⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣚⣭⢭⣭⢭⣭⣭⢫⡥⢦⣐⠢⠐⡄⡉⢑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣵⡞⡿⣜⡷⣺⡝⣶⡭⢷⡻⣭⡻⢿⣶⡠⠑⡌⡑⢎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠰⣎⣾⣛⣧⢟⣽⢺⡵⣻⢼⢧⣻⡭⢷⣳⣻⢭⣷⡹⣧⣐⠡⠊⡄⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⣧⣿⣛⡮⣗⢯⣳⢏⣟⡮⢷⣹⢯⡽⣷⣫⡞⣷⡌⢳⣌⠡⢂⡱⠽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣯⣟⣿⡱⣏⣞⣿⢧⣛⡾⣱⢫⢟⡼⣳⣽⣚⣷⡽⡖⡽⣌⣿⠀⠃⣧⢠⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣷⣻⢧⣻⢵⡞⣾⡭⣗⣯⡳⣭⢎⡵⣿⣟⡼⣹⡷⢯⠱⣉⠼⣇⡓⢹⣇⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣯⣟⡧⣟⣾⢅⡿⣳⡝⣾⡵⢯⣯⣛⡇⢾⣳⢭⣿⢮⣓⠬⣖⢿⣄⠙⣾⣱⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣹⣽⡾⢸⣏⡷⣽⢳⣻⢿⣖⣻⡱⢸⣯⡞⣽⣯⡽⢎⢧⣾⣏⡘⣧⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢾⣿⢷⣯⡧⢼⣾⡵⣫⢏⣯⢿⣞⣯⠇⠈⣷⡝⣯⣟⣿⡿⣯⣽⡷⣸⢣⡻⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣻⣿⣿⣿⣷⣨⣍⠉⠉⠉⠙⠛⢿⠃⠀⠉⣷⣟⣿⣯⢗⡧⣹⣹⣷⢩⣿⠙⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⣿⣿⣿⣿⣷⠈⢗⠘⢷⠀⠀⠀⠀⠀⡿⢿⣟⣾⣯⣞⡿⣟⢾⣸⣱⡧⣿⢣⠽⡂⣽⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢻⣽⣿⣿⣿⣿⠀⡪⠙⢚⠄⠀⠀⠀⢀⠨⠈⣀⣈⢛⡟⡿⣿⣯⣟⡿⣖⣿⣡⢛⡇⠆⢩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣸⣏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⢰⣿⣿⣏⠿⣇⣿⡆⣏⣸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢻⣳⣯⣿⣿⣿⣿⣿⣆⠀⠀⠐⠀⠀⡀⠀⠀⠀⠊⠂⠊⠴⣻⢿⣻⡾⣝⡿⣿⡜⢦⡏⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢗⠘⣧⢿⣽⣿⣻⣿⣿⣿⣿⣦⣄⡃⠀⠀⠠⠒⠒⠀⠈⠉⠚⢿⣿⣿⣽⣮⡗⣿⣟⣷⡸⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⣤⣿⣯⣷⠟⠉⠁⠈⠉⢏⠻⠛⣿⣶⣴⡆⢈⠞⠁⠠⠀⠀⠈⠻⣿⣼⡷⡇⣿⣿⣯⠃⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠉⠑⢇⢀⠈⠀⡠⠂⠀⠀⢹⣾⣿⢀⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢁⣴⣿⠀⠀⠀⠀⡀⠀⡃⡆⠀⠀⠀⠀⠀⠀⠙⠳⢠⡀⠀⢚⣦⡎⢿⣯⠰⣿⣿⣿⣶⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠈⣆⡇⣇⣀⣀⡀⡀⠀⠀⢠⢥⣤⣤⠼⠆⢿⣷⠞⣻⢾⡟⠋⠁⠀⠀⠀⠀⠈⢣⣀⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⣳⣿⣿⠋⡄⠀⠀⠀⠀⣿⠱⠀⠸⠃⠀⠰⠀⠈⠄⢂⠀⠐⠄⣀⠌⡆⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣿⣽⡟⠁⠀⢁⠀⠀⠀⠀⣇⣆⡤⢔⠖⠀⠒⠃⠐⠁⠈⢈⣉⣄⠀⠀⣸⠞⡑⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢷⠟⠀⠀⠀⠸⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⣰⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡾⡟⠁⠀⣜⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣞⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡞⠁⠀⢼⠓⠛⠚⠩⣷⡖⣒⡭⠭⠭⢕⣲⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⠀⢀⣀⣤⣴⣶⠀⠀⠀⠀⢹⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢮⠁⠀⠀⡆⠀⠀⣠⣾⠗⠋⠙⠿⣢⡄⠀⠙⠇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⣿⣶⣿⣿⣿⡿⣿⡀⠀⠀⠀⠘⣿⠰⠁⠀⠀⠀⠀⠠⢠⢎⡟⠀⠀⠀⡁⢀⣞⠟⠁⠀⠀⠀⠀⠉⢿⣦⡀⡃⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠾⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢡⠇⢸⡇⠀⠀⠀⢇⢮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠄⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣏⣟⡿⡋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠏⠀⣼⢃⠀⠀⠀⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣾⣽⡽⣦⣄⠰⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡿⡀⠀⠸⣿⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠻⣿⣷⣯⣿⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⡘⠘⢿⣄⡀⢻⣧⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⠀⠹⣿⣿⣿⡀⠀⠀⢠⠃⠀⠀⢀⣤⢴⠃⠀⠀⠙⠿⣦⣿⣆⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀ ⠀⢾⡟⠀⠀⢹⣿⣟⡇⠀⠀⢸⠀⢠⣠⢮⣴⠇⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀ ⣠⡿⡵⢶⣻⣟⠯⠟⠃⠀⠀⠘⣧⡞⠁⡇⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢓⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀ ⣩⣶⣿⠟⠋⠀⠀⠀⢰⠀⢀⣠⡟⠀⠀⢠⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⣧⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⣿⠟⠁⠀⠀⠀⠀⠀⠸⢊⠣⢼⡏⠀⠀⠈⠛⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⡸⠁⣿⢂⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⢀⣏⣥⠾⣿⡀⠀⠀⡄⠑⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⠀⢣⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀ ⣧⣀⠀⠀⠀⠀⠀⣀⠚⠉⠀⠘⣏⢳⠀⠀⢇⡀⠸⠗⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⢢⢛⠃⠀⢀⠆⠀⠀⢃⠀⠀⠀⠀⠀⠀⠱⡀⠀ ⣿⣿⣿⢿⣶⣶⠿⠁⠀⠀⠀⠀⣿⡀⣇⠀⠀⣇⠁⢀⣈⢁⣷⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡾⢿⣁⡎⠀⠀⣸⣀⠉⣏⢹⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⣭⠭⠩⠛⠉⠀⠀⣀⣀⣀⡤⠤⣼⣷⠘⠄⠀⠀⠉⠉⠄⠣⡘⠛⡲⠶⡦⠄⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠶⣖⣂⡩⠇⠀⠉⠀⢀⡼⠛⠟⠋⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⢠ ⠉⠑⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠳⢦⣖⣤⡀⡀⠠⠀⠁⠊⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠦⠦⠤⠤⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠊⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠑⠴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢇⠀⠀⠀⡰⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠈⠁⠒⠊⢹⠀⠀⠂⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠒⠠⣀⠀⠀⠀⠸⡐⢀⢇⢀⠰⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⢀⠀⠈⠠⣀⠀⠀⠠⡀⠀⠢⠀⠀⠠⡀⠀⠀⠀⡁⠀⠀⠀⠈⠉⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡄⠀⠀⢁⡀⠀⠘⡄⠀⠑⠀⠀⡥⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠙⠂⠒⠉⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀