⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠀⣿⣿⣿⡃⠀⠤⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡶⣿⡋⠀⠀⠀⠀⢸⡧⢎⡇⠀⠀⠀⠀⢹⡏⢛⡏⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⠀⢻⣧⣿⠇⠀⠀⠀⠀⠀⡛⠛⣃⣀⣀⣀⣀⡘⠿⠃⠧⠀⠀⠀⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⢀⣀⣤⡴⣾⣿⣶⣞⣟⢻⣛⡟⣻⣿⣿⡝⣯⢻⡝⣫⢿⣿⣿⣛⢛⠳⢶⣤⡀⠙⢦⣀⣀⣄⣀⡀⠀⠀⠀ ⠀⠀⣀⡤⢶⢶⡾⣶⣤⣄⡀⢀⡾⢋⡍⠦⣑⣿⡿⣿⢣⢎⠷⣬⢓⣿⣿⣿⣟⠦⣏⠼⡱⢿⣿⣿⡧⣏⠰⣨⠙⣿⣶⣿⣟⣯⣟⣭⠛⠶⣄⠀ ⣠⢞⡭⣞⣛⢮⣷⣻⢾⡽⣿⢿⡆⠡⡘⢑⣺⣿⣟⣿⢡⡛⡼⣒⢏⣿⣿⢿⣏⠳⣜⢩⠓⣿⣿⡿⣿⢌⡳⢆⣽⣿⢯⣷⣻⡾⣽⡾⣿⡵⣌⡧ ⣿⣈⠳⣽⣎⡿⢾⡽⣯⢿⣽⣻⡷⢁⠀⠃⢾⣻⢞⣿⢠⡙⢶⠩⢎⣿⣯⢿⣇⠣⡌⢂⡏⢼⣿⣽⣿⠢⡵⠚⣼⣿⣟⣷⢿⡽⣷⣟⣿⣿⣿⠇ ⠈⠻⣶⣩⢾⡽⣯⣟⣿⣻⢾⡽⣟⠀⠡⠈⢼⣟⠾⣿⠀⠌⡌⢣⠉⢿⣞⡯⣇⠋⠱⢆⡈⡘⣿⣞⣿⠱⡈⠒⣼⣿⣾⣯⣟⣿⣳⣟⣾⡽⠃⠀ ⠀⠀⠈⠛⠯⣿⣷⣽⣾⣽⣯⣿⠃⠠⠁⢌⣈⣿⡣⢽⠀⢂⠰⢀⠊⠼⣏⢷⣋⠠⠑⠠⠁⠌⣿⣻⡟⣡⣬⣉⡧⢿⣿⣿⣞⣷⠿⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡿⣿⠀⠡⡼⠋⠉⠉⠻⣞⠠⠁⠂⠄⡘⢸⣟⢮⣓⠠⢁⠘⠠⢱⣿⣷⠟⠉⠉⢳⣞⣿⣿⣿⡿⢿⣶⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠻⢿⡿⠃⠈⣼⠁⢠⣾⣷⣦⠹⣆⢈⣰⣤⣶⣾⣿⣿⣿⣶⣦⣬⡐⣼⣿⢃⣴⣿⣦⠀⢻⣿⡿⣿⣓⠚⠼⣿⢿⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢸⠀⢧⠀⣿⣿⣿⣿⣧⡿⡟⣏⠷⣣⢞⡿⡳⢯⡟⣾⡹⢿⣿⣧⣾⣿⣿⣿⡗⢸⣿⣟⣿⡿⢽⣳⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠀⠸⢀⠚⣄⠘⣿⣿⣿⣷⠙⣼⣍⣏⣗⡺⠜⡁⢛⡘⢧⡽⣙⣾⡟⣿⣿⣿⣿⠃⣼⠛⠻⠿⣿⣿⣾⣽⣹⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣷⡀⠂⠠⠙⠦⣄⣉⣼⣿⣏⠁⠌⣩⣄⣀⣂⣰⣠⣐⣠⣉⣛⡋⢷⣿⣧⣉⣀⣼⣿⡄⠀⠀⠀⡂⠉⠛⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡛⡆⢈⠐⡀⠂⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡛⡉⢉⠙⠿⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣧⠀⠂⠄⠡⢸⣷⣿⣿⡭⣿⣍⠛⡟⣿⣟⢻⡽⣏⢿⡹⣽⣿⣿⣿⣿⠐⢠⠂⡘⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡅⡌⠱⣹⣿⣿⣽⡷⡸⢿⣼⢽⣫⡜⣷⡺⣽⡶⣷⡟⣾⣿⣿⡟⣈⢆⣣⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢷⣖⣬⣍⣏⠷⣿⣖⠻⢿⣶⣿⣯⣷⣿⠿⣑⣿⢫⣐⣦⣼⢆⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣼⢩⡞⢻⣶⣮⣽⣿⣿⣴⣾⠛⢡⣦⣽⣿⣾⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣟⣾⣿⣿⣟⡿⢿⠟⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀⠌⣽⠿⣟⠿⡿⣟⡟⠀⠀⠙⢾⣵⣋⣯⣝⣭⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠾⠾⠾⠛⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀