⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠹⡟⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢿⣹⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠘⣿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⢻⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣿⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣿⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠛⢹⣟⠁⣀⣈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠶⠿⠷⣾⡃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣶⣾⡿⠋⠉⠙⠋⠘⠦⣄⡀⠀⠀⠀⠀⣠⣾⣫⠀⠀⠀⠀⠀⠙⢷⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⢠⣞⣉⣏⠀⠀⣀⠀⠀⠀⢀⣌⣙⣇⡀⣠⡾⠋⣾⠇⠀⠀⠀⠀⠀⠀⣎⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠀⠀⠀⢀⣴⣟⡋⠁⠙⠷⠈⠁⠀⢀⣰⣿⡟⠋⢻⡿⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣦⣜⣿⣷⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀ ⢤⣀⢀⣴⠟⠉⠙⣷⢲⣾⣆⠀⢸⣰⣿⠏⠀⢠⣾⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⡀⣉⣁⣤⠁⠀⠀⠀⠀⢸⡀ ⣀⠈⢻⠃⠀⠀⠀⢩⠿⣯⣿⣿⣿⣿⣧⣤⣶⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⣰⡶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢋⡽⠁⠀⠀⠙⠻⠷⣤⣤⣤⣤⣤⣴⠶⠾⠛⠛⠉⠉⢹⣯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣯⣤⣀⣀⠀⠀⠀⠀⠀⣀⣤⡵⠶⠷⠶⢶⣤⣄⣀⠀⢸⣈⣻⣷⠶⢦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⡴⠟⠁⠀⢀⣀⣀⣀⣀⠀⠀⠙⠻⣾⣟⠃⢹⣿⣿⣟⣿⣶⠶⢶⣿⣿⣭⣭⣿ ⠀⠀⠀⠀⠀⣰⣿⠋⣼⠏⠉⠁⠀⠀⠈⠉⢻⡆⠀⣾⠋⠀⡿⠉⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠙⢧⡈⢇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉ ⣤⣄⣀⣀⣴⠏⠀⠀⣿⠀⠀⠠⠀⠀⠀⠀⣾⢱⣾⠇⠀⠀⣷⠀⠀⠀⠰⠄⠀⠐⠆⣿⠀⠀⠀⠀⢨⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠻⠿⠿⣿⠇⠀⠰⣿⡄⠀⠀⠀⠀⠀⣰⠏⢸⡏⠀⠀⠀⣿⡀⠀⠀⠴⠘⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⢿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⠀⠀⠀⢿⡄⠀⠀⠉⢻⣦⡀⣀⡴⠛⠁⠀⢸⡇⠀⠀⠀⠈⠛⣦⣄⡀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿ ⢻⣄⠀⠀⠘⣷⡀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠉⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠶⠶⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⣿⣷⣦⣀⡀⢠⣴⡄⠀⠘⠳⢶⣶⣾⣿⣦⡀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⠈⢿⣿⣿⠉⠛⢿⣯⣤⣴⣷⣼⣯⣭⣿⣿⣿⣟⣻⣟⣁⣀⣤⣤⣤⣀⣴⣿⣟⣻⣥⡴⠖⢀⠀⠀⠀⢠⡤⢤⣤⣄⠀⠀⠀ ⠀⠠⠤⠤⣿⣦⣿⣿⡏⠀⠀⢻⣿⡿⠃⢻⣿⣿⠿⠏⠀⠉⠉⠛⢿⣿⠟⠛⢻⣿⣿⣿⠟⠉⠉⠁⠀⠀⢼⡷⠶⣦⣤⡤⠀⠙⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢉⡇⠀⢸⣻⡇⠀⠀⠀⠀⠀⠀⢈⣽⡀⠀⣼⣿⡟⣏⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⣯⠁⠀⠀⢸⣀⠀⠀

⠀⠀⣀⢸⠀⠀⠁⣯⢛⢰⠀⠀⠀⠀⠀⠀⠀⠀⣏⡟⣿⣼⠀⡀⣽⢈⠀⠀⠀⠀⠀⠀⡇⣻⢸⠀⡇⢉⠀⠀⠀⠀⠋⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠙⠀⡤⣤⣦⠶⡷⢼⠀⠀⠁⠉⠉⠟⣿⣿⣿⢻⠛⠟⣿⢿⠛⠉⠉⠀⠏⠿⣿⣿⢻⠃⡿⣿⢻⠀⠀⡏⣿⣿⣦⣿⠤⠤⠠⠀ ⠀⠀⠀⣄⣤⢤⡤⢠⠀⠀⠀⢀⠖⡴⣥⣻⣟⣿⣴⣀⣤⣤⣤⣀⣁⣟⣻⣟⣿⣿⣿⣭⣯⣼⣷⣴⣤⣯⢿⠛⠉⣿⣿⢿⠈⣿⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⢀⡀⣦⣿⣾⣶⢶⠳⠘⠀⡄⣴⢠⡀⣀⣦⣷⣿⣿⣶⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣽⠶⠶⠙⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢻⠉⠀⠀⠀⠀⠀⡀⣷⠸⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⡀⣷⠘⠀⠀⣄⢻ ⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠋⡾⣴⢀⡀⣄⣦⠛⠈⠀⠀⠀⡇⢸⠀⠁⠛⡴⣀⡀⣦⢻⠉⠀⠀⡄⢿⠀⠀⠀⣿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⢿⠀⠀⠀⠀⠀⠀⡿⣰⠀⠀⠘⠴⠀⠀⡀⣿⠀⠀⠀⡏⢸⠏⣰⠀⠀⠀⠀⠀⡄⣿⠰⠀⠇⣿⠿⠿⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣻⢨⠀⠀⠀⠀⣿⠆⠐⠀⠄⠰⠀⠀⠀⣷⠀⠀⠇⣾⢱⣾⠀⠀⠀⠀⠠⠀⠀⣿⠀⠀⠏⣴⣀⣀⣄⣤ ⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢇⡈⢧⠙⠀⠀⠀⣷⠙⠈⠀⠀⠀⠀⠀⠉⡿⠀⠋⣾⠀⡆⢻⠉⠈⠀⠀⠁⠉⠏⣼⠋⣿⣰⠀⠀⠀⠀⠀ ⣿⣭⣭⣿⣿⢶⠶⣶⣿⣟⣿⣿⢹⠃⣟⣾⠻⠙⠀⠀⣀⣀⣀⣀⢀⠀⠁⠟⡴⣤⢶⠛⠉⠀⠀⠀⠀⠀⠀⠁⠋⣿⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⣀⣀⣤⣤⢦⠶⣷⣻⣈⢸⠀⣀⣄⣤⢶⠶⠷⠶⡵⣤⣀⠀⠀⠀⠀⠀⣀⣀⣤⣯⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠟ ⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣯⢹⠉⠉⠛⠛⠾⠶⣴⣤⣤⣤⣤⣤⠷⠻⠙⠀⠀⠁⡽⢋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠞⡶⣰⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠿⣶⣤⣧⣿⣿⣿⣿⣯⠿⢩⠀⠀⠀⠃⢻⠈⣀ ⡀⢸⠀⠀⠀⠀⠁⣤⣁⣉⡀⠀⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠟⣾⢠⠀⠏⣿⣰⢸⠀⣆⣾⢲⣷⠙⠉⠟⣴⢀⣀⢤ ⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣦⣷⣿⣜⣦⢸⠀⠀⠀⠀⠀⠀⠀⠁⡾⢠⠋⡿⢻⠋⡟⣿⣰⢀⠀⠁⠈⠷⠙⠁⡋⣟⣴⢀⠀⠀⠀⠀ ⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠻⣎⠀⠀⠀⠀⠀⠀⠇⣾⠋⡾⣠⡀⣇⣙⣌⢀⠀⠀⠀⣀⠀⠀⣏⣉⣞⢠⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⣿⢷⠙⠀⠀⠀⠀⠀⣫⣾⣠⠀⠀⠀⠀⡀⣄⠦⠘⠋⠙⠉⠋⡿⣾⣶⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⡃⣾⠷⠿⠶⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣈⣀⠁⣟⢹⠛⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡄⣿⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⣿⠸⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣧⢻⠀⠀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡆⣿⠘⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣹⢿⠀⠀⠀⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣧⡟⠹⠀⠀⠀⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀