯⡀⠹⡀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡆⠀⠀⣯⡰⠎⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⣴⠁⠀⢀⠏⡰⠁⠀⠀⠀
⠀⠱⣀⢱⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠙⢿⡀⡇⠀⠀⠀⠀⠀⠀⢃⠀⠀⣼⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠠⡜⠀⠀⢠⢊⡴⠃⠀⠀⠀⠀
⢧⡀⠘⢆⣣⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠘⡧⡇⠀⠀⠀⠀⠀⠀⢸⡀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠁⠀⡞⠁⠀⠀⣈⡞⠀⠀⠀⠀⠀⠀
⠀⠙⢆⠀⠙⢯⡀⠀⠀⢘⡄⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⢀⣠⠄⠛⢻⠁⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⡬⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠑⢦⣀⠀⠃⠄⡀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⢿⣌⡆⠀⠸⡀⠀⠀⠀⠀⢸⡀⠀⠘⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠓⠶⢄⣀⡘⡄⠀⠀⠀⠀⢸⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⣇⣀⣰⡇⠀⠀⠀⠀⠀⣇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠇⠀⢹⡇⠀⠀⠀⠀⠀⠈⢦⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠀⣠⣆⡇⠀⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢮⡗⣴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀