⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡶⠶⠶⠿⠷⢤⣀⣀⠀⣤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠦⣤⣀⣠⣤⣤⡀⠀⠉⠛⠦⣄⠙⠲⣄⢠⡞⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣾⡁⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⠉⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⣱⣯⢤⣤⡏⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⣨⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢾⣿⢿⠋⠀⠀⢸⠟⢆⠀⠀⣠⣖⡯⠸⢤⡶⠯⠤⠤⣄⡀⠀⠀⠈⠉⠉⠉⠉⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢨⡏⡟⠀⠀⠀⠾⣇⢈⣷⡾⠛⠉⠀⣴⣏⠀⠀⠀⠀⠀⠙⢶⣦⣤⣀⣄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣸⢰⠃⠀⠀⢀⡀⣈⠉⠹⡆⠀⠀⡼⠁⠈⠉⠓⠒⠒⠤⠀⠀⠹⣿⣯⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⢀⣼⣿⢸⠀⠀⠀⠈⠙⢻⣿⣷⣧⠀⣸⠃⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠁⠀⠀⢀⣾⡷⢿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⠀⠀⢸⣿⣿⡏⠙⠂⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢁⡴⠃⠀⢀⣾⡟⠁⢀⡿⣄⠀⠀⠀⠀⠀⢉⡝⠉⠙⢿⠀⠀⢸⣿⡿⠛⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀ ⠀⠉⡿⠁⠀⠀⣼⣼⠀⠀⠈⡇⠈⠓⠤⣤⣤⠖⠋⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣀⡏⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⡼⠁⠀⠀⢸⠃⡟⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠖⠚⢹⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠾⠶⠟⠀⠀ ⢰⡇⠀⠀⠀⣞⠀⣷⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⢸⠀⠀⠀⠀⢿⠀⢻⡀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⡯⠀⠀⡄⠀⠸⡆⠀⠑⣄⠀⠀⠀⠀⠀⠈⠙⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⣿⢀⣠⡇⠀⠀⠹⡄⢀⣈⣭⣴⣶⣦⣤⣀⡀⣿⠈⠋⣻⡶⠒⡶⠒⠒⣀⡤⠖⠋⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠙⠻⠋⢷⠀⠀⣤⣾⡿⠏⠀⠈⠁⠀⠉⢻⣿⣯⠛⠷⣿⣿⣿⡵⠖⠋⠁⠀⠀⠀⠀⢠⣴⣿⡄⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⡇⠀ ⠀⠀⠀⠈⢳⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⢙⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣋⣹⣆⡼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⣸⠂ ⠀⠀⠀⠀⠀⢸⣿⠺⠃⣰⣦⠀⠀⠀⠀⢾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⡷⠟⠋⠁⠀⠀⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠛⠉⠀ ⠀⠀⠀⠀⠀⢸⣟⣐⣼⠟⠁⠀⠀⠀⠀⣾⣿⣿⣿⠷⣤⣀⡀⠀⢀⣠⣶⠿⠟⣏⣀⡀⠀⠀⠀⠀⣼⡿⠃⠉⠺⠛⢷⣦⣤⣀⣀⡀⣀⣀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠉⢙⣷⣿⣿⣴⣠⣾⣿⣿⣿⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡟⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⡇⠀⠀⠸⣿⡿⡿⠿⠛⠛⠿⣿⣿⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠁⣷⠀⠀⠀⠹⢷⣄⡀⠀⠀⢠⣾⠃⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠙⠻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⢸⠀⠀⠀⠀⠀⠉⠻⠿⣾⣾⠃⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡿⠇⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢠⣴⣿⠋⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣩⣿⡟⠀⠀⣠⣤⣤⣼⣷⠶⢶⣤⣤⣤⣤⣤⣤⣰⣿⣾⣧⣄⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⣰⡿⠋⠀⢠⣾⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣧⠻⣿⣷⡄⠀⠀⠀⢀⣼⠋⠀⠀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣦⣤⡶⠞⠋⠀⠀⣰⣿⣿⣋⣀⠀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⠇⠙⣿⣷⡀⠀⢀⣾⣇⣀⣀⣀⣁⣀⣀⣀⣀⣸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⣦⣠⣀⣀⣀⣀⣠⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀