⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠹⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢤⣄⠀⠀⠀⢀⣠⡤⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣀⣀⣀⣀⠈⠻⡄⣰⠟⠁⣀⣀⣀⣀⡈⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠹⣻⣄⠀⠀⠀⠀⠀⢸⡷⣿⣿⠛⢻⣿⣿⣿⣷⣿⡿⣾⣿⠟⠻⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢳⣄⠀⠀⠀⢸⠰⣿⣿⣶⣾⡿⣿⣿⣿⢸⡇⣿⣿⣷⣶⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢳⣄⠀⠸⣧⣻⣿⣿⣿⣿⣾⣿⣿⡿⣷⣹⣿⣿⣿⣿⣶⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⢿⣏⢛⠛⠿⠿⠛⣩⡿⠁⠘⢷⡙⠿⠿⠿⠿⣛⡹⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⢻⣯⢿⣿⣿⣿⣿⣽⣗⡄⠀⠀⢈⠛⠛⠛⠛⠉⠀⠀⠙⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠠⢌⣿⣿⣿⣿⣿⣿⣿⣏⡇⠀⠐⠐⠮⠀⠀⠀⠀⠀⠀⠀⠨⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠈⠀⡿⠿⣿⢟⡿⢏⠉⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡀⠨⠉⠀⠚⡇⠘⠒⢨⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣷⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠄⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠗⠂⠀⠀⠈⢠⣶⣤⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡃⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⢸⠻⣯⡿⠃⡀⠀⠁⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡡⠨⠀⠀⠀⡂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠀⠌⠈⠀⡀⢂⡀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠠⠂⠷⡇⣊⣤⠐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⠀⢌⢷⣎⣊⡮⣆⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠅⢿⣿⣿⣿⠳⠁⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠃⡜⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣻⣿⣡⡷⢭⣶⡆⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣿⠿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠓⠚⠒⠒⠒⠒⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠤⣤⡀⠀⠀⣠⠤⠖⠢⠤⣄⡀⠀⠀ ⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢀⡾⣵⡶⠶⢾⣶⣶⣽⣶⡾⣵⡶⠶⣷⣶⣦⣽⡆⠀ ⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⢸⡃⣿⣷⣤⣾⢿⣿⣿⢹⠡⣿⣧⣤⡿⣿⣿⡯⡗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠳⣽⣿⣿⣿⣿⣿⣿⠟⢷⣽⣿⣿⣿⣿⣿⡷⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⢏⡙⠒⢒⠚⠋⠁⡀⠄⠉⢛⣒⣖⠛⠉⠳⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠄⡁⢀⢢⣼⣶⡡⠀⠄⠡⠘⠿⠟⠠⠈⠄⡈⢳ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡈⠐⠠⠐⣀⡁⠚⢹⠭⠶⠶⢶⠄⠂⠌⠐⡈⠄⡐⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠠⠐⢀⠡⣡⣶⣺⣧⣵⠦⡐⢀⠂⠄⠂⡁⠌⢀⠐⠠⢀⠁ ⠀⠀⠀⠀⠀⠀⢸⡇⢀⠂⠌⠄⠟⣿⣿⣟⣿⡦⣧⠌⡀⠴⠂⠡⠀⠌⡐⠀⠌⠐ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠰⣬⣂⣵⠛⠯⠿⠟⠓⠊⠄⠠⢀⠁⢂⠡⠐⠀⠌⢤⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⢟⣋⣆⡐⢀⠂⠉⠐⠈⠐⢀⠈⠄⡐⢠⣁⣈⠾⠟