⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠿⢟⣿⣟⢻⣿⣭⣭⣭⣭⣽⣜⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠁⠀⠀⠀⠀⠒⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣼⡄⠄⢠⠘⡠⠐⠀⣠⠴⠒⠲⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣭⣽⠞⠢⠑⡠⠉⡛⢁⣤⠿⠆⢂⣀⠀⠀⠨⣝⠲⠦⠤⠤⠤⣄⣰⠤⣄⡀⠈⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢡⢡⣃⣤⣿⣿⠋⣀⣀⣀⡀⣈⠙⣶⣀⠈⠓⣶⣦⣶⠒⠛⠒⣶⣤⣉⢲⣌⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⢩⣼⣬⣿⢟⣫⣶⡿⢛⣻⣿⣿⣿⣿⣷⣿⡄⠀⡄⠀⠀⠀⠀⢀⠀⠀⠙⠃⠈⢸⣧⠀ ⠀⠀⠀⠀⠀⢰⡿⣿⡰⣿⣿⡿⢁⣦⠟⡙⢦⣾⣿⠿⠓⣎⣹⣟⣿⣿⣿⣿⣿⣇⠀⡁⠀⢰⣦⣦⣸⣆⡀⠀⠀⠀⠸⢸⡄ ⠀⠀⠀⠀⠀⣾⡇⣿⣿⣿⡿⢑⢂⣧⣈⣽⣿⣿⣮⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⢳⣿⣿⣿⣿⣿⣿⣷⠆⢤⠀⢸⡇ ⠀⠀⠀⠀⣴⡿⢷⣥⣿⢿⣅⡎⣈⠻⠮⣭⣙⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣯⣙⠂⠈⠀⢸⠃ ⠀⠀⠀⣾⣿⣿⣎⣿⢋⣿⣍⢣⠔⡂⠄⠀⠉⠹⠿⢾⣶⣶⣿⣿⠿⠛⢻⠏⠁⠀⠀⠀⢻⣿⣿⣿⣿⡿⣹⣿⣶⢀⠀⢸⠀ ⠀⠀⢰⣿⠇⡛⣿⡿⠀⣿⣟⠣⢎⡁⠆⠠⢁⣤⠶⠚⠋⠉⠁⠀⠀⣈⣩⡆⠀⠀⠀⣆⠀⢻⣿⣿⣿⣿⣟⣩⣿⣾⠀⡹⠀ ⠀⠀⢰⡟⢣⣾⣿⢧⣤⣿⢫⡱⢂⠾⢀⠣⠉⠀⢀⠀⠀⠀⣠⣴⣾⠟⡭⠐⣧⣄⠀⣸⠧⡄⠃⠙⠿⣷⡅⠁⣸⣿⢂⡇⠀ ⠀⠀⠀⣿⠹⣿⡿⣿⢏⡿⢢⣍⠣⡘⠠⠐⡀⠀⣀⣀⢺⣿⣿⣿⣿⣷⣿⣶⣻⣿⣶⡯⠀⠸⣦⡀⠀⠈⢻⣖⠉⢹⢺⠀⠀ ⠀⠀⠀⢿⣧⣈⣙⣻⣿⡌⢧⡘⢤⠑⢢⠑⡀⢃⢠⣸⣿⠟⠋⠙⣛⣿⣿⣿⣿⣿⣿⣥⣶⣿⣼⣷⣄⡀⠀⠘⡂⢁⡟⠀⠀ ⠀⠀⠀⠈⣧⠿⠉⣽⠿⣜⢦⡝⢢⡉⢆⠆⣡⠢⣵⡿⠁⢹⣤⣴⠾⢣⣿⣿⣿⣿⣿⠿⢿⢿⠿⣿⣿⠋⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠀⠹⠦⣽⣿⢃⡯⣞⡹⢦⡑⢎⠲⡄⣹⣿⣵⣯⣿⣿⣷⣟⣻⣆⡹⣿⣿⠿⣴⠃⢀⢸⡽⣿⣏⣉⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣏⣎⣗⡻⡟⣦⡙⣾⢣⠕⠸⣿⣿⣿⣿⣿⡟⣿⡻⠿⣿⣿⣿⣶⣍⢰⣾⣮⡆⢸⣿⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣾⣏⢷⡹⣹⠳⣿⣭⢚⡥⣿⡏⢉⡙⠳⣾⣦⣟⣶⣄⣀⣨⠭⠟⣿⢶⣿⡇⣸⣿⠟⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣯⢹⣿⢇⡞⢧⢣⢏⣽⣯⣟⣿⡿⡁⠦⡘⠡⠞⣯⣟⣿⣿⡉⡇⠀⠀⠀⢘⣿⣿⣿⣿⠠⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠋⣧⢚⣿⣯⡜⣎⡇⢮⢰⣿⡞⣿⡱⢌⡐⠀⠁⠊⠘⠻⢿⡿⠿⠅⠆⠀⠀⠄⢹⣿⡷⢃⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠃⠀⠘⣷⢻⡿⣾⡼⣷⣎⢆⣹⡯⠽⣷⣮⡐⠄⡀⠀⢀⠠⢀⠐⠀⡄⠀⠀⢰⡀⣼⠟⡥⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠈⠻⣷⣻⣿⣽⣿⣷⣦⠹⣑⠎⡽⢿⣿⣴⣭⡦⠵⣬⣶⣏⣰⣿⢸⠟⠐⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣬⠳⣌⢣⠙⡛⠟⠿⣶⣶⣿⣿⣣⣾⠋⢄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣎⣆⠓⡈⠰⢀⠀⢀⣠⣿⠟⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣥⠀⠁⡀⢨⣿⡟⠁⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣽⠃⢦⡇⢻⡇⠁⠀⢠⣿⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣍⠒⠨⡗⢨⠃⠀⠆⣾⣏⠛⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⠆⠀⣻⣧⠀⣰⣿⣿⣿⡀⠈⠀⠳⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⡈⢿⣂⢼⣿⡇⢠⣿⣿⣿⣿⠶⠀⠀⠀⠘⢄⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠙⣧⣿⠄⣈⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣿⢰⣿⣿⡇⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⢀⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠈⠲⣄⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀