⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⢂⡄⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢄⠀⠀⠀⣷⠀⠠⣄⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡼⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢠⠆⡆⠀⡇⠀⠘⢧⠀⠀⡻⡀⠀⠈⢷⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⠇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣼⣸⠃⠀⣷⠀⠀⠘⡆⠀⠀⢇⠸⠀⠈⢧⡸⡄⠀⠀⣷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⢿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⣯⠟⠀⢰⣿⠀⠀⠀⠃⠀⢰⠘⡄⠀⠀⠈⣷⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⣼⠃⡏⡇⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⡇⢸⠛⡇⠀⠀⠀⢸⢸⡄⣷⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣯⠏⢸⠃⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡇⢸⠀⢿⠀⠀⠀⠀⠈⣧⢻⠀⠀⠀⠀⠈⢻⠻⠛⡟⠉⣽⣿⡟⠋⠙⣿⣿⣿⣦⡈
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣸⡏⣠⡾⠴⡧⠀⡇⡇⢸⡀⠀⠀⠀⠀⠀⣿⠃⠀⡇⠸⡄⠈⡇⠀⠀⠀⢦⡟⣮⡇⠀⠀⠀⠀⠀⠀⢠⣧⣾⣿⣿⠃⠀⢸⣿⣿⠙⢿⣿
⠀⠀⠀⠀⠀⠀⣰⢸⠇⠀⠀⢀⣿⠁⠸⡇⠀⢷⠀⡇⠇⠘⡇⠀⠀⠀⠀⠀⡿⠐⢶⢿⠀⡇⠠⣼⡄⠀⠀⠈⡇⠘⡾⡀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡅⠀⠀⢸⣿⣿⡀⠀
⠀⠀⠀⠀⠀⢀⡏⢸⡄⠀⠀⢸⡟⠀⣆⢳⠀⠸⡆⠃⢸⠀⢹⡀⠀⠀⠀⠀⡇⠀⠈⡼⡆⡇⠀⠀⢻⡁⠀⠀⢳⠀⠹⣷⠀⠀⠀⢀⣼⣿⣿⠏⢀⡇⠀⠀⢸⡯⣿⠃⠀⠀
⠀⠀⠀⠀⣠⣿⡇⡏⡇⠀⠀⢸⠃⣴⣿⣷⣶⣄⠑⠀⠘⣦⡆⢷⡀⠀⠀⢀⠃⠀⠀⠐⢻⣹⠀⠀⠀⠳⡄⠀⠸⡀⠀⠘⣇⠀⢀⣼⣿⣿⠋⠀⣸⠁⠀⠀⢸⣿⣿⠀⠀
⠀⠀⠀⢸⣿⣿⡀⡇⢳⡀⠀⣸⠀⠋⠁⢀⣿⣿⣷⠀⠀⠙⣇⠀⢳⣄⠀⢨⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠹⣄⠀⠧⠀⠀⢹⡄⠘⣿⣿⡏⠀⢠⠏⠀⠀⠀⢸⣿⣿⠇⠀
⠀⠀⠀⠀⢿⣿⡇⠃⠘⢧⠀⣿⠀⠀⠀⣀⣹⣿⣿⠃⠀⠀⠈⠈⢢⡹⣆⢸⡤⢶⣶⣿⣿⣯⣻⣿⣷⣶⣶⣛⠂⠀⠀⠀⠀⢳⣸⡟⠉⠀⠀⡼⠀⠀⠀⠀⢸⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣆⢸⠀⠀⠀⣿🤍⣿⡇⠀⠀⠀⠀⠀⠀⠈⠚⢷⡶⠛⠉⠀⠰⢿⣯⠉⠙⠛⢿⣿⣿⣦⣳⠀⠀⠀⡟⠁⠀⠀⣰⠃⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣆⣰⣿⣿⣿⠀⠀⠀⢿⣋⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⣦⠾⠿⢦⣤⣤⣿⣿⠈⢻⡟⠀⢄⡼⠁⠀⠀⢠⠋⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡟⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷ 🤍⣿⡟⠩⣽⡟⠀⠀⠀⢀⡞⢁⡀⠀⣰⠏⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⡿⠋⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⠠⣍⠟⡛⠛⠀⠀⠀⢠⠟⢠⠞⠀⡴⠃⠀⠀⠀⠀⢀⡾⣽⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠟⠋⠀⢀⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠖⠛⠁⠀⠀⢀⡴⠋⣰⠏⢀⠞⠁⠀⠀⠀⠀⠀⡾⢳⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡞⠁⠀⠈⠀⠀⠀⠀⠀⢀⣾⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⠔⠀⠀⣠⣾⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⡴⠚⠁⠀⣠⣾⣯⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⣠⣤⡶⠛⠁⠀⠀⢠⡴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡿⠁⠀⠹⢦⣤⣄⣀⣠⣠⣤⣤⠤⠤⠴⢖⡶⠟⠁⠀⢐⣪⠝⠋⠁⠀⠀⠀⣠⡾⢋⣾⡋⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⡟⠁⠀⣠⠞⠋⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⣠⣾⠏⣠⡾⠋⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣼⢃⡴⠎⣁⣠⠶⠋⠁⠀⠀⠀⠀⠀⣀⡴⢛⡵⠋⣴⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠁⠀⠀⠀⢀⣀⡤⠤⠴⠶⠶⠒⢺⣏⣥⡶⠟⠉⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣠⠟⣠⡿⢃⣿⠀⠀⢸⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡴⠛⣀⣠⠤⠴⠚⠋⠁⠀⠀⠀⠀⣀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⢀⡜⠁⢠⡟⠀⢸⡏⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⢤⣶⡚⠷⡒⠋⠉⠀⠀⠀⣀⣀⣀⣤⣤⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠓⠒⣲⠖⢋⢀⠀⣾⠃⠀⢸⡇⠀⠀⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠳⣍⣻⣦⡜⠒⠒⠒⠚⠉⠉⢁⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠉⠉⠠⢴⣶⣶⣶⣤⣍⡛⠶⣄⣸⡇⠀⠀⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⣿⡷⠾⠟⠛⠋⠉⠉⠉⠉⠉⠙⠻⣟⢦⡞⠉⣷⠀⠀⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣛⣓⠲⠦⠤⠤⣤⣤⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣻⠯⠗⠛⠉⠀⠀⠀⢀⣀⣀⣤⠤⠤⢤⣄⠨⡳⣝⢦⣷⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀