⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⠴⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢨⣷⣤⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⡇⠀ ⢸⣿⣿⣿⣷⠀⠀⠀⢸⡷⠶⠒⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⡿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀ ⢸⣿⡿⠛⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⢿⡿⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠸⢿⣤⣤⣶⣶⣶⠶⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀ ⠸⣿⣷⣤⣤⣤⣶⣶⣶⣶⣶⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⣩⣟⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠴⣤⠴⠳⠤⣤⠤⠀⠀⠀⠀⢀⡟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣠⠤⣤⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⣀⣈⣭⣽⣷⣾⡯⠤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⣿⣿⣛⣋⠉⣽⣯⡷⠻⠿⣶⣬⣉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⠿⠛⣿⣿⠟⢋⡡⠞⢁⡏⢀⣤⠙⣶⣿⣿⣷⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⣾⣯⣥⣶⣿⣯⢀⣴⣿⣧⣴⣿⣠⡀⣿⣷⣼⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣯⣼⠿⠿⡿⣿⢿⡿⣿⢻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣄⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠞⡱⢃⣴⡿⢁⡵⢻⠇⠈⢸⡇⠸⣿⢿⣿⣿⡿⣽⣿⣷⣬⣿⣿⣿⣿⡶⠶⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡴⠃⣾⣿⣴⠏⣀⡟⣸⡀⣠⣿⡀⠹⣼⣟⠉⢳⡜⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣾⡁⣸⠟⢩⠏⣠⣾⣇⣻⣿⣿⣿⠿⢦⣿⣿⢷⢰⡏⢻⡉⣿⣿⣧⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢹⣿⣏⠷⢁⡜⠀⡼⣱⣯⣻⣬⣿⣿⣿⣷⡾⢹⠻⣦⡀⢧⢸⡟⠿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣋⣴⣿⠀⣼⣷⣧⣤⣬⣿⣷⠙⠻⣿⣷⡷⠆⢿⣳⠄⣼⣷⡀⢹⡀⣿⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠛⣿⣿⠈⣿⣰⠟ ⠿⠿⠈⣿⣧⣸⠻⠿⣟⣷⣶⣿⣀⣜⣽⣿⡦⣿⡟⠀⠙⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣿⣿⣿⠻⡇⠀⠀⠀⠤⠚⠋⠹⢻⡀⠈⠛⠛⠓⢻⣷⣿⣿⣿⣧⣿⡏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣿⣿⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣿⣟⢙⣿⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣭⣽⣿⠃⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠸⣷⡀⠀⠀⠀⠲⠶⠄⠀⠀⠀⠀⣠⣿⡟⣋⠋⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⢠⢿⠟⢦⡀⠀⠈⠀⠀⠀⢀⣤⣾⣿⠈⢧⢧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣁⡀⠙⢦⣀⡠⠔⠊⢡⡟⠟⠏⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣺⣿⣿⡟⣿⣿⠿⣿⣿⢿⣿⣿⣿⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣾⣿⣿⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⠁⠀⠀⢀⡟⠈⢧⡈⠏⠛⠻⠿⠿⠿⠟⠿⠋⠁⢹⡄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⡞⠀⠀⠀⠙⠦⣀⢤⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⣼⠃⠀⢰⠖⣆⠀⠺⠛⠧⢤⣄⣀⣀⡀⢴⠒⣿⠀⠀⠀⠀⠘⡟⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠋⠀⠀⠀⠀⢰⣿⡠⣤⣈⡛⠉⣀⢀⡀⢀⣠⡸⣍⣛⣓⣾⣷⣿⠀⠀⠀⡄⠀⠹⡀⠈⠙⠓⠦⢄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡮⠒⠂⠉⠳⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣻⣷⣶⣾⣿⣛⣻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠰⣀⠀⢳⠀⠀⠀⠀⠀⠀⠉⠑⠢ ⠀⠀⠀⠀⠀⠴⠓⠂⠉⠉⢣⠙⡄⢀⣿⣿⡇⢹⠉⠋⡟⢿⢿⡿⠿⠿⣿⢿⢻⡟⡟⢹⠋⣿⡇⠀⠀⠀⠈⠃⠈⣇⠀⠀⠀⠀⠘⠀⠀⠠ ⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢳⣵⣿⣿⡟⡇⣾⢰⠆⡇⡾⢸⠀⢀⠀⡇⢸⢸⡇⡇⢸⢰⣿⣿⣠⠤⠖⠶⣄⡀⠘⢶⠶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⡿⠛⢿⣷⡇⣿⣸⢸⡇⡇⢸⠀⠘⣿⡇⡿⢸⢀⣷⣿⣼⣿⡿⠿⠤⣀⡀⠀⠻⢷⣼⣠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡟⣿⣷⣄⠀⢰⣧⡀⠀⣹⣷⡏⣿⢾⢡⡇⣿⠀⠀⢸⡇⡏⣾⣸⣿⠉⣠⣿⠃⠀⠀⣀⡈⠑⠒⢤⡌⠁⣴⡷⠂⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⡿⠟⠀⣾⣿⣷⢶⣿⣿⡇⡿⢸⢸⡇⡿⠀⠀⣺⣧⣷⣿⡿⣯⣿⣿⡇⠀⣤⡾⢻⣿⣆⢀⣾⡇⠀⡀⠀⢰⢑⡆⠀ ⠀⠀⢀⣤⠄⠀⠙⠋⠀⠀⣸⡿⢿⣿⣾⣼⣟⣿⢷⣿⣾⣷⣷⣶⣟⣻⣭⣷⣶⣿⣿⢿⣾⠁⡀⠻⣿⣿⣿⣿⣿⣟⣁⡘⢿⣦⡈⠋⣀⢀ ⠒⢀⣸⠟⠀⠀⠀⠀⠀⢠⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⢹⣿⡿⣽⣿⣿⣾⠟⠙⢻⣿⣞⣹⣿⣿⣗⣓⡦⠙⠿⣼⡿⠯ ⠠⡼⠋⢀⠀⠀⠀⠀⢠⡟⠀⢠⣿⣿⣿⣿⣾⠉⡏⡏⢹⢹⣿⣿⣿⣇⣼⢿⣫⣿⣿⡇⡇⠹⠷⢾⣿⣿⣿⣯⣵⡿⠿⢋⣴⣾⡟⢻⣷⣆ ⡜⠁⡀⡆⠀⠀⠀⣠⡟⠀⠀⣼⣿⣿⣿⣿⣿⣸⠇⡇⣿⣿⣿⣿⠿⢋⣽⣿⢿⣿⣿⣧⡇⠀⠀⠀⢯⣿⣿⠀⠀⠉⠾⡿⣿⣟⣳⣿⣿⠏ ⠀⢠⢻⠁⠀⢀⣼⣯⣤⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣟⣫⣴⣷⣿⣿⣿⣼⣏⣿⣿⡇⠀⠀⢀⡼⠟⣧⡀⣀⡀⢸⣷⣌⢿⣿⣿⢏⡴ ⠀⣎⠃⠀⡰⠟⣿⣿⣿⣷⡿⠿⢿⡿⢿⢿⣛⣯⣽⣶⣿⣿⣿⣋⣿⡏⣍⠽⢿⣿⣿⣿⠁⠀⢀⣾⠀⠀⢸⣿⣿⠋⠙⢿⣿⣿⣿⣷⠛⠛ ⣰⠃⣠⠞⠁⠀⠛⠛⠛⢿⣿⣿⣿⣿⡿⡿⢟⠛⠛⠻⣿⣟⣿⣿⣿⢁⠀⠀⠀⠀⢿⣿⡆⢠⠿⣿⠀⠀⢸⣿⣿⠀⠀⠀⢹⣿⣿⣿⠀⠀ ⣡⡶⠁⢀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠉⠁⠀⠀⠀⢸⣿⣯⣿⡇⡄⠀⠀⠀⠈⢾⣿⣇⠟⠂⡿⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀ ⠟⠀⢠⠏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠀⢀⡀⠀⠀⣿⡟⠉⣹⢉⡅⠀⠀⠀⠀⠘⣿⣿⠀⠀⡇⠀⠀⠘⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⠈⠳⣦⣴⡿⠀⠀⣿⠛⡁⠄⠀⠀⠀⠀⣿⣿⠀⠐⣿⠀⠀⠀⣿⣿⡀⠀⠀⣾⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢹⡇⣠⣤⡏⠀⠀⠀⠀⠀⠀⢆⣿⣿⠀⠀⢸⣄⡆⢐⣿⠟⠁⠀⠈⠛⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢄⠀⢸⡇⣿⣿⡏⠫⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠘⠛⠻⢿⣿⡇⠀⠀⠀⠀⣾⣹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡉⠙⡉⢀⠀⠘⣧⣸⡀⠹⣿⠃⠀⠀⠙⣿⣶⣤⣿⢾⣿⡇⠀⠀⠀⢰⡿⡿⢻⡆⠀⠀⢰⣿⠛⢷⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⠈⣿⣦⡵⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠃⠈⢧⠀⠀⢸⠃⠀⠀⡃⠀ ⢀⣤⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⠙⢻⣿⠀⠄⠄⠐⠳⠶⠿⠿⣿⣿⣷⠀⠀⠀⠀⢣⠀⠀⢸⠀⠀⠘⣆⠀⠀⡇⠀ ⢸⣿⣿⡿⠀⣿⠿⠿⠿⣿⠿⣿⠽⠿⠿⠿⣿⣿⣼⣿⣤⣿⣿⡀⣀⣠⣤⣶⡾⠶⢿⣿⣿⣿⠀⠀⠀⠀⢸⡆⠀⢸⡄⠀⠀⣿⠀⠀⣇⠀ ⠀⠉⠉⠀⢸⣷⠀⠀⠀⠸⣿⠇⠀⠀⠐⢄⠀⠀⠀⠽⣿⠋⠉⠙⠛⠛⠛⠛⠓⠒⠛⢿⢿⣿⠀⠀⠀⠀⠘⠃⠀⠸⡇⠀⠀⣿⠀⠀⠙⠀ ⠀⠀⠀⠀⡿⣿⣿⣶⣶⣶⣯⣦⠤⣤⣀⣨⣷⣶⣥⣴⣥⣄⣀⣠⣀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⢰⡇⠀⠀⢸⠀ ⠀⠀⠀⣸⢡⣿⣿⣿⣿⣿⡤⣿⢠⣿⣿⣿⣿⣿⣏⠛⢿⣿⣿⢩⡿⢿⣿⡿⢸⣿⣿⣶⣷⣾⡆⠀⠀⢸⣿⣶⡀⢸⡿⠀⢰⣿⣀⡀⣸⠀ ⠀⠀⢀⣧⠞⠉⠛⠛⠿⢿⣷⣿⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣇⣾⣿⡇⢸⣿⣿⣿⣿⣟⢣⠀⠀⠀⠉⠙⠛⠋⠁⠀⠈⠙⠛⠛⠋⠀ ⠀⠀⣸⡏⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⣋⣹⣿⣿⣿⣿⣿⣿⣿⣟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⠿⠛⢉⡁⠼⣿⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀