⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣠⣡⣤ ⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠚⠻⢻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⡶⠾⠟⠛⠛⠛⠋⠉ ⠀⠠⢀⠛⠛⠻⠿⠿⠿⠧⣼⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡿⢠⣠⢇⡄⢻⣿⣿⠀⠀⠀⠀⢀⣀⣀⣤⣠⠤⠸⠟⠛⠛⠘⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠒⠶⢦⣤⣤⣤⣀⣠⣐⣿⣧⢯⣣⡶⢿⢿⣨⣿⡝⡗⠚⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡔⠶⠀⠂⠀⠀⠀⠀⠀⠀⠨⡇⣟⣈⠉⠋⢹⣷⢿⣀⠙⠛⠁⠈⡯⣯⢾⠛⠂⣇⣀⣀⠀⠤⠤⠀⠤⡔⠒⠒⠒⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⠐⢨⠖⠈⡤⡤⠆⡰⣵⣿⣞⠛⡠⠤⠧⠤⡀⢀⣀⠀⢀⡟⠀⠀⠶⡶⢺⠙⣮⡀⢀⢀⠀⢴⣟⣯⠎⠂⠀⡇⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠌⡰⠐⡊⠀⠀⢰⣹⣿⣿⣏⠰⡁⠎⠰⠁⡗⡀⢂⠐⠰⡇⠀⠀⠀⠃⠸⠀⡏⢇⠢⡥⠀⠞⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡈⢴⠀⠠⣥⠀⢰⢯⣿⣿⡏⠐⠄⡑⠂⠁⡇⠠⢁⠈⠀⡇⠀⠀⠀⡀⢘⠀⠣⠤⠆⠃⠀⠈⡠⠶⠤⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡈⠾⣈⣀⡰⣾⡿⣏⣿⡿⡇⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠈⠉⡉⠱⢈⡈⢀⠀⠀⠁⠀⠉⠀⢀⠀⠸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡡⡝⠮⣷⡾⠵⢳⣿⣻⣿⣟⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢐⣵⠳⢸⠁⣟⠀⠀⠀⠀⠀⠀⢌⠀⠄⠎⡁⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⣹⣿⣿⣿⡃⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣂⡔⢸⠀⡗⡄⡀⡀⠀⠀⠀⢥⣐⠀⠀⡇⢰⣢⣬⡞⡄⠇⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⣠⡤⡤⢠ ⣿⣿⣿⣿⣿⣤⣿⣿⣾⣿⣿⣇⡐⣂⠒⡄⡀⡇⢤⣉⠖⣤⣿⣽⠿⠯⠥⠀⠑⣷⡈⠂⠈⡀⠂⠐⠸⠇⠀⢠⣿⣶⣌⠉⢐⢿⡤⣀⣀⣀⣀⣐⣹⣻⣀⣯⠀⡖⢦⡀⢠⣗⡷⣿⢳ ⡛⣻⢯⣈⣼⣿⣿⣿⡿⢻⣿⣻⣴⣧⠫⡔⣡⡟⣦⣛⢾⣼⣿⣶⣤⠆⢀⣐⣄⡟⡈⠀⠀⠀⠀⠠⢻⠌⣐⡿⢹⠟⠛⠀⠈⢉⠟⠀⠀⠀⠀⠈⠉⠉⠉⣿⠀⣟⠦⣇⡸⠿⠷⣿⢯ ⠉⢿⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠀⣁⣐⣤⣿⣧⠿⣿⣾⣿⣶⣭⣍⣋⡤⣊⡗⠱⢂⠤⠂⠁⠰⢁⡇⣤⣾⣮⣀⣁⣀⡀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⢋⡿⠿⢗⣻⣿⢯ ⠀⣼⢻⡗⠚⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⣷⣾⣽⡞⣿⣿⣿⣶⣦⢹⠁⣯⣷⣷⣴⣦⡍⣷⣯⣿⣾⠛⢻⡏⠁⠀⠀⡄⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠉⡆⢡⣶⣶⣾⢣ ⣡⠦⢟⡴⣿⣿⣿⣿⣿⠿⣿⣿⠂⠀⠀⠀⢈⣿⢶⣯⣿⣿⣿⠿⢿⡿⠻⡤⣾⣿⠒⡭⣹⣏⠇⣎⡜⢿⣧⣞⠤⣶⠖⠂⢠⢶⡄⢇⠠⠀⢄⠠⢀⠀⠀⣿⢸⠠⠁⣇⣿⣓⣢⣽⠌ ⣿⣿⣟⡿⠟⢣⣍⣹⣿⣿⣿⣿⣠⠄⠤⠐⠚⠋⠉⠋⠡⢆⠱⠄⡤⣛⡴⣦⣟⢾⣻⣶⣭⣧⣿⢮⡱⢣⢽⣡⡐⣊⣿⣶⣾⣯⢠⢤⣿⣿⣶⣦⣥⣦⣡⣿⣼⡡⢃⣿⣟⡱⣚⣿⢌ ⣭⣿⡿⢿⣿⠟⢿⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠒⠐⠟⠚⠓⠞⠿⠻⠾⠦⠓⠛⢹⠷⠿⠞⠛⠛⠛⠛⠛⠊⠀⠀⢨⡛⣩⠛⠛⠿⢿⡣⢇⣏⣹⣿⣽⣿⢎