⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠷⠔⠾⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠄⢿⡏⡽⣶⣄⣠⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⢀⢯⢌⠦⠗⠒⠒⠓⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠋⠀⠈⠸⣿⢧⢠⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢻⢆⠘⠄⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⢀⣻⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣯⣦⣤⣀⡀⡀⠀⢀⢳⡀⠀⠀⠀ ⠀⠀⡇⠀⠀⢈⠞⣽⡝⢝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣽⣿⡷⠀⠘⢜⡇⠀⠀⠀ ⠀⠀⣇⠀⢠⠮⠃⠻⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠉⠀⠠⡠⠸⡅⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⡅⠈⡌⠊⠄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠂⠁⠘⠄⠉⢲⣲⠄ ⣤⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠁⠀⡈⡀⢰⠁⠀⠎⠀⠇⣼⡼⠀⢀⠀⠀⠀⠀⠀⠀⠈⠂⠰⣍⡆⢄⡞⠉⠀⠀ ⠀⠉⠉⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣸⠿⢆⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⣸⣻⠁⠐⡀⢄⠀⠀⠀⠀⠀⠀⢰⢆⠀⠘⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⣵⠂⠀⠀⠀⠀⠀⠀⠀⢣⢠⡯⠀⠈⢣⡀⠀⠾⢀⠀⠜⠀⠀⡴⠉⠸⠈⢰⡰⠁⠀⠀⠀⠀⠀⠀⢸⡌⡇⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⢂⠄⠀⠀⠀⠐⠀⢃⣟⣔⡀⠀⠀⠑⠀⠀⠀⠀⠀⣠⡞⠁⠀⠸⠀⠎⣰⣱⠀⠀⠀⠀⠀⠀⢸⡀⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⣠⠴⣏⠆⠀⠀⠀⡟⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢨⢀⡐⢹⠈⠄⠐⠀⠀⡀⣆⢸⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⠁⠀⠈⢦⠀⠀⠀⡇⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣥⣥⣤⣴⠈⠀⠀⠀⢰⠇⠈⢸⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠦⡀⠀⠀⢳⡄⠀⡭⠂⠈⢛⡿⠋⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠘⠏⢉⢍⡻⠀⢀⠀⢠⠯⠂⠀⣩⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢹⠒⠀⡙⠀⠈⠀⠀⠤⠃⠀⠀⢸⣿⠛⠛⠛⠛⠛⡻⣿⠇⠀⠀⠣⠃⢁⠼⠃⢀⢮⠤⢔⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠀⢧⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠛⡷⢦⣴⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡎⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠃⢘⡆⠀⠀⠈⠙⢲⢤⣄⣀⣀⡀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠊⠁⠀⢸⡉⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠈⡇⠀⠀⠀⠀⡟⢹⣿⡛⢿⡛⢷⣦⣿⣯⣿⣦⣾⠿⣿⢛⣿⡔⣦⠀⢀⡀⠀⠀⢸⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⢀⠀⢐⡇⠀⠀⠀⠀⡿⠈⠙⠻⣷⣿⣦⣴⣿⣿⣿⣿⣦⣾⡿⣿⠋⠁⢸⢀⡾⠁⢡⡴⣈⡏⠀⢰⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣴⣿⣃⣴⠐⠀⠀⠀⠀⣧⠀⠀⠘⠛⠿⢿⣽⣿⣷⣿⣿⣿⣿⠿⠋⠀⠀⢸⡾⢁⣄⣿⡷⣿⡿⣄⠀⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠙⣖⢿⣦⡀⠀⠀⠀⡟⢀⡀⢤⢤⣤⣴⣶⣾⣿⣟⠋⠀⢸⠀⠀⣀⣴⣾⣵⣻⣿⢏⣼⡿⡽⢫⡷⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢇⠈⠻⣽⣿⠦⠖⠲⢿⠛⠃⠁⠀⡏⠀⠀⠈⠉⠛⠿⣷⣾⣾⠿⠛⢉⡼⠿⠿⠤⣾⣯⠞⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠉⠁⠀⠀⠀⡼⡁⠀⠀⡈⠀⢯⠒⠒⠒⠒⠠⠄⠀⣭⣀⣈⣉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣷⣵⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠷⣿⣕⣚⣿⣿⣿⣭⣿⣿⡿⡿⢿⣿⡿⣟⣟⣻⢿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⣿⢯⠯⢿⣻⣿⠽⣿⢟⣿⣿⣿⡟⢳⣞⣿⠛⢾⢫⣏⢻⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠟⠻⠿⠗⣿⣿⣿⣿⣶⠿⣿⣿⣾⡿⢿⡿⠿⠿⠻⣟⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣤⣠⡼⠟⠀⠀⠀⠐⡍⠛⠻⠷⢶⣶⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⣉⣉⣀⠴⠁⠀⠀⠀⠀⠘⠦⠄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀