⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠏⠉⠙⢦⡈⠉⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠒⢦⣞⠉⠈⠙⢾⡀⠀⠀⣸⠇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⢸⣈⣳⠀⠀⠀⠁⢀⡴⠋⠀⠀⢀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⢠⠋⠀⠀⠀⠀⠀⣀⣀⣀⣉⡉⠀⠀⠀⠀⠈⠳⡄⠶⢾⡉⠀⣼⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⡏⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⣈⣷⡀⣀⣠⠤⠼⣇⣠⠞⠃⠀⣹⠟⠉⣧⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⡀⡇⠀⠀⣰⠃⠀⠀⠀⢀⠔⠋⠁⠈⠛⠁⠀⠀⠀⠀⠉⠓⢦⠞⠁⠀⠀⢸⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⠳⣹⡄⢰⠇⠀⠀⠀⣰⠿⡄⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠁⢈⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣀⣈⡴⠏⠀⠀⣶⣾⡿⢀⡇⠀⠀⣰⣿⠏⠉⠉⠿⣆⠀⠀⠀⠀⣠⠃⠀⢸⠃⢠⠤⠴⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⡽⠿⠤⠼⠀⠀⢠⠇⠀⠀⠀⠀⠈⣿⣀⡀⠀⠀⠁⠀⢀⡯⠴⠋⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠿⠏⠀⢀⣀⣴⠏⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠙⢲⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠁⠀⢤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡷⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢠⠤⠀⠀⠀⣠⠞⠋⠁⠈⠻⢭⡽⠂⢸⠶⠦⠤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡼⠁⠀⠀⠀⣄⡀⠀⠀⣠⡞⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠐⣇⠀⠀⠀⠀⠈⢯⠉⠩⣥⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⢀⡤⠤⠤⣄⡀⢰⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣸⠂⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⡞⠀⠀⠀⠀⠈⠋⣰⠞⠋⠓⣦⡖⠚⠛⠋⠉⠉⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣤⣶⣾⣛⣋⣉⣉⠉⠙⠛⠲⣤⡀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠹⣧⡀⠘⢿⣖⠒⠒⠒⠉⠈⠑⢦⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠉⠙⠦⣄⠀⠀⠙⣦⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⠺⡇⠀⠀⠀⠀⠈⢯⠙⠒⢻⠉⠁⠀⠀⠀⠀⠀⠹⣷⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⡇⠀⠀ ⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠘⣆⡇⠀⠀⠀⠀⠀⠈⢧⠀⡼⠀⠀⡾⢻⡄⠀⣠⣄⠸⣯⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡇⠀⠀ ⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠀⠻⡾⠀⢠⣏⡼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⠟⠀⠀⠀ ⣿⡇⠀⠀⠀⢱⡀⠀⠀⠀⠀⣰⠋⡆⠀⠀⠀⠀⠀⠀⣇⠀⠀⡆⠀⠀⠀⠈⠙⠁⢰⡿⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠴⠧⣤⣀⡀⠀ ⣿⡇⠀⠀⠀⠈⢷⡀⠀⣠⡾⠁⠀⠘⣆⠀⠀⠀⢀⡼⠋⠉⠚⡇⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⣄⡀⠀⠀⠀⠈⠙⢦ ⣿⡇⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠈⠓⠶⠖⠛⣇⠀⠀⠀⢻⡄⠀⠀⠀⠀⣾⣿⣍⠉⠉⠉⠓⠲⣄⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠈ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠀⠀⣹⡦⡀⠀⠀⠉⣿⡏⠳⢤⣄⣀⣠⡼⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢀⡴⠃ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⢰⡟⠘⣶⠶⠤⠤⢤⣤⣤⠤⠴⠚⠋⠀⢀⣠⠤⠞⠉⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⣿⠁⢀⡼⠀⠀⣠⠤⣤⠀⠀⠀⠉⠉⢹⠁⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡿⣖⡋⠀⠀⠘⢧⣀⠀⢳⡀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⢻⠁⠀⠀⠀⠀⠀⢸⡀⠀⢉⣷⠦⠄⠀⠉⠛⢺⡷⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠉⠁⠰⣏⠀⠀⠀⡤⠤⠖⢋⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀