⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠶⣦⣀⣠⡤⠴⠶⠶⠶⠦⢤⣞⠉⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡴⠞⠉⠁⠀⠀⠀⢠⠤⠄⠀⠈⠙⠲⢤⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠠⣄⠀⠀⠙⢦⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⠭⠤⠤⣀⠀⠀⠀⡜⣱⡿⠿⣷⡄⠀⠑⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠤⣤⣶⣼⣿⣿⡏⢹⣾⣩⣿⣝⣿⡵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡵⢁⣤⡶⣤⡈⢦⠀⢰⣿⣏⠀⣰⣿⣿⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⡠⠤⠔⣃⣶⣷⠀⠿⠟⠋⠛⢃⣼⡛⠙⢙⣛⣛⢣⡿⠟⠘⡐⠠⡀⠀⠀⠀⠀⣿⠁⣾⠁⢀⣼⣿⡜⡧⠄⢻⣿⢿⠋⠀⢸⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⣰⡿⠋⢉⣒⠀⠹⣴⠁⠿⢣⢷⠛⣾⣰⠁⣥⣈⠃⣠⠖⠑⠪⡇⣵⠀⠀⠀⢀⡿⡀⣿⣶⡞⠉⠙⣧⣧⢾⢯⠻⣿⡷⠴⠋⢀⡠⠋⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⠘⢾⠻⡀⢻⣀⠇⣰⢻⠀⣿⢸⢉⢿⣁⡟⢹⡋⡴⡟⠁⣀⠤⡺⡫⠃⠀⠀⠀⢸⠁⢳⡻⣾⣇⣀⣼⡝⠘⣏⠸⡆⠀⠉⠁⠈⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⢳⠉⡥⢠⠈⢹⠦⠥⣫⣿⠷⣿⣵⣶⣷⣄⡣⡄⠉⢱⢘⠀⠀⠀⠀⠀⠸⡆⠀⠙⠪⠭⠗⠋⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢶⣄⠀⠀⠀⠀ ⠀⠀⢼⢠⡇⠙⠋⣠⣮⠋⠉⠑⣶⣶⣶⡏⠀⠈⡩⣊⡤⣲⢝⠜⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣄⣠⠖⢋⡉⠙⢫⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠘⠝⣻⣭⣿⡫⠵⠢⢄⢼⠷⢿⠟⢃⠀⣸⣽⡳⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⢀⣀⡴⠖⠋⠁⢰⠋⠙⣾⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠰⠋⢹⠖⠋⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⣀⡴⠛⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠉⠉⠉⠉⠉⠁⠀⣀⡀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡇⠈⠑⠶⢤⣄⣀⣠⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⣤⠖⠉⢙⡏⠙⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢈⠀⠀⠏⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠉⠀⠉⡆⢀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡶⠛⠙⢦⣀⣀⣤⣇⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣀⠤⢤⠀⠀⠀⠀ ⠸⣇⠀⠀⠐⠋⠁⠀⠀⠀⣀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠙⣧⣀⣀⣀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠤⠤⠽⢧⣄⡀⣴⡏⠀⠀⠀⠀⡗⢤⡀⠀ ⠀⣸⠇⠀⣤⠀⠀⠀⠀⠈⠋⠀⠀⠈⢧⡀⠀⠀⠀⠀⠸⣇⠠⢔⣋⠉⠀⠈⠉⠙⠓⢿⡀⠀⠙⡇⠀⠀⢀⣠⣤⡴⠛⡥⠄⠀⠀⠀⠀⣠⠽⡟⢱⠐⢖⣀⠋⢱⡜⠃⠀ ⢠⡏⠀⠀⠁⡀⠀⠀⠀⠀⣖⣦⠀⠀⠈⢧⠀⠀⠀⢀⡼⠋⠀⢀⣬⠀⠀⠀⠀⠘⠛⠂⠁⢀⣠⠇⠀⢰⡏⠀⡜⢁⡔⠋⠉⠓⢤⠀⢸⠋⣼⣍⣇⡆⡀⡄⢆⡆⢡⠀⠀ ⢸⡇⠀⠀⠸⣾⡄⠰⠶⠀⠙⠋⠀⠀⠀⢸⡄⠀⠀⡞⠀⠀⠀⠸⡿⠁⠶⠆⠀⣿⡇⠀⠀⠈⢷⠀⠀⠘⢧⣸⠁⢸⡀⠀⢰⣿⣌⡆⡼⠿⠯⠭⠼⣳⠈⢧⣴⠛⠻⠳⡄ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠓⠶⣼⡇⠀⠀⠀⢰⡿⠋⠓⠒⠒⣌⠁⠀⠀⠀⢸⣧⠞⠛⠻⠻⣄⠀⠉⣀⡉⠙⠏⣗⠛⢻⠀⠀⠀⢧⡄⢼⠈⠁⠀⠀⣹ ⠀⠘⢦⣠⢴⠖⠲⣄⠀⠖⠀⠀⠀⣾⢁⠕⠒⢢⠘⢇⠀⠀⠀⠸⡁⠀⠀⠀⠀⡏⠀⠀⠀⠀⡼⠁⢰⠋⠉⢢⠼⡶⢫⠀⠩⠙⢦⠘⠤⠞⠀⠀⢀⡼⠋⠹⠀⠀⠀⢠⠏ ⠀⢀⡞⠁⠀⠀⠘⠀⢧⠀⠀⠀⠀⢧⠘⠆⡠⠞⠀⠘⢆⠀⠀⠀⠱⣀⢀⣠⠞⠀⠀⠀⠀⡴⠁⠀⠘⠢⠤⢊⣼⢣⠀⠀⠀⠀⠈⡤⠤⠤⠴⠲⡏⠀⠀⠀⠀⣀⡴⠋⠀ ⠀⢸⡁⠀⠀⠀⠀⢀⠏⢰⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⢶⡿⢿⡀⠀⠀⠀⠀⢰⠡⠤⠤⠤⠤⢽⣤⠤⠶⠋⠉⠀⠀⠀ ⠀⠘⢧⣀⣀⣀⠤⠋⠀⡞⠀⠀⠀⠀⠀⡄⠀⠉⣦⣠⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⢀⡀⠀⠀⢀⣴⡿⠛⡟⠀⠀⠣⣀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⡀⢀⠀⠀⣠⠃⠀⠀⡟⡏⠀⠀⠀⠀⠀⢰⢻⠀⠀⠇⠀⠙⡄⠀⠉⣇⣇⠀⡇⠀⠀⢀⡠⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡀⠀⠀⠀⠀⠙⠧⣼⠤⠖⠁⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀⢸⠈⢀⠔⠒⠦⠀⢹⡀⠀⣿⠈⠙⠻⣄⡔⠁⠀⠈⠇⠹⡆⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠒⣧⠀⠀⠀⠀⠀⠈⢧⡸⡀⠀⣠⠃⡼⠀⢠⢿⡄⠀⠀⢸⡇⠀⡔⠊⠉⣳⠇⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠏⠁⢀⠈⠀⠒⢶⠲⣶⠒⠀⠀⠈⠁⢹⡆⠘⣇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠉⢀⡴⠋⢀⡟⠀⠀⠀⠙⠓⠓⠒⠛⢻⡟⠋⠉⠉⠈⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢦⣿⣤⣤⠤⠟⠀⠻⢦⣄⣰⣀⣼⠞⠁⠀⠘⠣⣄⠀⠀⠀⠀⠀⣀⣤⡤⠞⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣠⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠈⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡆⢀⡄⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀