⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢥⡶⠀⠀⠘⠻⡿⢤⣶⠶⣶⣬⠿⠛⠃⠀⠀⢤⡽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢀⠞⠁⣿⣿⣿⣿⣿⠈⢳⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⠏⠀⠀⠉⠻⣿⠟⠉⠀⠀⢱⡀⢠⡀⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⣦⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢣⣷⣸⡇⡜⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⣿⣄⠀⠀⠀⢀⣾⠋⣯⢘⡿⠙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡄⣈⡿⢶⣤⣴⠋⠀⣹⣦⣤⣤⡾⠿⠐⠉⠈⠁⢠⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢽⡀⠀⡄⡄⢩⣧⡄⠀⠈⠛⠛⠛⠁⠀⢱⡄⠀⠀⠀⠀⠀⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠋⡾⣷⡀⣰⣿⢿⢺⢱⣄⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⢀⣰⣇⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⢀⣿⣿⣿⣿⣞⣿⣸⢟⣦⣝⣃⣠⡾⣍⡆⠀⠀⠀⣠⣼⡟⠀⠀⠁⣹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠂⠀⠀⠢⣫⣿⣿⣿⣿⣿⣻⣾⣧⣯⣛⣫⣦⣿⣷⡀⢠⣄⣷⣿⣿⢀⠆⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⡆⠀⠀⢣⡱⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣽⣿⣿⣿⢿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⡇⢤⢹⣿⣿⣕⣦⠈⠣⣹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⡟⠀⠀⠀⠀⢀⣿⡿⡾⡎⠺⣿⣿⣿⣻⣿⡿⡽⣿⣿⣟⣿⣿⣿⣿⡷⠁⠈⠸⢻⣽⣿⣯⣦⣤⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠰⣼⣿⡇⡇⠁⢀⢈⠉⠻⣿⣿⣏⣿⠙⢠⣿⣿⣿⡿⠛⠀⠀⠀⠀⠸⢿⣿⣿⠛⠋⠁⢹⡗⠀⠀ ⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⢻⣧⡘⠀⠀⠈⢷⣀⠘⢨⠻⣿⣿⣄⣼⣿⣿⣿⠧⠀⠀⠀⠀⠀⢀⣿⠏⠁⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠼⢿⣷⡀⠀⠀⠾⡻⣾⡀⠀⠊⠛⡏⠙⠋⠘⠃⠀⠀⠀⠀⢀⣖⣿⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢼⣟⣿⣆⡀⡀⣨⢫⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣿⠉⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣯⣿⣥⣯⢢⡁⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀ ⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠀⠀⠀⢘⣸⣿⣿⣷⢻⣥⣆⣆⡀⠀⠀⠠⡰⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠑⠙⠹⠛⠿⣿⣿⣿⣿⣶⢰⡷⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡼⠙⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣷⢻⣶⢀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠀⠆⠉⠙⠁⠈⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⡀⣰⣯⣤⡇⠀⠀ ⠀⠀⠀⠀⢀⡤⢶⣿⣿⣿⣿⣎⠀⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣿⣷⣻⣿⣿⠀⠀⠀ ⠀⢀⡴⠚⠁⣤⣼⢿⢿⡿⢻⣿⣿⣿⡼⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣹⣿⣿⣧⣷⣿⢻⣿⡆⠀⠀ ⡴⠋⠀⠀⡄⣿⠿⢛⠟⢷⣮⡾⣟⢿⣗⡟⢠⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⢷⣿⠟⡿⣿⣿⣿⣿⢻⣻⡀⠀ ⠀⢲⣀⢸⣿⣿⠀⡟⠀⣎⢿⣟⠝⡆⠙⢻⣦⣙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣴⣾⣿⢿⠛⣿⣿⡿⣡⡇⣿⠈⢹⣧⠀ ⠀⢸⣿⣿⣼⠃⢦⠃⠀⠘⠈⢹⣧⠘⠆⠀⠉⠻⢷⣄⢲⡠⡀⠀⠀⠀⠀⠀⢀⣖⣰⣾⡿⠋⠁⡠⢠⣿⠏⠐⠙⠸⣿⠀⠀⢸⡄ ⠀⠀⢿⣷⡏⠀⠘⠀⠀⠀⠀⠈⢯⢳⡄⠀⠀⠀⠀⢹⣷⣟⣿⣶⣵⡄⢀⣤⣾⣿⣿⠋⠀⠀⠀⢀⡼⠃⠀⠀⠀⠰⠃⠀⠀⠀⣇

⠀⠀⠰⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠁⠀⠉⠉⠙⠛⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⣋⡀⠀⠀⢰⣾⣿⣿⠀⣀⣀⣀⣀⠀⢿⣿⣷⡆⠀⠀⢀⡘⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠟⠁⠀⠀⠀⠀⣽⠏⣽⣿⣛⣛⣿⣿⠋⢩⡀⠀⠀⠀⠈⠙⢿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢠⡞⠁⠠⣿⣿⣿⣿⣿⣿⡇⠀⠻⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠻⣿⣿⠿⠋⠀⠀⠀⠹⣆⠀⣠⡀⢀⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⢠⢠⡟⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢢⣹⡄⣹⡅⠈⣷⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠙⠻⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢛⣷⣿⣧⢹⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢻⣦⡄⠀⠀⠀⢠⡿⢿⣦⠀⠀⠀⠀⢀⣾⡏⠐⣷⢠⣿⠃⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢰⢂⣠⣿⠿⣷⣶⣴⡟⠀⠀⣙⣷⣶⣤⣴⡟⠻⠇⠈⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣹⡆⠀⠀⡀⢀⠈⢹⣧⣄⠀⠀⠈⠛⠓⠛⠛⠋⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠾⢉⣿⡄⠀⠃⣾⣴⣿⣝⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⢠⡏⠁⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠠⠟⢹⣿⣆⣸⣿⣏⣹⣸⡗⣿⣧⡀⢠⣤⠀⠀⢠⣾⢟⠃⠀⠀⠀⠀⠀⢰⣶⣿⠳⠀⢠⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡿⣧⡟⣯⡿⣶⣽⣤⣴⣟⢷⣼⠇⠀⠀⠀⠀⡶⣾⣿⣇⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠐⠞⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣏⣙⣣⣿⣾⣿⣾⡇⠀⣤⣤⣿⣿⣿⣿⢀⠂⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠇⠀⠀⠀⠀⡖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⡄⠀⠀⠀⣦⠠⣽⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣯⣿⡿⠉⢿⣿⣿⣿⢀⠀⠀⠘⣶⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠧⡄⣿⣿⣿⢷⣩⣷⠀⠉⢤⣽⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠻⢿⣿⣿⣿⣯⣶⢤⣸⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡄⣼⣿⡿⢸⠉⠃⠀⠈⠙⠙⢿⣿⣿⣿⡟⣿⡞⠻⠁⣽⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡿⠿⠟⠉⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣷⡟⢡⡌⠀⠀⠀⢧⡀⠀⢠⡟⣿⣿⣿⣿⡇⢄⢸⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣬⣷⠿⠙⠁⠀⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⠀⠀⠀⠀⠈⣿⣄⢀⠀⠋⠙⠟⡿⣿⣾⣿⣿⡿⣿⡿⠏⠃⠀⠀⠀⠀⠀⢀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⠀⠀⠀⠠⠾⠿⣿⣦⡄⠀⠀⠸⠿⡹⣾⣆⠀⠀⠉⠃⢻⠀⠈⠋⠀⠙⠁⠀⠀⠀⠀⠀⢠⡼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡄⠀⠀⠀⢡⢟⡙⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡿⣷⡞⣰⡿⣄⠓⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣽⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢿⣿⣿⣷⡝⣼⣴⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⡿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⡸⣿⣿⣧⣿⣤⡀⠀⠀⡐⢠⣾⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠉⠏⠙⠿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⠁⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⡌⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠐⠀⢸⠉⠙⠛⠟⠁⠈⠙⢻⡿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣏⣀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣾⣿⣀⠦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣯⡇⣼⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠶⠋⣹⣿⣿⣿⣿⣿⣿⣆⡄⣷⡆⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣶⣿⣿⡿⣿⣻⣿⣿⣿⠀⠀⠀⠀ ⠀⢀⣤⠞⠋⠀⢀⣶⣿⢻⡿⣿⡿⢫⣻⣿⣧⣿⣇⢧⣀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣼⣽⣿⣿⣷⣿⣿⡟⣿⣟⣧⠀⠀⠀ ⣴⠟⠁⠀⠀⣀⠸⣾⠭⢋⣿⠻⣷⣿⡳⢽⡛⣿⣿⣺⡙⢠⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣱⣿⡿⢿⡿⣿⣿⢿⣿⣿⢻⣻⡆⠀⠀ ⠀⢰⡄⠀⢰⣿⣾⣿⠀⣿⠀⠀⡝⣿⣟⢮⢳⠀⠙⢿⣷⡌⠻⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣼⣿⣿⡿⢿⣿⣿⣾⣿⠟⣼⠘⡼⠀⢻⣿⡀⠀ ⠀⠸⣷⣿⣼⣯⣿⠋⡄⣿⠀⠀⣿⠈⢿⣮⡈⢷⡀⠀⠙⢿⣾⣦⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣡⣾⣾⣿⠿⠋⠋⠀⣿⣿⡿⢃⡾⡟⣾⡿⠀⠈⠛⣧⠀ ⠀⠀⢿⣿⣿⣿⡟⠀⣷⠀⠀⠀⠀⠀⠀⣿⢷⡀⠉⠀⠀⠀⠈⠙⢿⣦⡙⢾⣡⣄⠀⣀⠀⠀⠀⠀⠀⣴⡿⣴⣿⡿⠋⠀⠀⠠⠆⢸⣿⠏⠀⠀⠀⠀⢛⡿⠀⠀⠀⢻⡆ ⠀⠀⠈⣿⣿⣿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⣎⢻⣆⠀⠀⠀⠀⠀⠀⢻⣽⣻⣽⣾⣷⣾⣷⠄⢀⣤⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠘⣧