⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠶⠾⠋⠀⠘⠿⠶⣦⣄⡀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣤⣄⣀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣼⣿⡭⢍⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠈⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⠗⠂⠛⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⢦⠀⣴⢿⣯⢷⠸⣧⢀⣶⡄⠀⠘⢷⠟⠛⠛⠁⠀⠀⢀⣀⣠⣤⣤⣶⡟⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠒⠏⠨⣿⠶⢓⣿⠀⠉⠁⠀⣀⣀⣤⣴⡶⠶⣾⣛⣻⣽⣿⣶⡾⢾⣟⠛⠛⢿⡀⠀⠀⠀⠀ ⢀⣿⠁⠀⠀⠀⢀⣀⣒⣴⣾⣷⣶⣶⣿⣿⣯⣿⠿⠾⠛⠛⣿⡋⠉⠀⢿⡄⠀⠀⢻⣆⠀⠈⢿⣦⡀⠀⠀ ⠹⣿⡴⠶⠟⠛⠛⠋⢉⣿⡿⠿⠛⠻⣯⠁⠀⠻⣦⡀⠀⠀⠙⣷⡀⠀⠀⢻⣆⣀⣤⣿⠶⢶⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⢻⣆⠀⠀⠙⢷⣄⣀⣨⣷⣤⣤⡶⢾⣿⣻⣿⣿⣿⣿⡿⠾⠛⠛⠛⠉⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠹⣷⠟⣛⣻⣯⣭⣿⠾⠿⠿⠛⠛⠋⠉⠁⠀⢀⣀⣠⣤⣤⣶⠶⠶⠿⠻⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⡟⠉⠉⠀⠀⣀⢀⣀⣀⣀⣤⣤⡴⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠛⠂⠀⠀⢰⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣰⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣀⣀⡀⠀⠀ ⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⢰⡇⠀⣿⠁⠀⠉⠻⣦⡀⠠⠟⠀⠀⠀⠀⣿⣧⣶⠿⠛⠙⣿⠀⠀ ⣿⡋⠉⠙⠛⠷⣦⣄⠀⠀⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⣰⣿⠟⠁⠀⠀⠀⣿⠀⠀ ⠸⣷⡀⠀⠀⠀⠈⠛⣷⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡀⠀ ⠀⠘⢿⣆⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⡀⠀⢀⣴⡿⠃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⣷⡄ ⠀⠀⠀⠙⢷⣤⡀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⣼⡏⠀⠀⠀⠀⣾⣅⣀⣿⠀⠀⠀⠀⠀⠀⠀⣾⣅⢈⣷⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⢸⡇⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠻⠿⠟⠀⠀⠠⣖⢒⡶⠀⠙⠿⠿⠟⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢈⣏⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⢰⡆⠀⠀⢻⣧⡀⠀⠀⠀⠀⠈⠻⠶⣤⡴⠟⠙⠶⣤⡤⠞⠁⠀⠀⢀⣾⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠉⠛⣿⠛⢻⠿⠿⠿⠿⣿⡿⠿⠛⠛⠛⠛⠛⣿⠛⠉⠙⠛⣿⠛⠛⣿⠟⠛⠛⢻⡏⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣤⡾⠃⠀⣿⣀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣴⠟⠀⠀⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠙⠷⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠄⠀⠀⠸⢰⡏⠉⠳⣄⠰⠀⠀⢰⣷⠶⠛⣧⠀ ⢻⡀⠈⠙⠲⡄⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠈⠓⠒⠒⠛⠁⠀⠀⣿⠀ ⠀⠻⣄⠀⠀⠙⣿⠀⠀⠀⠈⠁⠀⢠⠄⣰⠟⠀⢀⡔⢠⠀⠀⠀⠀⣠⠠⡄⠘⢧ ⠀⠀⠈⠛⢦⣀⣿⠀⠀⢠⡆⠀⠀⠈⠀⣯⠀⠀⠈⠛⠛⠀⠠⢦⠄⠙⠛⠃⠀⢸ ⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⢠⠀⠀⢠⠀⠹⣆⠀⠀⠀⠢⢤⠠⠞⠤⡠⠄⠀⢀⡾ ⠀⠀⠀⠀⠀⢀⡿⠦⢤⣤⣤⣤⣤⣤⣤⣤⡼⣷⠶⠤⢤⣤⣤⡤⢤⡤⠶⠖⠋⠀ ⠀⠀⠀⠀⠀⠸⣤⡴⠋⠸⣇⣠⠼⠁⠀⠀⠀⠹⣄⣠⠞⠀⢾⡀⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠢⠄⣀⠉⠓⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀ ⠀⠂⠤⣀⠈⠑⠂⠤⣀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠀⠀⠀ ⠂⢄⣀⠀⠉⠒⠤⣀⠀⠉⠒⠤⣀⠈⠑⠢⢄⡀⠀⣀⠤⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⣀⠀⠉⠒⠤⢀⠀⠈⠑⠢⢀⡀⠉⠒⠤⣀⢨⠟⠛⠒⠦⢄⣀⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠉⠒⠤⣀⠀⠉⠒⠠⢄⡀⠈⠑⠢⣄⣀⡉⠀⢀⣠⣄⡀⠈⠉⠒⠦⢄⣀⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠉⠒⠤⣀⠀⠉⠒⠢⢄⠀⠈⠑⠢⢼⠉⢻⠣⠀⢸⠀⠀⡉⠑⠲⠤⣀⠀⠈⠉⠒⠢⣄⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠢⢄⡀⠉⠑⠢⢄⡀⠈⠑⠢⢄⣸⠀⢸⣷⠀⢸⠀⠸⠟⠀⠀⠀⢠⡿⣷⣶⢤⡀⠀⢳⠀⠀⢱⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠢⢄⣀⠈⠑⠢⠄⡀⠈⢧⡀⢻⠀⢸⣄⠀⠀⢀⣀⡀⠀⠘⡇⠈⠳⣿⠀⠀⡇⠀⢸⡤⠋⠀⡇⠀⠀⠀⠀⡠⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⠈⠉⠒⠿⣿⠀⢸⠁⠀⠀⠘⠚⠁⣤⣄⣣⠀⠀⠘⠒⠚⠓⠒⠚⠁⠀⠀⣷⠀⠀⠀⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣀⢸⠀⠘⣄⠀⠿⠇⠀⢀⡉⢹⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⣠⣄⠸⡆⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡴⠈⡟⠢⢄⣀⠙⠃⢸⣀⠠⢄⠻⠋⠀⠀⣤⡄⠀⠛⢛⠅⢿⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠿⠤⣀⠈⠙⠒⠼⣷⣄⠜⠀⢠⠀⠀⣸⠀⠀⡤⠘⣦⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠒⠦⣄⡀⠉⠒⢤⣌⣉⣉⣉⣉⣻⣥⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡎⠀⣴⡇⢀⣼⡂⠈⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠴⠋⠉⠉⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⡏⠙⣷⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣇⣈⢁⣀⣘⣶⣿⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⢯⣽⣸⣿⣏⣿⡟⠁⠀⠈⠻⣆⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢻⡟⢿⠛⠿⠀⠀⠀⠀⠀⠈⠉⣉⣁⡀⠸⣿⣿⣿⠋⢻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣄⠀⠀⢰⣋⣉⣁⣀⠀⠀⠉⠀⠀⠈⠛⠛⠋⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢉⣉⣹⡟⠀⠀⠸⣿⡆⠀⢠⣽⣿⠄⠀⠻⠟⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠚⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⣤⣄⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣠⣾⠛⢿⣿⠇ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣦⡾⠋⠀ ⠀⠀⠀⠀⠀⢛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠶⠞⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠾⠃⠀⠀⠀⣿⣁⡾⠷⠶⠤⢤⣤⣤⣻⣿⣋⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠂⣠⡴⠋⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀ ⣼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⣠⡄⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⣟⠛⠛⠿⠿⣿⣟⣛⡻⠖⠛⠁⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣦⣐⡆⠀⠀⠀⠉⠉⠀⠀⠀⠀⢶⣀⣤⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣶⣶⡞⠛⠉⢹⠀⠀⠀⠀⠀⠀ ⠙⢶⣄⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣀⣤⣠⡴⢶⠀⠉⠙⠛⠶⠾⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⢀⣴⠞⠉⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⠤⠤⠤⠶⠋⠁⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠳⣄⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣹⣆⣹⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⠶⢶⣶⣦⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⠋⠀⠀⢠⡶⠛⠛⠓⠶⢤⣀⡀⠀⢀⣴⠋⠁⠀⠀⠉⠓⠦⣄⡀⢀⡴⠖⠛⠛⢲⡆⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⢨⡏⠀⢀⣀⡿⣤⢷⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⡟⢳⠀⠸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣶⣶⣶⣶⣶⠾⠿⠟⠋⠀⣀⣀⣀⣼⠀⣾⠋⠉⠁⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⣤⣀⡀⠀⠉⠉⠀⠀⠙⢦⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠛⠛⡟⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⣯⠈⣍⡛⠲⢦⣄⡀⣀⣠⣾⣧⣤⣿⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣶⣦⣤⣶⣾⠿⠋⠁⠀⠀⠀⣰⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⡏⠛⠶⣌⡙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣄⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣴⣾⠿⢿⡇⠀⢰⠏⠀⠀⠀⠀⠀⠀⢰⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢳⠀⠀⣠⠙⢦⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠋⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⢸⡇⠀⢺⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣙⡆⠀⠀⢿⡀⠘⣇⡤⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣒⡒⠛⡿ ⠿⣷⣶⣶⣶⣶⣾⠿⠋⠀⠀⠀⠀⢸⡇⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠉⠀⠀⠀⠈⣧⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠱⠊⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠷⢾⡇⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠴⠚⠁ ⣀⣀⣀⣀⣀⣀⣠⣤⣾⠿⠋⠀⠀⠀⣷⠀⠀⢼⠉⠉⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀ ⠛⣿⡟⠛⠛⠛⠛⠉⠀⠀⢀⣀⣀⣀⣹⡄⠀⠸⣇⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀ ⡾⠁⠉⢳⣄⡀⠀⣀⣠⣴⡿⠛⠉⣹⡿⣧⣾⡆⢹⡧⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠰⣶⡶⠀⠀⠀⠀⣸⡇⠀⠀ ⢳⡄⠀⠀⠙⠻⠿⠿⠿⠯⠤⠖⠋⠁⢀⣼⣿⠃⠀⠷⠿⢴⡶⠲⠶⣤⣀⠀⠀⣀⣠⣅⡀⠀⠀⢀⣾⠁⠀⠀⠀⣰⢟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣤⠆⠀⢀⣴⠟⠀⠀⠀ ⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣯⣿⡏⠀⠀⠀⠀⢸⣧⣀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠛⠛⢻⡇⠀⠀⠀⢠⣿⡾⠁⠙⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⣙⣓⣒⣒⡚⠛⠉⣱⡿⠋⠻⣿⣧⠀⠀⠀⢀⡿⠈⠉⠉⠛⠛⠒⠒⠒⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠈⠉⠙⠓⠒⠒⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣾⠿⠛⠛⠛⠛⠻⠿⠿⠟⠁⠀⠀⠈⠻⢷⣤⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⣸⣿⣄⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣼⡿⠋⠁⢀⣴⣤⡀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠟⣿⡀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢰⡿⠁⠀⢠⣿⠟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⡄⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀ ⠀⠀⠀⢸⡟⠀⢹⡇⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡇⠀⢠⣿⠋⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣷⠀ ⠀⠀⠀⣿⠇⠀⢸⡇⠀⠀⠀⢀⣀⣸⣇⣀⣀⣸⡇⢠⣿⠏⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⢻⡇ ⠀⠀⠀⣿⠀⢀⣼⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣯⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⣸⡇ ⠀⠀⢀⣿⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⢸⣇⠀⣀⣴⣿⠋⠀⠀⠀⠀⢠⣿⠁ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡿⠿⠿⠟⠁⠀⠀⠀⠀⣠⣿⠏⠀ ⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⠀⠀ ⢀⣿⠃⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢠⣿⣷⣤⣀⣤⣤⣶⣾⡿⠟⠁⠀⠀⠀ ⢸⡏⠀⠘⠛⠁⠀⠀⣿⣿⣦⣰⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⢀⣾⡏⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⣾⣿⣷⣶⣤⣀⣀⡀⠀⠀⢀⣀⣀⣤⣾⣿⠟⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢏⣠⣭⣝⡛⠿⠿⠿⠿⠿⠿⠿⠿⠛⢋⣁⣀⣀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⠟⢁⣾⡟⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⠛⢿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⣠⣾⠟⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣦⡀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢁⣠⣴⣾⡿⠟⠋⠀⠀⠀⢀⣼⡿⠁⢀⣴⣿⠿⠋⠀⠀⠀⠉⢿⣇⠀⠀⣿⡄⠈⠻⣿⣦⡀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣾⣏⣠⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢸⣧⠀⠀⠈⠻⣿⣦⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⡋⠀⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠤⠤⠤⠴⠋⠉⣹⠋⢉⣉⠉⠉⠉⢉⠭⣉⠁⠂⢐⣒⠂⠤⣄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣀⡴⠋⢩⢁⡀⢧⠀⠉⠐⠒⠁⠀⠀⠁⠒⢱⠄⠅⠀⢸⠀⠀⠀⠀⠀⠀ ⣤⣀⣀⣤⠖⠋⡋⠘⡄⠀⠀⠀⠀⠀⠘⠋⠀⢠⠹⠔⡠⣤⠗⠚⠀⠠⢄⡀⠀⠀ ⠀⠉⠉⢀⡤⠚⡇⢰⠁⠀⠀⠸⠕⠀⠀⠀⡄⠈⡆⢃⠨⠂⠑⠀⠀⠀⠀⠈⠀⢉ ⠙⠛⠛⠉⢀⡤⡇⠀⣵⡀⠀⠀⠀⠐⠀⠀⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⡬⠔ ⣶⡶⠶⠚⢉⣀⣸⢀⢇⠀⠀⠸⠗⠀⠀⠀⠐⠆⠀⢃⠀⠀⢶⡿⠀⠀⠀⠰⠇⠀ ⢇⠈⠓⠾⠙⠂⡡⡿⠀⠿⡖⠢⢄⠠⠭⣀⣠⠀⠀⣜⢄⠀⠀⠀⠠⠼⠆⡠⠆⠀ ⢀⣁⣶⣶⣂⡽⠛⢦⡀⣸⠉⠐⠒⠒⠀⠀⢺⠀⢸⡇⢀⠉⠑⠒⠒⠂⠉⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢦⣤⣤⣄⣀⣀⣴⠿⠋⠉⠉⢙⡿⠋⠉⠁⠀⠀⠀⠀⠉⠉⠉⢉⣉⣉⠉⠉⠙⠛⠒⠒⠲⠶⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⠏⠀⠀⡴⠚⠓⠒⠤⣄⣀⣀⡴⠋⠀⠈⠙⠲⢤⣀⡠⠖⡛⠒⡆⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣤⡾⠋⠀⠀⡾⢀⡤⠼⢱⣳⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⡵⠀⢣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠛⠛⠛⠉⠉⢁⣠⡶⠶⢶⡇⠸⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⢻⠒⡦⢤⣀⠀⠀⢉⣶⣀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣶⣤⣤⣴⡾⠛⠉⠀⠀⣸⠀⠀⣹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⠒⠬⣙⠻⢭⡉⠉⠉⠉⠉⠉⠓⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⠀⢠⠃⠀⠀⠀⠀⠀⣿⣹⠄⠀⠀⠀⠀⢀⣀⠀⠀⣇⠘⡆⠀⣬⡳⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⢏⢉⣉⣉ ⣤⣄⣀⣀⣀⣴⡾⠋⠀⠀⢸⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠞⠀⠀⢹⡄⠹⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⣠⠎ ⠉⠉⠉⠉⠉⠁⠀⢀⣤⢶⣼⠀⠀⢨⣧⡀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠤⠊ ⣤⣤⣤⣤⣤⣤⡾⠛⠁⠀⠸⡇⠀⢸⠉⠁⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⡇⠀⠀⠀⠀⣀⣸⣦⡀⠀⠀⠀⠀⣀⣸⣇⠀⠀ ⣩⠿⣭⠉⠉⠁⠀⢀⣴⠶⢶⣷⢠⡘⢧⢀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠘⠓⠃⠀⠀⢧⠀⠀⠀⠀⢿⣿⡿⠀⠀⣀⡀⠀⠙⠛⢻⠀⠀ ⢇⠀⠈⠻⢶⣶⣾⣟⡡⠴⠊⢉⣿⠇⢸⣼⣃⡤⢤⣀⠀⠀⠀⣙⡋⠀⠀⢀⡞⠀⠀⠀⡼⣦⡀⠀⠀⠀⠀⠀⠀⡀⢙⣡⠀⠀⣠⠞⠀⠀ ⠈⠢⣄⠀⠀⠀⠀⠀⣀⣤⣶⣹⣿⠀⠀⠀⢸⣇⣀⠈⠙⠚⠋⠉⠉⠓⠒⣻⠁⠀⠀⢸⡷⠉⢻⠦⣄⡀⠀⠀⠀⠉⢉⣉⡤⠞⠁⠀⠀⠀ ⠀⠀⣀⣭⣭⣭⣭⣉⣰⡟⠉⠻⣿⡀⠀⠀⡟⠀⠈⠉⠉⠉⠉⠒⠒⠒⠒⣻⠀⠀⠀⣿⡀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠾⠟⠋⠁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣤⡟⠷⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⡄⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⠁⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣶⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣀⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣸⡇⠀⣸⡿⠀⠀⠉⠻⣿⣦⡀⠀⢰⡿⠀⠀⠀⠀⠀⣸⣿⣁⣴⣾⡿⠟⠛⣿⡄⠀⠀ ⣴⣿⠿⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⡇⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⣿⡇⠀⠀ ⢿⣧⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣤⣤⣤⣤⣼⣿⠟⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠈⢿⣧⡀⠀⠀⠀⠀⠀⠈⢻⣷⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀ ⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇⠀⠀⣾⡿⠁⠀⠀⠀⠀⢠⣾⠋⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠙⢳⡄⠀⠀⠈⢿⣷ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣶⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣾⣿⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⢸⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⢿⣉⣩⠿⠀⠀⠉⠛⠿⠛⠃⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⣀⣀⣴⠟⢿⣤⣀⣀⣀⣴⠇⠀⠀⠀⠀⢠⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⣴⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⠉⠉⣻⡟⠛⣻⡿⠛⠛⠛⠛⢿⣿⠿⠛⠛⠛⠛⠛⠛⠛⢻⣿⠏⠉⠉⠉⠉⢻⡟⠛⠛⣻⣿⠋⠉⠉⠙⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⠀⠀⣠⣾⠟⠁⠀⣿⠀⠀⠀⢀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣠⣿⠃⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠁⠀⠀⠀⠻⢿⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣶⡿⠟⠁⠀⠀⠀⠻⣷⣄⣠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⢀⣠⡴⠖⠚⠋⠉⠉⠀⠀⠉⠛⠲⣤⣀⣴⠶⢶⡄⠀⠀⠀⠀⠀ ⠀⣿⠙⠓⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠙⣯⠁⣷⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠐⠗⠊⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀ ⠀⣠⠗⠂⣴⢿⡜⣈⣇⢸⡦⠀⠘⠛⠛⠉⢀⣀⣠⣤⠶⢶⣾⣁⣤⡄⠀⠀⠀ ⢰⠏⠀⠀⠁⠘⠋⣩⣇⣀⣤⣤⣶⣶⣻⣯⣽⡷⠟⢻⡟⠋⠻⣄⠀⢳⣄⠀⠀ ⣿⣤⡤⠶⠶⠚⣻⣿⠿⠿⣟⠋⠙⣧⡀⠀⠘⣧⠀⠀⢻⣄⣀⣹⣦⣤⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⣏⠻⣆⠀⢘⣷⣄⣨⣷⣤⣤⣾⣿⣿⡿⠿⠿⠟⠛⠛⠋⠁⣿ ⠀⠀⠀⠀⠀⠀⠘⣦⠘⣏⣭⠽⠷⠞⠛⠛⠋⠉⠁⠀⣀⣠⠤⠶⠶⠚⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⡤⠤⠤⠴⠴⠶⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣯⣁⣈⡶⡧⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡎⠀⠙⣷⡿⠟⠁⠀⠈⠒⢒⡒⢶⣶⡖⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⠤⡼⠀⢠⡀⠀⣤⡀⢠⡄⠀⠯⠥⠤⠀⠀⠀⠉⠉⠈⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠒⠉⡇⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⡀ ⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢴⣎⣻⠇ ⠀⠀⠀⢐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠔⠋⠁⠀ ⠀⢀⡠⠋⠀⢸⣢⠤⢄⣀⣀⣿⣟⡀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠴⠓⠦⡀⠀⠀⠀ ⢰⠃⠀⠀⠀⡀⠀⠠⠴⠀⠀⢀⢀⠈⠉⠛⡍⠙⠛⠯⠭⣋⣁⣀⣀⠴⡇⠀⠀⠀ ⠈⠢⢄⡀⠈⠁⠀⠀⢠⣀⡀⠈⠉⠀⠀⣀⠇⠀⠀⢀⡤⣤⣪⠉⠓⠒⠧⠀⠀⠀ ⠀⠀⠀⠙⠤⣀⣀⡀⠀⠀⠀⠀⢠⠖⠉⠀⠀⣠⠖⠁⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠁⠀⠀⡴⣊⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣓⣎⡧⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⣀⠤⠒⠊⠉⠀⠙⠒⢤⣴⣲⡀⠀⠀⠀ ⠀⣇⠉⢀⣀⠀⠀⠀⠀⠀⠤⠸⠀⠃⠇⠀⠀⠀ ⠀⡜⠰⢻⠣⡇⠗⠈⣋⣁⠤⣴⣒⣶⠤⡄⠀⠀ ⢼⡠⠤⠴⣾⠿⢟⠛⡏⠉⢯⠀⢳⣀⣦⣸⣦⡀ ⠀⠀⠀⠘⣌⢦⢬⣷⣺⠶⠾⠟⠛⢛⣉⣉⡤⠇ ⠀⠀⠀⠀⠈⠾⠭⠤⠤⠤⠐⠒⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⠤⠤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⢀⣠⣤⣤⣤⣤⣄⣀⡀⠉⠉⠛⠷⣆⠀⠀⠀⠀⠀⠀ ⠀⢠⠿⡄⠀⠀⡜⠀⡞⢁⡴⢦⠀⠀⠈⠉⠙⠛⠶⣦⠀⠘⡆⠀⠀⠀⣀⣀ ⠀⡼⠀⣇⣀⣀⣇⣄⣇⡼⠁⠘⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠁⠀⠀⣼⠋⢹ ⠀⡇⠘⠋⠉⠉⠀⠉⠉⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⡾⠁⠀⣸ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡇⠀⣈⠉⠀⣀⡴⠃ ⡞⠘⠃⢰⣶⣶⠀⠀⠀⠰⠆⠀⣸⡀⠀⠀⠀⠀⢀⡼⠁⢠⠟⠛⠛⠉⠀⠀ ⠹⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⣫⣿⡛⠶⠶⢚⣫⣥⣤⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⢳⡶⠒⣶⣿⣯⣭⡼⠁⣠⣇⣀⣀⣼⣧⡀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡵⠞⠋⠀⢀⣟⣠⠞⠉⠀⠘⣇⠹⡈⠻⣦⣳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠻⠇⠀⠈⠛⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⡁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀ ⠀⠁⠂⠄⡁⠂⠈⠑⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⢀⠐⠠⢀⠀⠂⢄⡐⠘⠁⠀⠐⠠⢄⡀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⠐⠀⠈⠐⠀⠈⠐⠠⢹⡇⠀⠁⡁⠒⠠⣀⠁⠂⠤⠈⢂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠄⡀⠂⠄⡀⢀⡃⢰⡄⠀⡠⡀⠉⠉⢺⡀⠀⠀⡠⠊⡀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠁⠂⠄⠉⢃⠸⡀⢤⠉⠐⠾⠂⠀⠉⠉⠉⠁⡀⠃⠀⡰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⢘⡐⠠⢉⡸⠀⡈⠋⠀⡖⠀⠙⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠐⠠⠈⠙⠠⠌⣒⣑⡲⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠓⠚⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢸⠃⠀⢰⡿⠋⠉⣭⣭⠉⠉⠉⠉⠉⠛⠛⠿⢷⣶⣶⣤⣀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⢻⡄⠀⠀⠀⠀⣿⠀⠀⡿⠀⢀⣾⠏⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣠⣤⣤⠀ ⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣟⠀⠀⡇⠀⣾⠃⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⠀⢀⣾⠟⠉⠹⡇ ⠀⢠⡏⠀⣸⣷⣶⣶⡾⠿⠿⠿⢷⣿⣾⣏⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢀⣾⠏⠀⠀⠀⡇ ⠀⢰⡇⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⣀⣤⡿⠃⠀⠀⠀⣰⡇ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠛⠋⠀⠀⠀⢀⣴⡟⠀ ⣸⠇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣸⣧⣀⢀⣀⣠⣴⡿⠛⠀⠀ ⡟⠀⠙⠃⠀⢰⣾⣦⣰⡆⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⢠⡿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀ ⣷⡀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⡿⢷⣶⣤⣤⣀⣀⣀⣠⣤⣾⠿⠃⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢏⣶⣶⣯⡍⠉⠛⠛⠛⠉⣩⣥⣶⣶⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠿⠿⣿⣶⣶⣶⣶⣶⣶⣶⡿⠿⠟⠉⢀⣾⠃⠀⢈⡇⠀⠀⠀⠀⠈⢿⣍⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣸⣿⡿⠷⠶⢶⣶⡿⠁⢀⣤⣿⣷⣶⣶⣶⣶⢶⡿⢿⣦⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣏⣤⣶⡿⠟⠋⠀⠀⠀⣼⠟⢀⣴⡿⠋⠀⠀⠀⠈⢿⡄⠀⣧⠀⠙⢿⣦⡈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠸⢿⡾⠟⠋⠀⠀⠀⠀⠀⠀⠘⢿⣦⣹⡆⠀⠀⠙⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠁⠀⠀⠀⠀⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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