⠁⠉⠙⠛⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣅⡤⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀
⡶⠃⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣵⠛⠻⠋⢙⣳⣄⠀⠀⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣴⠋⠉⠒⠒⠊⠁⠀⠉⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣱⣿⠃⠀⠀⠀⠀⠀⢀⣴⠚⠛⠳⡄⠀⠐⢦⣄⡘⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡏⠊⠀⠀⠀⠀⠀⢠⣿⣭⣆⡀⠀⢹⠀⠀⠀⢿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⡇⡆⠀⠀⠀⠠⠀⣜⠈⠙⠻⠿⢷⡟⠀⠀⠀⢠⣿⡋⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣇⢠⡀⠀⠀⠀⣀⣼⣦⣀⣀⡴⠛⢲⡆⠀⠀⢀⡇⠁⠀⣦⠈⠈⠙⢶⡄⠀⠀⠀⠀⣀⣀⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡈⠯⢷⣄⠉⢿⣯⣂⠀⠈⡇⠀⢠⡞⠁⠀⠀⣼⣤⣇⠀⡟⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢭⠙⠷⢤⣹⣦⣲⣌⣙⣛⣶⡇⠒⠛⠀⠀⣠⣼⢻⠀⠉⢻⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⡄⢀⠈⠉⠛⡷⣍⣁⣤⣤⠶⠾⠛⣽⠃⣈⣷⣴⣿⣤⢤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢠⢀⣠⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠉⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠻⠮⣅⣈⡟⠀⠉⢶⠀⣧⡼⠿⣿⣿⣿⣿⣿⣿⣿⠛⠒⠲⢶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣦⡤⣶⣶⢶⣄⢀⣄⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⣠⡾⢦⣨⡤⠖⠋⠈⢻⡿⠟⠉⠉⠓⠶⢬⣉⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀
⣿⡿⠋⠩⠉⢩⢻⡿⡆⠀⠀⠀⣵⠸⡌⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣏⠹⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣷⠀⠀⠀⠀⠀⢷⢻⠀⠀⠀⢹⡇⢓⢸⣿⣿⣿⣿⣿⡟⠓⠶⣤⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⡇⡄⢠⡏⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⢸⠸⡄⠀⠀⠈⣃⠘⠈⣿⣿⣿⣿⣿⡟⠒⠲⠴⠿⡤⠀⠀⢰⣏⣉⣁⣬⠇⠀⠀⠀⢀⡤⠤⠤⢤⡶⠀⠀⠀⠈⢷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⡇⠃⢀⣉⣀⣀⣶⣤⣿⣿⣿⣿⡿⢳⡄⠀⠀⠀⠀⢾⠙⣯⡉⠉⠀⠀⠀⠀⠀⠀⠹⠦⠴⠤⣴⠧⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣤⣴⣷⣿⣿⠿⠿⠿⠿⠛⠛⠛⣻⣿⠙⠋⠁⢀⡾⣅⡀⠀⠀⠀⠘⣦⣈⡧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⠧⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⢉⣀⣤⣤⠶⠴⠶⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠘⡆⢸⣉⠙⠓⢶⡄⠈⠉⠀⠀⠀⠀⠀⠀⣏⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠋⣹⡇⠀⠳⢤⣟⡽⢶⠾⠋⠀⠀⠀⠀⠀⠀⣴⠒⢿⣄⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠖⠛⠉⠀⠀⣠⠞⠉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠤⠤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.