⠠⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⠀⠄ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⡭⣯⡽⣭⢯⡽⣭⡟⣞⡂⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠚⠋⠓⠛⠓⠋⠛⠙⢹⣽⠆⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢴⡖⣶⢯⣟⣼⠂⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣻⡝⣾⢎⣷⠃⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢳⡤⣤⢮⢷⣫⡽⣞⣻⡼⠃⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣳⠽⣞⢯⣳⡽⣳⡽⢾⡁⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⣧⢯⣟⣭⡟⣶⢻⣵⢻⣝⠆⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⣞⢧⠿⣭⣟⣼⣛⣮⠃⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣼⣷⣆⠀⠀⠀⠸⣏⣯⢟⣳⢮⢷⣹⡞⡅⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⣿⣷⡆⠀⠰⣟⣮⢟⡽⣞⢯⣳⡽⡂⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⣺⣿⣿⣿⣿⣿⡀⠀⠀⣿⡼⣫⡽⣞⢯⣳⡽⡁⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠠⣟⣼⡳⢯⣽⢫⣶⢻⡁⠀ ⠀⠠⣿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⢜⡿⣹⣞⣻⡼⣻⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣾⢿⣿⣿⣿⣿⣿⣿⡾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⡉⠹⣿⡤⡽⢿⣿⣿⣿⣿⣷⠎⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠟⠁⠈⢷⡀⠈⢷⣴⣿⣿⡿⠛⢻⣼⠀⢹⡄⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢽⣆⠘⣧⠈⢻⣷⣄⣾⡿⠃⠈⣿⣻⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⡀⠀⠀⠀⠀⠈⢳⢿⠀⠀⢨⣍⡽⠇⠀⠀⣧⣷⠀⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠁⠀⠀⠀⠸⣿⢐⣶⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⣠⡬⠿⢷⡄⠀⠀⠀⠀⠀⠀⣀⡿⣿⠵⠛⠻⢦⡀⠀⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣤⡶⠛⠁⢀⡴⠶⠿⠯⣗⣒⣲⡶⠛⣽⠃⠘⣧⠐⢀⣤⣿⣀⣿⣿⣿⣿⣿⡿⣿⣷⣶⣤⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⢹⣆⠀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⢶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄ ⠀⠀⠀⠀⣿⣧⠘⢿⣤⣀⡀⠀⠀⠀⢀⡀⠀⠀⣀⣘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠰⢿⣿⣷⣄⠀⠰⢤⣂⣀⣴⣿⣶⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠿⢿⡟⠉⠙⠛⠛⠃⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⠈⠉⠙⢿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢿⣿⣫⣿⢻⣏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣟⣼⡿⠹⣿⣿⣯⣵⠛⠻⣿⣿⣿⣿⣿⣿⣍⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡙⣇⣀⣶⣽⣿⣿⠃⠀⠀⠹⣿⣝⣉⣛⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣷⠟⢻⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣾⣿⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠟⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠹⠛⠛⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠶⡘⢏⣻⣿⣿⢻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⢜⡈⢳⡾⠁⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⠀⣨⢇⠀⠀⠀⣹⡾⠧⡀⣠⣄⡀⠀⠀⠀⠀⠀ ⠀⠱⡉⡰⠉⠙⠓⠋⠧⣵⣴⣷⣿⣿⣿⣿⣶⣶⣦⡄ ⠀⠠⣷⣍⣲⣀⣴⣦⣶⠿⠿⢿⣿⣿⡿⠻⠿⠛⠻⠃ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣟⢤⣿⡟⠀⠹⣭⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣤⠴⠞⣿⣿⡿⣳⣦⣴⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠳⠤⠤⠿⢯⣇⣸⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⢀⡾⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠷⠄⠀⢠⡾⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠿⠛⢉⣡⣤⠴⠲⡟⠁⠀⠈⢷⡀⠀⢰⡆⠀⠀⣠⡶⠀⠀⠀⠲⣄⠀⠀⢀⡄⠀⠀⢀⣾⣷⠒⠒⠒⠒⠲⠦⣤⡼⠛⠛⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⣠⡶⠋⠉⠀⠀⢀⣼⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠑⠲⠤⠯⠤⠴⠟⠁⢿⡖⠒⠦⣤⣤⣤⡼⢧⣀⣀⣠⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠛⠓⢾⣅⠀⠀⣀⡠⠶⠋⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⠿⠃⠘ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⢿⣀⣀⣠⡿⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠤⣾⡧⠤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⣼⡧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⢾⢧⣤⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡿⠋⠉⠀⠀⠀⠀⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠲⠶⠶⢤⣄⣀⣀⣀⣀⣀⣈⣿⣆⡀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠦⠤⢤⣄⣀⣀⣁⣀⣿⣿⣿⣉⠉⢉⠉⠉⠉⠉⠛⠛⠛⠛⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⢶⠦⣤⣀⣀⣀⣀⣀⣀⣀⣠⠴⢾⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡯⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣷⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣷⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡖⣲⣔⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢨⣵⣪⡅⠙⡆⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⠀⠀⠀⠀⠀⠘⡷⡠⢶⠐⡤⡠⡇⠀⠀⠀⠀⣠⣤⣄ ⠙⠫⡩⠒⣲⠀⣀⣤⣾⣋⡏⢹⢝⡎⢄⠀⠰⠔⢧⡜⠛⠛ ⠀⠀⠑⠒⡒⠉⢯⣥⡾⡀⠣⠂⡸⢯⣵⡟⠣⡘⠁⠀⠀⠀ ⠀⠀⠀⣬⠤⠼⢤⢻⡀⠣⣀⠰⠁⢸⢳⠤⠦⠬⠦⡀⠀⠀ ⠀⠀⢸⠀⠀⠀⢸⠾⣿⢺⠽⠶⢶⣻⢾⠀⠀⠀⠀⠈⡆⠀ ⠀⠀⣾⠀⠀⠀⣸⣸⡗⢁⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⡁⠀ ⠀⠀⢸⠤⢄⡴⢁⣼⠁⡀⠀⠀⡘⠘⠋⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠈⢿⠿⣴⣛⣻⣟⠯⡒⢲⠧⢼⣍⣉⣋⣷⠖⠁⠀⠀ ⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠉⠉⠉⣉⡩⠝⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⢱⠁⠀⠀⠀⠀⠐⡈⢂⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣧⣀⡆⠀⠀⠀⠀⠀⠀⢸⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠚⠛⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣠⢴⣶⣿⡶⢤⣶⡶⠶⠶⠶⠶⢤⣤⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⣋⣀⡀⠁⠀⠈⠳⠄⠀⠀⠀⣀⡠⠤⣀⠸⣷⣄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠱⢄⣉⠿⠶⠢⣤⠀⠀⣴⣏⡀⠀⠀⠈⠁⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠬⣉⣻⣟⣓⣲⠶⠀⠈⠛⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣦⣀⣀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡟⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⠀⢠⣤⣿⡖⠀⠀⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠀⣿⣿⠀⢀⣸⣿⡿⠦⠀⠸⣿⣿⡇⠀⣺⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣻⠯⡝⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⡆⠘⡏⠀⣷⣀⣠⣤⣿⣿⡇⣴⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢸⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣾⢿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣼⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣟⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣿⢿⣿⣿⣿⣿⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⠚⢷⡈⠻⣖⣹⣿⣿⣿⣿⠙⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⢹⣄⢹⡙⢿⣦⣠⡿⠇⢸⣶⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠈⣻⡇⠀⠨⠽⠃⠀⠸⣿⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⣿⣾⣫⢽⣄⠀⢀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⣤⠖⠋⢡⠤⠷⢶⣦⣤⡤⢲⡏⠹⣄⠀⣨⣇⣸⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀ ⠀⠀⠀⢻⡄⢤⡏⠀⠀⠀⠀⠀⠉⠉⠑⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⣸⣷⣌⠛⢒⣂⠀⢀⣤⣆⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠿⣿⠇ ⠀⠀⠀⠈⢻⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠿⣿⠿⠋⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣟⡿⢻⣿⣿⣷⠟⢿⣿⣿⣿⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⢻⣤⣶⣿⣿⠃⠀⠈⢿⣍⣭⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡿⠯⠼⠿⣿⠇⠀⠀⠀⠈⢿⡿⠯⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣤⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠛⠙⠂⠙⠛⠛⣿⣿⣿⣿⡟⣽⢻⡿⣩⠻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⡿⣟⠠⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡆⢡⣿⡄⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠲⠆⣠⡀⠀⠀⢸⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⣤⣤⣙⣡⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⠾⠟⠛⠛⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⡠⠄⠐⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠁⠉⠙⠛⠛⠻⠟⠉⠉⠀⠀⠀⢀⣀⣀⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⢚⣻⣆⣴⠞⠋⠉⠀⠀⠀⠀⠈⠙⠓⢶⢦⡤⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢶⣶⣿⡿⢿⣿⣿⣿⣦⣭⣀⣀⡴⠛⣠⠟⠉⠉⣧⠴⢶⡤⢤⣤⠴⠾⠛⠛⣷⣦⣄⣀⣀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣛⠉⠀⣿⣿⣿⣧⣄⣹⣿⣿⡿⠟⠉⢁⡴⠟⠁⣀⣴⠞⠁⣴⠏⠁⣼⠹⣷⠲⢦⣼⣿⣽⣿⣿⣿⡉⠳⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⠛⠦⣿⣿⣿⡿⢿⣿⡿⠉⠀⠀⠚⠉⢀⡴⠞⠋⠀⢀⣼⠃⢀⣼⡇⠀⠘⣦⡀⢻⣿⠁⠀⣩⣿⣇⣴⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠉⠙⠻⠶⣿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠟⠁⢀⡼⠃⢹⠀⠀⠈⠃⠀⠻⠀⠀⣿⡟⠉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⡄⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠈⠓⠾⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⡴⠶⠶⣦⣤⣀⣀⣸⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢹⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠈⠻⢦⣤⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣨⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠒⠒⠛⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣷⣌⣉⠉⠓⠒⠶⠶⠤⠤⡀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣸⣯⣾⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⡇⢸⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀ ⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠦

⠀⠀⠀⠀⠀⢠⠔⠊⠈⠉⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢔⡊⠛⠙⠍⠉⠉⣉⣉⡳⣄⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠁⠈⠂⠭⠥⠆⠀⣇⠤⡤⢀⡈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⠀⠀⠀⠐⠂⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠒⠀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣿⣿⡿⣿⡏⢉⣹⡄⠘⣿⣿⣿⣿⣿⣽⡿ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⣿⣿⣿⣿⠱⢸⣇⢠⠿⡗⠀⢻⣿⢀⣿⣿⣯⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⣿⡟⠀⣿⣿⣾⡶⣿⣿⣿⣿⠈⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣈⣠⣈⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣒⠛⠘⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⡔⠉⠀⠀⠀⠀⠉⠁⠂⢄⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠾⣟⠫⠤⠎⠐⢀⣠⣀⠠⠀⠠⡀⢠⠀⡱⡄⠀⠠⢤⠺⢆ ⠀⠀⠀⠀⣠⣾⣿⠓⢎⠀⠄⠊⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠉⠀⢡⠈⠉⠉⠑⠊ ⠀⠀⢀⣾⡿⠻⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⣇⠤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⡼⠉⠀⠀⠛⠀⠀⠀⠀⠀⢧⢀⣀⣀⠀⠀⣅⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⠒⠒⠒⠛⠓⠩⠭⠭⠭⡽⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠤⠄⠀⠀⠀⠠⡶⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠁⠀⠀⠀⠀⠀⠰⡘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⣿⣻⡛⠛⣻⣿⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠈⠳⠿⣎⠈⣹⡟⠝⠉⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢠⣄⢘⡿⢫⣿⣄⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠘⠿⠿⠋⠿⠿⠏⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣧⠀⠀⣴⣶⡦⢰⠤⡄⣀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀ ⠸⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣁⠷⣬⣉⣓⣇⣰⣈⣧⣭⢾⡉⡧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣿⣿⣿⣿⣿⡄ ⠀⠹⠿⠿⡏⠉⠙⣶⡤⠤⣤⡄⠀⠀⠀⠀⠀⢀⣨⣽⣾⠟⢉⣿⠙⢋⣿⠙⢷⣤⣍⡀⠀⠀⠀⠀⢤⡴⠲⢿⡥⣀⢰⡟⠿⣿⣿⡿⠃ ⠀⠀⠀⠀⢻⣶⠟⠁⢀⡴⠻⡄⠀⣀⣤⣶⢺⣿⣿⣿⣁⡤⢾⠃⠀⢸⡟⠒⢾⣿⡉⠛⢦⣀⠀⢀⡼⠛⢦⡀⠙⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⢤⣰⣋⣀⣀⡿⠚⢹⠿⠟⠋⠉⣉⣿⡁⠀⠸⡄⣠⡞⠀⠀⣿⡙⠻⠶⣶⣿⣷⣾⡀⠀⣈⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⣾⠿⣿⣉⣙⣿⠿⣇⠀⠀⠻⠏⠀⠀⣸⠿⢿⣿⣶⡦⣿⠃⠈⠙⢯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡿⠀⢈⡟⣿⠀⠀⢸⡄⠀⠀⠀⠀⣰⠇⠀⠀⣿⢻⡇⠙⢧⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⡴⠶⣿⣤⣤⣼⡇⣿⠀⠀⠈⢳⡀⠀⢀⡴⠃⠀⠀⠀⣇⠈⣧⣤⣤⣬⢽⠶⠦⠤⠾⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡏⠉⠀⠀⠀⠀⠀⠀⣿⠃⣿⣷⣆⣀⣀⣹⣾⡉⠀⠀⠀⢀⣼⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣏⣹⡿⢻⣏⣉⣿⣯⣛⣻⣿⠛⣿⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⣿⠛⣠⡿⠏⠀⠁⠀⠉⠉⣿⢻⣿⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢰⣾⠷⣴⣿⡟⠀⠀⢴⠀⠀⠀⠀⠀⠀⣿⢸⣿⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⠀⠀⠀⢠⡾⠁⠀⣸⣿⠇⠀⠀⡀⠀⠀⠀⠀⠀⢸⡏⠀⢻⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣍⠉⠛⠳⣶⠟⠀⢀⣾⣿⣿⠀⠀⣠⡁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⢿⡏⠀⣠⣿⣉⣛⣛⣛⣿⣿⢓⣶⣤⣤⣤⡴⠷⢶⢶⣾⡟⠛⠿⠿⠿⠿⣿⣷⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣍⠻⢾⣿⣞⣋⣈⣈⣙⣿⣯⣩⡽⠟⣯⡉⠉⠛⣿⠻⠷⠶⣿⣷⣤⣤⣤⣤⣤⣼⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠙⠒⠺⠿⢶⣶⣦⣤⣤⣤⡿⠿⠿⠛⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢓⡶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⡏⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣸⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣯⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠳⠿⣿⡿⡿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣇⠀⠀⠀⢹⡗⣷⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣴⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠐⣈⣀⣉⡉⢭⣄⡤⠒⠒⠒⢤⡄⠀⠈⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⡒⢻⣿⣙⣿⠗⡂⠕⡡⠜⡝⡹⢮⢭⣿⢶⡖⢴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣉⠛⢿⠁⠀⠀⠉⠀⠊⡰⠳⠈⠂⠃⠰⢛⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣀⣈⠛⢣⣀⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡼⢇⠀⠀⠀⠀⠀ ⠀⠰⡀⠀⠀⠀⠈⠘⡄⠀⣩⣿⣿⣿⣿⡏⠉⠙⢲⣤⣴⣶⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⢠⣿⣖⠀⠤⠄⣀⣹⣶⣿⣿⣿⣿⡟⠈⠉⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠘⠗⢻⣿⣿⣿⣿⣿⡇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡥⠖⢺⣿⡷⣶⣶⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⡐⠛⠛⠓⠛⠛⣻⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠒⠛⠓⠒⠒⠲⠶⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠟⠃⢀⣴⠋⠀⡄⠀⠀⡀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⣀⣀⠀⢀⣼⣶⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡿⠛⣩⠤⠒⠊⠉⢸⡇⠀⠀⠙⠂⠘⠓⠒⠒⠋⠀⠀⠈⠓⠤⢄⣧⣀⡤⠛⢿⠤⢤⣀⣉⣹⣏⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡟⠒⢾⣁⣀⣀⠤⠚⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠙⠟⠘ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠧⠤⠴⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣒⠒⢻⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⡿⠋⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠨⠭⣽⣉⡛⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠟⠉⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠛⠒⠒⠤⠤⠤⢤⣤⣿⢤⣤⣤⣤⣤⣤⣄⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⠛⠒⠒⠒⠾⠛⠷⠦⠴⠤⠤⠤⠤⠤⢤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢻⠖⠦⠤⠤⠤⠤⠤⠤⠚⢏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣹⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⠾⢷⣶⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠉⠻⣅⣸⡿⠋⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢰⣶⣼⢯⣶⡆⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⡄⠀⣠⣤⢀⡄⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀ ⠸⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡹⣮⣝⣻⣐⣦⣤⠕⣏⠇⠀⠀⠀⠀⠀⢀⡠⠴⣿⣿⣿⣿⡄ ⠀⠉⠙⢧⣀⡽⠓⢐⡖⠀⠀⠀⣀⣤⣶⣿⠋⣸⠇⢁⣾⣈⣷⡶⣄⡀⠀⠀⣲⣍⠛⢧⣤⡟⠛⠛⠛⠁ ⠀⠀⠀⠈⢯⣀⡔⠋⢸⡶⢲⡿⠿⠛⢛⣟⠉⢹⠀⣸⠃⢨⡿⢷⣤⣽⣦⣴⠁⠈⣦⠔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣩⠋⠀⢸⠶⣶⣼⠿⠿⡀⠈⠿⠁⠀⡼⠻⣿⣶⢾⡏⠈⠛⢏⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⢀⣠⠞⠀⡼⣿⠀⠀⢇⠀⠀⠀⡼⠁⠀⣾⢹⡄⠓⠦⣄⡀⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠛⠋⠉⠉⠉⠙⡇⣿⣦⡀⠈⣢⡴⠊⠀⠀⢀⣿⠈⡟⠋⠉⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⣷⣿⣏⡿⢛⣏⣹⣿⣛⣿⡟⣻⣶⡇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠇⢸⣿⣡⠞⠁⠀⠀⠀⢸⡏⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢠⣿⣄⣾⡿⠁⢀⠀⠀⠀⠀⢸⡇⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣀⡀⠀⢀⡾⠁⢈⣿⠇⠀⠀⠀⠀⠀⠀⣸⠁⠻⡟⠃⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀ ⠀⠀⠀⠀⠐⣷⣭⣉⣹⠏⠀⣰⣿⣿⣀⣠⣆⡀⠀⠀⢀⣏⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⢿⣿⣤⡞⠛⠲⣶⡖⢻⣿⣿⠿⠿⣿⣯⣏⣿⣇⣈⣉⣉⣉⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡈⠉⠙⠛⠛⠛⠉⠁⠀⠉⠓⠲⠿⠤⠦⠬⠭⠭⠿⠿⢟⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡽⠉⠉⠉⠉⠉⠉⠁⠀⠈⣆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣱⣤⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠙⠛⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠶⠋⠉⣁⡀⠈⠙⠳⣄⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⣉⡉⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⢀⡖⠉⠉⠉⢳⡀⠀⠘⣇⠀⠀⠀⡼⠁⠀⠀⡴⠋⠉⠉⠳⡀⠹⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡇⠀⠸⡄⠈⠃⠀⢠⠇⠀⠀⡿⠀⠀⠠⡇⠀⠀⠐⡇⠀⠀⠉⢀⡇⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢻⡄⠀⠙⠲⠤⠔⠋⠀⠀⣰⠃⠀⠀⠀⢷⡀⠀⠀⠈⠲⠤⠴⠋⠀⣸⠇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⠲⢤⣄⣀⣀⣤⡤⠞⠁⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⣤⠞⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣤⠶⠚⠛⣿⡿⠓⣶⠒⠒⠒⠒⠒⠒⠲⠶⠶⠿⠿⠿⢧⣤⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠁⠀⠀⢸⡁⠀⠀⢈⡷⠒⠒⠒⠢⣄⣀⣀⡤⠾⠷⠀⠀⠀⠈⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣧⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣇⠀⠀⠀⠀⠈⢛⣓⣒⣒⣒⣲⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⠋⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠜⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⢉⣿⣉⣉⣉⣭⣉⡉⠉⢉⣉⠉⣿⣿⣏⢉⣉⣛⠛⠛⣛⣛⣒⣒⣾⣿⡿⠳⢦⡀⠀⠀⠀⠀ ⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⠉⢙⡏⠉⡿⣿⣿⡟⢻⠁⣿⡛⠉⠉⠉⠉⠉⠉⠉⢷⠀⠀⠙⢶⡀⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⡤⣤⠤⠖⠛⡇⠀⠷⠽⠿⠷⢻⠀⢹⠳⠦⢤⣤⣤⣤⣤⣤⡾⡆⠀⠀⠀⠹⣆⠀ ⠀⡼⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣶⠒⠒⠒⢲⣶⣿⣾⠓⠒⠒⠒⠚⠓⣻⣶⣒⣒⣛⣶⣤⣤⣤⣤⣷⣤⣤⣤⣤⣿⣦ ⠛⡇⠠⠀⠀⠀⠀⠀⠈⠻⢶⣶⣶⠶⡞⢩⡷⠶⠶⠛⠛⣹⢿⣋⡼⠋⠉⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣭⡁⢈⡿⣆⠀⣀⣈ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠁⠘⠓⠒⣚⣲⣤⣇⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡅⠻⠏⠀⠸⠶⠁⢹ ⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠸⣯⣉⣿⠉⡏⠁⠀⣳⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠖⠚⠉⠀⢠⠇⠘⢷⡀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠈⠓⣦⣄⡀⠀⠀⠀⠐⠁⠀⠀⢀⡤⠴⠛⠙⣷⣷⣶⣞⡽⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠊⠀⠀⠈⢳⡶⠀⠐⠀⠐⠃ ⠀⠀⢰⠋⡟⠉⠙⢯⡉⠛⠒⠒⠚⠷⣄⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⠼ ⠛⠛⠋⢀⡇⠀⠀⠀⠙⠲⠒⠒⠒⠶⠬⣝⣉⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠈⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡠⢄⣀⠀⠀⠀⠀⠀⢀⣀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠋⡄⠒⠠⠈⠳⠀⠀⡠⠊⢁⠔⠒⢌⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⢇⠀⢄⣁⡠⠃⢠⠃⠀⢇⠀⠘⣀⢈⠜⢠⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠈⠲⠤⣤⣤⡴⠃⠀⠀⠈⠢⢤⣀⣠⠤⠋⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡎⠉⢩⠋⠉⡯⠭⠭⡉⠉⡩⡭⠉⠑⡆⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡇⠀⠀⠱⢄⣀⣈⣀⣀⣀⣐⣀⣀⣀⣀⣀⡠⠇⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⣠⠞⠉⠛⠒⠒⠂⢈⡿⠉⠭⢍⣉⣉⣉⣿⣏⡙⣟⣒⣒⣒⣾⡗⠢⡀⠀⠀ ⠀⡐⠁⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⡀⠤⡇⡯⠿⠧⡇⡧⢄⣀⣀⣀⣴⠀⠈⢢⠀ ⢰⠁⠀⠀⠀⢄⣀⣀⣀⢤⣀⣸⠉⣭⢿⠿⠍⠉⠍⠩⠷⠥⠭⠶⠶⠶⠶⣶⠶⠷ ⠘⡄⠀⠀⠀⠀⠈⢁⠊⠘⣒⣲⣼⡨⢇⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡏⠞⠉⠖⢹ ⠀⠈⠢⣄⡀⠀⠀⠇⠀⢀⠳⠾⣼⣤⣼⠄⠀⠒⠒⠒⠚⠥⠤⠄⠀⠹⡤⠀⠄⠜ ⠀⠘⠙⠉⠻⣍⣉⣉⣢⠬⠂⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠤⠐ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠈⢆⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠬⣑⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠨⠢⡙⠮⡙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢆⢫⣆⠈⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣷⡌⠀⠀⠀⢠⣷⣦⣡⠀⠀⡘⡄⠙⣦⡘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⠊⠀⠀⠀⠀⠚⠿⠋⠀⠀⠈⢻⣄⠸⣿⣾⡆⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⢡⠀⢹⠋⠱⠤⣀ ⠀⠀⢀⡔⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠈ ⠀⢠⠊⠀⡠⠔⠂⠉⢃⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣼⡿⠒⠒⢢ ⠔⠁⡞⠋⠀⠀⠀⠀⠘⡆⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⡼ ⠊⠰⠁⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⢠⡞⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⠀⣷⣀⠀⢸⣿⣷⣶⣄⠀⠀⠀⠘⠋⡇⠀⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⡿⠋⠉⠉⠉⠉⠉⠑⡄⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠰⢹⠀⠀⠀⠀ ⠀⠀⢀⣀⡤⠖⠲⣎⣭⠄⠀⠀⠱⡀⠀⢀⣀⠤⠴⣶⣊⠁⢀⠀⠀⢈⣇⠀⠀⠀ ⡶⠭⢥⣀⠤⠤⠠⠨⠗⠚⠒⠚⠺⠕⢉⣁⣀⣔⣂⣀⣈⡿⠦⠤⠼⠾⠛⠀⠀⠀ ⠀⢀⣀⢀⢀⣀⡀⠀⡀⢀⢀⢀⡀⡀⢀⢀⢰⢤⡀⠀⡀⡠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠃⠛⠑⠃⠁⠑⠒⠋⠚⠑⠊⠑⠃⠋⠹⠘⠓⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⠶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡏⠁⠀⠀⠀⠀⣿⣿⣿⢣⣇⠛⣶⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠈⣽⡿⢸⣿⠀⣿⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⢂⣄⠀⢀⣻⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢿⣷⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠿⠾⠛⠛⠉⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠙⠛⠿⠿⠿⠟⠛⠛⠉⠉⢀⣀⣀⣁⡀⠀⠀⠀⠀⠉⠛⠛⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢁⣀⣀⣀⣀⣀⣠⠤⢖⡻⣄⣶⡛⠉⠀⠀⠀⠉⠛⣶⠦⠄⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⢺⣿⣿⠛⢿⣿⣷⣶⠦⠔⣫⠔⠉⣀⠵⢋⡷⢲⣶⣋⣉⢩⡿⣶⣦⣤⣤⣀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⢤⣸⣿⣿⣿⣾⡿⠋⠁⠤⠚⣁⡤⠚⠁⣠⠏⢀⡞⠈⢷⡉⢿⡿⠋⢛⣿⢀⣽⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠉⠙⠶⢿⠁⠀⠀⠀⠀⠁⠀⠀⠘⠁⢀⡞⠸⠀⠀⠛⠀⠟⠀⢸⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠿⣐⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣁⣀⣀⣀⠀⠉⣷⣤⣀⣀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣇⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⠒⠛⠉⠳⢤⣄⣀⣀⣠⣤⣶⣿⣿⣿⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠇⣀⣀⣀⡠⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⡛⠲⠤⠤⢄⣀⣀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣶⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⠁⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠿⠿⠀⠿⠗⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠷⠦