⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠠⣄⡀⠀⠀⠀⠀⣾⠀⢹⡄⠀⣀⠈⠻⣿⣿⣿⣿⡿⢛⠀⢻⡀⠀⠀⠀⢀⣠⠄⠀⠀⠀
⢤⣅⢀⣀⣠⡙⠲⣤⡀⢰⠏⠀⢸⣇⡤⠃⠀⠀⠀⠉⠉⢶⢰⡟⠀⠘⣧⠀⣀⡴⢛⣧⣄⠀⢀⣶
⠀⠉⠉⠁⠀⠙⢦⡀⠙⠻⠆⠀⣼⢿⡆⢤⣤⣤⣤⣤⣤⣀⣿⢿⡀⠀⠛⠛⠁⣠⠞⠁⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣶⣾⠃⣸⣿⣤⣅⣃⣘⣁⣤⣾⣧⠈⢷⣶⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢀⠀⣉⢙⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⣉⡁⢀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣴⠃⣴⣾⣿⡟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠹⣿⣿⣶⣄⠀⠀⠀
⠀⠀⠓⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠖⠀⠀
⠀⠀⠀⠐⠂⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠹⣄⠉⠙⠓⠶⡦⠄⣤⣿⣿⣿⣿⡆⢠⠤⠶⠶⠚⠉⢀⣿⠁⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣶⣀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡏⢁⡿⠓⠦⠀⠀⢠⠖⠻⣅⠉⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⣠⠀⠀⠀⠀⢧⠀⠘⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠤⠴⠃⠀⠀⠀⠀⠈⠳⠤⠼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⠟⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣟⣃⡤⠤⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣴⡶⠦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⢿⣿⠁⠀⠀ ⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠯⠀⢠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⣿⡏⠀⠀⠀⢠ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⠀⠀⠘⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣜⣷⣿⣿⠁⠀⠀⢸ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⠀⠀⠘⣿⢠⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣇ ⠀⠀ ⡇ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⣾⣾⣷⣿⣿⣿⠿⢿⣿⣶⣾ ⣿⣿⣇ ⢸ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣇⣾⣿⢿⡟⠀⠸⣿⡄⢹⡁⠀⢹⣿⣿⣿⣿ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡟⠉⠘⣇⠈⠀ ⠀⠀⠀⠀ ⡏ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣷⠀⠀⣼⡿⠧⠒⠒⠛⠛⠒⣶⢤⣄⣳⡀⣀⣀⡤⠥⠤⠬⢷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀ ⠈⠙⠓⠢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⢰⣷⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀
⢠⡴⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⡇⠀⠀⠀⠀⠀⠀⠀
⠈⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀
⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀
⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⢿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⡾⡟⠀ ⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡷⠖⠒⠲⢄ ⠚⢁⣢⠀⠀⠀⣇⠙⠒ ⡞⠀ ⠀⠀⢀⣀⡀⠀⠀
⢠⠞⠀⠀⠀⠀⠀⠹⣶⢤⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠈⡇⢀⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡴⠊⠁⠀⠈⢦⡀
⡞⠀⠀⠀⠀⠀⠀⠀⠙⠳⣽⣷⡀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⣶⡿⠀⠀⠀⠀ ⠀⠀⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢦⡀⠀⢠⢿⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⣀⡤⠤⠤⠤⣴⣻⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣏⡇⢹⡀⣸⡏⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠋⠁⠀⠀⠀⢰⣳⣧⡇⠀⡆⠀⠀⠀⠀⠀⠀⢀⡟
⠘⣆⠀⠀⠀⠀⠀⠀⣄⢧⣾⣿⣿⠁⠀⢷⡿⠀⠀⠀⠀⠀⠀⠀⢱⠀⡴⠃⠀⠀⠀⠀⠀⣾⣿⢧⣧⠀⡇⢰⠀⠀⠀⠀⠀⣼⠃
⠀⠸⡄⠀⠀⠀⠀⠀⠈⣿⣿⡽⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠻⣿⣮⣿⣷⡇⠀⡄⠀⠀⠀⣔⡏⠀
⠀⢰⠻⡄⠀⠀⠀⠀⠀⢹⣏⡄⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡌⠒⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⡟⠁⡀⠀⠀⠀⠀⠙⡇⠀
⠀⡼⠰⢿⠀⠀⠀⠀⠀⠈⠛⣶⣦⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣠⠤⠴⠚⠉⠀⡼⠁⠀⠁⠀⠀⠀⠀⢹⠀
⠀⡇⠀⠈⠀⠀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀ ⠀⠀⢠⠀⠀⠀ ⢸⠀
⠀⢧⠀⠀⠀⠀⠹⢤⡀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⢲⠇⠀⠀⠀⠀⠞⠀⠀⠀ ⣸⠀
⠀⠈⠳⠤⣀⣀⣀⣀⡤⠤⠤⠤⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠯⢤⣀⣀⡤⠤⠤⠤⠤⠴⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢛⠚⣉⢋⡙⢩⠙⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠰⡈⢆⠱⢠⠒⡌⢢⠉⡜⡐⢂⠌⡙⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠞⡡⠒⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⠠⡑⢨⠐⡡⢂⣽⠶⣀⠀⠀
⠀⠀⠀⠀⡼⢃⠜⡠⢃⠜⡠⢃⠜⡠⢊⠔⡡⢊⠔⣡⣿⣿⣆⠡⢂⢿⣿⡙⣄⠀
⠀⠀⠀⣼⠃⡌⢢⠑⡌⢢⠑⡌⢢⠑⡌⢢⠑⡌⢢⢸⣿⣿⣿⡆⢡⠺⣿⣷⠘⡆
⠀⠀⢰⡇⡘⢄⠣⡘⠄⢣⠘⡄⢣⠘⡄⢣⠘⡄⢣⠈⣿⣿⣿⡇⢢⠁⢿⣿⢀⢻
⠀⠀⢸⠆⡱⢈⠆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⡈⠿⡿⢃⠂⣍⣠⣦⣬⣺
⠀⠀⢺⡁⣆⣥⠬⠵⣔⠈⢆⠱⣈⠢⡑⡈⢆⠱⡈⢆⡑⢢⢰⣷⠛⠉⣁⣤⣿⢗
⠀⣠⠟⢋⣡⠴⠚⢋⣁⣮⠶⠛⢉⣹⡽⠅⡌⢢⠑⢢⠘⠤⣈⠻⢿⣿⡿⠿⢋⢸
⡿⢃⡴⢋⠔⡨⢑⣦⠏⣀⡴⠚⡉⢄⠒⡌⠰⡁⠎⠤⣉⠒⡄⢃⠆⡄⢢⠑⡌⡿
⣿⢊⠑⡌⢢⢡⡿⣡⠞⠡⢄⠣⡘⢄⠣⢌⠱⡈⠜⡰⢀⠣⡘⢄⠊⡔⢡⢊⣼⠁
⣏⠄⢣⠘⢄⢺⣗⠠⡘⠰⡈⢆⠱⢈⠒⡌⢢⠑⡘⢄⠃⢆⠱⣈⠒⢌⢂⡾⠁⠀
⠻⣌⠂⡍⢄⠚⣿⡄⢡⠃⡜⢠⠊⡄⢣⠘⡄⢣⠑⡌⡘⢄⠣⢄⣉⣦⠛⠀⠀⠀
⠀⠙⠳⣌⠢⢑⡘⢿⣦⡑⠄⢣⠘⡄⠣⡘⢠⠃⠜⡠⠑⣨⣰⠶⠋⠀⠀⠀⠀⠀
⠀⠀⠀⢈⡙⠓⠚⠒⣚⠻⠞⢦⡥⢦⡵⠶⡳⠞⠶⢳⠛⢃⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣠⡶⠞⠛⠉⠉⠉⠙⠳⣦⡀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢾⡧⣆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠉⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⢶⡄⠀⠀⠈⢷⡹⣆⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣤⠞⠁⢀⣴⠞⠉⢿⣜⣀⣀⣤⡴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⠛⠃⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠋⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⣠⣤⣴⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢛⣿⣉⣁⣀⣠⣠⣤⣴⣶⣶⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣯⣵⣶⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀
⠟⠛⠛⢿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⣷⣶⢶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣀⣀⣤⣤⣴⣶
⣠⣤⣴⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⣀⣀⣤⣬⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠿⠿⠟⠛⠋⠉
⟡ pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
completely free, NO signup required (ever), and unlimited!
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣂⣂⢂⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣄⣿⣗⢛⢻⡯⣗⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡸⣿⣯⣷⣯⣭⡗⣯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢟⣿⣿⡏⣞⣥⣿⡏⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡓⣯⣿⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⢀⠀⢳⣋⣇⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣟⣿⡷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢠⣖⣯⣿⣿⣤⣍⡿⢿⣇⡢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⣟⣿⢿⡹⣆⣅⠯⣏⡏⢻⣒⠖⣒⣆⣥⣀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣏⡏⠈⠉⠉⠆⢉⣓⣎⡛⡣⡏⡿⡯⠸⠙⢀⠑⠁⡇⠄
⠀⠀⠀⠀⠀⢀⣏⡏⠀⢀⡠⠊⡉⠟⡋⡽⣕⣧⣕⣍⣟⠇⠸⣘⢃⣔⡅⡃
⠀⠀⠀⠀⠀⣮⡷⡁⡄⢃⠔⣈⡤⣆⣥⡥⣏⡗⢟⡛⠩⠐⢌⣱⣾⡺⡃⠁
⠀⠀⠀⠀⣞⣿⣡⢅⡇⣯⣋⡵⠗⡋⣹⣄⡄⣤⣄⣍⣀⣀⡁⢈⠉⠈⠀⠀
⠀⠀⠀⠀⢣⣻⣁⣏⡷⣟⣝⡟⡟⡏⣏⡇⡽⠅⠇⠉⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⡯⣏⡇⡯⠉⠐⠬⣯⡟⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡹⡗⣁⡐⣝⡄⠀⠋⢿⣏⣾⡗⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡪⡯⣍⣧⣹⠙⣄⠀⠀⣗⡆⡿⡏⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢨⣟⡓⡏⣷⡳⡌⠀⠀⠘⡌⣅⠉⢿⡝⠧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⡧⡋⡯⠆⠄⠀⠀⠇⠀⣧⡈⠻⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⡤⣊⣭⣿⡄⠀⠀⢔⣆⠗⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠋⠉⠀⠶⣦⠌⠙⠿⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠃⡀⣀⣤⣤⡤⠶⠷⣤⣽⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⢸⡟⠋⠉⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢶⣴⣶⣤⣀⣀⣀⣀⣀⣘⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣏⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢠⣄⣍⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣄⣀⣀⠀⠈⣿⣿⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢛⡛⠉⠉⠛⣿⣿⠀⢿⡇⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠄⠁⠀⠀⠀⣿⣿⠀⢸⣧⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⠀⣽⣿⠀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⠂⠀⠀⠀⠀⢰⣿⡇⠀⠊⣿⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢸⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⠀⠀⠄⠀⠀⢠⣿⡟⠀⠀⣸⣿⣷⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⣤⣠⣼⣿⠃⠀⠀⣿⡏⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠉⠛⠛⠿⠿⠿⠟⠁⠀⠀⠀⢻⡇⢸⣆⢿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣽⣿⣿⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠋⠛⠶⣦⣀⠀⠀
⠀⠀⠠⢸⣿⢰⡇⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠘⢃⣆⣈⢻⣷⠀
⠀⠀⠀⢸⣿⠘⠃⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣀⣠⣴⣾⠟⠏⣺⣿⡇
⠀⠀⠀⠈⢿⣧⣀⡀⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠛⠉⠉⢀⣤⣿⡿⠀
⠀⢀⣠⣤⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤⣴⣿⣿⠟⠉⠀⠀⠀⢀⣠⣶⣿⠿⠋⠀⠀
⢰⣿⠛⣷⠦⠀⠀⣩⣿⠿⠛⠉⠉⠙⠛⠿⠿⠿⠛⠛⠉⠁⠀⢀⣀⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀
⠘⢿⣿⣦⣤⣄⣸⣿⣷⣄⡀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⣴⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠙⠻⠿⠿⠿⠟⠿⣿⣷⣶⣶⣶⣶⣾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢘⣨⣧⡿⢿⣶⣿⣷⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣴⠾⠛⠋⠉⠉⠛⠛⠷⣦⣠⡶⠛⠁⠀⠀⠀⠀⠈⠙⢿⣷⣄⠈⢿⣟⠛⠛⣶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣷⡾⠋⠁⠀⠀⢀⣀⣤⣤⣤⣤⣈⡙⢷⡄⠀⠀⢀⣀⣤⣤⣤⣤⣽⣿⣷⣦⣽⡶⣄⣸⣿⢷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⡟⣴⡆⢀⣠⡾⠛⠉⠁⠀⠀⠉⠉⢛⣿⣿⣶⡾⠛⠉⠁⠀⣀⣤⣤⣭⣽⣿⣿⣿⣿⡏⢻⡿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⣰⠏⠀⠸⠋⠀⠀⠀⣀⣤⡶⠶⠶⠿⠿⠿⢿⣿⣄⣠⣴⢾⣿⣿⣤⡄⠀⠀⠙⠻⢿⣿⣿⠀⢸⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣽⣿⣿⣧⡟⠀⠀⢀⢰⣦⣤⡾⢻⣿⣿⣿⡶⠀⠀⠀⠀⠈⢻⣿⣿⣦⣿⣿⣯⡁⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⣿⡿⣿⠟⠁⠀⢀⣿⢷⣿⣿⣷⣶⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣴⣿⡿⣹⡏⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣏⣙⣿⣿⡏⠀⠀⠀⣸⡿⢿⣿⣿⣿⡿⠟⠁⠀⢀⣴⣿⡷⠟⣻⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣿⣿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⡿⠿⠋⠀⢀⣠⡾⠛⠀⠚⠿⣿⣥⣤⣶⡶⠾⠛⠻⣯⡇⣴⣯⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⣿⣿⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⡻⠶⠶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡞⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣛⠻⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣿⣿⣧⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⢿⣶⣦⣭⣿⣻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣯⣿⣼⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⣉⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣹⣿⡿⡽⠻⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⠟⠋⠉⠉⠛⠻⣿⣯⣭⣭⣭⣶⣶⣾⡿⢟⡉⠃⣠⡾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠲⣿⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣟⣩⣷⣶⣾⣷⣾⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣀⣼⡿⣿⡏⣿⠟⠿⠿⠿⠿⠟⠛⢻⣿⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣍⣽⣿⢿⡟⠹⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⢚⣿⠋⣰⡟⣼⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡍⠻⠼⣇⡼⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠉⣻⡟⠁⢰⡿⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠈⢿⣄⠸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠙⢷⣶⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⣿⠋⠀⢀⣿⢃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠻⣦⣈⡻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠻⣧⡜⠻⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣴⡿⠁⠀⠀⣼⠏⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠈⠙⠛⠛⠛⠻⣶⣄⡀⠀⠀⠀⠀⠘⢷⣎⠉⢳⣄⡤⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⣴⣿⣿⣿⣿⣿⡀⠀⢀⣴⣿⣀⠀⠛⠻⣶⣶⣶⣶⣶⣶⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣀⣀⣠⣶⣾⣿⣇⣈⣿⡀⠈⡀⠀
⠀⣠⣴⣶⢾⣿⣷⡿⢋⣭⠉⢉⣽⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠿⠶⢶⣤⣀⠀⠀⠀⢀⣠⣼⣿⠿⠟⠛⢻⣍⠁⢸⣏⢿⡝⢻⣿⣇⠀⠀
⢀⣿⠁⡿⣿⢇⣿⢁⣾⠋⣴⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣶⠾⠛⠉⠀⠀⠀⠀⠀⠈⢻⣆⠀⣿⡈⣿⢸⡏⢿⡄⠀
⠸⡇⢸⣿⣿⣾⠟⠛⠁⣾⠏⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣧⣿⣿⢷⠿⣧⠀
⠐⡇⢸⣿⣯⠇⠀⠀⢰⣿⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⡟⠁⠀⠀⠀⣿⠻
⠀⣿⡈⢿⣻⣧⠀⠀⠸⣿⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⣰⡟⠀
⠀⠈⣷⡘⣧⣹⣷⡀⠀⢿⣧⡀⠀⠀⠘⢿⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣴⠟⡃⠀
⠀⠀⠀⠁⠙⠣⠬⢻⣦⡈⠻⣷⣄⠀⠀⠈⢻⣧⡀⠀⠀⢻⡇⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣴⠟⣁⠞⠁⠀
⠀⠀⠀⠀⠀⠀⠀⣶⡼⣿⣷⣍⠻⢷⣦⣄⠀⠙⢿⣦⡀⠈⢿⣆⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⣠⡶⠟⢁⡜⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢻⠛⢷⣄⠉⠛⠿⢷⣾⣿⣿⣶⣦⣿⡿⣿⣿⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣠⣤⣶⡾⢿⡿⠋⠀⠀⠀⢀⣤⡾⠿⢤⡶⠛⢣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣿⡶⠾⠟⠀⠀⠀⠀⠀⠹⣿⡙⠳⣶⠟⠉⠀⠉⠉⢛⣛⣛⣛⣛⣛⣻⠋⠉⠀⣸⣥⡿⠁⠀⠀⠀⠀⠈⠛⠷⠾⣷⣤⣄⡛⢃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠨⡉⢹⣷⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣶⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⣉⡍⢉⡙⠛⠛⠛⠛⢟⠛⠻⢿⣭⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢛⣋⡏⢩⠁⠀⠀⠀
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