⣧⠈⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢩⡇⣿⣿⣿⣿⡟⣮⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⣿⣿⣿⣿⣿⠏⠀⠹⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣧⠀⢧⠀⠀⠀⠀⠀⠀⢹⢫⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⢀⣿⡿⠛⠉⠀⠀⠀⠐⣌⣙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡄⠸⡄⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣾⣯⣶⣶⣷⣷⣿⣿⣿⣿⣿⣤⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠻⣾⡛⠛⠻⠿⠿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣿⣿⡟⢁⣴⣾⣿⣿⠟⠙⡖⠛⣿⣷⣿⣷⣤⣦⡬⡛⢷⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⠀⢿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣡⣞⠩⢯⡞⠀⠲⣽⣿⠿⣿⣿⣶⡶⣻⠀⢧⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠇⠀⠀⠀⠀⠀⣼⣭⣿⣿⣿⡿⠁⣼⣿⣿⣿⠏⠀⠀⢀⣿⡿⠋⢹⣿⣿⡟⠁⠀⠀⠀⠀⢀⠀⠈⠙⠲⡝⠛⠃⠹⡳⡀⡁⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⡾⢻⣿⡿⣿⡏⠀⣠⣿⣿⠟⠁⠀⠀⠀⢸⡟⠀⠀⣼⣟⡿⢻⣷⣶⣶⠟⠀⢿⣷⣶⡖⢒⣻⠇⠀⠀⠀⠙⠈⠀⠈⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠈⡇⠉⣧⠀⠀⠘⢁⣤⣴⠇⡇⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠈⠀⢠⣴⡯⡝⢀⠈⠉⠋⡡⠤⣀⠀⠙⠫⠍⠉⠃⠉⠉⠁⠀⠁⠀⠀⠀⠀⢉⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢹⡄⠸⡄⢠⠞⠸⠟⣿⠀⡇⠐⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⣾⢾⠀⠁⠀⠀⠘⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠠⠀⠀⢻⡿⠦⠤⠤⠤⠤⠤⠤⠤ ⡇⠀⠀⠀⠀⠀⣇⠀⢳⡀⠀⢀⡾⠁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⢿⡛⢄⠀⢀⣦⣷⣤⣤⣤⣤⠤⣤⣀⣀ ⠃⠀⠀⠀⠀⠀⢸⡀⠘⣧⢠⠞⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠀⠀⠈⣏⢣⠃⢘⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢻⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠟⠀⠀⠀⠀⡟⠀⢠⣸⡿⠍⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠿⣄⠉⠳⣶⣖⣒⣒⣚⣯⣽⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠮⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⢹⡄⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣴⡺⣆⠀⠀⠍⠛⠫⠭⠽⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⢛⢂⣓⣊⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⣷⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠚⣿⣷⣀⣿⣥⣤⣍⣽⡛⠾⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠉⠠⠄⠙⠦⢄⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠋⢻⣿⡵⢚⡁⢬⣟⣿⣦⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠓⢄⡽⠀⠀⠀⠀⠀⠀⠙⣶⣄⣠⣤⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣴⡿⢚⣉⠙⢻⣷⡀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠋⢿⣋⣡⣾⣿⣿⣶⣮⣯⣇⠀⠀⠸⡀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠘⡘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢘⣿⣌⠀⢸⡉⠉⢻⡝⠛⢆⡀⠀⡷⠉⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⣽⠉⣠⠇⣹⡟⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠤⠴⠚⠉⠁⠀⠈⠑⢼⣧⢰⡐⢷⠀⠀⠀⢳⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣈⠉⣥⠖⡧⢏⣠⣿⣻⣿⣿⡋⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⢶⡖⠒⠊⠙⣆⣳⣼⣧⣥⡌⠘⡟⠀⠀⠤⠀⠀⠀⠨⣀⣴⠿⠋⣉⡴⠋⠀⣫⠁⣿⡟⢩⠽⢈⡇⣧⠀⡙⢷⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⣀⡀⠨⠥⠔⠢⠒⠻⢫⠁⠹⣿⣃⣠⢵⡆⠤⠀⠀⠀⠀⡾⢟⠟⢀⣾⡟⠁⡴⣺⣳⡟⡞⠀⠀⠀⡾⢸⡧⣹⣷⢰⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⠊⠤⠂⠀⠂⠀⠀⣠⣁⣸⡇⣀⣯⣿⣶⣿⣿⠀⠀⠀⠀⠀⢰⠥⣶⣿⠟⠁⠞⡰⣱⠋⣤⡇⢰⠀⡆⣷⣼⣰⣫⣜⣿⡼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⣡⡀⠂⠬⠍⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠁⣠⣿⡵⣀⣜⡼⣿⠁⢸⡟⡏⡆⣦⣇⣧⣿⣹⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢟⣿⠀⠀⠀⠀⠏⢰⢫⣿⡟⢹⡟⣿⣿⢸⢸⢹⠀⡇⣿⢻⣿⡿⢧⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⡟⢿⡅⠀⠀⠀⣠⣶⡇⣼⣿⡇⢰⠏⢨⣧⣈⠌⠀⠀⡞⣸⣿⢿⣷⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⡤⠴⠒⠋⠁⠘⡇⢳⠾⡇⠀⠀⢀⣽⠑⣅⣧⣿⣧⠃⡄⣠⢳⣿⠃⠠⠀⠸⣧⣧⣼⠎⣻⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣀⡠⠄⠤⠤⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⣷⡄⠀⣾⠇⡟⢱⣿⣿⡟⢘⣴⠃⣾⢃⠀⣀⡄⡄⢺⢇⡞⣸⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠿⠇⢠⢿⠸⢳⢸⣿⣿⡇⣾⠖⢜⢁⠞⡾⠸⠀⡇⡟⢨⠏⡗⠃⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀