⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡄⠀⢹⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡶⢶⣠⣾⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡞⡇⠀⠘⠈⣇⠀⠀⠀⠀⠀⢀⡰⡿⠃⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⠷⠞⢿⡜⠀⠀⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡞⠀⣇⠀⠀⢆⣿⡀⠀⠀⣀⡴⡋⠊⠀⠀⣼⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⣏⣯⡀⠀⠸⡃⠀⠘⣿⠿⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠹⣄⠀⢸⡟⢟⣶⣾⡿⠂⠀⠀⢀⠜⠁⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀
⢰⣿⠉⠀⣱⠀⠀⠙⠄⠀⠙⠆⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⣴⣿⡗⠛⠛⠾⠻⣏⠀⢀⣠⠖⠁⠀⢰⠇⣼⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡟⠛⠻⣷⣼⠟⣧⠀⠀
⠘⣿⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡞⢁⠝⢉⣢⠀⡜⠀⠀⠰⣯⣗⢄⠀⠀⢀⡎⢰⡇⠀⠀⠀⠀⠀⢀⡴⠛⢼⣾⠆⠀⠀⡟⠙⠛⢿⣧⡀
⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢸⠀⣿⣿⢠⠁⣴⣧⠈⢻⠋⠈⣆⡴⢋⣰⠏⠀⠀⠀⠀⠀⠀⡟⠀⠀⡸⠇⠀⣠⠞⠀⠀⡠⢾⣿⡇
⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⣷⣿⣧⢮⣰⠿⠞⠀⣰⠀⢀⣹⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⢀⡰⠁⠀⢸⡷
⠀⠀⠀⠀⠈⢿⠳⡒⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠸⣆⢸⠀⢳⣾⣙⣩⠟⠉⠐⠈⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠈⠳⣝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠙⠳⢤⣄⠀⠀⠙⣾⣄⠀⡏⠁⠀⠀⠐⡟⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡴⠏⠹⣿⣿⣶⡶⠖⠉⢀⣀⣠⠴⠛⠁⣀⣀⣤⠤⢤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣵⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣘⠋⠀⠀⠉⠉⠉⠈⢷⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢟⣹⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢧⣲⣄⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣊⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠻⠷⣶⡾⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣺⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⣀⣀⣀⠤⢤⣠⣦⡥⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠉⠉⣹⠟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣀⢞⠇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡧⠞⠡⠎⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢼⠇⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠚⠁⢤⡀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⢸⠀⠀⠀⢠⡖⣧⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠑⠲⢤⣈⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠸⡆⠀⠀⢰⣗⣼⡇⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢰⣃⡼⠃⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠑⢄⡀⠸⡄⠀⠀⠀⠀⠀⢧⠀⠳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡽⠶⠷⢄⣀⢀⣠⣤⣞⣆⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢇⣤⠘⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⠣⠌⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠿⠶⠦⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠀⠀⠀⠀⣀⣀⣠⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣶⠟⣡⠋⠀⢀⣠⠤⠤⠄⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠓⠀⠀⠀⠀⠉⠀⠀⠀⠉⠻⣟⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⢿⣾⢶⡧⣤⢀⣎⡀⠀⠀⠀⠀⣠⠔⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠣⡀⠀⠀⠀⠉⠉⠉⠳⡄⠀⠈⣧⣈⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣾⣡⣾⣫⣾⡟⣺⡽⠒⠒⢋⣡⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣈⠑⠢⠤⣀⣀⢠⡶⣾⣴⡛⢽⣟⠽⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠉⠉⠉⠛⠋⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣬⣿⣮⣽⠿⣶⡿⠳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
