⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠀⠉⣉⣠⡶⠶⠶⢶⢶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⢀⣠⣴⠞⣋⡥⣾⣭⣛⠛⢿⣷⣦⣿⣿⠴⢶⣶⡲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣯⡶⢚⣿⠿⠿⣿⣿⣛⠈⣿⣿⣿⣍⣀⠀⠀⠈⠑⢯⡻⣶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⣀⣀⣤⣴⣚⣥⣤⣾⠟⢡⣿⣿⣶⣿⣿⣿⣿⣿⠋⢹⣿⣿⠻⣿⣺⣾⣷⣦⡽⣾⣿⣶⣽⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢋⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⡀⠈⢷⡈⠙⠙⠛⠿⢿⡎⠻⣮⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠒⢉⣉⣷⣶⣼⣿⣶⣿⡿⠿⠛⢋⣼⣿⡉⢿⣿⡿⠟⠉⠉⠛⣻⣿⡀⢰⡄⠘⣷⡄⠈⢿⣄⠀⠀⠀⠈⠁⠀⠈⣧⣽⣆⠀⠀⠀⠀⠀⠀ ⠀⠈⢡⡾⠛⠉⠙⢻⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⡇⠀⢿⢧⠀⠀⠀⠀⣿⢿⣧⡜⣿⢦⡈⠳⡀⠘⢿⣆⠀⠀⠀⠀⠹⣷⣾⣮⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣏⠤⠤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡞⡎⡆⠀⠀⠀⡇⣞⣿⣿⣾⣿⣻⣦⣉⠻⣾⣿⣆⠀⠀⠀⠀⠙⢿⡿⣿⣿⡆⠀⠀⠀⠀ ⠀⠐⠁⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣸⣠⣤⣤⣷⣬⣿⣿⣿⣿⣿⣯⣝⣿⣿⣿⣿⣾⣦⡀⠀⠀⠀⠳⣞⣷⣿⡄⠀⠀⠀ ⠀⠀⠀⢺⢣⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣿⡏⢸⢿⡟⡏⠉⠉⠉⠻⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣄⡀⢹⣾⣿⣟⣆⠀⠀ ⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠟⣼⡿⠁⢀⠤⢀⣀⣨⠽⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⡈⣆⠀ ⠀⠀⠀⢸⢻⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⠿⠿⠏⠁⠐⠵⠟⠋⠉⠉⠙⠛⠯⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣇⠸⡄ ⠀⠀⠀⠀⠁⠑⠘⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠞⠕⠀⠀⠀⠀⠒⠀⣠⠟⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇ ⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⣿⣿⣿⣿⣿⠿⡁⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⡿⠛⢱⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⢻⣿⣿⡔⠙⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣶⣦⡀⢹⣿⣿⣿⣿⡿⠋⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠀⠀⣠⠖⣋⣥⣤⣼⣦⣤⣤⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠙⣿⡼⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷⣚⢛⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⠿⣫⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢛⣦⣀⡤⠄⠒⠻⡀⠀⠘⢿⣿⣿⣿⠿⠛⠋⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠛⠭⠭⣭⡒⣒⢴⠛⠙⢶⡄⠀⠐⣷⡄⠀⠘⣿⣁⡀⠤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣆⠀⠙⣻⡆⡴⠉⠐⠚⠚⢁⣰⠶⠮⢿⡄⠀⠈⠓⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⣸⠛⡟⠀⢠⠖⠛⠩⣙⣱⠻⣏⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⣝⠼⢀⡠⢤⣲⣶⡻⢋⣡⣶⣿⣿⣟⣿⣆⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡠⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡼⢯⢵⠞⡫⡾⠋⠘⢿⣿⣿⣿⡿⠟⢻⠈⡗⠒⣲⣿⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⡤⢲⠋⠥⣇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠋⣴⢿⡡⣪⠊⠀⠀⠀⠀⠙⢅⠀⠀⠀⡌⠀⠘⡼⣳⡫⠔⢻⣿⣿⣿⠇⠀⣀⠴⢎⠁⢃⠀⠳⠀⠈⣦⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⡿⢋⣿⣥⡀⢀⡄⡄⠀⠀⠀⠉⠒⠊⠀⢀⣼⡵⠓⠤⣀⠀⢿⣿⣯⠴⡏⠘⡄⠈⢣⠀⢣⠀⢧⠀⢠⠑⢷⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠾⠁⢸⢹⠗⠀⠀⠐⠀⠉⢉⣛⡻⠲⠶⠭⠞⢹⠃⠀⠀⠀⢉⠶⡋⠱⡄⠘⣄⠈⣄⠀⢣⠀⢧⣈⣦⣴⣷⣾⣦⡖⢋⡀⠀⠈⠱⡄⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣢⣄⠀⠀⠀⠀⠀⠀⠈⠑⠶⣤⠤⣻⢠⠇⠀⢰⡻⣄⠑⢄⠈⢆⠈⢆⣘⡶⠞⠉⠉⠀⠀⠀⠀⠀⠀⠙⢏⠀⢈⠗⠠⣳⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣋⠀⠀⠀⠀⠀⠀⠢⡤⣤⡀⠀⠁⢹⣸⡀⠀⢏⠙⣌⢢⡈⠣⣨⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⢀⠎⢣⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣠⣤⡤⠤⠖⠃⠈⠐⠲⢤⡉⢳⣖⡚⠙⡌⢆⣱⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠶⣉⣠⡿⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠉⠑⠚⣑⠺⢾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠹⣇⠀⠀