⣿⢀⣀⠀⠈⣓⣮⣖⡛⠛⣶⡀⠀⠀⣩⡴⣾⡉⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡏⠉⠛⠛⠛⠛⠉⠹⠷⠿⣶⣿⣷⠒⠀⠀⢸ ⣿⢳⣽⣷⣿⣿⢺⡎⣷⣧⣿⣇⣠⣾⣭⢷⣄⣳⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸ ⣿⢿⢿⣾⣿⣿⡆⣟⣿⣿⡿⠛⠁⠈⢟⣎⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⣿⠁⠀⠉⠉⠉⠉⠓⣶⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠇⠀⠀⠀⢸ ⣿⠸⠈⣿⣽⣭⣷⣿⡟⢝⢿⣧⡀⣤⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⣻⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⢀⣦⣼⣷⣿⠟⠉⠙⢾⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⡇⠀⠀⠀⠀⠀⢀⣀⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⢈⡾⢿⣿⡟⠀⣀⡀⠀⠁⠙⢿⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⡄⠀⢀⣳⣧⣤⣬⣀⣐⢂⡀⠀⣿⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠋⠀⠀⡸⢀⣤⣽⣿⣷⣄⣀⣠⣿⣿⣿⣿⣛⣻⡀⠀⢀⣼⣿⣿⣿⣿⢻⢹⡟⠻⢷⣤⣿⣿⣿⣿⣤⣤⠀⠘⣯⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⢀⣵⡟⠷⣤⣽⣿⣿⣿⣿⣿⠿⡿⢃⣾⣿⠿⠂⣼⣿⣿⣿⣿⣿⣏⣴⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⢀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⢻⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⡿⠋⠀⠈⠹⢿⣿⣿⣿⣿⡦⣮⣿⣿⣿⣿⡛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣠⡀⠻⡿⠿⣄⣈⠓⢮⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣟⣷⣨⣛⣦⣀⡀⠘⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⠛⠉⣡⠷⢄⣈⢻⠲⢬⣿⣿⣿⣿⣿⣿⣎⠉⠻⣿⣿⣷⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠁⠀⠀⠀⠀⠀⠰⣶⠯⠽⣿⠿⠿⣿⣿⣿⡍⣿⡛⣶⣤⣄⣀⡈⠙⠋⠻⣿⣏⢀⡾⣧⠾⠷⢤⣄⡈⠙⣷⢦⡈⠙⢿⣿⣿⣿⣿⣧⣤⣬⣽⣿⣿⣿⣿⣿⣾⣗⣤⡀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣷⣿⣿⡿⣥⣤⣤⠤⡈⠳⠿⣤⣜⣶⡿⠷⢮⣽⣓⡿⣷⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⢄⢠⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣷⣿⡷⡃⣽⠀⠀⠀⠉⠻⠧⠬⠬⠭⠭⣽⣿⣿⣿⣿⣧⣉⠻⠿⠿⠿⢿⡿⠿⠿⠟⠻⣿⣿⣿⣶⣝⣿⣿⢾ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠟⢿⣿⣿⢯⢿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠉⠛⠻⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⢺⣽⠃⣼⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣷⣤⣴⠀⠀⣸⠛⣀⡟⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣸⣏⡠⢿⠁⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣰⢻ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⡀⡀⣀⣄⠀⢐⠀⡀⡀⢀⠀⠀⣀⣀⣀⠀⠀⣀⡀⢀⣀⡀⣀⣀⢀⡀⢀⡞⢉⣸