⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠊⠉⠉⠉⠉⠙⠋⠛⠻⠶⣢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣈⣑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣟⢿⣷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠊⡁⠀⠀⠀⠀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠐⠒⣓⡛⠊⠈⢷⢤⠜⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡯⠟⢀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣁⣂⣀⡀⠹⠕⡢⢝⡢⢄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣴⠞⠁⠀⠀⣤⠀⠀⢀⣀⡠⣴⣶⡋⠉⠩⢿⡧⠤⠹⣿⣿⣿⣿⣶⣶⣬⣝⣻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⢀⣩⢴⣾⠟⠛⠙⠂⡇⠀⠀⠀⠈⢷⠐⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⣀⣴⣾⡿⣿⡿⢿⣿⣶⡀⠈⠀⠀⠀⠀⠀⠀⢠⣤⣤⡘⡏⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠀⠀⣠⣴⣿⣿⣿⣿⡿⠋⣼⣿⣿⣽⣆⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣆⢹⣿⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⢀⣴⣿⣿⣿⣿⣿⣿⣿⢧⣄⢻⢟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⢸⢸⣿⣿⣿⡟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠈⢸⡞⠋⠈⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⣿⣿⣿⣿⣿⣿⠷⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡼⡇⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⡿⣇⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⠒⠒⠛⠭⠷⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⠀⠀⠀⠸⣿⣿⣿⣶⣦⣤⣄⣀⣀⠀⠀⢀⣀⣀⣤⣴⣾⣉⣀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠻⢷⣤⡀⠀⢿⢿⡿⣿⣿⣿⣿⣻⣶⡭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⢀⠀⠀⠈⢙⣦⣁⠈⠧⣿⣿⣿⡉⠻⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢋⢳⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟⣿⡩⡤⠖⢾⠉⠀⠊⠳⢬⣸⣿⣿⣷⠂⠄⠙⢿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣦⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⢰⠛⠂⠘⡆⠀⢸⣿⣷⠙⣿⣿⣿⡇⠀⣠⠵⡭⠛⠿⡟⣿⣿⣿⡤⠖⠻⣻⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡏⠀⠐⠀⢹⡀⢸⣿⣟⠁⣿⣿⡟⣿⠚⠁⠀⢯⣀⠀⡎⠹⣿⣿⣿⡀⠄⠐⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⠀⠀⠀⠀⠀⣇⢸⣿⡇⢀⣾⣿⣿⣿⣄⠀⠀⢸⡹⣿⣹⠯⣿⣿⣿⡇⠀⡸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢸⣾⣿⣠⣿⡼⣿⣿⣿⣧⠤⣄⡀⣇⠙⠋⣇⠘⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡇⢴⣿⣿⣿⣿⣇⣸⡀⢸⠂⠀⢸⣶⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠰⠀⠀⠀⠠⢀⠀⣿⣿⣿⣯⣯⠉⣿⣿⣿⣿⡿⡉⣇⠌⡗⢛⢣⣽⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀