⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢮⣶⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠴⠶⡦⠉⠀⠒⣿⠁⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡸⠥⠼⠛⠒⠶⣾⣷⢢⣴⣿⡶⣄⣤⣈⠡⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠥⠖⠀⠀⠀⠤⠺⠧⣬⣎⣺⡌⣤⣄⡉⢳⣍⠇⠘⡿⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡥⠒⢁⣤⣤⣶⣶⣶⣾⣶⣿⣿⣿⣿⣟⠉⠉⠉⠠⢄⠀⠢⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⣣⡯⢰⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⠓⢔⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢰⡏⢰⣿⢟⣝⣿⡽⣯⣀⢤⣄⡤⣀⡈⣿⢟⡛⠉⠛⠿⣿⣿⣿⣧⣻⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡂⢸⢁⣾⣿⡿⢻⣿⣽⣿⢡⠊⠁⠉⠻⡽⣷⣩⣴⣂⠀⢀⡁⣿⢹⣿⡇⢻⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣸⣜⢁⣾⣿⣾⡿⠛⢿⣮⣦⡀⠀⠀⠸⠟⠉⠀⢈⡗⢰⡱⣻⢻⣾⣿⢰⢸⠀⠀⠀ ⠀⠀⠀⣠⣤⡀⠀⣹⡯⣼⣿⣿⣿⠀⠀⠀⠈⢳⡇⠀⠀⠀⠀⠀⡰⣫⡶⢟⠷⣿⣿⣿⣣⣼⡿⠀⠀⠀ ⠀⡔⢉⠀⠀⠘⡟⣾⢧⣿⡿⢞⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⢳⢹⣿⣇⢸⡿⠁⠀⠀⠀ ⠀⠀⠞⠒⢤⡀⠁⢻⠼⣿⣷⣸⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣹⣿⣧⣸⣃⠄⣀⡀⠀ ⢠⡾⢫⠔⢦⣹⣰⠟⠾⢏⣿⣿⣾⠉⣙⣿⣿⠧⠖⠂⣰⠒⢤⡦⣤⣤⣾⠛⣿⣿⣿⣿⡏⢞⠀⠀⠙⣦ ⠀⠈⠉⠁⠉⠉⠡⣖⠲⣮⣿⣿⡻⢤⡀⠀⠀⠀⢴⣷⣿⡇⠀⠉⠚⠤⢽⣾⣿⣿⣿⢏⣀⡤⠤⠴⠆⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⢙⡪⢝⣻⣻⣖⠿⣷⣶⠤⣚⣿⣯⣁⣀⡤⣴⣖⣿⣿⠟⠁⠀⢸⣯⠤⠤⢤⣄⡄ ⠀⠀⠀⠀⠀⠀⢸⡤⣾⣀⠀⢩⣿⣿⠝⡿⠁⠀⠶⢼⣷⣽⣟⠉⠉⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠛⠿⢱⢠⡾⠛⣆⠁⢠⣶⡯⣽⡿⡿⡝⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢵⡶⣦⣳⣱⣼⣿⣾⣿⣿⣦⡿⣵⡷⢃⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⢟⢿⣿⣿⡿⠿⠏⣠⣼⣿⡄⠘⠄⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣺⡏⢀⢿⡏⢀⣴⡿⠟⠓⢿⣿⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⠊⡏⡇⢘⢨⣷⣾⠃⠀⡀⢀⣤⡏⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⢙⣿⢅⣼⠞⣿⠃⠀⠀⢠⣿⣿⣏⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⡏⠀⠀⠀⠺⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠸⢸⣷⠀⠀⣤⣶⣿⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢊⠡⠠⢲⣍⣲⡎⡸⡆⠀⠀⠙⠛⠿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢃⠀⣀⣄⣠⣵⢹⣌⡇⢹⡄⠁⠀⢀⣴⢛⢇⡇⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣿⠷⠛⠊⣩⠔⣯⣿⡋⡇⣾⢹⡦⠖⣫⠟⠁⣨⣿⣆⡿⡈⠳⢦⡤⢤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀