⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣀⣀⣀⣠⣤⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⠉⠀⣀⢀⠀⠀⠀⠀⢉⡀⠈⡛⠷⢀⠑⠄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⠯⠴⠆⠛⠉⠉⠄⠀⠘⠟⠒⠀⠀⠉⠓⡓⠀⡀⠑⠄⠀⠀⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⡿⠃⠀⠈⢀⠀⠂⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⣁⣸⡇⠀⠀⡀⠊⠀⠀⡠⠀⠀⡀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠚⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⡐⠁⢸⡇⣠⠎⠀⠀⠀⠊⠀⠀⢀⠀⠀⠨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀⠀ ⠀⢠⡿⢣⣾⠁⢀⠸⠀⡁⠀⠀⠐⠀⠀⢶⠀⠋⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⣇⠀⠀⠀⠀⠀ ⠀⣼⠃⠸⠉⠀⠘⠇⠀⠀⠀⡀⠀⠀⢰⡇⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⠳⡀⠀⠀⠀ ⢸⡏⠀⢸⡦⠂⠀⠀⠈⢦⡀⠑⠀⣰⠟⠁⠀⡀⠀⢀⣧⠀⠀⠀⠀⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠦⢡⠀⠀⠀ ⠈⡇⠀⢠⠀⢠⣀⡀⢀⠀⠉⣁⠾⠁⠲⢀⣀⣇⠀⠀⠙⢦⡀⠀⠺⢿⣀⡀⣀⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⢷⠀⠘⠀⣸⡯⣉⣫⣵⣾⣿⣦⣤⣤⣤⣉⣉⣍⡁⠀⠀⠣⣰⣼⣀⣀⣉⣉⣁⣀⣤⣤⣴⣶⣶⣆⣿⠲⢄⡀⠀⢸⡃⠀⠀ ⠀⢸⣇⠠⣾⣿⣿⠿⠛⠛⠉⣻⠿⠿⢿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠁⠙⠿⢿⡿⠿⠟⠛⠛⠋⠉⠉⢙⠛⠿⢦⣉⠓⢠⡇⠀⠀ ⠀⢸⡿⠀⠘⠫⣀⠇⠀⣸⣿⣛⡟⣛⡛⣛⣛⠳⣤⣄⠓⠀⠀⠀⠀⠀⣠⡴⠛⢛⣛⣛⣛⣛⣿⣷⣼⠆⠀⠀⠉⠃⠘⡆⠀⠀ ⠀⠘⣷⠀⠐⠃⠈⣧⣾⠋⠹⣿⣿⣿⣿⠻⣿⡁⢸⣿⠀⠀⠀⠀⠀⠀⣿⡀⢈⡿⠙⣿⣿⣿⣿⠀⠙⢻⣄⠀⠀⠀⢠⠃⠀⠀ ⠀⢠⣿⡄⠘⠀⠈⠁⠿⠿⠟⠟⠿⠛⠿⠚⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠛⠛⠞⠻⠛⠛⠛⠓⠛⠋⠀⠀⠀⠀⢚⠀⠀⠀ ⠀⠘⢷⡙⠓⢤⠠⠄⠠⠀⡀⠀⠈⠀⡠⠲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀ ⠀⠀⢀⡏⡲⣤⡀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠒⠂⢠⠀⠀⠈⠓⡄⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀ ⠀⠀⣾⢷⠰⣆⠙⠲⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠀⣤⠀⠈⠀⡞⠀⠀ ⠀⠀⠹⣆⠁⢘⢳⣤⠆⠀⠀⠀⠘⠃⠄⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣶⠀⣠⠀⠀⣼⠃⠀⠀⠀⢹⡀⠀ ⠀⠀⠀⢸⣦⣘⣦⣆⠀⠂⠂⠀⣦⠀⠀⠈⠈⠁⢦⣀⡀⠀⢥⡀⠀⠀⣀⡰⠀⠀⠀⠀⠀⣠⡆⡀⢀⣾⠃⠀⠀⠀⠀⢀⡇⠀ ⠀⢀⣴⡿⠽⣏⠀⠀⠓⢆⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠑⠠⡄⠀⣀⣀⠀⠂⠀⠀⢀⣠⠾⠋⢀⠀⣸⠃⢀⠀⠀⠀⠀⠐⢹⠀ ⠀⣿⡇⠃⠀⠈⠀⠀⠀⠀⠁⠀⢠⣶⣤⣌⣠⣤⣤⣤⣤⣤⣤⣴⣶⣷⣶⠿⠟⠛⠉⠀⠀⠀⠀⢀⡏⠀⠈⠀⠃⠀⠀⠠⠸⡇ ⠀⣿⠙⢦⡀⣘⠀⠀⠔⠄⡀⠀⢄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⣰⡧ ⠀⠸⣶⠀⠈⠋⠑⢢⣤⣤⣀⣠⣄⡨⠉⢲⢤⣀⠀⢀⡴⠒⠮⠭⠑⠴⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇ ⠀⢠⣿⣄⠀⠀⢀⣼⣏⣷⡶⠴⣬⠖⠉⠉⠁⡠⠘⢻⡀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⡇ ⠀⡘⠉⢻⡗⠆⠈⠻⠷⠏⠀⠀⠁⠀⠀⠀⢿⡀⠀⠀⠙⢲⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁ ⠀⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠀⠆⠀⠀⠀⠀⠁⠀⣠⡀⠀⠀⣀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀ ⠀⢹⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠈⠳⡄⠀⠢⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⢻⣶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠘⡇⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⢿⡇⠀⣹⢮⡀⠀⠀⠀⠀⣐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀ ⠀⠀⠀⠻⣾⢁⡀⠁⠆⡀⠀⠀⠙⢇⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠻⡈⠀⠀⠬⡄⠀⠀⡆⠀⢁⡀⠈⠀⠀⠀⠁⠀⠀⠉⢠⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⣄⣅⣘⣀⡤⠔⠚⠉⠉⠙⠲⠦⣀⡀⠀⡀⠈⠆⢀⡠⠴⠒⠦⣤⣀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀