⠀⣤⣠⣀⠘⢿⣿⣀⣸⣷⡀⣿⣷⣾⣦⡀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢰⡇⣼⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⢧⡈⡿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⠀⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠛⣿⣿⣷⣹⣿⣿⣬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡆⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣣⣾⣿⣿⠷⠙⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠚⠇⣼⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠏⣀⢹⣿⣦⠀⠈⠉⠛⢿⣯⣀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⠾⢫⠏⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣸⣾⠛⢿⡉⠻⣦⣤⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⡷⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣿⠇⠀⢸⣷⣴⡞⠉⢣⣀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⢸⡇⢰⠁⠸⢇⣀⣠⣤⣤⠤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠘⣿⣿⣤⠀⣦⠀⠉⠀⠘⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⣼⠀⢼⡟⣿⡝⠻⣿⡋⢙⣻⣿⡿⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡏⠀⠀⢷⠀⢻⣿⠀⢿⣶⣸⣇⣸⣿⣿⣀⣿⣿⣿⡿⠀⠀⠀⠀⡏⠀⢸⣷⣿⠃⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⣶⣿⣛⣻⣿⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣦⣶⡏⠀⠀⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⡇⠀⣿⣿⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⠉⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠋⣰⣠⣾⣿⣿⡿⢛⡿⢛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⡇⠀⢹⣿⡄⠻⢟⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⣰⢿⣿⣿⠏⣿⠃⠒⠀⠨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⡀⠀⢻⣷⠰⠛⠛⠛⢧⣤⠀⠀⠀⠀⠀⠀⣠⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⢸⠏⢸⣿⣿⠀⢁⣼⣯⣆⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠇⠀⠇⠀⠀⢿⣿⡙⠉⠉⠁⠀⠀⠀⠀⢀⣠⡿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⡟⠀⢸⣿⣿⣴⠟⢏⣼⠿⠛⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⠀⠀⠸⠀⠀⠈⢿⣷⣤⣶⣾⣷⣤⣤⣾⡿⢋⣀⠀⠀⠀⠀⠙⠛⠛⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣇⣷⡄⢸⣣⡟⢓⣴⡿⠋⢀⠀⠸⢟⣿⣿⣿⣿⡇⠀⠀⠀⡿⢀⣤⠆⠀⠀⠀⠈⠉⣻⣇⣸⣿⣿⣏⠙⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢦⣄⡀⠐⠀⠀⠀⠀⠀ ⡄⣻⣿⣷⢸⣾⡇⣾⡏⠀⠄⠸⠉⠛⠻⣿⣿⣿⣿⠁⠀⢀⣴⡷⠟⡦⠀⠀⠀⣠⣶⣿⣯⣿⣿⣿⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀ ⣗⣿⣿⣿⣾⡟⢤⣿⣷⣄⣀⣠⣤⣤⣴⣿⣿⣿⣿⣠⡶⠋⠁⡁⠶⠟⢿⣿⣿⣿⡿⠟⠉⠉⠋⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀ ⣧⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣠⠋⣠⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡄⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠉⠉⢉⠉⠙⠛⠿⠛⠛⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⣇⣴⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⢚⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀ ⠀⠈⣁⠀⠀⣤⠀⠀⢉⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣒⠀⠰⠯⣥⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⣠⠎⠁⠀⠀⠀⠀⠀⠀⣀⣁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⣠⡾⠃⠀⠀⠀⢀⠔⢲⣄⡴⠋⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡶⠀⢹⠃⠀⠀⠀⠀⠸⢤⣤⡏⠀⠀⠀⢰⣿⣿⣿⣍⣻⣧⠀⠀⠀⠀⠀⠍⠀⠀⠠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠁⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣾⡿⣟⠛⣫⣿⡟⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⠟⢹⡇⠀⠀⡿⠀⠀⠀⠀⢀⣼⠀⠀⢹⡀⠀⠀⠀⠘⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣀⣤⠞⢁⣠⠟⢃⠀⢰⡇⠀⠀⠀⣠⣿⠇⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣦⣀⣈⣉⣉⣉⣡⡴⠟⠁⠀⠘⠃⢼⣅⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⢀⡴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢶⣶⣤⣤⡶⠶⠟⠉⠁⠀⠀⢀⣾⣱⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣟⠉⣹⡷⢿⣉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡶⠟⠋⠀⠀⠦⠙⢧⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⠉⠛⠲⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⢀⡾⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣿⠀⠀⠐⠶⢤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣸⢏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠞⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⡟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠟⠉⠁⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⡟⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⣶⡿⠛⠋⠁⠀⠀⠀⠀⣾⠟⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣼⡇⠀⠀⠻⠷⣄⣀⣀⣀⣀⣀⣀⣀⣤⣶⣾⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⢹⡇⠀⠀⠀⢰⡆⠉⠙⠓⠒⣛⣿⠭⠍⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡞⣼⠀⠀⠀⣶⠋⠀⢀⣼⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⢣⡇⠀⠀⢰⡏⠀⢠⡟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠰⣿⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣾⠁⠀⠀⣼⠁⢠⡟⠀⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡏⠇⡇⠀⠀⠁⢠⡎⠀⠀⡿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⠟⠿⣭⣝⡳⢾⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠁⢰⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⣸⣿⠀⠀⠀⠈⠙⠛⠻⠦⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⡇⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⠁⠀⠀⠀⠀⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢨⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣽⡟⠀⠀⣀⡲⢶⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀