⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣿⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣲⣽⣷⣶⣮⣥⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⢿⡻⣝⢶⣣⢟⡼⣿⣿⡿⠋⢸⣿⣿⠟⣿⣿⠁⠈⠻⣿⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣾⢿⡹⣎⢷⡹⣎⢷⣫⣾⣿⣿⠁⡄⢸⡿⠃⠀⠘⡏⠀⠀⠀⣷⣙⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⡿⣏⢾⡱⣏⢾⡱⣏⢾⣱⡿⢧⣿⠀⣷⠘⠁⠀⠀⢀⠀⠀⣀⠀⣿⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⣳⣽⣎⢷⡹⣎⢷⣽⣷⡿⠽⠷⣿⠀⠀⢀⣿⠀⠀⣿⣆⣀⡿⠶⡞⠒⠲⢮⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡾⣟⠿⣿⣎⢷⣹⣿⠟⠁⠀⠀⠀⣺⠀⠀⣾⣿⠀⠀⣟⢫⠕⠋⣁⠀⢀⣶⡆⠘⣧⡜⠙⠺⣕⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣾⡟⣼⢫⣿⣯⢷⣿⡏⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣧⠀⢻⡮⠿⣯⣤⣀⣀⣻⣤⣴⣟⠒⠓⠀⣹⢯⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣾⡿⣜⢧⡻⡼⣿⣯⣿⠂⠀⠀⠀⠀⠀⣿⠀⣼⣿⡏⠹⣧⠸⠇⠀⣻⣠⣼⣿⣿⣿⣿⣿⣿⣿⠿⠝⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣝⣿⡽⣎⡷⣹⣷⣻⣯⢿⣇⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⣾⣿⣷⣄⠀⠙⠢⠜⠁⠛⠴⣾⣝⣟⡣⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢾⣿⣽⣿⣞⣿⣿⣿⣿⢯⡿⣦⣄⣀⣀⣤⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠉⠙⢛⣲⣿⢶⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣾⣿⣿⠹⣿⣿⣟⣻⣿⢧⡻⣝⡻⣟⣻⣛⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣼⠋⢿⡻⡷⠶⠶⢶⣾⣻⠿⠝⠚⠉⠀⠀ ⠀⠀⠀⢀⢠⡀⡀⣀⣤⢴⣿⣿⣞⣿⣿⣿⡄⠻⢸⣟⡶⣹⢯⣷⣭⣳⡝⡶⣭⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⠛⡆⢼⣿⣃⣠⣤⣼⣿⠣⣔⣬⠀⠀⠀⠀ ⠀⠈⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⡇⠀⢸⡿⣜⣧⣿⣿⡷⣭⣿⣿⣿⣿⠀⠀⣠⣾⢻⡹⣌⣷⠿⣛⣛⡿⣯⣿⣻⣿⣷⠶⠛⠉⣿⢲⠀⠀⠀ ⠀⠀⠀⠀⠉⠫⢿⣿⣿⣿⣽⣿⣻⣿⣿⣾⣷⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⣰⡿⣡⢇⣳⢯⡙⢮⣱⣿⠉⠉⠉⠉⠀⠀⠀⠀⢰⣿⣻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠻⡟⣟⠛⣟⠛⣿⠀⢸⣿⠟⣿⠛⠛⣿⡟⠛⢦⣄⣿⠀⣿⢳⡱⢎⡵⢣⡝⢦⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡾⣤⣼⣿⠀⣿⡣⢟⡜⣜⢣⠞⣥⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣿⡿⣿⡏⠀⠀⠘⣿⣿⣿⣻⣿⣿⡿⠛⣾⡧⣿⡀⢿⣟⡼⡸⣌⠧⣛⢴⣻⡏⠀⠀⠀⠀⠀⠀⠀⢰⡟⡹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣇⠀⠀⠈⣿⣿⣟⣿⣯⣿⣵⣼⣿⣇⣹⡇⠈⠻⣶⣷⣌⣳⣽⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⢳⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⣖⣄⠈⡷⣿⣿⣷⣿⣿⡀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⢙⣿⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣴⣻⠀⢀⣾⢧⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣔⡵⠋⠉⣙⣤⣺⡞⣿⣿⣯⣿⣧⠀⠀⣿⣿⣿⣿⣻⣽⣿⣿⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡵⠃⢀⣾⣯⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢵⣏⠀⢴⣯⣝⣊⠉⢈⡿⠛⠉⠙⠻⣆⠀⣿⣿⣿⣾⣿⢿⣯⣷⣿⣿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣠⠈⠉⢀⣴⡿⡻⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⠤⣾⡸⣦⣈⡙⠓⠶⠴⠋⠀⠀⠀⠀⠀⣀⣁⣿⣿⣿⣷⣿⣿⢿⣻⣽⣾⣿⡿⣿⣿⣷⣤⣀⠀⠀⠀⠉⣀⣠⣴⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠀⢸⣎⠉⡁⠋⣙⠿⣄⠴⠂⢀⡤⣶⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣯⣛⣻⡿⠿⠛⣛⡩⢖⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣇⣀⡈⠳⠧⠷⠖⢉⣠⣥⣤⣿⡿⡄⠹⣄⡝⢿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠙⠻⣽⣶⣦⡴⢋⢵⡏⢰⣿⡿⠇⢀⣾⠟⠉⠚⠽⡻⢿⣯⣿⣿⣿⣿⣶⣵⣅⠀⠀⠉⠊⠽⣛⡿⣿⣿⣿⣿⣿⣿⣦⠱⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡷⠻⢭⣼⠟⠀⡾⣮⣧⢴⠻⠃⠀⠀⠀⢀⢐⣶⣿⣿⣿⣽⣿⣿⣿⡼⠃⣀⣀⠀⠀⣀⣨⣿⣿⣿⣯⣿⣿⡿⠁⢀⣤⢴⡾⢻⣷⡀⠀⠀ ⠀⠀⠀⠀⠨⣛⣄⣠⢴⠒⠻⠿⠏⠁⠁⠀⠀⠀⣠⣴⡷⣿⠿⣿⣿⣿⣿⣿⠟⠛⠁⣜⡿⡗⠿⣍⡪⠩⣱⣿⣿⣿⣿⡿⣅⢶⣿⢹⡟⣠⢞⣿⣵⣄⠀ ⠀⠀⠀⠀⠀⠊⠿⠕⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠞⠁⠘⣫⡿⣷⣿⣕⠢⣀⣴⡟⢀⣹⠀⢀⣹⣾⠋⠀⠸⠛⠒⠓⠛⠛⠃⠈⢀⣕⣩⢤⠿⣭⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣾⣧⠞⠁⠀⠀⠞⠛⠉⠉⠉⠉⠉⠙⠚⠋⠉⠤⠾⠿⣇⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠉⣇⡠⠋⢠⢿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣴⣛⣉⣀⡘⠉⠁⠀⠀⠀⢀⠀⢀⣀⣀⣀⡀⠀⢀⡀⠲⢤⣄⣠⢿⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⢹⠳⣄⣀⣴⢯⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠉⠉⠋⠋⠉⠉⠉⠉⠉⠉⠙⠍⠟⣽⡇⢸⣆⣻⣶⣶⢿⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠟⠓⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠞⠛⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀