⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢿⣿⣙⣏⣹⡙⠓⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠚⠏⣹⡿⣜⣾⣽⣿⣿⣷⡆⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠚⠋⣉⣦⣴⣾⣟⣻⣽⣿⣿⡿⣟⣿⡿⣿⣆⣼⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⢋⣥⣶⣾⢻⣽⣿⡿⣻⣽⣿⣿⣿⣿⣿⣛⣿⣻⣿⣿⣭⡄⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⣭⣤⣴⣿⣿⢻⣽⣿⣿⣿⠿⣟⣯⡿⠿⠿⠿⠛⠛⠿⡿⢻⠿⣛⣶⣦⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢾⣉⣡⣴⠶⣾⣻⣽⡿⢿⣹⣿⣿⣿⣶⣿⣿⣿⣟⣿⡇⠏⣭⠉⣭⠉⠃⣿⣿⣿⣿⠏⣡⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠲⣋⣩⣤⣾⡿⡟⢿⣯⣿⣟⣿⣿⠾⣟⣿⡿⢟⣻⣿⣿⠿⣿⣿⣿⡧⠀⠿⠶⠿⠀⣼⣿⣿⡏⠐⣦⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⢛⣩⣴⠶⢾⣿⣿⡿⡿⣵⣿⣿⣛⣿⣿⣿⡶⡟⡿⢯⣿⣾⣟⣯⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠉⠁⡉⣇⠺⣏⣻⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⠖⣋⣁⣵⣶⡿⣻⣭⣶⣿⣿⣫⣵⣶⣿⣿⣿⣷⣿⢿⣻⣷⣾⣿⣿⣿⣻⡟⠿⣼⡟⠋⠀⡁⣿⠟⠃⠠⠐⠠⢈⠠⠁⡀⣿⡄⠈⠙⢋⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠒⣏⣩⣤⣾⣿⢿⡟⣛⣿⣽⣿⣿⣿⡿⢟⣻⣭⣽⣿⣚⣭⣷⡿⢟⣭⣶⣾⣿⣏⣶⣷⣾⣿⣿⡇⢀⠂⠀⣿⡇⠈⡀⠂⢁⠠⠀⠂⠄⣿⡿⠿⠶⠛⣠⣿⡄⠀ ⠀⠀⠀⣀⣀⣤⡖⠋⣉⣵⡶⣾⣿⣿⣿⢿⣟⣶⣿⣿⣻⣭⣟⣿⣿⡿⢟⣫⣝⣫⣾⣿⣿⣷⠟⡯⢿⣻⢛⣯⣿⢿⡻⢟⢻⣿⡇⠠⠀⡁⣿⡃⢀⣥⣬⣤⣵⣬⣤⣭⣿⡇⠀⠀⠀⠈⣩⣷⡀ ⢠⡶⡿⢿⣹⡾⢟⣿⣭⣷⣾⣿⠻⣭⣶⣾⣾⣿⣿⣻⣷⣿⣿⣿⣽⠷⣿⣿⣿⣿⢛⡷⢛⣬⣻⣽⣿⣿⠿⢿⡏⠐⠘⢩⢞⢻⣿⣿⡟⠛⠿⢷⣦⠘⠿⠛⢻⣿⣽⣿⣿⣗⠀⠀⠀⠀⠰⣿⠃ ⢸⡇⢼⡿⣟⣾⣿⣿⣟⣿⣯⡿⢿⡟⣯⣽⣿⡞⣫⣭⣿⡿⡟⣍⣶⣿⣿⢿⣽⣶⣻⣶⣿⣷⣿⠟⢋⣽⡤⠞⠛⠳⢦⣀⡈⠐⠀⢙⣿⣶⡤⣼⣿⠶⠶⠶⣿⡉⣿⣿⣿⠛⣤⣴⣶⣶⣶⡿⠀ ⠘⣿⣠⣽⣿⠿⣿⣿⣿⣟⣧⣿⡷⢿⣻⠟⣽⣿⣿⣯⣵⡿⣹⠿⠿⣽⠟⣿⣷⣿⡿⠿⢛⣩⡷⠞⠋⠉⠀⠀⠀⠀⠀⠉⠙⠓⠶⢾⣿⣿⡄⢀⣼⣀⣄⢠⣿⢐⡹⣿⠉⠉⠉⠉⣻⣏⣿⠀⠀ ⠀⠈⠹⣦⡀⢛⣿⣿⣿⣿⣻⣴⣿⣿⣶⣿⣿⢯⣟⡿⢳⣹⢷⣿⣿⠿⠿⢿⠛⣡⣤⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠉⠉⠋⠉⠉⣿⠛⢶⣏⠀⠀⠀⠀⣽⡧⣿⠀⠀ ⠀⠀⠀⠀⠑⢿⡏⠱⣿⠟⣫⣿⣷⣿⡟⣯⢶⣻⣴⣾⣿⢿⠿⠋⠁⢀⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⠂⠙⠓⠒⢹⣿⣿⣿⣿⠁⠀⠀⠀⣻⣷⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠸⢿⣿⣿⣟⣿⢿⣿⡿⣿⡟⡿⠃⣀⣠⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣬⣬⣼⣿⣃⣿⡟⠁⡀⢰⣤⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⢯⣹⣿⡿⠋⠁⢀⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣥⠘⢿⣭⣽⣭⣿⣿⣷⡿⠀⣸⡇⢨⣷⠿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣉⣉⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠜⣹⣤⡄⠀⠀⣸⣷⢴⣿⠋⢹⣷⢶⣻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢠⠟⢸⣿⠃⠀⢀⠸⣿⡿⠃⢀⣿⣿⣾⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣿⠇⢘⣿⠀⠀⠂⢠⣿⠟⢶⣾⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣼⣧⠀⠀⠋⠀⢈⠀⢸⣿⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠛⣿⡀⠀⢹⢿⣿⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠂⢻⡇⠀⠀⠰⠷⡾⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⣿⡄⠀⠛⢛⠛⢳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⣿⠇⠀⠀⢘⠻⡾⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡏⠀⠀⢨⣒⣻⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⡈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀