⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣠⣾⣷⣄⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⢃⣼⣿⠃⠘⣿⣧⡘⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣧⣾⢻⣿⣦⣴⣿⡟⣷⣼⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⣾⡇⠈⠁⢸⣷⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠃⠀⢰⣿⠀⠀⠀⠀⣿⡆⠀⠘⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠏⠀⠀⣾⠇⠀⠀⠀⠀⠸⣷⠀⠀⠹⣿⣧⠀⠀⠀⠀ ⠀⠀⢀⣾⡿⠁⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠘⢿⣷⡀⠀⠀ ⠀⢠⣿⠋⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠙⣿⡄⠀ ⠀⣿⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⣼⣦⠀⠀⠀⢸⣧⠀⠀⠀⠀⠸⣿⠀ ⠀⣿⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣿⠀ ⠀⢹⡇⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢸⡏⠀ ⠀⣾⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣷⠀ ⢰⡿⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢿⡆ ⣾⠇⠀⠀⠀⢰⣿⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⣿⡆⠀⠀⠀⠸⣷ ⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿ ⢿⣆⠀⠀⠀⠘⣿⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⣿⠃⠀⠀⠀⣰⡿ ⠈⢿⣦⠀⠀⠀⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⠀⠀⠀⣴⡿⠁ ⠀⠀⠻⣷⡀⠀⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⡿⠀⢀⣾⠟⠀⠀ ⠀⠀⠀⢹⣧⠀⢸⣷⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⣾⡇⠀⣼⡏⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⠀⢿⣇⠀⠘⣿⣿⣿⣿⠃⠀⣸⡿⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⡈⣿⡄⠀⠈⠛⠛⠁⠀⢠⣿⢁⣠⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣾⣿⣄⠀⠀⠀⠀⣠⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡖⠀⠀⢲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢇⡞⢳⡘⡆⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⢫⠗⠺⡝⢿⡄⠀⠀⠀ ⠀⠀⢠⡿⠀⡼⠀⠀⢧⠀⢿⡄⠀⠀ ⠀⢠⠟⠀⢸⠃⠀⠀⠘⡇⠀⠻⡄⠀ ⠀⡏⠀⠀⡏⠀⢸⡇⠀⢹⠀⠀⢹⠀ ⠀⡿⠀⢸⠁⠀⠀⠀⠀⠈⡇⠀⢿⠀ ⢰⠇⠀⢸⠀⠀⣼⣧⠀⠀⡇⠀⠸⡆ ⢸⡀⠀⢸⠀⢠⣿⣿⡄⠀⡇⠀⢀⡇ ⠀⠳⡄⢸⠀⢸⣿⣿⡇⠀⡇⢠⠞⠀ ⠀⠀⢹⠈⣇⠈⣿⣿⠁⣸⠁⡏⠀⠀ ⠀⠀⠈⠳⣼⣆⠈⠁⣰⣧⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠛⠦⠴⠛⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡿⠻⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠃⠀⠀⢀⣿⠃⠀⢻⣇⠀⠀⠀⠛⢷⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⠟⠁⠀⠀⠀⢀⣾⣏⣠⣤⣈⣿⣆⠀⠀⠀⠀⠙⢿⣆⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⣰⣿⠟⠛⠉⡉⠙⠛⢿⣧⡀⠀⠀⠀⠀⢻⣧⠀ ⢀⣿⠇⠀⠀⠀⣠⣶⠟⠁⠀⣠⣾⢿⣦⡀⠀⠹⢷⣦⡀⠀⠀⠀⢿⣇ ⢸⣿⠀⠀⠀⢸⣿⠁⠀⢀⣼⠟⠁⠀⠙⢿⣆⠀⠀⢹⣷⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⢘⣿⡄⠀⣾⡏⢀⣴⣶⣄⠈⣿⡆⠀⣼⡏⠀⠀⠀⢀⣿ ⢸⣿⠀⠀⠀⣼⡏⠀⢠⣿⠀⣼⣏⣈⣿⡄⢸⡇⠀⠈⣿⡀⠀⠀⢸⣿ ⠀⣿⡆⠀⠀⣿⡀⠀⠸⣿⠀⣿⠛⠛⢿⡇⢸⡇⠀⠀⣸⡇⠀⠀⣾⡇ ⠀⠸⣷⠀⠀⠹⣧⡀⠀⣿⡆⣿⡄⠀⣼⡇⣾⡇⠀⣠⡿⠀⠀⢸⡿⠀ ⠀⠀⢻⣇⠀⠀⠙⣷⡄⠸⣷⣹⣧⣠⡿⣱⡿⠀⣴⡟⠁⠀⢀⣿⠃⠀ ⠀⠀⠈⢿⣆⠀⠀⠘⣿⡀⠹⣧⠙⠛⣡⣿⠃⣸⡟⠀⠀⢀⣾⠇⠀⠀ ⠀⠀⠀⠈⢻⣦⠀⠀⠘⣷⡄⠹⣷⣴⡿⠁⣴⡟⠀⠀⢠⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⡀⠀⠘⢿⣦⡈⠉⣠⣾⠟⠀⠀⣠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠙⠻⠿⠛⠁⠀⠀⢾⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣾⣿⣿⣿⣷⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀ ⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠋⠉⠛⠛⠻⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀ ⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀ ⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡟⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀ ⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⠁⠀⠀⠀⣠⣾⣿⡿⠋⠈⠙⢿⣿⣷⣄⠀⠀⠀⠈⠉⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⣸⣿⣿⠁⠀⠀⣠⣶⣶⣶⣄⠀⠀⠘⣿⣿⣇⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⣿⣿⡇⠀⠀⣼⣿⡿⠛⢿⣿⣧⠀⠀⢹⣿⣿⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢸⣿⣿⠁⠀⢸⣿⣿⠁⠀⠈⣿⣿⡇⠀⠘⣿⣿⡇⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⡟ ⢸⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⡇ ⠀⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⡟⠛⠛⠛⢿⣿⣿⡀⢀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⠀ ⠀⠸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠘⣿⣿⡆⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠃⢸⣿⣿⠃⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⢠⣿⣿⠇⠀ ⠀⠀⢻⣿⣷⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⢿⣿⣧⠀⣿⣿⣇⠀⠀⠀⢸⣿⣿⠀⣼⣿⡿⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠀⣾⣿⡟⠀⠀ ⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠸⣿⣿⡄⢻⣿⣿⡀⠀⢀⣿⣿⡟⢠⣿⣿⠇⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀ ⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⢻⣿⣷⡈⣿⣿⣧⣀⣼⣿⡿⢁⣾⣿⡟⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠈⢿⣿⣧⠈⠿⣿⣿⣿⠿⠁⣼⣿⡿⠁⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠈⢿⣿⣧⡀⠈⠉⠁⢀⣾⣿⡿⠁⠀⣠⣿⣿⠇⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠈⢻⣿⣷⣄⠀⣠⣾⣿⡟⠁⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⣿⠋⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠈⠛⠿⠛⠁⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣦⣄⠀⠀⠀⣠⣴⣿⣿⠟⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣿⣿⡿⠟⠁⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣴⣀⣀⣦⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠿⣷⣿⣠⠀⠀⠀⠀⣄⣿⣾⠿⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡾⣠⢁⣿⢠⠀⠁⠛⠛⠈⠀⡄⣿⡈⣄⢷⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢠⠀⡿⣸⠀⠃⣿⣿⣿⣿⠘⠀⣇⢿⠀⡄⣿⠀⠀⠀⠀ ⠀⠀⠀⡏⣼⠀⡇⣾⠀⠀⡏⣿⣿⣿⣿⢻⠀⠀⣷⢸⠀⣧⢹⠀⠀⠀ ⠀⠀⠟⣾⢀⠀⡿⢸⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⡇⢿⠀⡀⣷⠻⠀⠀ ⠁⡿⣴⠀⠀⠀⣿⢀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⡄⣿⠀⠀⠀⣦⢿⠈ ⡿⣰⠀⠀⠀⠃⣿⠀⠀⠀⣧⣿⣿⣿⣿⣼⠀⠀⠀⣿⠘⠀⠀⠀⣆⢿ ⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⡆⣿⣿⣿⣿⢰⠀⠀⠀⣿⢸⠀⠀⠀⠀⣿ ⣷⠸⠀⠀⠀⡆⣿⠀⠀⠀⠀⣧⣿⣿⣼⠀⠀⠀⠀⣿⢰⠀⠀⠀⠇⣾ ⡆⢿⠀⠀⠀⠀⣿⠈⠀⠀⠀⡀⣿⣿⢀⠀⠀⠀⠁⣿⠀⠀⠀⠀⡿⢰ ⠀⣷⢸⠀⠀⠀⣿⢸⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡇⣾⠀ ⠀⡏⢸⠀⠀⠀⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⠀⠀⡇⢹⠀ ⠀⣿⢀⠀⠀⠀⡄⣿⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⣿⢠⠀⠀⠀⡀⣿⠀ ⠀⣿⠸⠀⠀⠀⠀⣧⢸⠀⠀⠀⣦⣼⠀⠀⠀⡇⣼⠀⠀⠀⠀⠇⣿⠀ ⠀⡄⣿⠙⠀⠀⠀⡄⣿⠈⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠋⣿⢠⠀ ⠀⠀⡀⣷⢿⠘⠀⠀⣇⢻⠀⠀⠀⠀⠀⠀⡟⣸⠀⠀⠁⡿⣾⢀⠀⠀ ⠀⠀⠀⠀⣧⣿⠹⠀⠀⣷⠸⠀⠀⠀⠀⠇⣾⠀⠀⠏⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⠘⠀⡆⣿⠀⠀⠀⠀⣿⢰⠀⠃⣿⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣿⠻⠈⣷⢸⠁⠈⡇⣾⠁⠟⣿⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣼⣷⡟⣿⣴⣦⣿⢻⣾⣧⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⡘⣧⣿⠘⠃⣿⣼⢃⣿⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⣄⣷⣾⣠⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠀⠀⠀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠛⠴⠦⠛⠀⠀⠀⠀⠀ ⠀⠀⠁⠞⣧⣰⠁⠈⣆⣼⠳⠈⠀⠀ ⠀⠀⡏⠁⣸⠁⣿⣿⠈⣇⠈⢹⠀⠀ ⠀⠞⢠⡇⠀⡇⣿⣿⢸⠀⢸⡄⠳⠀ ⡇⢀⠀⡇⠀⡄⣿⣿⢠⠀⢸⠀⡀⢸ ⡆⠸⠀⡇⠀⠀⣧⣼⠀⠀⢸⠀⠇⢰ ⠀⢿⠀⡇⠈⠀⠀⠀⠀⠁⢸⠀⡿⠀ ⠀⢹⠀⠀⢹⠀⡇⢸⠀⡏⠀⠀⡏⠀ ⠀⡄⠻⠀⡇⠘⠀⠀⠃⢸⠀⠟⢠⠀ ⠀⠀⡄⢿⠀⢧⠀⠀⡼⠀⡿⢠⠀⠀ ⠀⠀⠀⡄⢿⡝⠺⠗⢫⡿⢠⠀⠀⠀ ⠀⠀⠀⠀⡆⡘⢳⡞⢇⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢲⠀⠀⡖⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠁⠟⢾⠀⠀⠁⠛⠿⠻⠙⠀⠀⠆⠿⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡿⣠⠀⠀⠟⣾⣠⠉⡈⣦⢿⠘⠀⡀⣷⠻⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣾⢠⠀⠀⡟⣴⠁⡿⣴⣷⠹⡄⣷⠘⠀⠀⣦⢻⠈⠀⠀⠀ ⠀⠀⠇⣾⢀⠀⠀⡟⣸⠃⣿⣡⠛⠙⣧⠹⡀⣿⠘⠀⠀⣆⢿⠈⠀⠀ ⠀⠃⣿⢀⠀⠁⡟⣴⠀⡿⣱⡿⣠⣧⣹⣷⠸⡄⣷⠙⠀⠀⣇⢻⠀⠀ ⠀⡿⢸⠀⠀⡿⣠⠀⡇⣾⡇⣼⠀⡄⣿⡆⣿⠀⡀⣧⠹⠀⠀⣷⠸⠀ ⡇⣾⠀⠀⡇⣸⠀⠀⡇⢸⡇⢿⠛⠛⣿⠀⣿⠸⠀⡀⣿⠀⠀⡆⣿⠀ ⣿⢸⠀⠀⡀⣿⠈⠀⡇⢸⡄⣿⣈⣏⣼⠀⣿⢠⠀⡏⣼⠀⠀⠀⣿⢸ ⣿⢀⠀⠀⠀⡏⣼⠀⡆⣿⠈⣄⣶⣴⢀⡏⣾⠀⡄⣿⢘⠀⠀⠀⣿⢸ ⣿⢸⠀⠀⠀⣷⢹⠀⠀⣆⢿⠙⠀⠁⠟⣼⢀⠀⠁⣿⢸⠀⠀⠀⣿⢸ ⣇⢿⠀⠀⠀⡀⣦⢷⠹⠀⡀⣦⢿⣾⣠⠀⠁⠟⣶⣠⠀⠀⠀⠇⣿⢀ ⠀⣧⢻⠀⠀⠀⠀⡀⣧⢿⠛⠙⡉⠉⠛⠟⣿⣰⠀⠀⠀⠀⠃⣿⢠⠀ ⠀⠀⣆⢿⠙⠀⠀⠀⠀⣆⣿⣈⣤⣠⣏⣾⢀⠀⠀⠀⠁⠟⣾⢀⠀⠀ ⠀⠀⠀⡀⣦⢷⠛⠀⠀⠀⣇⢻⠀⠃⣿⢀⠀⠀⠃⠟⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣷⠻⡿⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠙⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠋⠿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣾⣠⠀⠀⠀⠀⠁⠟⡿⣿⣿⣶⣿⣿⣿⠻⠈⠀⠀⠀⠀⡄⣷⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣰⠀⠀⠀⠀⠀⠟⣿⣿⣴⣠⠀⠀⠀⣄⣦⣿⣿⠻⠀⠀⠀⠀⠀⣄⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣾⢀⠀⠀⠀⠀⠁⡿⣿⣾⣠⠀⠁⠛⠿⠛⠈⠀⡄⣷⣿⢿⠘⠀⠀⠀⠀⡀⣷⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣴⠀⠀⠀⠀⠀⠋⣿⣿⣴⠀⠀⠋⣿⣿⣿⣿⣿⠹⠀⠀⣦⣿⣿⠙⠀⠀⠀⠀⠀⣦⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠏⣿⣿⣰⠀⠀⠀⠀⠀⠏⣿⣿⣰⠀⠁⡟⣿⣾⣠⠀⣄⣷⣿⢻⠈⠀⣆⣿⣿⠹⠀⠀⠀⠀⠀⣆⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣿⣿⣠⠀⠀⠀⠀⠀⠇⣿⣿⣠⠀⠁⡿⣿⣾⢀⠁⠉⠈⡀⣧⣿⢿⠈⠀⣄⣿⣿⠸⠀⠀⠀⠀⠀⡄⣿⣿⠹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣿⣿⢠⠀⠀⠀⠀⠀⠃⣿⣿⣼⠀⠁⡿⣿⣼⠁⠿⣿⣿⣿⠿⠈⣧⣿⢿⠈⠀⣇⣿⣿⠘⠀⠀⠀⠀⠀⡄⣿⣿⠹⠀⠀⠀⠀ ⠀⠀⠀⠃⣿⣿⣰⠀⠀⠀⠀⠀⠏⣿⣿⣴⠀⠀⡟⣿⣾⢁⡿⣿⣼⣀⣧⣿⣿⡈⣷⣿⢻⠀⠀⣆⣿⣿⠹⠀⠀⠀⠀⠀⡆⣿⣿⠸⠀⠀⠀ ⠀⠀⠁⣿⣿⣸⠀⠀⠀⠀⠁⡟⣿⣾⣠⠀⠀⠇⣿⣿⢠⡟⣿⣿⢀⠀⡀⣿⣿⢻⡄⣿⣿⠸⠀⠀⣄⣷⣿⢻⠈⠀⠀⠀⠀⣇⣿⣿⠈⠀⠀ ⠀⠀⡟⣿⣾⠀⠀⠀⠀⠁⡿⣿⣼⢀⠀⠀⠀⡿⣿⣼⠀⣿⣿⢸⠀⠀⠀⣇⣿⣿⠀⣧⣿⢿⠀⠀⠀⡀⣧⣿⢿⠈⠀⠀⠀⠀⣷⣿⢻⠀⠀ ⠀⠇⣿⣿⢠⠀⠀⠀⠀⡟⣿⣾⠀⠀⠀⠀⠃⣿⣿⢸⠃⣿⣿⢸⠀⠀⠀⡇⣿⣿⠀⡆⣿⣿⠘⠀⠀⠀⠀⣷⣿⢻⠀⠀⠀⠀⡄⣿⣿⠸⠀ ⠀⣿⣿⣼⠀⠀⠀⠀⠀⣿⣿⢸⠀⠀⠀⠀⡇⣿⣿⢀⡀⣿⣿⢿⠛⠛⠛⡟⣿⣿⠀⠀⣿⣿⢸⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⣇⣿⣿⠀ ⡇⣿⣿⢠⠀⠀⠀⠀⠀⣿⣿⢹⠀⠀⠀⠀⡇⣿⣿⠀⠀⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣿⣿⢸⠀⠀⠀⠀⡏⣿⣿⠀⠀⠀⠀⠀⡀⣿⣿⢸ ⡟⣿⣾⠀⠀⠀⠀⠀⠀⡆⣿⣿⠘⠀⠀⠀⡇⣿⣿⠘⠀⡇⣿⣿⠈⠀⠁⣿⣿⢸⠀⠁⣿⣿⢸⠀⠀⠀⠃⣿⣿⢸⠀⠀⠀⠀⠀⠀⣧⣿⢿ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠘⠀⠀⠀⣿⣿⢹⠀⠀⣧⣿⢿⠛⡿⣿⣼⠀⠀⡇⣿⣿⠀⠀⠀⠃⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢰⠀⠀⠀⣇⣿⣿⠘⠀⠀⣄⣶⣶⣶⣠⠀⠀⠁⣿⣿⣸⠀⠀⠀⡄⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⠀⠀⠀⠀⠀⣧⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣼⠀⠀⠀⠀⠀⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠈⠀⠀⠀⠀⠀⣦⣿⣿⠻⠀⠀⠀⠀⠀⠏⣿⣿⣴⠀⠀⠀⠀⠀⠀⡿⣿⣾⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿ ⡇⣿⣿⠈⠀⠀⠀⠀⠀⠀⡀⣷⣿⢿⠻⠉⠈⠀⠀⠀⣄⣷⣿⢿⠙⠈⠋⡿⣿⣾⣠⠀⠀⠀⠁⠉⠟⡿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠁⣿⣿⢸ ⠀⣷⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⢿⠈⠀⠀⠀⠀⣄⣷⣿⣿⣿⣾⣠⠀⠀⠀⠀⠁⡟⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣾⢀ ⠀⡄⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠻⠉⠀⠀⠀⠀⣄⣤⣠⠀⠀⠀⠀⠉⠟⡿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⢠⠀ ⠀⠀⡄⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠿⠻⠛⠛⠉⠋⠛⠟⠿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⢠⠀⠀ ⠀⠀⠀⡀⣷⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣾⣶⣷⣿⣿⣿⣾⣶⣷⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣾⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠘⠀⠀⠀⠀⠀⠃⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠈⠀⠀⠀⠁⡿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⣿⣿⠺⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⠀⠀⠀⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠗⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⠙⠀⠋⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀