⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠈⠙⡇⠘⣷⡄⠀⠀⠷⣄⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡿⢛⣿⠃⠀⠀⠀⠀⠀⣠⠀⠀⠀⢰⡀⠀⠀⠀⠁⠀⣿⣿⡄⠀⠀⠈⢷⣄⠈⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠋⢀⡿⠁⠀⠀⠀⠀⡄⢠⡏⠀⠀⠀⢸⡇⠀⠀⠀⢰⡄⣿⢿⣷⠀⠀⠀⠸⣿⣷⣄⠹⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⣼⢁⡀⠀⠀⠀⢰⣇⣿⠁⠀⣀⣀⣸⡇⠀⠀⠀⢸⡇⡏⠀⢻⡆⠀⠀⠀⣻⡙⣿⠿⣾⣿⣷⣄⡀⠀ ⠀⠀⠀⠀⣾⣿⠃⢠⡏⣼⠃⠀⡀⠀⢸⣿⡟⠘⠋⠉⢉⣿⡇⠀⠀⣠⣿⣿⠋⠘⢺⣧⠀⠀⣠⣿⡇⠸⣇⠀⠉⠙⠛⠛⠒ ⠀⠀⠀⢸⣿⠏⣀⢸⢁⡟⠀⠀⣇⠀⢸⣿⣁⣠⣤⣾⣿⣿⣷⣾⣿⡿⣿⠣⣤⣄⣀⣻⣶⣾⣿⣿⣷⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣣⣾⠃⣾⢸⡇⠀⠀⣿⠀⢸⣿⠿⠿⣿⣿⡓⠛⠛⠛⠋⠀⠁⠈⣭⣿⡏⠛⣿⣿⣿⣿⡏⢻⣿⡆⠀⠀⠀⠀⠀ ⠚⠛⢻⣿⣿⡿⠀⣿⢸⣇⠀⠀⢹⣇⢸⣧⠀⢸⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⢿⠀⢹⣿⣿⣿⠁⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⡇⢰⣿⣾⢿⡆⠀⠘⣿⣾⣿⣄⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢇⡀⢸⣿⣿⠇⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⡇⢸⣿⣿⣸⡆⠀⠀⢻⣿⢿⣿⡑⢆⠈⢲⣶⡤⠄⠠⠤⣤⣤⠀⠑⢜⣿⡿⢿⣿⡆⠀⢸⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⠙⣷⣘⢻⣿⣿⣧⠀⡄⠀⢿⣇⠙⠳⠤⠀⡏⠀⠁⠀⠀⠀⠘⢻⡇⠀⠀⠉⠀⣸⣿⡇⠀⣼⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠙⠛⠿⢿⣿⣿⣦⠠⡤⠰⢿⣄⠀⠀⠀⠳⣀⠀⠀⠀⠀⣀⡴⠁⠀⢀⣠⣾⣿⣿⣿⢠⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⡷⣶⣶⣾⣿⣟⠲⠤⣄⣀⡈⠁⠀⢉⣡⠤⣶⣾⣿⣿⣿⠿⣿⣧⣿⠟⠻⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⠓⠒⠒⠛⠻⣿⣿⣗⠀⠀⠀⠉⠛⢻⠟⠀⣴⣿⡟⠓⠛⠛⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⡀⠀⠀⠀⢻⠻⣿⣷⡦⢤⣤⣄⣨⣴⣟⣿⡏⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⣿⡏⢧⣀⠀⠀⠀⠃⠀⠀⠀⠘⣆⠈⠙⠓⠒⠒⠾⠟⠛⠉⢠⡇⠀⠀⠀⠀⠸⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⢠⣿⠀⠀⠀⠉⠑⠒⣿⠦⠤⢀⣀⣹⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⣠⣇⣀⡠⠚⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡄⠀⠈⣧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢻⡀⠉⠀⠀⠉⠉⠉⢉⡏⡠⠈⠀⠀⣸⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⣧⠀⠈⣿⣦⡀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣀⣤⠴⡾⠉⠀⠀⠀⢠⢻⣀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠄⣼⡆⠀⠙⡟⠿⣍⡉⠉⢉⣿⠦⣀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣰⠁⠀⠀⠀⢠⢷⡟⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⣧⠹⡀⠀⣻⡄⠀⠉⢛⡿⢿⣆⡀⠉⠓⠒⠤⠤⢤⣿⣄⣀⣴⣃⣀⣠⣤⡶⠃⣼⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣷⡽⡄⣻⣤⡏⠛⠀⠀⢸⡇⠀⠋⠙⠓⠲⠶⠤⢤⣼⡏⠈⠉⠉⣿⠤⠴⠿⠖⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⠇⠙⣧⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⡾⢁⡀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⠀⠀⣟⢧⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣨⣭⡯⠭⠶⠚⠀⠀⢘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢳⣴⣿⡄⠉⡿⠛⠓⠒⠒⠢⢶⣌⣉⣉⠉⠁⣀⣀⣀⣀⣀⣀⡤⠴⠒⢾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢾⠒⠴⡤⣀⣀⣀⣀⣀⣀⠁⠉⣉⣉⣌⢶⠢⠒⠒⠓⠛⡿⠉⡄⣿⣴⢳⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢘⠀⠀⠚⠶⠭⡯⣭⣨⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡀⢧⣟⠀⠀⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠠⠀⠀⡀⢁⡾⣠⣦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⣧⠙⠇⣿⣿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢻⠖⠿⠴⠤⣿⠉⠉⠈⡏⣼⢤⠤⠶⠲⠓⠙⠋⠀⡇⢸⠀⠀⠛⡏⣤⣻⡄⡽⣷⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣡⣼⠃⡶⣤⣠⣀⣃⣴⣀⣄⣿⢤⠤⠤⠒⠓⠉⡀⣆⢿⡿⢛⠉⠀⡄⣻⠀⡀⠹⣧⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⡟⢷⢠⠀⠀⠀⠁⣰⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⣀⠦⣿⢉⠉⡉⣍⠿⡟⠙⠀⡆⣼⠄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⣀⣀⢻⢠⠀⠀⠀⠉⡾⠴⣤⣀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⡆⣀⠀⠀⠀⡀⣦⣿⠈⠀⣧⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠁⣸⠀⠀⠈⡠⡏⢉⠉⠉⠉⠀⠀⠉⡀⢻⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣧⠈⠀⡄⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⣿⠚⡠⣀⣇⣠⣀⢀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡀⣄⣹⣀⢀⠤⠦⣿⠒⠑⠉⠀⠀⠀⣿⢠⠀⠀⣇⢸ ⠀⠀⠀⠀⠀⠀⠀⣧⢘⠀⠀⠸⠀⠀⠀⠀⡇⢠⠉⠛⠟⠾⠒⠒⠓⠙⠈⣆⠘⠀⠀⠀⠃⠀⠀⠀⣀⢧⡏⣿⠀⠀⠀⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⡏⣿⣟⣴⣨⣄⣤⢤⡦⣷⣿⠻⢻⠀⠀⠀⡀⠀⠀⠀⠁⡟⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⠿⠛⠛⠓⡟⣿⣴⠀⠟⢻⠛⠉⠀⠀⠀⣗⣿⣿⠻⠛⠒⠒⠓⠛⠿⣴⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠻⠟⣿⣧⣿⠿⣿⣿⣿⣾⣶⠤⣡⢉⠀⠁⡈⣀⣄⠤⠲⣟⣿⣾⣶⣶⡷⣿⣙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⣿⣾⣠⢀⠀⠁⡴⣀⠀⠀⠀⠀⣀⠳⠀⠀⠀⣄⢿⠰⡤⠠⣦⣿⣿⢿⠿⠛⠙⠀⡇⠘⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣼⠀⡇⣿⣸⠀⠉⠀⠀⡇⢻⠘⠀⠀⠀⠁⠀⡏⠀⠤⠳⠙⣇⢿⠀⡄⠀⣧⣿⣿⢻⣘⣷⠙⣿⢿⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⢸⠀⡆⣿⢿⡿⣿⢜⠑⠀⣤⣤⠤⠠⠄⡤⣶⢲⠈⢆⡑⣿⢿⣿⢻⠀⠀⡆⣸⣿⣿⢸⡇⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢸⠀⠇⣿⣿⢸⡀⢇⣤⢰⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⣄⣿⣾⣿⠘⠀⡆⢿⣾⣿⢰⡇⣿⣿⣼⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢸⠁⣿⣿⣿⢹⠀⢿⣹⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⠀⣧⢸⣇⢹⠀⠀⣇⢸⣿⠀⡿⣿⣿⢻⠛⠚ ⠀⠀⠀⠀⠀⡆⣿⢻⡏⣿⣿⣿⣿⠛⡏⣿⣭⠈⠁⠀⠋⠛⠛⠛⡓⣿⣿⠿⠿⣿⢸⠀⣿⠀⠀⡇⢸⣾⠃⣾⣣⣿⣰⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢀⣷⣿⣿⣾⣶⣻⣀⣄⣤⠣⣿⡿⣿⣾⣷⣿⣿⣾⣤⣠⣁⣿⢸⠀⣇⠀⠀⡟⢁⢸⣀⠏⣿⢸⠀⠀⠀ ⠒⠛⠛⠙⠉⠀⣇⠸⡇⣿⣠⠀⠀⣧⢺⠘⠋⣿⣿⣠⠀⠀⡇⣿⢉⠉⠋⠘⡟⣿⢸⠀⡀⠀⠃⣼⡏⢠⠃⣿⣾⠀⠀⠀⠀ ⠀⡀⣄⣷⣿⣾⠿⣿⡙⣻⠀⠀⠀⡆⢻⠀⡏⡇⢸⠀⠀⠀⡇⣸⣀⣀⠀⠁⣿⣇⢰⠀⠀⠀⡀⢁⣼⠀⠀⣿⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣷⠹⣄⣷⣿⠸⠀⠀⠀⣷⢿⣿⡄⢰⠀⠀⠀⡇⢸⠀⠀⠀⡏⢠⡄⠀⠀⠀⠀⠁⡿⢀⠋⡿⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⢿⠈⣄⢷⠈⠀⠀⡄⣿⣿⠀⠁⠀⠀⠀⡀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠃⣿⢛⡿⣿⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠉⣄⠷⠀⠀⡄⣷⠘⡇⠙⠈⠀⠀⠀⠀⠀⠁⠋⡰⠀⠀⠁⠟⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀