⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⢀⣀⠀⢀⣀⣠⣀⣀⣴⢶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣷⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⡠⢖⡪⠟⣚⣽⡿⠟⠋⣻⣿⣿⢿⣿⣿⡷⣾⣘⢻⣷⣶⣖⣊⣩⡥⠶⠚⠉⠁⣴⠋⣾⡇⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣭⠭⠽⠿⠿⠷⢾⣿⣶⣾⣿⠋⠀⢠⣾⣿⠟⡹⢿⡋⢳⣝⢦⡝⠻⣯⡙⠿⣿⣶⣄⠀⠀⠀⡾⠁⠀⣙⡇⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢥⡀⠀⠀⠀⠀⠀⢿⣿⣿⡟⣅⠃⣠⣿⣿⡏⠀⡇⡞⣧⠀⢻⡆⠙⢦⠻⣿⣆⠀⠙⢿⣿⣿⠟⠛⢤⡀⢩⡇⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣯⠀⠀⠀⠹⢦⣀⡀⠄⣰⣿⣿⡿⣰⢚⣾⢿⣿⠏⠀⢠⠀⡁⢻⡇⠀⢿⠀⠈⢳⡘⣿⣧⣠⢋⡘⣮⣿⣷⠀⣽⣾⡇⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⠁⢻⠃⠀⠁⠀⢀⡿⠷⣾⣿⣿⡟⢙⢻⣿⣯⣿⡏⢤⡀⣾⠀⠀⠘⣯⠀⠘⡇⠀⠈⣷⡺⡏⢿⣶⣟⠛⠹⣿⣄⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀ ⠀⢀⠎⠀⠀⠘⣦⠀⢀⣤⡏⠀⢨⣿⣿⡏⠀⠀⡈⣿⣿⠇⠕⡶⡝⡿⢅⣠⠀⣿⠀⠀⢿⠄⠀⠘⣧⣇⠘⣇⢹⣵⠖⠻⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⠎⠀⠀⠀⠀⢹⣇⠈⢉⡏⠀⢸⣿⡟⠀⠀⠀⢸⢷⣿⠄⠀⠀⢀⣇⣀⢸⡀⣿⠀⠀⠸⡄⠀⠀⢿⣻⠃⠸⡆⠀⢰⡄⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀ ⠀⠀⠀⠀⠀⠀⡞⢻⣧⡨⡦⠀⠸⡏⢹⠀⠢⠀⣼⣿⡏⠀⠀⠀⢸⡇⠘⢸⡇⢸⠀⠀⠀⠁⡀⠀⢸⣿⡇⠀⢿⡄⠈⣇⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⢹⣯⣙⢶⣤⣗⣿⣀⠀⠀⣿⣿⠀⠀⠀⠀⣸⡇⢀⣼⡇⢸⠀⠀⠀⠀⡄⠀⢸⣿⡇⠀⢸⣧⡄⢹⡒⠗⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⣷⡏⢻⣿⣯⠙⢛⣿⢸⣿⣿⠀⠠⠀⢀⣿⠁⠀⣿⣇⣾⠀⠀⠀⢀⣿⣄⣼⣿⡇⠀⠸⣿⣧⢺⢽⣦⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⣿⢧⣶⠶⠟⣾⣾⡇⠀⡇⢠⣸⣿⣀⣴⣿⣿⣿⠀⠀⣄⣼⣿⣸⡟⣿⣷⡧⣴⣿⣧⢸⣸⣿⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣾⣿⠀⠀⡟⣿⣃⣰⡧⣴⣿⣿⣿⣿⣽⣿⣿⡄⣼⣿⣿⣟⣿⡗⣿⣟⣿⣿⣿⣻⣾⣿⣿⠘⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠟⠹⡌⢸⣯⣿⠁⣾⢰⣿⣽⣿⣿⡟⣿⣿⣿⣽⢻⣿⣿⣿⡟⠀⣿⣿⣷⠟⢿⣟⢹⣿⣿⣸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⣰⠀⠀⠀⠀⠀⢠⠇⠀⠀⢳⣿⢻⣟⣸⣏⣾⣷⣿⡿⠋⣸⠿⣿⣿⣿⣿⣿⠿⠟⢀⣤⣿⣿⣥⣤⠈⣿⣿⣿⣿⣿⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢣⠃⡀⠀⡀⠀⠀⠈⢰⡆⠀⠈⣿⣼⢽⣿⣿⣿⣿⣯⣴⣾⣗⣺⠉⠉⠁⠀⠀⠀⢘⣿⠿⠛⠛⠛⠛⢶⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⠏⣸⡇⠀⢣⠀⣠⢠⣿⠃⠀⠀⡇⢻⠾⢿⣿⠿⠟⠛⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠇⢳⠀⢈⣷⡷⢻⣿⡄⠀⠀⡇⠘⣇⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⡿⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣭⠿⠦⣀⠀⠉⠹⣧⣼⡟⡇⠀⠀⡇⠀⣿⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢹⡏⣿⠟⢉⡔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠸⣜⣄⣠⢼⣷⣦⢤⣤⣙⡇⡇⠀⠀⡇⠀⣿⣽⠷⣌⠳⣄⠀⠀⠀⢠⠞⠋⠉⠉⠻⡇⠀⠀⠀⣠⣾⣿⣿⣿⣼⠇⡿⢉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆ ⢣⠀⠀⠈⠓⠒⠋⢰⢨⡉⠩⢉⡅⣿⠆⠀⣿⣀⣿⣥⣖⣯⣷⣮⣳⣄⠀⠘⢦⣀⣀⣠⠼⠃⢀⣤⣾⣿⣿⣿⣿⣿⣿⢤⡿⠽⠛⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⢆⠀⠀⠀⠀⠀⣀⣷⣝⠳⣾⢰⢿⠀⠀⢹⣬⣿⡟⠫⠾⢿⣿⣏⡙⠻⠤⣄⣀⣀⣀⣤⡞⠉⠿⣿⣿⣿⣿⣿⣿⣧⣸⣧⡀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠈⢆⠀⠀⣠⠚⠁⠀⣹⣟⣿⢸⣾⡄⠀⠘⣿⣇⠙⣢⣴⡿⠛⠳⣿⣄⠀⠀⠉⠉⠻⣿⣷⣀⠀⢸⣿⠛⠛⢻⣿⣿⣾⣷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠈⢣⡀⠃⠀⢀⡴⠛⠉⠸⣼⣷⢳⡄⠀⢹⣏⣉⣽⣫⠟⠀⠀⠀⠉⠓⠒⠶⣤⣶⣏⠀⠋⣷⣮⣛⣯⣙⣿⣟⣿⣧⠿⣿⣆⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⣠⣾⢎⣤⡤⢶⣿⠿⠭⣟⣳⣶⡏⢻⣿⣄⠀⢀⣀⣤⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠋⠀⠈⠹⣾⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣿⠏⢠⠛⡇⠀⡇⠀⢹⠈⢿⣸⣿⡿⣶⣯⡴⠾⠛⠛⠉⣩⣿⣠⣿⣤⡀⠀⠀⣸⣇⢻⣿⣿⣀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⣿⠀⡇⠀⡇⠀⢸⠀⢸⡿⠛⡇⢿⣷⡇⠀⠀⠀⣼⣫⣿⣿⣷⣌⣉⠀⠀⣿⢹⣿⣿⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡑⠀⢳⠀⢸⡆⠸⡇⠀⢻⠀⢻⣿⠂⢀⣠⠾⡿⣽⣿⣿⣏⠻⡟⢿⣇⠀⣧⣿⠇⠀⠀⠀⠀⢰⡟⢸⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢼⣆⡀⣇⠀⣇⠀⢸⠀⠀⡿⣿⡟⠁⠀⡇⢸⢸⣿⡞⠆⠀⠀⣿⡄⠸⣿⠀⠀⠀⠀⢀⡿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠴⣿⣀⢸⡄⠀⠇⣿⣁⣀⣀⣱⣼⣾⣿⣧⣠⣤⣶⣿⣧⢠⣿⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡲⠤⠿⠿⣿⣿⣿⣿⣟⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀