⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠒⠒⠒⠒⠒⠂⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣄⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⡀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠒⡿⠛⠃⠀⠀⢠⠂⠛⣿⠟⠃⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣛⣯⠭⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠞⢉⡰⠊⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠏⢀⡜⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠏⠀⠸⠁⠀⠀⠀⠀⠠⢬⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⠼⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣟⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡶⠉⠀⠀⠀⠈⢷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠉⠲⢦⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣆⠉⠙⣶⠦⢄⣀⣀⣀⣠⡤⠶⠋⠁⠀⡀⠈⣇⠀⣀⣀⢀⢀⣀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣾⠀⢀⣉⣉⣉⠉⠉⠉⠉⠉
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠳⣗⠒⠒⠚⠉⠀⠀⠀⣠⡌⠘⣀⠽⠤⠇⠒⠶⣖⡢⢭⡓⣤⠀⡜⠀⠀⠀⠀⠀⢀⡏⠀⡘⠈⠓⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢀⠞⠀⠀⠄⠒⠺⠤⢴⢲⠀⠀⠀⠀⠀⠉⠁⣿⠀⡇⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠛⣤⠀⠀⠀
⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠹⠀⠀⠀⢠⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠰⢲⠶⡶⣿⠀⠀⠀⠀⠀⠀⠀⣿⢠⠁⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⣄⠀
⠀⠀⠀⠀⣇⠀⠘⡇⠀⠀⠀⣇⠀⠀⠀⠱⢄⡀⠘⡤⠶⠶⢄⣀⣀⠴⠉⠀⠀⠀⠀⠀⠰⢚⠤⠍⡇⠀⠀⠀⠀⠀⠀⢠⠇⡾⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠹⡀⠀⢱⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠉⠙⣤⣄⡔⢫⠁⠀⠀⢀⠖⢦⡤⠤⠔⠛⠢⡐⡧⣤⣀⠀⠀⠀⣤⠟⢀⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⠀⠘⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣴⠁⠀⠀⢸⡀⠀⣠⠋⠀⠀⠈⠓⠄⠀⠀⠈⠁⠀⢸⡏⠉⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡀⠀⢱⠀⠀⠀⠀⣹⡀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢣⡎⢷⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢇⠀⠈⡇⠀⠀⢠⠁⣱⡄⠀⠀⠈⠃⠀⠀⠀⠀⢈⡗⠞⠀⠀⢀⣉⣉⣑⣲⣦⠄⣀⣠⢾⣁⣀⣀⠀⠀⡿⠀⠀⠀⠀⠀⣾⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⠛⢹⣸⡧⣄⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠈⠉⠓⠒⠒⠠⢤⡈⢻⠀⠀⠀⠀⠈⠙⠛⡇⠀⠀⠀⠀⢀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡆⠀⠀⠀⠀⢡⠓⠚⠛⠒⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⣤⣄⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢯⡩⡍⠛⠶⠤⣀⡀⠈⢇⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠷⠶⠾⠗⠛⠘⠳⢄⡀⠀⠀⡞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠶⣄⣀⠀⠙⠲⢾⣆⠀⠀⠀⠀⠀⠈⡇⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣀⡇⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢿⠀⠙⠢⣄⡀⠀⠙⠛⠲⣤⡀⠀⠙⢢⡀⠀⠈⠛⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡿⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⣆⠀⠀⠀⢙⣳⣤⠀⠀⠀⠈⢳⡏⠁⠈⠓⢤⡀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⡀⠀⠈⠛⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣹⡶⠭⣍⡉⠀⠀⢷⠀⠀⠀⢈⡇⠀⠀⠀⠀⠈⠑⠦⣄⡀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⠦⠤⠤⡠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣿⣿⢟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡄⠀⠀⠀
⠀⢀⣼⣿⡿⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀
⠀⣾⣿⡟⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢿⣇⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠇⠀⠀⢸⣿⠀⠀⠛⠃⣶⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⢠⣤⣴⣶⡾⠿⠟⠛⠙⠻⣿⣦⠀⠀⠀⠀⣾⣇⣤⣾⠿⣿⣦⣤⣀⣠⡄⣠⣿⣿⠏
⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⣀⢠⣿⣏⣤⣤⣤⣶⣶⣤⣤⣬⣿⡇⠀⠀⢸⣿⡿⠋⢁⣀⣀⣈⣉⠻⣿⣥⣿⣿⡃⠀
⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣟⢻⣿⠛⠉⠹⣿⣿⣿⣿⣿⠋⣿⡇⠀⠀⠸⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡿⠋⠉⠀⠻⣷⣤⡀⠈⠉⠉⢉⣡⣾⣿⠁⠀⠀⠀⠙⢿⣦⡀⠙⠿⠿⢿⣿⡿⠛⢿⣿⡆⠀
⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⣷⣶⣶⣾⠿⠋⠁⠀⠸⣿⣷⠀
⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠿⠿⠿⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⣿⢿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠿⠿⠙⢿⣿⣷⣦⣄⡀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣿⣿⣷⣶⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣴⣾⣿⣿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣬⣿⣿⠉⠉⢻⣿⣿⣶⣦⣤⣄⣠⣤⡀⠀⠀⠀⣰⣿⣇⣴⣷⣶⣄⠀⠀⠀⠀⠀⢻⣿⡇⠀⢠⣾⣿⢟⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⠉⠉⠛⠛⠛⢻⣿⡇⠀⠀⢠⣿⠛⠿⠿⠿⠙⢿⣷⣄⠀⠀⣀⣼⡿⣿⡀⣿⣿⡏⠈⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⠋⠁⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣿⣿⠃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠸⣿⡇⠀⣼⡟⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣶⣶⣄⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠛⠃⢠⣿⠁⠀⠀⢀⣴⣿⠟⢉⣤⡍⠛⢡⣽⣿⡆⠈⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣾⣿⣥⣶⡿⣿⣷⣶⡿⣿⣾⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠉⠁⢀⣴⣿⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣴⣶⡿⠟⠁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⣷⣦⣄⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣾⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠛⠿⣿⣿⣷⣦⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣦⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠹⣿⣿⣶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠈⠻⢿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣰⣿⣿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠻⣿⣿⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣶⣾⣿⣿⠿⣧⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠉⠙⠛⠿⠿⣿⣿⣿⣷⣶⣶⣾⣿⣿⡿⠛⠉⠙⠛⠉⠛⠻⠛⠀⠀⠀⠀

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