Volleyball Emojis & Text

Copy & Paste Volleyball Emojis & Symbols ☀🏅 🏐🏑 🏓 🏸🥊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡞⠻⣿⣟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⢠⣿⣿⣿⣗⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⢋⣽⠟⠒⢺⣦⠀⠀⠀⠀⠀⠀⢨⢷⣤⠀⣨⣿⡍⠁⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣴⠟⠁⢀⠔⢉⠼⡆⠀⠀⠀⠀⢠⣷⣤⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡇⠀⢠⠃⡴⠃⢠⡏⠀⠀⢀⡴⣿⣿⠿⠛⠉⢀⣀⣠⠀⣠⡾⠛⠀⡸⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⣄⣳⣄⣀⡠⠟⠀⣀⠔⠁⣠⠟⠁⠀⠀⢀⣾⣽⣶⠿⠿⣿⠚⠉⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⢀⣾⠁⣠⣾⠀⣠⣆⡔⠚⣏⣿⣻⣿⣗⣾⡃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⣣⣾⠟⠁⣠⡿⠋⠀⠀⠈⢳⣾⢷⣾⣽⣛⠷⣦⠄⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢏⣴⡟⣁⣴⡿⠟⠀⠀⠀⠀⠀⠘⣄⢿⣆⠀⠉⠓⠶⠤⣀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⡷⠛⣥⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠹⣷⣀⠀⠀⠀⠀⠑⣀⡀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡟⠁⠀⢸⡟⠁⣀⣤⡤⠖⠒⠒⠒⠺⣿⣿⣶⣾⣷⣾⣿⣦⣄⣀⣀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢿⣿⣄⣀⡴⠏⢠⣟⠋⣁⢄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⠈⠓⢬⡑⢝⢻⣷⢶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⠛⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⣯⣻⣿⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣶⣾⣏⠁⠹⡍⠉⠉⠛⢿⣿⣿⠀⠀⠀⠀⢀⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡇⢀⣠⣷⠀⠀⠀⠀⢉⣛⡷⠤⠤⣧⣀⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠁⠀⢸⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢯⢣⠀⠀⠀⠀⠳⢄⡀⠀⢰⠏⠀⠉⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⣧⡆⠀⠀⠀⠀⠀⠈⠑⠻⣤⣠⡶⠋⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠙⠚⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠋⠁⠀⠀⣀⣠⡤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⡛⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⢶⣾⠿⠿⢷⠶⢶⣾⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⣿⠾⣿⡉⣁⣰⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⣤⣴⣿⣽⣿⣿⣤⣀⣤⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠻⢟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢔⡦⠤⣄⠀⠀⠀⢘⢤⠀⣺⡛⠓⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠋⡠⡢⢺⠄⠀⢀⣾⣾⠟⠁⢀⢀⡄⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠄⠧⠡⠊⡠⢊⠼⠋⠀⣠⣯⣖⢻⠖⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⣡⠞⣠⠗⠁⠙⣵⣯⣾⡦⡄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣮⢞⡵⠞⠉⠀⠀⠀⠱⡽⣤⠈⠁⠂⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠋⢀⢏⡠⠤⠒⠒⠒⣷⣶⣿⣿⣷⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠁⢈⠃⢜⣖⢶⣦⣸⣿⣿⣿⡿⠿⣿⣿⡻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⣀⣨⠟⢟⠿⠿⣿⣿⠀⠀⠈⣾⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢺⠠⠼⡆⠀⠈⣽⠒⠺⠬⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢫⠄⠀⠈⠆⡀⢰⠋⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠤⠣⠀⠀⠀⠀⠙⠒⠇⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠆⢈⣀⣠⣤⣒⣃⣀⣀⡀⠀⠀⠀⠈⠑⢯⣉⠒⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⢸⣪⣽⣷⣿⣥⣤⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣫⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣠⠞⠉⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀ ⠀⠀⢠⣞⡵⠞⠉⠹⣇⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⣾⠋⠀⠀⠀⠀⠹⣦⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⡆⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⢷⣄⢠⡞⠁⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡏⠀⠀⣷⠀ ⢸⠇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠁⠀⠀⢿⡀⠀⢸⡄ ⣼⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠘⡇⠀⠀⠈⣇⠀⠘⡇ ⢿⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢻⡀⠀⠀⢹⡀⠀⡇ ⢸⣇⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⡇ ⠈⣿⡄⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣗⢰⠇ ⠀⢹⣿⣆⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣇⡿⠀ ⠀⠈⢯⠙⢷⣄⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⠃⠀ ⠀⠀⠘⢧⡀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⡾⠃⠀⠀ ⠀⠀⠀⠈⠻⣄⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⣀⡿⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⢀⡾⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠈⠉⠓⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡾⠀⠀⠀⠀⠀⣠⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣩⠿⠋⠀⠀⠀⣀⣠⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣤⣶⣯⡥⠴⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⢲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠾⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠢⢤⠺⢅⠀⡸⠀⠀⠀⠀⠀⣰⡮⡻⢋⣦⠀ ⠀⠀⠀⠀⠀⡠⡇⡄⠀⠉⠂⣏⠁⠢⢀⡀⠀⠘⡇⠬⠉⡇⣾⠀ ⠀⠀⠀⠀⡰⠁⡇⢁⠀⠀⠀⠀⠑⠠⠀⠀⠉⢱⠊⠷⢆⡓⠋⠀ ⠀⠀⠀⡜⠁⠐⡇⢸⠀⠀⢄⠤⠄⣀⠀⠉⠛⠛⢲⠶⠤⠤⢵⣄ ⠀⠀⠌⠀⠀⠘⡇⢈⡠⠐⠁⠀⠀⠀⠈⠉⠁⠐⠊⠉⠉⠒⠼⠋ ⠀⡊⠀⠀⠀⠀⠐⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠉⠀⠤⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢛⣩⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠛⠉⠉⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢁⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⣠⣴⠖⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⣼⣯⡾⠋⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⣿⡀⠀ ⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠻⣿⠀⠀⠀⢸⣇⠀ ⠀⣿⠁⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⠹⣇⠀⠀⠈⣿⠀ ⠀⡏⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠙⣷⡀⠀⠀⠀⢿⡆⠀⠀⢿⡆ ⢸⡇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⢹⡇⠀⠀⠀⠘⣷⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡆⠀⠀⡇ ⠀⣷⡀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⢠⡇ ⠀⢿⣇⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡀⢸⡇ ⠀⢸⣿⣆⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣽⡅⣿⠁ ⠀⠈⣿⡻⣷⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⢰⡟⠀ ⠀⠀⠹⣏⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⡾⠀⠀ ⠀⠀⠀⢻⣆⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⣿⠃⠀⠀ ⠀⠀⠀⠀⠹⣧⡀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⣦⣤⣤⣀⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠉⠛⠷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣰⡟⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⠤⠤⣤⣤⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⢀⣼⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⢀⣀⣤⡴⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣤⣀⠀⠀⣀⣤⡶⣛⣉⣤⣤⣤⡶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⚽️ 🏀 🏈 ⚾️ 🎾 🏐 🏉 🎱
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⠇⠙⠿⢿⡇⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⣸⣯⣭⡟⣟⡓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠞⣻⣶⡶⠦⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣀⠀⠀⢻⣿⠛⠛⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣤⣾⠟⠉⠀⣠⠼⠻⣆⠀⠀⠀⠀⠀⠀⠀⣴⠋⠹⣿⣥⣴⣫⡽⠋⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢾⠟⠁⠀⢀⡜⠁⣤⠞⣿⡄⠀⠀⠀⠀⠀⣼⣿⡛⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⢸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣿⠀⠀⢠⠏⢠⡞⠁⢀⣿⠁⠀⠀⠀⣠⠶⣮⢿⡽⠛⠋⠉⠀⢀⣀⣤⡤⢀⣴⡾⠋⠉⢀⡼⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣀⠀⣿⡀⠈⠁⢠⡾⠋⠀⢀⣠⠞⠁⣨⣿⠋⠀⠀⠀⠀⢠⢟⣹⣤⣾⣿⡿⣗⡶⠖⠋⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠑⠒⠛⠒⠚⠉⠀⢀⣴⠋⠀⣠⠞⠋⠁⣀⠀⢀⣴⡶⢾⣿⣿⣿⣶⣈⢭⣗⠂⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢀⣴⡵⠇⠀⣴⣏⡞⠁⠀⠳⣝⡶⢾⣹⠳⢾⣽⣆⣀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⣴⣿⠟⠀⢠⢴⡽⠋⠀⠀⠀⠀⠈⣻⢿⡻⣿⣶⣮⣝⠛⠭⣖⠂⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⣱⣿⠟⢁⡴⣫⡷⠟⠀⠀⠀⠀⠀⠀⠀⢷⡐⢿⣶⠄⠀⠉⠛⠶⣮⣄⡀⠀⠀⠀⠹⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⣡⡾⠋⢹⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡞⠫⣗⣤⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⣶⡿⠟⠉⠠⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣀⣀⣀⢻⣦⡸⢿⣲⡄⠀⠀⠀⠀⢀⣨⣦⣦⣴⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣫⣾⠟⠀⠀⠀⣸⡟⠀⣀⣤⣔⡾⠛⠋⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡷⢤⣤⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢿⣟⣿⣔⣀⣠⣴⠏⢠⣿⡟⠉⣀⢤⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠈⠉⠁⠀⠀⢸⠉⠛⢦⡈⠳⢝⡻⣷⣗⢮⡢⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠈⠓⢦⣽⣮⡹⡕⠝⠾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⢿⣛⠿⣿⣶⡘⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢈⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢼⣧⣭⣿⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⢾⣟⣏⠀⠀⠻⡆⠉⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠀⡄⠀⣡⣹⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡨⡦⠀⠀⢀⣷⡄⠀⠀⠀⠀⠈⠛⢿⣧⡤⠤⣤⣇⠀⢸⣿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠖⠋⠉⢹⣧⠀⠀⠀⠀⠀⢹⣶⠉⠀⠀⠈⠉⠙⢾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠘⣏⢧⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⣠⡿⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠻⡌⢧⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⢰⡟⠀⠀⠀⠉⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⠀⠀⠻⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⣧⣄⣀⣴⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠙⢷⣤⡾⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠧⣄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⢠⣼⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⡉⠁⠀⠀⠀⠀⢀⣤⣶⣶⡒⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣌⠉⠉⠉⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⣿⣿⠿⠿⠿⡿⠿⢿⣯⣽⡷⠶⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢺⣿⠿⣯⣍⡉⢉⣁⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡖⣏⣀⣀⡶⢏⣹⣿⣶⣭⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
💭 🕊🍚🏐👻🐩🐚🕸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠒⠒⠒⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⡩⠞⠁⠀⠀⠀⡠⠒⠉⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⢀⠜⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⠤⠚⠉⠈⠳⣄⠀⠀ ⠀⠀⣜⠔⠚⢇⠀⠀⠀⣠⠊⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⢦⠀ ⠀⣼⠁⠀⠀⠈⢢⡀⡴⠁⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢀⠤⡖⠚⡇ ⢰⠈⢆⠀⠀⠀⠀⠙⢦⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡠⠖⡇⠀⢱⠀⢱ ⢸⠀⠈⢆⠀⠀⠀⠀⠀⠈⠛⠤⣀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠀⠀⡇⢸ ⠘⣇⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢎⠀⠀⠀⠀⠀⡇⠀⢸⢸ ⠀⢻⢧⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⣸⠇ ⠀⠀⢣⡙⢦⡀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⢸⠂⠀⠀⠀⢸⠀⢠⠏⠀ ⠀⠀⠀⠑⢄⠈⠲⢄⡀⠀⠀⠀⠀⠉⠉⠒⢺⠀⠀⠀⢀⠎⡠⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠉⠒⠒⠠⠤⠤⡤⠃⠀⠀⣠⠮⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠶⠭⠄⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⡿⠿⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⢠⣴⣾⠋⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡿⣿⣷⠶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠙⠻⣌⠉⠡⢤⣠⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⣿⣵⠋⣠⣾⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢸⠀⠀⠀⠀⠉⠲⣞⠁⠀⠙⠦⣀⠀⠀⠀⠀⠀⠸⡗⠦⣀⣉⣉⣣⢸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠈⡇⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠉⠉⠒⠦⠤⣀⡙⢦⣤⣀⠀⣼⣸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⢻⠉⠉⠛⠻⠭⣍⡉⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠀⠀⢰⡇⠀⢸⡄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠿⣶⣦⣤⣄⣀⠀⠉⠓⣄⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⢰⡇⠀⢸⠀⠀⠀⢀⡴⠋⠈⠉⠒⠒⠠⠤⣀⣀⣀⠀⠀⢀⣇⣈⣉⣉⠉⠉⠹⣿⡧ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⡇⠀⢘⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠲⠴⠟⠁ ⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠹⡀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⢄⣀⠀⠀⠀⠀⠀⠀⠀⡹⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠈⠉⠂⢄⣀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠁⠊⢕⠢⡄⠀⠀⠀⠀⡇⠃⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠑⡌⢦⠀⠀⠀⡇⡀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡀⠀⠀⠰⠈⢇⠀⠀⢃⢣⠀⠀⢹⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼⢵⡀⠀⠀⠃⠈⡀⠀⢸⠀⢆⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠳⣄⠀⠸⠀⠱⠠⣘⠀⠈⣆⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠇⠀⠂⠊⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⣲⠉⠙⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⡇⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠿⠵⡄⠀⠀⠀⠇ ⡠⡤⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⢧⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⣀⣠⠖⠁ ⠀⠈⠢⠤⠬⠦⡀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢎⠳⢤⣀⣀⡴⢓⡄⠄⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⢎⠐⠠⠤⠴⣊⣀⣀⡀⡔⠛⠐⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠈⢦⣀⣀⣤⡸⠀⠀⠀⠀⠒⠒⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⛸ 🥌 🛷 🎿 ⛷️ 🏂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠉⠛⢦⡀⠀⠀⢀⣼⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠙⣶⠻⣏⠿⠄⠀⠀⠀⠀⠀⠹⣦⠴⠚⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⠁⠀⢀⢀⡄⢠⣦⡄⠀⠀⠘⣷⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⢶⡿⠶⠶⠆⠀⠀⢰⣦⠈⣹⡾⠾⠓⠀⠉⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠠⣾⠓⠚⠛⠁⠀⠀⠀⠉⠀⠁⠀⣸⠛⢶⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠳⣄⣄⡀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠯⣤⡍⠀⠀⠀⠈⣇⠀⠀⠀ ⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣁⡼⠀⠀⠀⠀⠀⣀⣹⣦⣄⠀⠀⠘⣆⠀⠀ ⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣠⡤⠶⠚⠉⠉⣀⣠⠟⠀⠀⠀⢹⡄⠀ ⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣀⣠⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⣧⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣸ ⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣳⠀⠀⢀⣠⠴⠛⠁⠀⠀ ⠀⠀⠀⠙⢦⣄⢠⣿⣿⡶⠶⣤⣤⡤⠤⣤⣤⣄⣉⣰⣧⠴⠚⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠿⣥⣼⣿⣿⣇⣀⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🏒 🥅 🥌 🇨🇦
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠟⠛⠛⠛⠛⠛⠛⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠰⠿⣷⢀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⣼⣿⣷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⡞⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠈⠉⣹⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠉⠛⠛⢛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⠀⠀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣷⠀⠘⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣷⠀⠀⠀⠀ ⠀⠀⠹⣇⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀ ⠀⠀⠀⠙⢿⣔⠤⡀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⣷⣶⡄⠀ ⠀⠀⠀⠀⠀⠉⠻⢦⣝⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠰⢾⣷⣐ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⡦⣤⣤⣄⣀⣀⣀⣴⣧⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⠀⢀⣰⣿⣿⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠙⠛⠛⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣀⣠⣤⣤⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⢀⣘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠙⡄⠀⠀⠀⠀⠀⠀⠘⠾⠓⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣶⠾⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠢⠤⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠒⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣴⣿⡷⠶⠿⠿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⣉⠙⣿⣒⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣤⡾⢿⠛⠥⢥⣀⣠⡴⠚⢲⡎⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣿⣿⠛⠛⡿⠿⣶⣵⡢⠀⠀⠀⠀⠀ ⠀⠙⢻⠆⣈⡷⣶⡾⠥⡀⠐⠺⠭⠆⢠⡶⠏⢰⡿⠀⠈⠀⣀⠤⠖⢠⠿⣥⣌⣻⣿⣿⠓⠢⣍⣻⣷⣦⣄⡀⠀ ⠀⣰⣗⠋⣯⡴⠉⢔⠾⠋⠁⣀⠴⠚⠁⠀⠀⢸⡯⠄⠂⠄⠀⠀⢠⣟⡁⠨⠉⠉⠉⠓⢶⡄⠞⠋⢀⣹⣿⠧⠄ ⠘⣻⠟⠻⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠑⠖⢀⠉⠥⠄⠀⠀ ⠈⠁⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⣀⣀⣀⡈⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣿⡁⠀⢿⣿⣿⣿⣿⣿⣷⣦⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠉⠀⠀⠉⢉⢸⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⣠⣤⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠓⠒⢲⡒⢻⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢱⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠉⣉⣩⠭⠭⠉⠉⠩⠭⠉⠉⠉⠙⠛⠛⠛⠻⢿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⠤⠒⣉⠤⠔⠒⠒⠒⠋⠙⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠮⠙⠻⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⠤⠊⡡⠖⡩⠔⠂⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠠⢒⠒⠒⠀⠒⠢⣄⠀⠀⠀⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠠⠊⠴⠋⠀⣀⣀⣤⣤⣤⣀⡀⠀⠑⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⣠⣾⣟⣀⡀⠀⠀⠀⣀⡀⢠⣶⣿⣿⣿⣿⣿⡋⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠻⣧⣄⠀ ⠀⢠⣾⣻⠋⠉⣡⣤⣤⣤⣌⡉⠔⠈⠛⠛⠉⢉⣭⠉⠛⠻⣶⣶⡿⠃⠀⠀⠐⢾⣿⡿⠿⠛⠛⠛⠋⠉⠀⠀⠉⠉⢍⡳⢌⢻⣦ ⣰⡿⢱⠃⢠⡾⠋⠁⢰⣌⠙⠛⠷⢶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣄⣀⣴⡶⠶⠶⣶⠹⠀⢳⣿ ⢿⡇⢸⠀⣿⠃⣀⣤⣾⠿⢷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣤⡤⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠈⠙⠛⠋⢠⣇⠀⠀⢠⠇⣸⣿ ⢸⣧⠘⡆⢹⣇⠉⠉⢿⣆⠀⠈⠙⢿⣷⣦⣤⣉⡁⠀⠀⠸⣿⡀⣶⡶⠶⠄⠀⠀⠀⣠⣿⠿⠗⠦⣄⠀⠀⣼⣿⡇⢀⣣⠴⣿⠏ ⠀⠹⣧⣘⠲⠅⠀⠀⠘⢿⣿⣶⣤⣸⣿⡀⠈⠙⠛⠿⢶⣦⣭⣅⣀⡀⠀⠀⠐⠷⡾⠟⠁⠀⠀⢀⣠⣴⣿⢿⣿⣷⠈⠀⣼⡟⠀ ⠀⠀⠈⠻⣿⡀⠀⠀⠀⠈⢻⣦⠉⢻⣿⣿⣶⣦⣄⣀⣸⡏⠉⠉⠉⠛⢿⡿⠿⠶⢶⣶⠶⠿⠛⢿⡏⠁⣿⣄⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⢷⣼⡟⠀⠉⠛⠻⢿⣿⣷⣶⣤⣤⣤⣼⣧⣤⣤⣤⣿⣤⣤⣤⣾⣷⣴⣿⣿⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⣸⡟⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⢀⡀⠀⢀⠀⠉⠻⣷⣴⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⣽⡏⠉⢹⣿⠋⣽⡟⢸⣿⡿⠃⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡓⠦⣍⠒⠤⣀⠉⠙⠛⠿⠶⢶⣤⣾⣧⣄⣀⣠⣿⣄⣠⣾⣧⣴⡿⠷⠿⠋⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣉⠒⠦⢍⣑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⡆⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⡉⠑⠒⠩⠭⠍⢐⣒⣒⠒⠂⠐⠒⠒⠒⠒⠒⠉⠀⢀⡤⠚⠀⠀⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⠀⣀⠀⣀⡀⢠⣤⠀⣤⡄⠰⣶⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⡿⠀⣿⡄⢹⣿⠘⣿⡆⠸⣿⡄⠹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⡇⢰⣿⣧⠈⣿⡆⢹⣿⡄⢹⣿⡄⢻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⠇⢸⣿⣿⡄⢹⣿⠀⠛⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⠿⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣷⣦⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠻⠿⠿⠿⠿⠿⠟⠋⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣶⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠴⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠳⣄⢀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⡇⠀⠀⠀ ⠀⠀⠈⢻⣦⣀⣴⠿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⢿⣦⣀⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⢿⣦⣾⠟⠋⠉⠀⠉⠉⢤⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠄⠉⠁⠀⠉⠙⠻⣦⣼⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡱⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡇⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⡀⠠⠤⠒⠁⠀⠀⠈⠳⣤⣄⣀⣀⣀⣤⠾⠋⠀⠀⠈⠢⠤⠀⡀⠠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣰⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠋⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣲⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢆⠀⠀⠀⠀⢀⣤⠀⠘⣿⡿⠿⠇⢀⡠⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⢦⠀⢀⣾⣿⠟⠃⠀⠀⣠⠖⠂⠘⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠙⢡⠖⠋⢙⣳⠇⣴⣿⣶⣄⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡏⠀⢰⣿⣿⣷⣿⣿⣿⣿⠀⣼⠉⠋⡳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⢼⣧⣄⠸⣿⣿⣿⠃⡈⠉⠁⢀⣇⠀⣰⠟⢂⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠼⣦⢾⣀⠈⠳⡄⠉⠀⣠⠟⠓⠒⣋⣽⣿⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⠴⠋⠉⠀⠀⡴⠁⠀⠈⠳⣄⢿⣟⠋⠁⠀⡀⢎⣼⡿⣿⠀⠀⠠⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⢠⢖⡏⠙⡶⠋⠉⢙⠞⠁⢀⢀⠀⢀⠞⢢⢤⡀⠀⠀⠘⡆⠻⣿⣿⣾⣧⣶⣿⠃⢹⡀⠀⠀⠁⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠃⡾⠀⠀⠁⠀⣰⠃⢀⡞⠁⡜⢠⠃⢠⠎⡰⠃⠀⠀⠀⣧⠀⠈⠙⠻⠿⠛⠁⠀⢸⡇⠀⠀⠀⠀⢦⠀⡻⣆⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⢠⡇⠀⠀⠀⣼⡏⢀⡜⠀⣸⢁⠎⢠⠋⡴⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⢇⠹⡌⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⢀⣼⡿⠁⣮⠁⠀⠇⡜⣠⠃⡼⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⢇⠘⣄⠹⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⣰⣿⡿⠃⠀⢿⠀⢸⢀⡷⢃⡞⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠢⠈⠁⢣⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠉⢿⠀⠀⠀⠘⡄⡜⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣖⣐⣂⣀ ⠀⠀⣿⡀⠀⢸⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣨⣿⣦⣀⣀⣀⣀⣠⣞⣉⣉⣉⣩⣥⡤ ⠀⣠⠆⠳⣄⣠⠇⠀⠀⠀⠀⠘⣆⢠⢤⣤⣤⣶⣶⣶⣾⡿⢿⣿⢶⡶⠿⠷⠖⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠞⢷⣤⣤⣭⣴⡶⠒⠒⠛⠛⠏⠙⠉⠉⠉⠉⠛⠉⠘⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⠠⠄⠴⠆⠐⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠠⠅⠉⠉⣉⣁⣠⣤⣤⠤⠀⠄⠀⠀⠒⠀⠉⠉⠉⡙⣁⡉⣡⣀⠀⠀⠀⠀⠀⢀⣶⡀⢀⣻⣭⣤⠀⢀⡀⣀⣀⠀⠀⠀⢀⠀⠀⠀ ⠛⠚⠋⣉⠉⡁⢡⣤⡠⣀⣠⣤⠄⠀⠼⣷⣤⣤⣾⣷⣦⣩⣷⣖⣛⡛⢛⣛⣃⣈⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⢷⠀⢈⠃⣤⠀ ⣿⣥⣬⣤⡄⢈⣉⠁⣤⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⡿⠿⠟⠻⠿⠋⣉⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣤⡼⠛⢿⣿⣽⣉
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠾⠿⠿⠛⠻⠿⠿⠶⢶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⢀⣠⣶⡶⢶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣿⠏⠀⠀⠀⠈⠙⢿⣦⠀ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⣠⡶⢶⣄⠀⢹⣇ ⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠙⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠛⠀⠀⣿⠀⠈⣿ ⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣼⠟⠀⢸⡟ ⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠁⠀⣠⣿⠁ ⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡾⠟⠁⠀ ⢠⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣤⣄⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀ ⢸⣿⡭⣷⡀⠀⠀⠀⠀⢀⣶⢟⣭⣴⣶⣶⣬⣝⢷⣄⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⢸⣿⣿⢸⡇⠀⠀⠀⠀⣿⢃⣾⣿⣿⣿⣿⣿⣿⣆⢻⡆⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⢸⣿⣿⢸⡇⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡷⠀⠀⠉⠻⣿⣦⣀⡀⠄⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⢸⣿⣿⣼⣷⣶⣶⣶⣾⣿⡄⢻⣿⣿⣿⣿⣿⣿⡟⣸⡇⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀ ⢻⣷⣾⣿⣗⠙⣿⠋⠀⠈⠻⣦⣍⣛⣛⣛⣛⣩⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠸⣷⣿⠳⠿⣸⣿⠀⠀⠀⠀⠈⠻⣿⡛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⣿⡏⠀⣰⣿⢿⡄⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⣿⡇⣂⣿⡘⢘⣿⡄⠀⠀⠀⢀⢠⣜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢾⠃⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⡟⡛⠛⣿⣦⣀⣀⣈⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠁⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡙⠿⠷⣦⣬⣿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡆⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡙⢻⡿⢷⣶⣶⣤⣄⣿⣇⠀⠀⢠⣶⠀⠀⠀⠀⣀⣀⣀⣤⣶⡾⣿⠋⠹⣷⡀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠈⠉⠙⣿⡄⠀⣸⡟⠛⠛⠛⠛⠛⠛⠉⠙⠿⠾⠋⠀⠀⢻⣧⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⡿⠀⠂⠀⠀⠀⠐⠠⠠⠄⠯⠋⠁⠐⠄⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠤⠢⢄⠀⠀⠀⠀⢷⡛⠉⠈⢿⡲⢲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠀⠀⢀⡇⠀⠀⠀⡜⠑⢤⣤⡿⡇⠆⠀⢠⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠲⣾⢟⢅⡀⠀⡸⠀⠢⡀⠀⠰⠁⠈⠒⠚⢖⠲⠁⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⠣⡀⠉⡇⠒⢢⠳⡠⠐⠤⠤⠀⣀⡬⠃⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠔⠁⢀⡸⠤⣇⠀⡀⠯⠄⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠑⢄⠲⢟⠒⢂⠍⠒⡹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⣠⣇⠔⠣⣀⠔⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠂⠞⠁⠀⠀⠀⠀⠛⠣⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⢘⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠲⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠭⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠠⠤⠤⢤⠤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⢀⠠⣒⠨⠅⢀⡀⠉⠭⠄⠐⠀⠈⠭⠭⠓⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⢂⢕⠜⠊⠁⠀⠀⠈⠆⠀⠀⠀⡌⠉⠉⠐⢂⠀⠈⣇⠀⠀ ⠀⠀⣠⣾⠥⠄⠀⢤⢄⣶⣿⢿⣿⣉⠳⣄⠀⢀⣀⣥⣶⣶⣶⠄⠤⠀⣘⢦⡀ ⠀⡞⡍⣠⠞⢉⡝⠲⠤⠤⠴⠊⠀⠈⠙⠁⠀⠀⢹⡏⠀⠀⣀⣠⢤⠦⠕⠡⣿ ⠘⣇⠃⢿⠰⢻⡉⠓⢦⣤⣀⠀⠀⢲⡚⣃⣄⠀⠀⢉⣷⠄⡀⠁⣸⡄⢐⣱⡟ ⠀⠙⢮⡂⠀⠈⢻⡶⢤⣧⣉⠙⠓⡶⠥⢤⣀⣀⣳⣋⣀⣠⡤⢾⢻⣷⠁⡞⠀ ⠀⠀⠀⠹⡄⠀⠀⠙⣤⡏⠙⠻⢿⣧⣤⣤⣼⣤⣤⣿⣤⣤⣧⣼⣾⡿⠀⡇⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠈⠛⢦⣄⡞⠀⠀⠉⡟⠛⢛⡿⢛⡿⣻⢿⣿⠇⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠓⢮⣔⡩⢐⡨⢉⠛⠒⠶⠷⠶⠾⠷⠾⠷⠛⠛⡉⢀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣅⠘⠓⠰⠄⢀⡀⡀⠀⠒⣒⣈⠠⠘⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⢤⣀⣀⡀⠀⠀⠀⢀⣀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠛⠛⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣄⠀⠘⢶⣤⣀⣀⣀⣀⣀⣹⣧⣤⡾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠻⣿⡿⠿⠿⣭⡭⠽⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠈⢳⣄⠀⢠⡹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣀⣀⠀⠙⢧⡀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⠀⠀⠀⣰⣏⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣇⣹⡆⠀⠀⢻⡄⠙⣧⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⣠⣾⡟⠉⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⣷⡄⠀⠀⠀ ⣰⠺⢿⠃⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⣷⡄⠀⠀ ⣿⢀⡟⠀⠀⢸⣿⠟⠇⢠⣤⡄⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⣿⠻⡀⠀ ⣿⣾⠁⠀⠀⠟⠃⣸⠀⣟⣠⡇⠀⠀⠀⠀⠀⢠⡞⠀⢀⡤⠞⠛⢿⡙⠛⠒⣶⠬⣝⠒⠶⠤⠤⠤⠤⠖⠛⠁⠀⠀⠀⠸⣇⢷⠀ ⢻⡇⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⠋⠀⠀⠀⠀⢳⣀⡴⠃⠀⠘⣟⠶⢤⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢹⣾⠀ ⢸⡇⠀⠀⢀⣀⡼⠛⢧⣀⠀⠀⠀⢀⣴⠟⠁⢀⡾⠻⣆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⠤⠬⠟⠋⠈⢳⡄⠀⠀⠀⠀⠘⣿⠀ ⣾⡇⠀⠀⠀⠋⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⣸⠁⠀⠹⠷⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢻⡆ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠇⠀⠀⢸⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⠀⠀⠀⢸⡇ ⢸⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠈⢷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠈⣿⢷⡀⠀⠀⠀⠀⠀⠀⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⢻⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⠈⣧⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠐⣤⠽⠖⠒⠋⠉⠉⠙⠓⠒⠾⣤⠔⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⣀⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣏⠉⠁⠋⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠘⠁⠉⢉⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⠒⠒⠉⠀⢀⣠⣴⡶⠶⠶⠶⣶⣤⡀⠀⠈⠑⠒⠚⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⡠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣀⣠⣤⣤⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡠⠔⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠤⠤⠤⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠶⠶⠿⠿⠿⠶⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠸⣦⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⣠⡟⠀⠈⠉⠒⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢉⡏⠉⠉⠉⠉⠉⠉⢙⡏⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡏⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⢉⣹⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣿⣉⡉⠉⠑⠲⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⡤⠚⠉⠉⡟⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡉⠉⠙⢦⡀⠈⠳⣦⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢸⡇⠀⠀⣸⠃⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠀⠀⠸⣿⠀⠀⠀⠀⠙⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣐⣠⢞⣿⣆⠀⣿⡄⠀⢠⡟⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠸⡇⠀⠀⡽⡂⢀⡿⡷⢦⣀⡽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠀⠙⠲⠞⠁⠀⣼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢻⠀⠀⠳⠶⠚⠁⠙⠚⠉⠀⠀ ⠀⠀⠀⣀⡤⠴⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠊⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣀⠀⣀⠴⠶⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠁⠀⠀⠹⡄⠀⠀⢳⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠑⠤⠤⠤⠴⠚⡇⠀⠀⠀⠀⠈⠲⢄⣀⣀⣀⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢸⡄⠀⠀⠀⠀⠉⠙⢒⡶⠒⠒⠶⣖⠚⠉⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣞⠋⠉⠉⠉⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠉⠉⣓⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⣟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠤⠤⢤⣤⡜⢨⡷⠋⠑⢦⡀⠀⠀⢈⠇⣀⡀⣰⢋⠟⣆ ⠀⠀⠀⠀⠀⠀⣀⣴⠶⠺⢿⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠹⡷⢤⣍⡉⣻⠏⡴⢩⡟⡡⢋⢞⣽ ⠀⠰⡄⠀⢠⡾⠋⠀⠀⠀⠀⠈⠉⠛⠲⢤⣄⡀⠀⠀⠀⢻⠀⢐⡻⣆⡈⠉⣸⠋⢹⠃⠸⡆⠀⢿⢎⡜ ⠰⡀⠘⣦⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣼⣆⠻⣿⣿⣥⠞⠁⠀⢸⠀⠀⠸⠀⢠⠏⠀ ⠀⠹⣆⠘⣷⣜⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢷⡶⠞⠁⠀⠀⡀⠈⡇⠀⠀⣰⠋⠀⠀ ⠀⠀⠹⣷⣌⢯⠳⣍⢻⣿⡛⠛⠛⠻⣿⠛⠛⠛⠓⣷⠀⠀⠀⠀⠹⣦⣤⣤⣤⣧⣀⣷⠀⠈⠈⢧⠀⠀ ⠀⠰⣄⡘⢯⡻⣷⣌⠛⢿⡙⢦⣄⠀⣿⠀⠀⠀⢼⢹⠇⣠⢀⠀⡀⢈⡷⠀⠀⠀⠈⠙⢳⡄⠀⠈⣧⠀ ⠀⠀⠈⠻⣿⣿⣮⡙⠷⣄⠙⠢⣌⠓⢿⣇⣀⠀⠈⠿⢴⣧⣞⣠⢃⡞⠀⣀⣄⡀⠀⠀⠀⣷⠀⠀⠘⣇ ⠀⠀⠀⠀⠈⠛⢮⣝⠢⢌⡙⠲⠌⠑⠂⠈⠙⠛⠶⢦⣤⣄⣸⣧⣾⣄⢸⡅⣀⣿⠀⢀⣼⠇⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠛⣿⣿⠟⠓⠚⠛⠷⣤⣀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠤⠤⠤⠤⠤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
ヽ(^o^)ρ┳┻┳°σ(^o^)/
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠚⠛⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⢶⣏⠙⣇⠀⠀⢀⣾⡟⢳⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠀⠀⠀⠀⠉⠙⠝⠷⠶⠛⣉⡴⠾⠇⠀⠈⢣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠀⢠⡄⢠⣤⣝⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⣀⣀⣀⣤⣶⣶⡶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⣿⣿⣯⢻⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⣴⠿⠋⠉⠉⣽⣏⠙⠛⠲⠤⠄⡀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⣿⠀⠙⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⡼⠋⠁⠀⠀⠀⠀⣿⣿⡿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠉⠻⣇⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⡇⠙⠒⠬⠉⠑⠂⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠙⠷⣦⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠙⢿⣤⡤⠀⠀⣄⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠂⢠⣤⣼⣷⣄⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠄⠀⠀⢈⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢀⣾⠁⠀⢠⡾⠛⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⢷⣾⡇⠀⢠⡟⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⣿⣷⣾⡶⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠻⣦⠀⠀⣻⣿⠋⠁⠀⠰⣦⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⣀⣹⣷⣾⣿⠇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⠛⠋⠉⠀⠀⣴⡞⠙⠛⠋⠙⣿⡄⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡄⠀⣀⣤⣼⣿⠇⢠⣾⣦⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣤⣤⣴⠟⠁⠀⠀⠀⣸⣿⠟⠉⠀⠸⣇⣄⡀⠛⠋⢀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⣈⠉⠀⣀⣀⡤⠶⠞⠛⠋⠉⠀⠀⠀⢤⡿⠿⣿⣦⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠃⠀⣹⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠋⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠿⠿⠿⣿⠿⣿⠿⢿⡟⠛⣿⠛⢻⣏⠉⠉⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⠇⠀⠀⠀⢀⣿⠀⢻⡆⠀⣧⠀⢹⣇⠀⢻⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⠀⠀⠀⢸⡏⠀⠘⣷⠀⢹⡆⠀⢻⡆⠀⢻⡄⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⠀⠀⠀⣸⡇⠀⠀⢻⡆⠀⣿⣤⣬⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⣀⣀⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠈⠙⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⣄⣀⣀⣀⣀⣀⣠⣴⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠉⠉⠉⠉⠉⠉⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⣉⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⡈⣿⣦⡀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⣿⠀ ⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⢸⡄⠉⢨⡇⠀⠀⠀⠀⠀⣰⠟⠈⢳⡘⡞⢧⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠄⢸⠀⠀⣿⠀ ⠀⠀⠀⠀⢸⠈⢳⡄⠀⠀⠀⠀⠀⠙⠴⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⣿⣹⡜⢧⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣷⣦⢸⡄⠀⣿⠀ ⠀⠈⠀⠀⢼⠀⠈⠻⣦⡀⠀⠀⢀⣠⣤⣶⠟⠻⣦⡶⣟⠁⠀⠀⠀⠀⢸⣧⢳⠈⢧⠀⠀⠘⢿⣤⣤⣶⠖⢾⡟⠉⠉⢯⠉⢿⡷⣶⣤⣤⣶⣶⣆⠀⣼⣽⣿⡀⢸⣿⣿⡇⠀⢹⠀ ⠀⠀⢀⡄⢸⠀⠀⡷⠀⠙⣆⠀⢸⠁⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣿⣟⣆⣈⣧⣀⣘⣿⣿⠤⠾⢷⡶⡷⠦⠤⠼⣦⠀⠹⣿⣏⠉⠙⣮⣝⣷⣿⣻⣿⣷⣈⣻⣿⡇⠀⢸⠀ ⠀⠀⠋⠀⠸⡄⢠⡇⠀⠀⢻⡆⠘⡇⠀⠀⣷⠀⠀⠀⣾⡄⠀⢸⡀⠀⠈⢹⣿⣯⠉⠙⣯⠁⠈⢛⡇⠀⠈⢷⡁⢶⡄⠀⠸⡄⠀⠈⠻⣆⠀⢸⣿⣷⣍⠙⣿⣿⣿⣿⣿⡇⠀⢸⡀ ⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⣿⡆⣧⠀⠀⣸⣆⠀⠀⢹⣇⠀⠀⣇⠀⠀⠀⢿⣿⠀⠀⠈⣧⡀⢸⣽⠀⠀⠈⢳⣎⢷⣄⡀⢻⡀⠀⠀⠈⢷⠀⢻⣷⡙⣷⣼⣿⣿⣿⣿⣿⡀⢸⡇ ⠀⠀⠀⠀⠀⢻⣸⣷⠀⠀⠀⠙⢿⣿⣠⠾⠁⢹⣦⠀⠀⣿⡆⠀⢸⡆⠀⠀⠸⣿⡆⠀⠀⠸⣧⠈⣿⡇⠀⠀⠀⢿⡄⢻⣧⠸⡇⠀⠀⠀⠀⢷⡈⢿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠸⣿⣿⠀⢀⣠⣴⣿⣿⠁⠀⠀⠀⢻⣧⠸⢹⣷⠀⢀⣷⠀⠀⠀⣿⣧⠀⠀⠀⢹⡰⣯⣧⣀⢤⣤⣤⣷⣤⣿⣶⣿⠀⠀⠀⠀⠀⢳⡹⣿⣧⣽⣿⣿⠿⠻⣿⣷⢸⡇ ⠀⠀⠀⠀⠀⠀⢳⣿⣾⡏⠁⠀⢹⣿⡆⠀⠀⠀⠀⢻⣦⣱⣿⣷⡈⣿⣧⢠⡰⣼⣿⡀⠀⢀⡼⣷⣿⣿⣿⠿⠿⠿⠿⣿⣿⡛⠿⣿⣶⣤⣀⡀⠈⢷⣿⣿⠶⠟⠁⠀⢀⡈⢿⡌⡇ ⠀⠀⠀⢀⡤⠚⠙⣿⡇⠳⡀⠀⠈⢿⣷⠀⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣻⣼⡇⢻⣿⡇⠀⢀⣴⢿⣿⣿⣥⣤⣤⣶⣯⠬⣽⣷⡀⠀⠈⠛⣿⡛⠛⠛⣿⣿⡇⠀⠀⣰⡟⠙⠈⢿⡇ ⠀⠀⠐⠉⠀⠀⠀⠻⣽⡀⠻⣄⠀⠈⢿⣇⠀⠀⠀⠀⠀⠱⡝⢿⣷⡹⣷⡹⡇⠀⢻⣇⠀⠺⠃⢸⣿⠻⢿⡉⠛⠉⢹⡇⠀⠙⢧⠀⠀⢰⡟⠛⠓⠒⠚⣿⣧⠀⠀⣿⠓⠀⠀⠈⡇ ⡄⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣨⠷⠶⠶⣾⣦⠀⠀⠀⠀⠀⠙⢦⡙⢿⡌⠻⣄⠀⠀⠛⠀⠀⠀⠘⣿⡀⠀⠙⢦⣀⠏⠀⠀⠀⢸⣄⡴⠏⠀⠀⠀⠀⠀⢻⣿⠀⠀⠘⣆⠀⡀⠀⡇ ⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⠀⠙⠂⠈⠓⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠛⠒⠲⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣰⠃⢠⡇⠀⡇ ⠀⠀⠀⠀⠀⣠⣾⡿⣿⡟⠉⠀⢀⣀⣤⠾⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣠⠎⠀⢰⢃ ⠄⠀⠀⢀⣾⡿⠋⢠⡟⠀⣾⡛⠛⠋⢹⡟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡿⠁⠀⠀⡾⠋ ⢰⡀⣤⣿⡿⠁⠀⢸⣇⢰⣿⠓⠢⠔⠋⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⠁⠀⠀⠀⠒⠞ ⠀⣿⣿⣿⡀⠀⠀⠈⣿⣼⠃⢀⣠⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⡇⠀⠀⠀⠀⠀⣁ ⠋⣼⣿⣻⡷⢤⣀⠀⠸⢧⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⡇⢀⣀⠀⠀⠀⠰ ⠀⠀⠸⣿⣷⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠀⠀⠀⠀⢸⢿⢯⣀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠘⠆⠀⢱⣤⡀⠀ ⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣦⠌⠙⠻⣷ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⢒⣲⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⢦⣴⠛⣦⡀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⡤⠤⠖⠛⠉⠀⠀⠀⠈⠉⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠙⣦⡈⠿⣶⣄ ⠠⠤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣤⠟⠀⠈⠳⣤⣌⠛ ⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢠⣄⣱⣄⠀⠀⠀⠀⠉⠙ ⠓⢤⣀⠀⠀⠈⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣠⣄⠈⠀⠀⠀⠄⢀⠜ ⣤⣀⠈⠉⡉⠉⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣠⠞⣿⠁⠀⢀⡼⠳⢬⡳⣄⠀⠀⠀⠂⠀ ⠿⣿⣄⣀⣿⠀⠀⣿⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⠞⠁⠀⣿⠀⣤⣿⠀⠀⡆⠙⢾⣳⣄⡀⠐⠀ ⢀⣿⣿⣿⣿⣀⣀⣼⣦⠀⠙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡴⠋⠀⢠⣦⢻⣿⣿⣿⠟⠛⣧⠀⠀⠉⠛⠻⢦⡀ ⣼⡿⢻⣿⡟⠋⢹⣿⣿⠓⠶⠋⠙⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣤⣤⣤⣤⠖⠋⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⠉⢷⣯⣿⣷⣦⡇⠀⠀⠀⠀⠀⠀⢹ ⠉⢠⣿⡟⠀⢤⣿⣿⡟⠀⠀⢠⡀⠀⣀⣈⠉⠛⠿⣗⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠄⠀⠈⣿⠀⣿⣐⣿⢀⣀⡥⠀⠀⠀⠀⠀⠀⠠ ⣴⣿⠋⣰⣷⡿⣿⣿⡇⠀⠀⢸⣧⠞⠉⠉⠛⠂⠀⠈⢳⡀⠀⠀⠉⠉⠓⠲⡆⢠⣤⣀⣀⠀⠀⠈⡇⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠹⣷⠭⠿⠳⣄⡀⠀⠀⠀⠀⡀ ⠟⣠⣮⡿⢫⡾⣿⣿⠇⠀⠀⣾⠃⠀⠀⢠⡶⢦⣄⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⢉⡀⠀⠈⠉⠉⠉⢻⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⢇⠀⠀⣀⡽⠶⠆⠀⠀⠀ ⡚⠛⢉⣰⣟⣻⣿⡿⠀⢀⡼⣁⣄⠀⠀⢸⡿⠀⢻⣟⡶⠤⢿⣄⠀⠀⠀⢠⣄⣈⣿⣿⡃⠀⠀⠀⢸⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀
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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
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⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣶⣶⣾⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⠛⠉⠁⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠴⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀ ⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣾⡿⠁ ⠀⢙⣿⣿⡟⠛⠛⠛⢿⡟⢿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣿⣙⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⣼⣿⡟⠁⠀ ⠀⠈⠻⣿⣷⡀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⡀⠄⠚⠻⡏⠀⠀⠀ ⠀⠀⠀⠈⠹⠛⠓⠦⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⠤⠀⣀⣀⣀⣀⣀⣀⣀⠠⠔⠒⠉⢀⡰⠁⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⡍⠐⠂⠤⠤⠀⣀⣀⣀⡀⠤⠔⠂⠁⡈⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢱⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧⣿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⣆⠀⢸⢠⠀⠀⢸⠀⠀⠀⠀⠀⡸⠛⠁⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠸⠀⡄⡀⠀⡰⠁⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠁⡰⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠈⣿⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡄⠀⠀⠀⠀⠀⢠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⡀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⣴⡾⠿⣷⣄⡀⢹⣷⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⠟⠋⠀⠀⠈⠙⢿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⢹⣿⠟⡅⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⢨⡻⣿⡎⢿⣆⠀⠀⠀⠀ ⠀⠀⢀⢶⣿⠇⣟⣥⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⣻⠸⣿⡷⣄⠀⠀ ⠀⢠⡟⢸⣿⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣿⡇⢹⡄⠀ ⠀⣾⣷⢸⡿⣋⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣍⢻⡇⣿⣷⠀ ⠀⣿⣿⠘⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⣿⣿⢀ ⣧⠸⣿⣼⡿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣌⠻⣿⣿⠇⣼ ⣿⡆⢹⡟⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠹⡿⢠⣿ ⢻⣿⡄⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢀⣿⡟ ⡌⢿⣷⣾⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣏⢹⣿⣾⡿⢁ ⣷⡌⢻⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⠟⢡⣾ ⠘⣿⣦⡙⠃⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣶⣤⣀⣀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⢫⣴⣿⠃ ⠀⢸⣿⣿⣦⣿⣇⢸⣆⠀⠀⠀⠀⢀⣠⣾⡿⠉⠁⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⡏⢸⣿⣴⣿⠟⡁⠀ ⠀⠈⢧⣉⠻⢿⣿⠀⣿⣆⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠉⠻⣿⣿⡆⠀⠀⠀⣰⣿⠁⣾⡿⠟⣡⡼⠁⠀ ⠀⠀⠈⠻⣷⣤⣙⠃⢹⣿⡖⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⢲⣿⡟⢈⣩⣴⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣦⣿⣿⡌⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢃⣾⣿⣶⣿⡿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣬⣉⣙⣛⠛⠎⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⣁⣚⣛⣉⣩⣤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⣿⣿⡿⠿⠿⠟⢛⣩⣤⣶⡶⠖⣲⣶⢶⣶⡚⠶⣶⣶⣮⣙⡛⠻⠿⠿⠿⠿⠿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣤⣤⣴⣶⣾⣿⡿⠟⣉⣴⠟⠉⠀⠀⠈⠻⢷⣌⡙⠿⣿⣿⣷⣶⣶⣶⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⡦⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀ ⠀⢰⣿⢋⠉⠉⠲⢤⡀⠀⠀⠀⣀⣠⢄⣀⡠⠴⠋⠀⠀⠉⡷⡄⠀⠀ ⠀⠈⣿⣿⡇⠀⠀⠀⣏⡿⠽⣿⠿⠋⠉⠈⠉⠙⢂⣀⠀⠀⢸⡇⠀⠀ ⠀⠀⢿⣍⢧⡄⠂⠀⠀⠀⠀⣠⡴⠒⠊⢀⠐⠒⢢⣌⠉⠁⠈⠧⡀⠀ ⠀⠀⠈⢻⡀⠙⠦⠀⠀⣰⠋⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⢹⡄ ⠀⠀⠀⠀⢱⣦⣤⣀⣼⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿ ⠀⠀⠀⠀⠀⢻⢸⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼ ⠀⠀⠀⠀⠀⠀⡷⣿⡷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⡇ ⠀⠀⠀⠀⠀⣠⠯⢹⠇⠀⠀⠀⠈⠛⠟⠿⠿⠿⠿⠿⠿⠋⠀⠀⡿⠁ ⠀⠀⠀⠀⢰⣓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠀⢀⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⢀⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣙⡛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⢛⣋⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⢀⡾⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠛⠃⠀⠻⠷⢶⣤⣄⡀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⣤⣶⣶⠿⠟⠀⠘⠛⠛⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⠀⠀⠀⠀⢀⣾⢟⣩⣶⣾⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣦⠀⠙⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠋⢀⣼⣿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣷⣦⣌⠻⣷⡀⠀⠀⠀⠀⡄⠀ ⠀⠈⢳⣤⣤⣶⣿⣇⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣹⣿⣦⣤⣴⡞⠀⠀ ⢀⢴⡫⠿⠿⠟⠻⠿⣷⣶⣦⣤⣭⣭⡍⠉⣭⣭⣽⣷⡾⠟⠋⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠙⠿⣷⣾⣯⣭⣭⠉⢛⣯⣭⣭⣥⣶⣾⠿⠿⠿⠿⠿⣟⡦⡀ ⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠃⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡆⢠⡟⠁⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⢻⡄⠰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⢹⣷⣤⣀⡀⠀⠀⢀⣀⣀⣤⣴⣶⡿⠿⠛⠉⠀⢸⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢀⡇⠀⠈⠛⠿⢿⣶⣤⣄⣀⣀⡀⢀⣀⣀⣠⣴⣾⠃⠀ ⠀⠀⢿⣿⣿⠛⣿⣿⣿⡛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣦⣌⠻⣷⣤⣀⣀⣀⣠⣤⣾⠟⣠⣴⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⣿⣿⣿⠛⣿⣿⡟⠀⠀ ⠀⠀⠈⢿⣿⣧⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣤⣤⣍⣉⡛⢛⣋⣩⣥⣤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⣼⣿⣿⠁⠀⠀ ⠀⠀⠀⠈⣿⣿⣆⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⣸⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣦⠀⠹⣿⣿⣿⣦⣀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⠟⠁⠈⠻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣀⣀⣀⣀⣴⣿⣿⣿⠏⠀⣴⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢀⡴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠈⠉⠒⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⠉⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⣿⢻⣿⠿⣿⣿⣿⣿⣟⣙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣴⡾⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡏⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣾⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⢿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢧⡴⠶⢤⣤⠀⠀⣠⡴⣶⠿⢶⡆⠀⠀⢸⡞⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⠰⠿⢻⣿⠀⠀⢻⣿⠾⣿⠶⡅⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠛⢁⠀⠀⠀⣉⠙⠒⠋⠀⠀⠀⠀⠻⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠧⢠⡤⠠⡹⣷⡀⠀⠀⠀⠀⠀⣹⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠔⣡⣶⣾⣿⣷⣷⣾⡻⠀⠀⠀⠀⠀⢡⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⣠⣾⣿⡿⠿⠿⢿⣿⣿⣿⣦⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⠁⠀⠸⠿⠿⠇⠈⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⡛⠛⠻⣿⣿⠖⠈⠁⠀⢀⣾⣷⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣴⣺⣿⣿⣿⣿⣿⣿⣢⢀⠸⢿⡄⠀⢀⣠⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀ ⠺⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣢⣧⣰⣿⣿⣿⢯⣻⢿⣿⣿⣿⣿⣿⠗ ⠀⠀⠙⠿⢿⣿⣿⣿⡿⣠⣸⣟⣿⣿⣿⠎⣿⣿⣿⣿⣿⣸⣬⡇⣿⣿⡿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣾⡿⢋⣾⡛⣿⣿⣿⡇⣿⣿⡇⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠔⡓⠊⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡲⠤⠔⣡⡤⠄⠈⣁⣀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠊⢀⡤⠀⠱⢦⡤⣀⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⢼⡀⠐⠶⠬⠵⠂⠀⡀⢀⡇⠀⡸⠙⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠺⠸⢻⡈⠢⢄⡀⠀⣀⠔⣠⠞⠺⢣⢡⠀⠀⠀⠑⣄⠀⠀ ⠀⠀⡜⠀⢠⢰⣇⠙⠦⡀⠠⢀⣶⡓⠁⠀⠈⠀⢸⠀⠀⠀⠀⠀⠢⠀ ⠀⡜⠀⠀⠈⡇⢀⠀⡈⡟⠛⠃⢃⠤⠰⠦⠀⠠⠤⠲⣤⣜⠄⠀⠀⡇ ⢰⠀⠀⠡⢰⣧⠽⠒⠒⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⢰⣻⠀⠀⠀⠀⡇ ⠘⡀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠰⠀ ⠀⠑⠄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠉⠐⠒⡇⠀ ⠀⠀⠈⠢⡎⢸⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⣆⣀⣀⡀⠇⠀ ⠀⠀⠀⠀⠈⠛⠀⠙⠻⠶⠶⣶⡶⠶⠿⠛⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡔⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠉⡗⠒⠂⠀⠐⢲⠋⠉⠀⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⢱⠀⠀⠀⠀⠀⠂⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢁⠀⠀⠎⠀⠀⠀⠀⠀⢆⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣤⣤⡆⠀⠀⠀⠀⠀⢸⣀⣤⣼⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠒⠁⠀⠀⣀⡱⠀⠀⠀⠀⠀⢠⠋⠋⠁⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠤⠔⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠤⠴⠶⠒⠋⠉⠁⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣓⢤⣤⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣿⡿⠟⢛⣛⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡍⢿⡯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⢰⣾⢸⡈⣆⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⡇⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠛⢧⢈⣧⣧⣷⠿⣎⣿⡘⣿⣿⣿⡿⠛⡻⣿⣿⣿⣿⣿⣿⣧⠰⠥⠴⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠳⣦⠘⡞⡎⠛⢢⡄⢹⣸⣇⡿⠛⢉⣵⣶⣷⣿⣿⣿⣿⣿⡻⣝⡛⢿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡄⣹⡇⣣⠹⣸⣿⠿⢾⠉⣀⣤⣖⣋⣾⣷⣾⣿⣿⣿⠻⣝⣎⡐⡄⣁⢱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠥⠿⢷⠛⣋⣩⣤⠶⣾⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣷⢸⡻⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣉⣉⣏⣉⣉⣉⣏⣉⣭⣤⠴⠶⠞⠛⠋⣉⣤⠾⣫⣴⣿⣟⣛⡧⣦⣽⣿⣿⣿⠋⣿⣿⣿⣿⣿⣀⠳⣤⠆⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣶⡾⣋⣷⣿⣏⣻⣷⠿⣗⣲⡾⣿⣿⣿⡇⣸⣿⣿⢹⣿⣷⠺⢍⠭⠟⠉⠀⠀⢀ ⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣾⣿⣿⣫⣷⣾⣿⡷⡿⡿⢿⣋⡏⣀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣾⢿⠻⣷⠈⡇⠀⠀⡠⠒⢉ ⠀⠀⣠⠎⠀⠀⠀⠈⠙⠛⠛⠛⠛⣛⣻⡿⢿⣿⣿⡿⠛⣺⣯⣾⣛⣧⠤⠞⠊⠁⠀⢸⣿⣿⣿⣿⣾⠿⡟⣿⣌⣧⣹⡧⠜⣦⠞⢀⣴⣾ ⣠⠾⠁⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⣋⣵⣾⣿⣿⣿⠟⢿⡟⠁⠀⠙⢏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣠⡾⣿⣿⣿⣿⣷⣘⡏⣰⣿⣿⣿ ⠋⢀⣀⣤⣴⠶⠟⢛⣋⡭⠴⠚⠋⢻⣿⣿⣿⠿⠿⡆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣾⣿⣧⣿⠀⣶⣶⣶⣾⣿⣿⣿⣿⣿ ⠚⢛⣉⣩⡴⠶⠚⠋⠉⠀⠀⠀⠀⠸⡿⡏⠁⠀⢰⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣏⣉⣁⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⠤⢷⢱⠀⠀⠸⢤⣤⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡿⠋⢁⣴ ⡇⠀⢦⣬⣭⣭⣍⣍⣀⣀⣤⣤⣤⠶⠞⢣⡀⠀⠀⠀⠈⢉⠠⣀⣀⣀⡀⠀⠀⠀⠀⢀⣿⣿⡟⣽⣿⣿⣿⣿⡇⢸⣿⣿⡿⠃⠀⣴⣿⣿ ⣧⠀⢸⣿⣩⣉⣉⣉⣩⠭⢭⣥⣴⣶⣾⣿⣷⡄⠀⠀⡼⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⣸⡿⢋⣼⠋⣿⣿⣿⣿⣷⠀⣿⣿⠃⠀⢸⣿⣿⡏ ⣿⠀⢸⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢢⣤⣶⣶⣶⣶⠎⠀⠀⢸⢏⣴⣿⡏⠀⣿⣿⡏⠀⠘⡄⣿⣿⠀⠀⣿⣿⣿⣿ ⣿⡄⠘⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠀⠀⠉⠉⠉⠉⠁⠀⠀⢠⣿⣿⠿⣿⠁⠀⣿⣿⣧⠀⠀⣧⢸⣿⠀⠀⣿⣿⣿⣿ ⣿⡇⠀⡿⠿⠮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⡏⠀⠀⢻⣿⣿⡄⠀⣿⣼⣿⡆⠀⢻⣿⣿⣄ ⣿⣇⠀⢳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣷⣤⣤⣤⣴⣶⡿⠋⠁⠀⠀⡜⠀⠀⠀⠸⣿⣿⣿⣦⡏⣿⣿⠙⣄⠀⢻⣿⣿ ⣿⣿⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⠙⠿⣿⠿⠋⠀⠀⠀⠀⡜⠀⣠⠀⠀⠀⠟⠛⠻⠿⠿⣿⠇⠀⣾⣦⣀⢹⣿ ⣿⣿⠀⢸⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠘⡆⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡟⠀⢠⣶⣶⣶⣶⣾⣿⣿⠀⠀⣿⣿⣿⣿⣽ ⠛⠉⠀⠉⠉⣉⣽⣿⣿⣿⠿⢿⣿⣿⡿⠁⠀⢀⣰⠁⠀⢸⠏⢻⣿⠆⠀⠀⡠⠊⠀⠀⢀⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣠⠟⠉⢉⣿⣿ ⢀⣤⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠈⠛⠷⠤⠤⣀⡀⠀⠀⣸⠀⠀⠁⢀⠴⠊⠀⢀⣀⡤⠞⡄⢀⣿⣿⣿⡫⣵⣿⣿⡿⠋⠀⢀⣴⣿⣿⠟ ⣿⣿⣿⣿⣿⣋⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠁⢀⡠⠴⠧⠤⠄⠊⠉⠁⢀⡰⠁⠘⣡⡟⣩⣿⣿⣿⣿⠁⠀⣰⣿⡿⠋⠁⠀ ⣿⣿⣿⣟⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⡰⠋⠀⠀⠀⠀⠀⠀⠠⣴⣿⠃⠀⣴⣿⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣇⠀⢀⣴ ⣿⣿⡟⣾⣯⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠜⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⡇⣿⣿⣿⣯ ⣿⣿⢡⣿⣿⢦⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⣧⢻⣿⠟⠿ ⣿⢇⣾⡏⠹⡀⢣⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠏⢣⡀⠈⢿⣿⣿⡄⠀ ⡏⣼⣿⡇⠀⢣⠀⠣⠈⢫⡢⢄⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣷⣄⡀⠙⣿⣧⡀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣧⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⠿⢋⢧⡀⠀⠀⣰⡟⣡⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢶⣽⣦⣴⠏⣸⠛⡉⠙⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⣀⣽⡀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣰⣿⢀⣚⣛⣻⣶⣿⣷⣄⠀⣀⣤⣤⣾⣿⠿⢿⣀⣠⠴⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠉⠻⢿⣼⣿⣇⣹⣿⠟⠋⠉⢻⣿⣿⣿⡿⣄⠀⢈⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⢉⣩⠙⠆⠀⠀⠀⠀⠙⠿⢽⣓⡛⠑⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⣾⣶⣶⣶⣿⣯⣴⣷⣄⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢤⠶⢾⡿⣿⣄⠀⠈⠉⠙⠻⠿⢿⣶⠶⠶⠛⠛⠿⣦⣄⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⢀⣀⣴⣿⡇⢸⠀⢸⡇⠸⣯⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠻⣿⣿⣿⣿⣿⣧⠸⣄⢀⣿⠛⠛⢷⡝⠲⢤⡈⠉⠑⠒⠒⠒⠒⠒⠛⠉⠘⠃⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣧⠙⠚⣿⡆⠀⠈⢷⡐⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣴⣿⠇⠀⠀⢸⣇⣀⣀⡴⠂⠉⠀⠠⣄⠈⡆⠀⢀⣴⣿⣿⣿⣿⣿⠛⠁⠀⠈⠁ ⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⣀⣬⠿⠁⢠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣹⣿⣿⣏⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠟⠋⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣀⣀⠀⢀⡰⠞⠛⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣤⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⢀⡠⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠖⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣶⡟⠛⠛⠿⠿⠿⠿⠖⠒⠛⠓⠦⣄⡀ ⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠐⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⣶⡾⠿⠟⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⣠⡄⢢⣰⡜⠿⣿⠁⠉⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⡾⣟⣿⡶⣌⡞⠀⠀⠀⠀⢸⣿⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⣴⣻⣿ ⠯⠯⠀⠀⠀⠀⠀⠀⣀⣾⣧⡀⠈⠙⠦⣄⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡄⠀⠘⣦⠀⠀⠀⠀⠀⢀⣨⠀⠀⠀⠀⠸⠿⡏ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠻⣿⡶⣄⡀⠈⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⡄⠀⢸⣧⠀⠀⣠⡴⣋⠀⠀⠀⠀⠀⠀⢰⣇ ⣿⠁⠀⠀⣀⣀⣀⠀⠙⢦⣄⠀⠙⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣄⡘⡟⣯⠉⢻⡍⢠⠀⠀⠀⠀⠀⠀⢠⣿ ⡏⠀⠀⠀⠈⢩⣿⠀⠀⠀⠈⠳⢦⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⢻⡏⢳⣧⠘⣆⠸⣿⡌⣧⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢘⣿⢈⣿⣤⣽⣄⣻⢻⣼⣧⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⠀⡏⠀⢹⣿⢸⠀⣻⢽⡆⠀⠀⠀⠀⢸ ⡅⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⣼⠃⣠⡜⣿⣼⣦⣼⡈⣿⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⢸⡇⢈⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢻⡇⢠⣿⠏⣼⣿⣿⣿⣿⣏⠉⠻⣿⠀⠀⠀⠀⠨ ⣿⠀⠀⠀⠀⡄⠀⢸⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣥⣭⣉⡙⢳⡄⠀⠈⠀⠈⠛⠀⣾⣿⣿⣿⣋⡉⠀⠀⣿⠀⠀⠀⠀⡀ ⡇⠀⠀⠀⢠⠇⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣿⠷⠈⠙⡟⠁⠀⠀⠀⠀⠀⠀⠛⢧⣩⣭⣿⣃⣠⠾⣿⠀⠀⠈⠀⡇ ⠁⠀⠀⠀⣾⡄⣤⡿⠛⠛⢿⣿⡆⠀⣀⣀⣨⡿⠋⣿⡿⢻⣿⡿⢥⣤⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠋⠁⠀⣠⣤⣀⢤⣿⠀⠀⡀⠀⡇ ⠀⠀⠀⢰⣿⣷⣿⠁⢰⠛⢄⠙⢧⡀⠈⠉⠙⠧⡀⠘⢷⣤⠤⠖⠛⠉⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⢪⠙⣿⣿⠀⠀⡇⢀⠗ ⠀⠀⣠⣾⢏⣿⣟⠉⢻⠤⠬⣧⠀⢳⡄⠀⠀⠀⠈⢑⣫⣄⡀⠤⣈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⡇⢰⠀ ⠀⠀⣿⡏⢸⣿⣿⡀⠸⡆⡏⢻⡀⠀⠇⠀⠀⠀⠈⠳⢌⡙⠻⣶⣬⡑⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⢸⣿⠀⢸⠁⠈⠀ ⠠⣼⡿⣶⣾⣿⣿⣷⣶⠛⠧⣀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠂⠀⠁⠈⣦⡀⠀⠀⠀⠀⣀⡠⠤⠐⠊⠁⡏⠀⠀⠀⠀⣾⡏⠀⢸⠀⢀⠟ ⣴⣿⣿⢿⣿⣿⣿⣿⣿⣷⣦⣈⠉⠉⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠩⣉⡉⠉⠀⠀⠀⠀⣀⠴⠁⠀⠀⢀⣼⣿⡇⠀⡞⠀⠈⠀ ⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠉⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠤⠴⠒⠊⠁⠀⠀⠀⣰⣿⣿⣿⡇⠀⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀ ⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣦⣤⣄⣀⣀⣀⣠⣾⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣟⣁⣬⠟⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⡿⣼⠟⢻⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡍⠀⠀⠀⠀⠵⢤⣄⣀⣀⡠⠤⠴⠒⠋⣹⡁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⠋⠀⢸⣿⣿⡇⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⡿⣷⡄⠀⠀⠈⢻⠿⠿⠿⠟⠋⠘⡀⠀⢸⣿⣿⣇⣿⠀⢀⣠⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠸⣧⠙⣷⠀⢠⠢⠀⢣⡀⠀⠀⠀⠀⢇⠀⢸⣿⣿⣿⣿⠞⠉⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡖⠤⣀⡀⡏⢦⠀⡠⠐⢡⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⣹⠀⠀⠙⠃⠈⠉⠀⠀⠘⠂⠉⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢉⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠞⠉⠀⠀⢀⣴⡶⠟⠛⠻⣷⡀⢠⡐⡀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⡋⠀⠀⠀⠀⣴⠟⠱⡀⠀⠀⢀⣸⡿⠦⣿⣾⣦⠰⡀⠁⠀⠀⠀⠀⡠⠢⣀⣠⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⡹⠂⠀⢠⠅⠀⠸⣀⠴⢊⠋⠀⣀⠀⠀⠈⠛⠗⡱⣤⣤⣤⣤⣴⡇⠀⠘⣿⡿⠟⠛⠉⠁⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡜⠁⡀⠀⢸⣆⣀⡜⠁⠀⠀⠀⠈⠀⠀⠀⠈⠉⣸⠃⠏⠛⠛⠛⠛⡇⠀⠀⢰⠀⠀⠀⠀⣠⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣦⢸⣿⠃⠔⣥⡀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠃⠀⠀⠘⢀⣠⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠻⠻⢄⠀⠉⠀⠀⠀⠀⠠⠂⠀⡆⠀⠀⢋⠰⣦⣤⣤⣤⡄⠀⠀⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠀⠀⠀⣀⠁⡠⠐⠈⠀⠀⠀⢨⣿⡏⠉⢙⢫⢽⠀⠀⠀⢷⣶⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⡀⠀⠁⠐⠉⠀⠀⣠⣴⣿⣿⣷⣎⡡⠒⣳⠀⠀⠀⠸⠛⠉⠉⢻⠟⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠀⠀⠀⠘⡄⠀⠀⢃⠉⠢⢄⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⡶⠶⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠑⢇⠀⠀⠀⠐⡀⠀⠈⠆⠀⠀⣸⣿⠿⠛⠛⠛⠉⠉⣉⡤⠖⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣀⣀⣈⡆⠀⠀⠀⡅⠀⠀⡸⠀⢰⣿⣿⣧⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡀⠀⠉⠉⣙⠫⠭⠭⠭⢤⠒⣴⢒⢾⠉⠈⡈⡇⠀⠀⢀⠁⠀⣰⡁⣰⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡤⠒⠉⠐⠆⠀⣠⠄⠀⡏⡠⠿⠜⠒⠃⠹⡀⢀⡠⠆⡀⠔⠁⣨⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠈⠉⠉⣉⣀⡤⠒⢍⡁⠀⠀⠀⠀⠀⠁⢈⣨⣥⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⠟⣠⠊⠀⠹⣶⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣿⣿⣿⡇⣿⣿⣿⡿⠋⠀⡔⠁⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⢹⣿⣷⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣸⣿⢧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⡏⣾⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⢷⣿⣿⣿⡇⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⣿⢸⣿⣿⣿⣇⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠛⠶⣾⣿⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠾⠿⠿⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⠤⣾⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣀⠀⣀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆ ⣼⣿⣿⣿⣿⣧⣤⣿⠿⠉⠿⠿⠿⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢩⣿⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⢹⠟⠉⠀⠀ ⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣴⣿⡈⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠁⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠛⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠿⠟⠋⠁⢸⡿⠿⠋⠀⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠉⠉⠉⠛⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣶⣶⣶⣤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀ ⠀⠀⢀⣼⣿⠛⢿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢠⡟⠁⠀⠀⠹⣇ ⠀⢀⣾⣿⠃⠀⢘⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡇⠀⣏⡱⠀⣿ ⠀⢸⣿⣿⠀⠀⣸⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠀⠀⠀⢠⠏ ⠀⢸⣿⣿⣷⣶⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡤⠀⣀⡀⠘⣆ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⢅⡔⠀⡿ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⢷⣄⣀⣠⡼⠃ ⠀⣀⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⠿⣿⡟⠀⠀⠀⠀⠙⠛⠉⠀⠀ ⣸⠏⠀⠀⠈⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠶⠶⠶⠶⠶⠶⠞⠛⠳⣦⣤⣤⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢲⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⡑⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣆⠙⢦⡄ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢀⡤⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⢦⠈⢧⣸⠀ ⠀⠀⠀⠀⠀⢀⣴⣏⣀⠀⠀⠀⠀⣠⡟⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣄⠀⠀⠙⣄⠀⠀⡀⢷⡀⣿⠁ ⠀⠀⣾⡉⣹⣿⣿⣿⣯⣷⡄⠀⣾⡟⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⢧⠈⢳⡘⣦⡀⠘⢮⣿⡇⠀ ⠀⣤⡙⣵⣾⣿⣿⣟⣿⣿⣿⣾⣿⠅⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢳⠘⣶⠒⠳⡜⣷⡄⠈⢿⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⡄⠀⢠⠈⡆⠸⡄⠀⢱⡝⣿⠀⢘⠀⠀ ⠀⠹⣽⣿⡿⢿⣿⣿⣿⣷⣿⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢳⠀⠈⡇⢱⠀⣷⠤⠒⢿⠘⡇⠀⡆⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣧⠘⡄⠀⢸⢸⣶⡿⠀⡠⢸⣇⡇⠀⣧⠀ ⠈⣿⣿⣿⢿⣿⣿⣿⣿⠣⡙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢘⣟⡄⣇⠀⠘⣿⡟⠁⠀⣠⣾⣿⣿⣶⣿⠀ ⠀⠧⡹⣿⡿⣿⢿⣿⡻⠀⠈⣽⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⢠⡀⠀⢀⡧⠞⢉⣇⡇⢸⢀⡸⠋⠀⠀⣼⣿⣷⠈⡿⣿⠿⡄ ⠀⠀⠘⠻⣷⣏⠟⠮⠉⡀⠀⢹⣿⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⡆⠘⣷⡖⠋⢱⠚⠉⣿⣇⡼⠋⠀⠀⠀⢸⣿⣿⣛⠀⠃⣏⣠⡿ ⠀⠀⠀⢀⣿⠀⠀⠀⠀⢣⠀⠈⣿⣧⣇⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣷⠞⢻⡀⠀⠈⣦⡴⠳⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⣿⣿⠃ ⠀⠀⢠⣿⡿⣇⠀⠀⠀⠀⠆⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⡄⠀⣠⠞⠙⡆⠀⢿⣀⣴⣋⣤⣒⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢸⠟⠀ ⢀⡴⣿⡿⠁⣿⣾⡍⡏⠑⠒⣦⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡀⠁⠀⠀⠹⣄⣸⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀ ⠊⣸⡿⢁⣾⠿⣿⣷⠃⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣷⡀⠀⢀⣴⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠ ⡼⢋⡴⠟⠉⠀⣿⡿⠀⠀⢀⣿⣿⣿⣿⣿⠿⢧⡀⠀⠀⠀⠀⢹⡳⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏ ⠞⠉⠀⠀⠀⢴⣿⠇⡄⠀⢸⣿⣿⣿⣿⣿⡄⠚⠳⡄⠀⠀⠀⠀⢷⣿⡏⢧⣟⠛⣻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇ ⠀⠀⠀⢀⣤⠟⣻⠀⡇⠀⢸⢹⣿⡏⢻⣿⣿⣄⠀⠈⠢⡀⠀⠀⠀⠳⡉⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣴⣿⡇⣿⡇ ⣠⡴⠞⠋⠁⢠⠇⢰⠇⠀⡌⣸⣿⡇⢸⣿⣿⣿⣿⣦⣤⣼⣦⡀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠀⢀⣾⣿⣿⡇⠸⣷ ⠀⠀⠀⠀⢀⠎⢀⣾⠀⣀⣷⣿⣿⠀⣸⣿⣿⣿⡿⠿⣻⡇⠘⠙⢦⡀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠋⠙⣿⣿⣇⠀⢻ ⠀⠀⠀⢠⠎⠀⣼⡇⠀⡏⠀⠈⠉⠉⠛⠋⠀⠀⢠⠞⠙⡇⠀⢣⠀⠙⢦⡀⠀⠙⣟⠒⠲⠤⣤⣤⣤⣀⣀⣀⣀⡼⠓⣄⠀⠘⡏⢿⡀⠀ ⠀⠀⣠⠋⠀⣼⡿⠀⠀⣸⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡇⠀⠀⠑⠤⡀⠙⢤⠀⠈⠣⡀⠀⠀⢙⣟⠀⠀⠀⠀⢸⠀⠈⢆⠀⢹⡘⣷⡀ ⣀⡔⠁⣠⣾⣿⠇⠀⢠⣿⣧⡤⠤⠒⣶⡿⠃⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠉⠐⠓⢤⡄⠈⠲⠤⠚⢻⣤⣄⣀⡀⠀⡇⠀⠈⡀⠀⢧⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣟⣋⣩⣩⣤⣄⣀⣀⣀⣉⣉⠙⠛⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠭⢿⣲⣤⣄⣀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⢽⣲⣄⡀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⡄⠀⠈⠑⠿⡲⣄⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⡳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣣⡀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣵⡀⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⢸⠀⠀⠀ ⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠎⢈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⡧⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠟⠉⢿⣆⠘⢧⡹⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠇⠀⢸⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⠟⠃⠀⠀⠀⠀⠹⣧⡄⢽⢮⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢳⣄⣷⣝⠪⣝⣆⠀⠀⠀⠀⠀⢀⣴⣏⣼⠁⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⢤⣤⣽⣷⣛⣷⣌⠙⢷⣤⣤⣤⣾⡽⠛⠉⠁⠀⣀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢈⢽⣿⣋⠉⢿⣮⣻⢷⡂⠙⢆⠀⠀⠀⢀⢠⠀⣩⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢥⣠⣔⡿⠛⠛⠷⠧⠤⣿⣿⣷⣝⠳⠬⣳⣤⣖⡾⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡞⠓⠦⣤⣿⣿⣭⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⢷⣝⢳⣄⠀⠹⣦⡀⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠿⣼⣦⣴⣿⠿⠛⠛⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⠛⠊⠛⠳⣧⣀⣘⡽⢦⡄⠀⠀⠀⠀ ⠀⣿⣿⠀⠘⣿⡞⢊⠠⢾⣇⡄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⣶⡄⠙⢺⡿⢀⡘⣿⠀⠀⠀⠀ ⡾⡍⠙⢾⡀⠈⣹⡳⣾⣿⣿⡿⡄⠀⢸⢧⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⣻⡋⠹⣿⡉⠀⣠⠾⠛⣷⠀⠀⠀ ⣻⢯⡦⡀⠙⣿⣧⣿⣿⡟⠯⠀⠀⠀⠘⢸⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣸⣿⣷⣤⣷⢥⠞⡁⡠⣤⣿⡀⠀⠀ ⡇⢀⣙⠺⣾⣽⣿⡿⡿⣇⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠠⠿⣿⣟⢳⣄⡽⠟⠉⣉⣿⠀⠀ ⣽⣷⣿⣄⣿⣿⣿⡟⠀⢹⠀⠀⠀⠀⠀⢨⣧⡀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⢺⠋⡿⣦⣯⣂⣴⣮⣟⣧⡀⠀ ⠹⣿⣿⣿⣿⣿⢏⠀⡀⠀⠀⠀⠀⠀⠐⠻⠍⠳⡄⠀⠀⢠⡾⠾⡀⠀⠀⠀⠋⠀⠀⠈⠻⡄⠹⣥⡹⣿⠹⣆ ⠀⠈⠉⠛⠋⠉⠓⠾⠤⣤⣶⡃⠀⠀⠀⠀⠀⠀⠘⢦⣠⠏⠀⠀⠸⣷⣄⡀⠀⡠⠲⣀⡴⠛⢧⠹⠜⢾⣷⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡁⢀⣀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢛⡷⠛⠁⠀⠀⠀⠳⠖⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢐⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠃⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢰⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣞⣩⣶⣾⣷⣤⣤⣤⣷⣤⣀⠀⠀⠀⠘⣿⣿⠋⠉⠈⠉⠉⢨⣿⣿⣿⣿⣿⣿⡆⢨⣤ ⢻⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⢀⡄⢀⣀⣀⣤⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠛⢀⣐⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⠀⠈⡟⣹⣿⣿⡅⠀⠀⠀⠀⢰⣿⣿⣿⣽⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿ ⠀⣼⡇⢿⣿⣿⣇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⠿ ⣤⣿⡇⠘⣿⣿⣿⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⣿⡿⠁⢠⣿⣿⣿⣷⣿⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠀⠀⠀ ⢋⣤⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⠙⠻⣿⣿⣦⠙⢿⣋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣐⣚⣛⣿⣿ ⣟⠀⢰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣌⠀⠀⠹⣧⡙⣷⡀⠉⠳⢬⣻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠋⢻⡇⠀⠁⠙⠈⠙⢄⣤⣴⣟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⡀⠀⢠⣿⠿⣿⣿⡍⢶⣿⡟⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣵⣿⠟⠿⠟⢿⣿⡖⠘⣇⠢⠬⠋⢁⡜⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣟⠋⠁⠀⣸⣿⣷⠀⠈⠓⠂⠒⠉⠀⣏⠁⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠡⡀⠀⠈⠓⠒⠉⢀⣿⢿⡀⠀⣀⠀⠀⠀⢰⡿⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⣿⣿⣿⣿⣿⡆⢰⣀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⡀⠀⢸⠃⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣩⠿⠛⠉⠀⠀⢀⡠⠀⠀⠈⠻⣿⣿⣿⣷⣼⣿⣦⣤⡀⠀⠠⠤⠴⠶⠒⠊⠉⠀⢠⣏⠀⠀⠀⠈⢛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠁⠀⣠⡤⠶⠛⠒⠀⠀⠐⠦⢄⡘⡆⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡇⢹⣤⣀⠀⠀⠈⠻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⢠⡎⠁⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠾⢠⠀⣿⣿⣿⢿⣿⣿⣷⣦⣀⣀⣀⡠⢤⡞⠀⣸⣿⣿⡍⠹⠶⠿⠿⣤⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣿⣤⣤⠴⠶⠾⠿⠿⠷⠒⠒⢚⣿⣿⠀⠙⠻⣧⡀⠘⠉⠉⠈⠉⠉⠀⣠⠏⠀⢠⣿⣿⣿⣷⣦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⡿⠟⠛⢐⣂⣀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣧⠀⠀⠀⠉⠢⣀⠀⠀⠀⣤⣾⢏⣼⣷⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⣾⣦⡀⠈⠙⠲⣾⠟⢋⣼⣿⣿⣿⣿⣿⣿⣿⣧⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⢿⣿⣿⣿⣾⣁⣴⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⢻⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡄⠀⠈⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⡟⠀⠀⢀⡀⠀⢀⣴⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⣿⡇⡠⠒⢉⣽⢛⡋⣡⣴⣶⣷⣦⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢋⡴⠒⠒⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣇⣠⣾⣿⢷⣸⡀⠛⠋⠙⠛⠿⣿⣿⣿⣿⣿⣷⠤⣀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠈⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⠁⠀⠉⠃⠀⠀⠀⠀⢀⣤⣄⣀⠀⣀⣽⣾⡭⠄⠀⠀⠀⠀⠸⠿⡿⠃⠀⠀⣸⠙⠒⠀⣶⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠟⠉⠉⢓⣦⣧⠀⢸⡀⠀⣿⠛⠋⠉⣉⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⣿⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⣠⣶⠟⠛⢛⣿⡆⠀⠀⠀⠈⠓⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠖⠋⠁⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⡦⠤⠒⡻⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠁⢀⡞⢀⠏⠀⠀⠀⠀⠴⠲⣞⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⡜⢠⣾⡀⠀⠀⣀⠤⠤⠤⠏⠀⠀⠈⠳⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠠⣧⠜⠻⠟⠀⠈⠁⠀⠀⣀⣀⣀⣀⡀⠀⠘⡆⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⣇⠀⠀⣀⡴⠒⣊⣯⣿⣿⡿⠿⠿⢿⢿⣦⣽⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢣⠘⢆⠸⣿⣿⡛⡏⢫⣨⣤⣷⣾⣿⣿⣿⡿⠘⢻⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠙⣿⣟⢿⣿⣿⠿⢿⣫⡿⠟⢋⡼⠁⠀⣼⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⢿⠳⣌⣉⣁⣀⠤⠤⠒⠋⠀⠀⢠⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠇⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣀⡠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⡄⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠈⠒⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀
⣿⢿⣿⡿⢿⠟⣟⠫⣟⢿⡿⣟⠻⢿⠿⡿⠿⠿⣛⠛⠻⢟⠻⡛⢿⣿⣟⡻⢻⣿⣿⠿⣛⡛⣟⡿⣿⣿⣿⢟⣝⡾⣹⢏⣯⡝⣯⣻⡭⢷ ⢎⡳⣌⠳⣌⢫⡔⣣⠜⡢⠱⣭⢛⠬⡓⠥⢃⠒⠠⢈⠐⠌⠠⠈⠄⠚⢿⣵⢃⡴⢌⢳⣡⢛⡾⣷⣿⠿⣿⡾⣹⢞⣭⢟⣶⣻⢷⢫⠓⣿ ⢏⠶⣩⠷⣌⠳⡜⡡⢎⠱⣡⠢⢌⠢⠑⡌⢠⠈⡐⠂⠀⠄⡁⠌⢀⠢⠠⠙⣎⠲⣍⠖⣻⣷⣼⣶⠏⡞⡽⢳⣽⣚⢧⣛⠶⣉⢦⢇⡇⡿ ⠊⢇⢃⠓⣌⠓⡌⠱⣈⠒⠄⢃⠄⢃⠡⠐⡀⠂⠀⠄⠁⠐⠀⠐⠀⢂⠑⡈⡐⢫⠤⡉⢒⢿⣿⡟⡸⢌⣳⣏⢶⢫⢗⣯⢾⡱⡞⢮⡑⣿ ⢣⠜⣀⠇⡘⠼⡀⢇⡀⢛⡘⠄⡘⠀⠄⢃⠠⢀⠃⠄⠘⡀⢃⠘⠠⠀⢄⠠⡀⠇⠄⢃⠘⡸⣿⢇⠣⡘⣿⣿⡜⢧⡜⡸⢟⡧⢿⡄⡇⣧ ⠌⠚⠤⢩⢐⠣⡉⠆⡜⢠⠂⡅⢂⠡⠊⡀⠂⠄⢂⠈⠄⠀⠠⠈⢄⠡⢂⠡⡘⠠⠌⡀⢂⠐⡁⠊⠄⠱⢸⢿⣿⣣⢎⡱⢋⠞⣧⣛⡖⣷ ⡘⠰⡁⠆⡌⢢⠑⡌⡰⢡⠘⣀⠂⡄⠡⢀⡁⠂⠄⡈⠄⡁⢂⠁⠢⠌⢄⠃⡌⡁⠆⡐⢀⠂⡄⠃⡌⢢⠑⡺⣿⣿⡧⣘⠡⢊⡔⣣⢗⣻ ⠠⡑⢌⠒⡌⢢⣱⣤⣷⣦⣷⣦⣷⣬⣣⡒⢬⡑⢎⡔⢢⢁⠆⡌⠱⣈⠢⢑⠰⠐⡌⢐⠂⠔⠠⢡⠐⢬⡘⣱⣽⣿⠗⡬⢌⠳⢎⡱⢋⣽ ⢠⠑⣌⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡚⡥⢊⡅⡊⠔⡈⠥⢀⠢⠁⢎⠡⡘⠠⠌⢂⡑⢢⡙⢦⡱⢣⡟⣼⣙⠶⣉⢞⡰⣡⣃⣿ ⣢⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⠣⠐⡁⠎⠐⠠⢁⠂⢡⠈⠤⣁⠣⠘⡄⢪⡑⣎⢧⣝⣳⣽⣶⣿⣿⣿⣿⣿⣷⣧⣿ ⢿⣿⣻⣿⣿⣏⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠅⡐⠈⠄⠁⠂⡈⠄⠨⢀⠄⢂⠱⢌⢣⠹⡜⢾⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢂⠠⢀⠀⠂⠁⠀⠠⠁⠀⠐⠈⠒⠌⢢⠣⡙⢦⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣻ ⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣉⠀⡀⠀⢀⠀⠀⠈⠀⠀⠰⠈⠀⠁⠎⡀⢁⠱⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠔⡡⢈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠟⡛⢃⠀⠄⠀⡀⢀⠀⡀⢂⠐⡀⢂⠁⡀⠄⣀⠂⡜⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻ ⢧⣑⠧⡚⡴⢤⣉⡙⡛⡛⢛⠛⠛⠛⠉⠁⠀⡈⠄⣀⠀⡈⠀⠀⠐⠀⡀⢐⠠⣒⣼⣶⣻⣿⣶⣵⣮⡔⢡⠊⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠩⢌⠣⡑⡌⠒⠄⢉⠀⠈⣀⣤⣷⣦⡄⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠺⣷⣦⣽⣿⣿⣼⡵⣎⣷⣽⣿⣿⣦⣅⢂⠉⡙⠿⠻⠿⢿⣿⣿⣻ ⢁⠎⡖⡩⠝⡄⠈⡀⣤⡿⡛⣍⠲⣸⣿⠀⠀⠈⠀⡀⠐⠀⠀⠂⠄⠁⠈⠉⠛⠻⢿⣿⣹⣿⣿⣿⣿⠿⡛⢁⠂⡐⠄⠠⠂⠄⠠⣤⣿⣽ ⢎⡜⡱⢍⡚⡔⣠⣿⢋⣶⠟⣂⠧⣿⡇⠀⠈⡀⠀⠀⠐⡀⢁⠠⡈⠤⢡⠈⠄⣁⠚⠷⣿⣿⠿⠟⡁⢂⠐⠤⢈⠐⡈⢁⠂⡘⠤⣋⢷⣻ ⠌⡘⢠⢳⡘⠴⡡⣾⠟⠁⠀⢻⣿⣿⠇⠀⠄⠠⢀⠂⡁⠐⡈⢀⠐⡀⢂⡌⡲⢄⡩⢲⠥⣏⡲⡐⡀⠆⡌⢠⠀⢊⠔⠡⢒⡡⢓⡌⡓⣿ ⠐⣀⠣⢖⡩⠖⠛⡁⠂⠠⠀⠄⠀⡀⠠⢀⠀⠡⡀⠆⡰⠡⡌⡅⢋⠍⠣⣌⠱⡌⡞⣥⣛⣿⢧⡱⡘⠴⡘⠤⡙⠤⣊⠔⡡⢌⢃⠒⡡⣟ ⠐⠈⡆⢡⠒⡌⠐⠀⡄⢡⠈⡄⠂⠀⠁⠂⡎⠑⢨⢰⠑⢳⣾⣼⣥⠚⢱⡌⣧⠙⣾⣵⣿⣿⣾⣵⠙⣦⠙⣦⢱⢢⡅⡎⢱⠊⡆⢣⡄⣯ ⠢⡑⠄⠂⡄⢠⠁⡀⠄⠠⠀⠄⡈⠤⢁⠢⡐⠤⣃⢎⡱⢣⢞⡻⣿⣿⣧⣽⣾⣿⣿⢿⡿⣹⢿⣿⣿⣮⡷⣌⡳⣜⢢⡙⢦⠚⡜⢦⡁⣧ ⡰⡐⢌⡑⠈⠄⢂⠀⠄⡁⢂⠐⠠⡁⠎⡰⢁⡚⢴⡊⣕⢣⢎⡱⢣⠞⣭⠫⣝⢣⢏⢮⡱⢋⠶⢬⡙⢿⣿⣷⣝⢮⣣⡝⣬⢛⡜⣢⠅⡷ ⠄⡱⢀⠢⡉⢆⠢⣌⠐⣀⠂⡉⠄⠡⢂⡑⢎⡜⡥⢓⡬⢎⡬⢱⢣⠹⣰⠙⢦⢩⠚⣦⡝⡭⢊⠥⡛⢦⡳⣝⡾⣣⢗⡞⣥⢫⡜⡱⢎⡗ ⠚⡐⠣⡑⠜⣂⠹⢄⠋⡔⢂⡁⠎⡑⠢⢜⠢⡜⡔⢫⠔⡣⢜⡡⢎⡱⢂⠏⣆⠣⡝⢦⡝⡲⣍⢞⡱⣣⢟⡼⣳⣟⣮⢿⣜⣧⢻⣱⣋⣞
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠟⠋⠙⠡⠁⡌⠡⢉⡉⠛⠳⣦⡄⠌⠠⢉⠉⡙⠛⠳⠿⣟⣦⢤⡀⠀⠀⣠⣴⣾⠿⠟⠛⠻⠴⣄ ⠀⠀⠀⠀⠀⠀⠀⣠⢶⡿⠚⠉⠀⠀⠀⠠⠁⢂⠡⣀⢁⠂⡄⢃⠂⠌⡉⠄⢃⠂⢌⠠⣁⠃⢆⡈⠙⠻⣾⣳⣾⠿⠉⠀⠀⢀⣠⣤⠶⠾ ⠀⠀⠀⠀⠀⢀⣼⡿⢋⠞⠀⠀⠀⣔⣒⣥⣭⣦⣵⣬⣬⣵⣬⣦⡥⠒⣐⠈⠄⠌⡀⠆⠙⠻⣦⣌⡡⢃⠠⠙⢿⣤⣧⣄⡐⠏⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⢁⠎⣰⣮⣶⣿⠿⢛⠩⢄⠡⢂⠴⠠⢌⠡⣾⡁⠰⣿⠀⢊⠐⠠⠈⠄⠡⢀⠙⢷⣦⡀⠡⠈⠻⣯⣛⣿⣎⢀⡀⢄⡀ ⠀⠀⠀⠀⠀⣿⡏⢰⠾⣻⣴⣟⣁⠊⣄⣳⠞⠋⠉⠉⠉⠸⡆⢻⣇⠐⣿⣆⠀⠌⠀⠡⠈⡐⠀⢂⠀⠹⣷⠀⠁⠀⠘⣿⡜⣿⡇⠈⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⠈⣶⡿⢉⡻⠛⠛⠛⠋⠀⠀⢀⠀⠀⢀⣿⠄⡹⢷⣼⢻⣆⠀⠀⠐⠀⠀⠈⠀⠈⠀⢹⡇⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣼⡟⢡⡞⠁⠠⠀⠄⠠⠀⠂⢀⠠⠁⠈⠻⢿⣦⣤⣌⡂⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⢻⡅⠬⡑⠢⢄ ⠀⠀⠀⠀⠀⣀⣿⣿⣷⣿⠿⣿⣶⣅⠈⡄⢁⠂⠄⠂⡐⢀⠀⡀⠀⠉⠙⢿⡂⢿⡆⠀⠀⠀⠸⡄⠀⠀⢀⣿⡄⠀⠀⢀⣿⣯⣰⣁⣋⣤ ⠀⠀⠀⢀⣴⣿⡟⠁⢾⣀⠐⡢⢻⣿⠇⡐⠂⣌⠠⠡⠐⣀⢂⣀⣄⣂⣀⠀⢷⡘⣿⡀⠀⠀⠐⡇⠀⣘⢨⡗⡧⢀⣤⠿⠁⣿⡗⠋⠛⠒ ⠀⣠⣼⠟⢡⡿⢀⠃⠌⠻⣤⠙⢧⣔⠘⣦⡡⠘⣧⡁⢃⣼⡿⠟⠿⠻⢿⣷⣄⠣⢹⣧⠀⠀⡘⡄⢰⠃⣿⢘⣷⠞⠁⠀⢸⣗⡇⠀⠀⠀ ⣴⡿⠋⠀⣿⡇⠠⢈⠂⠅⠨⢁⠂⡉⢓⠈⠳⣦⠘⣷⡈⢳⣄⠌⡰⣀⠢⡻⠿⠀⠹⣿⠀⢀⡧⢡⠏⣼⠏⣸⡇⠀⢀⡴⣿⣿⡇⠀⠀⠀ ⡿⠁⠀⢸⣿⠀⠐⢀⠈⠠⠁⢂⣡⣾⣟⡛⠶⣌⠡⠘⣷⡀⠻⣦⡀⢿⡄⢳⡄⢊⠰⣿⠁⣼⠁⢎⡾⢡⢂⣿⣃⣔⣭⡞⣽⣾⠀⠀⠀⠀ ⡇⠀⢀⠾⣿⡀⠈⠀⡀⠄⢬⣾⡹⢲⠬⣝⡛⢻⣦⠁⠄⡁⢂⠙⣧⡘⣷⠈⣷⠠⢸⡿⢸⠃⣬⡿⠁⡏⣼⡟⠹⣿⠐⣰⣿⠋⠀⠀⠀⠀ ⡇⢠⢋⡐⣿⡇⠀⢀⠀⠀⣾⢣⠕⡫⢜⠢⣍⢣⠜⣇⠀⡀⠂⡐⢀⠡⢉⠡⠘⠓⣼⡏⢱⣸⡟⠁⣸⢱⡿⠁⢰⣿⣹⣏⠏⠀⠀⠀⠀⠀ ⢁⠒⣤⣿⣿⣿⣦⣀⠀⠀⢻⡜⢬⡑⢎⡱⢌⠖⣩⣟⠀⠀⠐⠠⠀⠂⠄⢂⠡⣸⣟⣰⡿⠋⠀⢠⢇⣿⠃⢀⣾⣟⣧⠞⠀⠀⠀⠀⠀⠀ ⡄⣽⢫⠏⠀⠹⣻⣯⡲⣄⠈⠳⣆⡙⢢⡑⢎⡜⢡⡞⠀⠀⠈⠀⠀⡁⠐⠀⣴⣿⠏⠁⠀⠀⣰⢏⣾⢃⣴⣿⣛⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⣷⣣⠏⠀⠀⣴⣿⠟⣻⣷⣟⡲⢬⣙⡓⠮⠶⠼⠋⠀⠀⠂⢀⣈⣤⣤⣶⠿⠋⠁⠀⠀⣠⠞⣱⣾⣟⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⠃⠀⠀⣾⡿⢡⣾⣟⣯⢿⣿⣿⣦⡍⢫⠙⣉⢋⠥⣩⣾⠟⠋⠉⠀⠀⢀⣀⣠⠴⣋⣵⡿⢟⡛⠟⠿⢻⠿⣿⣖⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣿⣿⠰⣿⣞⣭⣟⣾⣳⣿⣿⣄⣃⣐⣬⡾⠋⢀⣠⣐⣮⣽⣭⣯⣶⡾⢟⡛⣍⢖⡣⢞⣩⠝⣦⠳⣌⠻⣿⠆⠀⠀⠀⠀⠀⠀ ⣴⣿⠿⣻⡹⢿⣷⡹⣾⣳⣾⣿⣿⣿⡿⣿⣿⣿⢟⣴⡿⠟⡛⣍⠳⣌⣦⡽⣶⢶⣧⢿⡼⣮⡽⣏⣾⣻⣼⣻⣼⢻⣿⡃⠀⠀⠀⠀⠀⠀ ⣿⡏⡽⣱⣭⣿⣿⣷⡽⣿⣟⣷⣻⢾⣿⣷⠟⣯⠏⣥⣶⣽⣾⡾⢿⢟⣟⣻⢛⣛⡛⠿⣿⣽⣻⣽⣷⣟⣾⣳⣿⣟⠏⠁⠀⠀⠀⠀⠀⠀ ⣿⡿⣽⣻⡿⡯⠒⢽⣿⣿⢿⣾⣽⡿⣋⣴⣾⣾⢿⣿⢿⡿⣽⣞⡹⣎⡞⣜⣫⠞⡽⢶⡄⠹⣿⣷⣻⣌⠻⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡻⣷⣟⠝⠀⡌⠠⠙⣯⣿⣿⣷⣾⣿⣿⣽⣾⡿⣩⢞⣿⣷⣻⣟⣿⣿⡿⢿⠿⣿⣯⣿⣦⢹⣷⡿⣿⢦⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣤⣤⣶⣶⣾⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⢿⣿⣶⣶⣾⡿⠿⠿⠟⠛⠛⠛⢿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣀⠀⠀⠀ ⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀ ⢀⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣿⣿⣷⠀ ⣼⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⢿⣿⣿⠀ ⣿⣿⣟⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⢸⣿⣿⡀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⢸⣿⣿⡇ ⢻⣿⣿⠀⠀⠀⣶⣄⡀⠀⣰⣿⣿⠋⠀⠀⠀⠛⢶⣤⡀⢀⣾⣿⡏⠀⢸⣿⣿⡇ ⢸⣿⣿⡀⠀⠀⠈⢻⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠀⠀⠈⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⣿⣿⡇ ⠘⣿⣿⡇⠀⠀⣰⣿⣿⠟⢿⣷⣄⠀⠀⠀⠀⣠⣾⣿⡿⠁⠹⣿⣦⠀⠀⣿⣿⣷ ⠀⣿⣿⣇⠀⣾⣿⡿⠃⠀⠀⠉⠙⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⢻⣿⣿⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⢸⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡟ ⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢹⣿⣿⡇ ⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁ ⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀ ⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⢤⣤⣤⣤⣤⣤⣶⣶⡿⠿⠟⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⣿⣿⡄⠀⠀⢠⣤⠀⠀⠀⢀⡀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣦⣤⣼⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣽⣿⡏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣿⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⡀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⠶⢶⣦⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣿⡿⠟⠿⠷⠶⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣇⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠁⠀⠈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠿⢿⠉⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⡿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣴⣿⣿⣧⡄⠀⢠⣼⡿⠛⢿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠛⠋⠀⠀⠘⠿⠁⠀⠀⠙⣿⣿⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠠⠤⠤⠤⠶⠶⣶⡇⠀⠀⠀⡴⠋⠀⠐⢆⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠠⠔⠒⠒⠓⠒⠒⠤⠄⡀⠀⠀⠙⡀⠀⠀⠈⠀⠀⢨ ⠀⠀⢠⣴⣿⣷⡆⠀⡐⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠈⠢⡀⠹⣿⣷⣄⠀⠀⢀⠎ ⠀⠀⠘⠛⠟⠛⠁⠀⡇⠀⢀⠖⠉⠀⠀⠀⠀⠈⠑⢄⠀⢰⠀⠈⠙⠋⠑⠲⡏⠈ ⠀⠀⠀⢀⣀⣠⣤⣄⣱⣀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠂⣀⣧⣤⣤⣤⣀⠀⠈⢆ ⠀⣠⣾⣿⠟⠛⠻⣿⣿⣿⣷⣮⣑⡀⠀⠀⠀⢀⣴⣥⣾⣿⣿⣿⠏⠉⠻⣷⡄⠀ ⢰⣿⣿⡏⠀⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⡀⢻⣿⡄ ⢸⣿⣿⡇⠀⢏⡇⠀⢻⣿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⣿⠀⠳⠃⢸⣿⡇ ⠈⢿⣿⣿⣄⠀⠀⠀⡸⠃⠀⠀⠀⠀⢴⠒⠀⠈⠉⢐⡄⠀⠀⠈⢆⠀⢀⣼⣿⠃ ⠀⠀⠙⠻⢿⣶⣶⣶⡇⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠉⠀⠀⠀⠀⢈⣿⡿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡠⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
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⣦⡾⢃⣤⡿⠛⣒⡛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⢊⠉⢱⠖⣲⢤⣀⠀⠀⠀⠀⢠⡾⡗⡛⠒⠈⣤⣤⡀⠀⠀⠀ ⣻⣿⠿⢛⣣⠜⠸⣟⣿⡇⠀⠀⠀⡀⠀⠀⠀⣀⣤⣤⣶⣶⣿⠿⠿⠿⠿⠿⠿⣿⣶⣦⣍⡛⢻⣦⣄⠀⢼⡿⡇⠥⠙⢘⣹⣿⣟⠀⠀⠀ ⣿⣭⠘⣁⠀⠀⠀⢫⣩⡽⣦⠞⠉⣠⣴⣾⡿⠟⠛⠉⠉⢀⠀⠖⡌⠀⠀⠀⠁⠀⠈⠙⡻⢿⣶⣄⠙⢷⣞⣛⣧⣇⡤⣈⣿⣿⣿⠀⠀⠀ ⣿⡟⢸⣷⠀⣰⣾⣫⣭⡿⢛⣶⣿⠟⢋⠡⡐⢌⠱⣀⠠⢄⠢⢑⡈⢆⠑⣂⠒⡰⢄⠀⠀⠈⡙⢿⣿⣟⣿⡿⢻⣿⣿⣷⡿⠟⢟⠀⠀⠠ ⢸⣸⣹⣿⣼⣿⣿⣿⣷⣿⣿⣏⣰⡈⠢⣁⠃⠎⡰⢀⡃⠦⡘⠤⡘⢄⠣⢄⢣⠐⡌⢒⡀⢀⠜⣤⣿⠿⠉⠀⠀⢻⣿⣿⡅⠀⠈⡆⠀⣶ ⠈⢇⡦⣿⣿⣿⠏⠁⠩⢿⣿⠛⢿⣿⣿⣶⣬⣴⣁⣢⠘⢠⠑⣂⠱⣈⠒⡌⢢⠑⡌⠂⣌⣶⡿⢿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣶⡍⠀⣀⠛ ⠀⠘⣿⠸⣿⣿⣦⣀⣔⣿⣿⣧⠀⢿⣿⡌⠙⠛⠻⠿⣿⣶⣮⣤⣒⡠⠑⢌⢂⠡⣨⣾⣿⣿⣇⠘⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⡧⣼⡇⠀ ⠀⠀⠸⣧⠹⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣮⣾⣿⣿⣿⣿⣿⡔⠸⣿⣷⡀⠀⠀⠀⠸⣿⣿⢹⡟⠀⠀ ⠀⠀⠀⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⠹⣿⣷⠀⠀⠄⠀⣿⣟⣿⡇⠀⠀ ⠀⠀⠰⢙⣹⣿⠇⡠⠿⢿⣿⣿⣿⣿⡀⠹⣿⣧⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣇⠀⠀⢸⣿⡏⠹⣇⠀⠀ ⠀⠀⡈⠋⣿⡿⠐⡄⠣⢼⣿⣿⣿⣿⣿⡀⢹⣿⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣆⢠⣿⠟⣿⣆⠙⣇⠀ ⢀⠒⢁⣾⡿⢃⠱⣈⠱⢠⢸⣿⣿⣿⣿⣷⠀⢿⣿⣆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣾⡟⢠⠹⣿⡆⣿⢷ ⣾⣤⣿⠏⡁⠦⡑⢄⠃⢆⣹⣿⣿⣿⣿⣿⣧⠈⢿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠏⡐⢂⠆⣿⣿⣹⣛ ⠿⣿⢋⡐⢌⠱⡈⠆⡹⢼⣿⣿⠣⡝⢿⣿⣿⣆⠘⣿⣿⡀⠀⢀⣤⣼⣿⠿⣋⠷⡘⢆⠣⢒⠰⡘⡐⢣⠍⠭⣉⠡⢂⠱⡈⣴⣿⡇⢿⣿ ⠀⣿⠠⢐⠊⡔⢡⠊⡵⢫⣿⣧⢫⠜⣣⣮⡻⢿⣷⣾⣿⣷⣾⡿⢟⡹⢢⠝⡨⠑⢌⠂⠓⡌⢲⡄⣉⠒⡌⢒⣠⣥⣮⣶⣿⡿⢋⣰⠾⠡ ⠙⣿⢀⠃⣍⠰⡁⢎⡵⢋⣿⣟⠠⢉⣾⣿⠋⠶⣩⢛⠿⢫⠕⡊⠇⡉⢆⡘⠤⡉⠜⣿⠔⡠⢛⠡⣄⣶⣾⣿⠿⠟⢛⣿⡿⠲⣾⠋⠀⠐ ⠀⢹⠀⠎⡄⢣⠘⣬⢚⡥⣿⣿⠀⡙⣿⣷⣌⡐⠠⠉⠌⢡⢘⣀⣣⣬⣤⣶⣴⣧⣮⣤⣶⣤⣷⣾⡿⠟⠋⣄⠢⣩⣾⣟⣱⡾⠃⠀⠀⠀ ⠀⢈⠘⡰⠘⡄⠳⣌⢳⡘⣿⣿⢀⠡⠌⠻⠿⣿⣿⣿⣿⣿⡿⠿⠿⢛⠛⠛⠛⠛⠛⠛⡛⠿⢛⠩⠐⢌⢒⣠⣾⣿⣯⣍⡉⠅⠂⡀⠀⠀ ⠀⠀⠐⡡⢃⢌⡳⣌⢧⡙⣿⣯⢀⠃⢎⡑⢢⠐⡄⢢⠐⠤⡐⢢⠑⡌⠬⠡⢍⠊⢅⠣⢐⠂⣡⣊⣵⣾⣿⠟⠻⣿⣏⠻⢿⣷⣤⡙⠲⣤ ⠀⠀⠘⡄⢃⢬⢳⡘⢦⡙⣿⣿⣿⣮⣄⣘⡠⢃⠘⠤⠉⠆⠱⡈⢆⠱⣈⣑⣈⣬⣴⣶⣿⣿⡿⢟⠛⡩⡔⠎⠁⠘⣿⣷⠠⠌⠻⣷⡘⣿ ⠀⠀⢈⠔⣩⠞⢦⡙⢦⣙⣿⣯⠘⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⢛⠻⣿⣯⠰⡐⢎⡱⠁⠌⠠⢁⠠⠘⣿⣧⠈⡅⢚⣿⣯ ⠀⠀⡐⢮⡱⢎⢧⡙⢦⢹⣿⡇⡱⢘⢆⠳⢄⠢⡔⡰⠢⢔⠢⡔⡒⡔⢪⡑⠎⡥⢊⠽⣿⣇⠉⡀⠄⡐⢈⠂⠂⢀⣤⣿⣿⡆⡘⠌⣿⡧ ⠀⠀⡘⣇⢞⡩⢖⡹⣌⢻⣿⢃⡌⢣⠜⣌⢊⡕⠬⣑⠩⢆⡓⢬⡑⠬⠑⠌⢃⢈⠁⡀⢿⣿⡀⠄⠂⠀⣄⣠⣶⣿⡿⠛⣿⣇⠰⠁⣿⡗ ⠀⠀⠸⡜⢪⡕⡫⣔⢣⣿⡿⠐⠬⠡⠎⠰⠁⠎⠒⠁⡉⠂⠌⠀⠄⠂⠡⠈⠄⠂⠄⢀⣸⣿⣧⣴⣶⣿⡿⠿⠛⠁⢀⠀⣿⣯⠐⡁⣿⣟ ⠀⠀⠈⢉⣃⣞⣑⣬⣚⠛⠁⠀⠠⠁⠄⠂⣁⢀⡁⢌⠠⠅⠌⠰⠈⠤⠡⣒⣒⣛⣾⣛⣟⣿⣛⣯⣭⣥⣄⣠⣀⣤⡶⣴⣟⡃⠸⠴⡷⠋
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⣟⣿⣻⣿⢏⡚⣿⣻⣟⣿⣻⣟⣿⡻⣟⣿⣻⢟⣿⣻⣟⣿⣻⢿⣹⣿⣟⣿⣻⢿ ⣿⣾⡿⢃⠎⡴⢹⣷⣻⢾⣽⣞⣷⣻⡽⣾⣽⣻⣞⣷⣻⢾⡽⣿⠐⣿⣿⣾⣽⣻ ⣿⡿⢷⡿⣶⣾⣭⣷⣟⡿⣾⣿⣞⣷⣻⢷⣯⢷⣻⣾⡽⣯⢿⣷⡿⠿⣿⣾⣳⢿ ⡟⡜⢢⡐⠰⡀⢎⡙⣿⣽⣻⣿⣞⡷⣯⣟⡾⣯⢷⣿⡿⣽⣿⠃⡔⢣⠺⣿⣽⣻ ⡜⢌⣡⣌⣥⡬⣄⣒⠸⣿⣳⣿⣯⣟⡷⣯⢿⡽⣯⣿⣿⣳⡟⣨⢴⣳⣿⣿⣿⣽ ⣼⡾⢟⣿⣿⣿⡷⣮⡕⠚⢿⣟⣿⣾⣻⣽⣯⣟⡷⣿⣻⣿⢋⣽⢿⣿⣿⣿⣿⢾ ⣿⠉⢻⣿⣿⡿⣿⠬⣻⠖⠀⠙⢿⣷⣟⣾⣿⢾⡽⣿⣿⡿⠹⠇⢻⡟⣿⣟⣿⣻ ⡘⢧⡈⢧⣻⣽⡛⠀⣀⠝⢀⢡⣾⣿⣾⣿⡿⣿⣽⣻⣷⡇⠲⢄⣈⡣⣿⣜⣽⡿ ⣧⠈⡙⢒⠚⠓⠒⡉⢁⠐⣠⡿⠟⠋⠔⠻⢿⣿⣷⣟⣿⠁⠄⢂⠠⠉⢄⠁⡟⢰ ⣿⡆⠡⠌⢨⠐⠡⠐⡀⢂⠡⠐⡈⠐⡈⠄⠩⢙⢿⣿⣾⣧⠈⠄⢂⠁⢂⠂⡄⣻ ⠻⢧⡑⠌⢂⠌⢂⡁⠒⡀⠆⠡⠠⢁⡐⠨⠐⢂⡄⢉⠛⠿⣷⡈⠄⠌⢂⠡⡐⣱ ⠀⠈⢷⡈⢆⡘⢠⠐⡁⠒⣈⠡⢂⠅⡄⢃⡉⢼⣻⡄⢊⡐⠠⢉⠰⢈⡐⢂⣱⠉ ⠀⠐⠻⠿⣄⠢⢡⠘⣀⠣⠐⢌⠢⢘⠠⠃⡄⠻⠞⠠⠡⠄⡃⢌⢂⠡⢄⣿⡷⡄ ⠀⠀⠀⠀⠈⠳⢆⡱⢀⠎⡑⢂⠱⠈⢆⠱⢈⠡⠌⡡⢃⠘⡐⠌⣄⡷⠋⠹⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡶⣌⣰⠁⠎⡑⢊⠒⣃⠚⡡⢡⠉⣆⣱⡾⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡄⠀⠀⠀ ⠀⠀⠀⡀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⢀⠀⠀ ⠀⠀⢀⡏⢹⠀⣿⣿⣿⣿⣿⣿⣿⠟⡠⠖⠉⠲⣜⢿⣿⣿⣿⣿⣿⣿⣷⢸⡏⣽⡀⠀ ⠀⠀⣿⡇⢸⠀⢹⣿⣿⣿⠿⢋⡥⠊⠀⠀⠀⠀⠈⠳⣍⡛⠿⣿⣿⣿⠃⢸⡇⢹⡇⠀ ⠀⠀⠛⡇⢸⠱⣄⠈⠁⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠉⠀⣠⢻⡇⣺⠃⠀ ⠀⠀⠀⣻⢿⠀⠈⠛⠛⠉⠀⠀⠀⠀⢀⣤⢤⣄⡀⠀⠀⠀⠀⠉⠛⠛⠁⢸⢿⡛⠀⠀ ⠀⢠⢾⣿⠀⢧⠀⠀⠀⠀⠀⠀⣠⣾⣹⣿⣴⣿⣹⣦⡀⠀⠀⠀⠀⠀⢀⡞⢰⣮⢦⠀ ⠀⡎⢸⣿⣧⡈⠓⠤⣀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⣠⠔⠋⣠⣾⣿⠈⡇ ⠘⡇⠀⠻⠟⢉⣠⠴⠚⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⠒⠤⣀⠙⢿⠋⠀⡼ ⠀⠳⡄⢀⡴⠋⠀⠀⠀⠀⠀⢣⠀⢀⡴⣋⣿⡑⢦⠀⢀⡞⠀⠀⠀⠀⠈⠑⢄⠀⣠⠃ ⠀⠀⠙⡏⠀⠀⠀⠀⢀⣀⣀⠀⣆⡞⣠⣿⣿⣧⡄⢣⡜⠀⣀⣀⠀⠀⠀⠀⠈⡷⠁⠀ ⠀⠀⠀⢳⡀⠀⢠⠞⢩⣿⣿⡍⠉⢰⣿⣿⣿⣿⣿⡆⠉⢩⣿⣿⠉⢳⡀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⠳⣄⡘⢧⣈⣛⣛⣁⠤⢾⣿⣿⣿⣿⣿⡷⢤⣈⣛⣛⣀⠜⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠲⠬⠥⠤⠖⠋⠀⠙⠛⠃⠀⠙⠦⠤⠬⠽⠒⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⢤⠏⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⠡⠙⡾⠉⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠊⠀⠙⠒⣺⡏⠉⣄⣸⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠻⡳⡀⢹⠜⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠔⠢⡀⠀⠀⢀⠀⠀⢠⡖⠂⠒⠊⠀⠀⠀⠀⠀⠀ ⢀⠤⠀⠤⠄⠀⠀⠀⠸⠆⠀⠀⢀⣇⡀⡀⠘⣤⢴⣿⠀⢀⡤⠤⠐⠒⠒⠒⢦⠀ ⠘⠦⠤⠤⣤⣤⣤⡤⣴⠶⡦⡤⣍⣼⣿⡇⢀⢸⡾⠿⠂⣼⢇⣀⣀⣀⡀⠤⠼⠃ ⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⢹⠀⢀⣴⠗⠛⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠛⣀⠀⡸⠁⡸⠇⠀⠀⣸⠁⠀⠀⠀ ⠀⠀⣠⢤⡔⠒⡚⠓⠊⠉⢉⣀⠉⠉⠀⠀⠉⠋⠐⠲⠦⢤⡠⠏⠀⠀⠀⠀ ⢀⣾⠗⠁⠀⠀⢹⡀⠀⢿⣷⡎⢙⡦⣤⢶⣶⡒⢦⡀⠀⠀⠉⠑⢦⡀⠀⠀ ⢸⡇⢰⡆⠸⡷⢸⡇⠀⠀⠈⠉⠁⠀⠈⠛⠝⠰⠚⠁⠀⠀⠀⠀⠀⠙⣦⠀ ⢸⣇⠀⠀⠀⢄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⠘⡄ ⠀⠉⠷⣒⣒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠁⠚⠓⠶⢤⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠲⠶⠶⠶⠶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠐ ⠀⡀⠠⠤⠀⢀⡀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡰⣻⠀ ⠐⠤⠀⠀⣀⠠⢜⠀⠀⢠⣼⣷⡢⢄⡀⠀⠀⠀⠀⠀⢀⣀⡤⣔⣭⣾⢿⣷ ⠁⠀⠀⠀⠀⢀⣠⠀⢀⣽⣿⡷⠿⣷⡶⡯⣭⠭⠭⠭⢶⡾⠿⢍⣋⣘⠉⣿ ⠀⠀⠀⠀⠀⠀⠙⢀⣀⣥⣤⢴⢶⣿⣿⣷⣿⡄⡰⠾⠿⠷⢦⣾⣿⣿⡄⣿ ⢰⠀⠀⠀⠀⠀⠰⢠⣿⣿⠧⠾⠻⣿⣿⣿⣿⣧⣶⣶⣾⣷⣿⣿⣿⣿⡇⣿
⠀⠀⠀⡠⠒⠉⢉⣑⠢⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠎⢦⠀⣨⠞⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀ ⠀⢸⠀⠀⠀⢂⠈⡟⢡⠎⣀⣤⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⡠⠊⢠⠞⢁⡽⡄⠀ ⠀⡇⠀⠀⠀⠀⣜⣤⡷⠉⠘⡠⠱⡴⠀⠀⠀⠀⠀⡏⠈⠳⠁⠀⠁⠠⠃⢀⠇⠀ ⠀⡇⠀⠀⠀⡸⢸⠁⠔⠒⣄⠃⢸⠜⠊⠉⠑⡄⠀⠈⡆⠀⡀⡀⠀⠀⠀⠎⠒⢢ ⠀⡼⠀⠀⠀⡗⠉⠀⠃⠀⢿⠄⠉⠀⠀⠀⠀⡸⠀⠀⣥⠀⠁⠡⠂⠀⢀⠤⠴⠊ ⢸⠀⠀⠀⢀⠑⠤⠤⢄⠀⢉⠀⢀⣀⣀⣀⣴⡇⠀⠘⣄⠀⠀⠀⢀⡤⠃⠀⠀⠀ ⠀⠣⢄⡰⠊⣑⠢⠄⠴⠁⢸⣿⣿⣿⣟⡛⡟⠀⢀⠎⠀⠑⠢⡤⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠊⠑⠀⣀⠀⠀⠈⢟⠁⠲⡇⣧⡔⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠒⠊⢣⠙⠦⡀⠀⠐⠂⡰⢻⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⡀⢸⣀⠦⢞⡖⠊⠹⠀⠸⡀⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠉⠉⠉⠐⠃⠀⢱⡀⡠⠔⢏⠱⡀⡇⠀⠀⠙⠦⣀⠀⡘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⡯⠀⠠⠇⠈⡽⠋⠀⠀⠈⢢⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⡼⠂⠀⠈⠀⠈⣄⠀⢀⡤⠊⢉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⢸⣀⡠⢄⡀⠀⠀⠀⢉⠥⠓⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠈⠉⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠊⢇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠸⡂⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢏⢆⠀⠑⠦⢀⣀⡀⠴⢻⠈⡇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⢕⡢⢤⣀⣀⣀⡠⡞⢠⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠔⠚⠁⡜⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⣁⣀⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠤⢄⡀⠉⠲⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠈⠑⢌⢢⠀⠈⢦⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⣇⢣⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢣⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡏⡆⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣴⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀ ⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⡛⠿⠿⠿⠿⠿⠿⣿⠇⠸⣿⠿⠿⠿⠿⠿⠿⢻⣿ ⣿⣷⣶⣶⣶⣶⣤⠀⠿⠶⠶⠿⠀⣤⣶⣶⣶⣶⣾⣿ ⠹⣿⣿⣿⠙⠛⢿⣷⣶⣶⣶⣶⣾⡿⠛⠋⣿⣿⣿⠏ ⠀⠀⠉⣿⣿⠀⠘⣉⣠⣤⣤⣄⣉⠃⠀⣿⣿⠉⠀⠀ ⠀⠀⠀⢻⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⡟⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⢸⣿⣿⣿⣿⣿⣿⡇⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣸⣠⣤⠽⣦⣀⠀⠀⠀⣠⠔⡿⡏⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⣶⣬⡙⠶⠋⠁⢸⢰⠃⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠋⢹⡤⠦⢍⢻⣿⠀⠀⠀⣿⢻⡄⢸ ⠀⠀⣠⣾⣿⣿⣿⣟⡛⠻⠼⠿⠆⣥⠶⢄⣳⡥⠤⠤⠀⣉⣸⠏⠋ ⢠⡞⢹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠒⠚⠁⠠⢤⡄⠀⠈⢻⡀⠀ ⢿⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡴⠚⣂⣀⢸⡇⠀⠀⠘⣧⠀ ⠘⢧⡀⢀⢙⡏⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⠙⣿⠀⣴⣄⠀⢿⠀ ⠀⠈⠳⠀⠂⢧⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⡞⠓⡞⠀⣿⡇⠀⢸⡇ ⠀⠀⠀⢧⣄⣠⠗⢦⡀⠀⠀⠀⠀⠀⢀⡾⠳⣼⠁⠀⡿⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠶⢶⣶⣞⢉⣧⠼⠁⠀⣸⠇⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⡶⢤⡄⠈⠉⠀⠀⠀⣰⠏⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣦⣀⣠⣀⣀⣀⣤⠞⠋⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡞⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣏⣹⡿⢿⣿⣤⣀⣀⣀⣀⣀⣤⣤⡶⠞⠛⢁⡏⠀ ⠀⠀⠀⠀⠀⠀⠹⠿⠤⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠠⠴⠞⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠈⣽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠯⠤⠴⠯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡶⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠻⣆⣀⣴⢇⡴⠒⠉⠉⠉⠉⢙⠢⣄⠀⠀⠙⢢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣀⠛⠀⠙⣧⡀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡴⣤⡀⠀⠀⠀⢸⠁⠀⠀⣀⠀⢀⡈⠋⠀⠀⠀⢸⡇⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠎⠀⠈⠻⣷⣄⠀⠸⡶⠓⠈⠉⠁⠘⠋⠀⠀⠀⠀⢸⣿⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠃⠀⠀⠀⠀⠈⠙⢦⡀⠙⢦⡀⠀⠀⠀⠛⡃⠀⠀⣠⣿⡟⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡾⠁⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠶⣦⣤⣀⣻⣴⡾⠟⠋⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⡿⠁⠀⢠⡿⣄⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠉⠉⠉⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⡟⠁⠀⢠⠟⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⡟⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⡿⢁⡟⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⢀⣿⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡾⢃⣾⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄⠀⡾⣳⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⡟⢩⣇⠉⠳⡻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠞⣽⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢸⣿⣿⣆⢹⣄⡈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡰⢃⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠘⣿⣿⡿⠀⣯⣉⠙⠒⠮⣓⢦⣀⠀⠀⠀⠀⠀⣠⠎⣠⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢠⣤⣴⣮⣁⠀⢸⣿⣿⣿⣶⣤⡈⠳⡌⠛⢤⣀⢀⡜⣡⠞⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣷⠀⠉⠉⠛⠺⢿⡞⠁⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠐⢻⣿⣿⣯⡉⠉⠉⠀⠀⠀⠀⠉⠛⠿⠉⣠⣾⣿⣿⣦⡀⠀⠁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⡈⢻⣿⣿⡟⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠟⠃⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠃⠀⣾⣿⣿⣾⡏⠁⠀⢸⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⣀⣀⠈⠛⠿⠟⠁⢀⣤⡀⠙⠿⣿⡿⠇⢀⣀⣀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⣿⣿⣿⣲⠀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠠⣿⣿⣿⣿⣶⠄⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⣀⣀⡙⠿⠟⠃⠀⣤⣤⣀⠙⠛⠛⠛⠀⣀⣀⣈⠻⠿⠟⠉⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⢸⣿⣿⣯⡇⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⡄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠈⠛⠛⠃⠀⢀⣠⣀⡉⠛⠛⠋⠀⢠⣶⣤⣀⠙⠋⠉⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡅⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠀⠀⠀⠘⣿⣿⣿⡷⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⣀⣤⣄⠈⠉⠉⢁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠛⠋⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⢶⣦⢤⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠽⠅⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⠛⠉⠉⠉⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣯⣭⡉⠉⠉⠉⢓⡢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠁⠀⠈⠙⠻⣟⡒⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠶⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⣦⣧⣶⣹⣆⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⣰⢣⣿⡿⣻⣿⣧⣿⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⣿⣷⣿⣿⣿⢸⣧⣀⡤⠊⠁⠀⠀⠀⡴⠛⠿⠍⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀ ⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⣿⣿⣿⣿⡿⣼⠏⠁⠀⠀⠀⠀⠀⠸⡿⠦⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠬⠛⡆ ⢰⣡⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣿⣿⣿⣿⣿⢣⡟⠀⠀⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡿⣄⠀⠀⠀⢀⣠⡇ ⠘⢿⣿⠟⠙⠳⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡔⣿⣿⣿⡿⣛⣵⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣄⣀⣀⣠⡼⠁⠈⠳⢤⣤⡤⠾⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⢮⣭⠵⠞⠉⠉⠉⠉⠙⠛⠛⠉⠛⠋⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠋⣉⣥⡿⠿⣤⣀⣀⣀⡀⡰⠟⠛⠻⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⣫⣶⠿⢋⡴⠖⠒⠶⣍⠀⠁⠀⠀⣠⡶⠋⢉⣽⡿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠋⠉⠉⢰⠏⣀⣀⠀⠀⢸⡇⠀⠀⢠⡏⠀⠀⠈⠉⢁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠇⠀⠀⠴⢾⣆⡿⠟⠁⠀⣸⠇⠀⠀⠀⠷⢤⣤⣤⢴⣾⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠋⠈⠙⠓⠒⠚⢁⣀⣀⣀⣀⣠⡴⢋⣴⠶⣤⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠌⠉⠀⣾⠁⡿⣿⢶⣾⣇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠭⠤⠴⣇⢸⡏⠉⠉⠉⣿⣸⠁⠀⣀⣀⠀⢀⣀⠀⢀⣀⣀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀ ⠸⡆⢧⢰⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⠀⠀⢰⢣⡇⠀⠀⠘⣿⣶⣿⠋⣼⡿⠛⢻⣷⡄⣿⡏⠀⢀⣾⡿⠛⢻⣷⡀ ⠀⢷⠈⢧⢇⠈⢢⡀⠀⠠⠤⣀⡀⠀⠀⠀⣸⢸⠃⠀⠀⣿⠘⡇⠀⠀⠀⢸⣿⠃⠀⢿⣷⣀⣼⡿⠃⣿⣧⣀⡘⢿⣧⣀⣼⡿⠁ ⠀⠘⣇⠈⢿⡄⠀⡇⠀⠀⠈⠭⣛⠦⡀⢀⡏⣼⠂⠤⡀⢹⡀⢿⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠀⠀ ⠀⠀⠸⣆⠘⡽⡀⠐⢄⠀⠐⠦⢌⡑⢤⣼⠁⣯⣤⣤⣬⢾⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⠈⢿⡢⢄⡓⢄⠀⠀⠈⠢⣼⠀⢿⡞⠾⢼⡾⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⡉⠒⠽⣦⣥⣀⣀⣀⠹⣆⠀⠙⠓⠋⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣈⠉⠑⠒⠛⢉⠙⣲⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀⠀⣿⣷⡀⠀⠀ ⠀⠀⣀⣴⣿⡇⢀⣤⣾⣿⣿⠿⠛⠉⠉⠉⠙⠻⣿⣷⡄⠘⣿⣷⠀⠀ ⠀⠸⡿⠛⣡⣶⣿⣿⠟⠋⢀⣠⣶⣶⣶⣄⠀⠀⣿⣿⣇⠀⣻⣿⠀⠀ ⠀⠀⠀⣾⣿⡿⠋⠁⢀⣴⣿⣿⠿⢻⣿⣿⠀⠀⣿⣿⡏⢀⣿⡿⠀⠀ ⠀⣠⣄⠈⠉⠀⢀⣴⣿⣿⠟⠁⠀⣾⣿⡟⠀⣰⣿⣿⠃⠘⠿⠃⠀⠀ ⣀⠙⠋⠀⠀⢀⣾⣿⡿⠁⢀⣀⠶⠈⠉⠀⣴⣿⣿⠃⠀⠀⠀⡀⠙⠃ ⠙⠀⣴⣦⠀⣼⣿⡿⠀⢠⣿⣿⠇⠀⣠⣾⣿⡿⠁⠀⢀⣀⠸⠿⠀⠀ ⠀⢸⣿⠇⢸⣿⣿⠁⠀⣿⣿⣯⣴⣾⣿⡿⠋⠀⣠⣾⣿⣿⠃⠀⠀⠀ ⠀⢾⣿⠀⢸⣿⣿⡀⠀⠘⠻⠿⠿⠟⠉⣀⣤⣾⣿⡿⠋⣡⣤⡀⠀⠀ ⠀⠸⣿⣆⠀⢻⣿⣷⣄⣀⣀⣀⣠⣴⣾⣿⡿⠟⠋⣴⣾⡿⠛⠀⠀⠀ ⠀⠀⠹⣿⠇⠀⠙⠻⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⠻⣦⣄⢀⣀⡆⠄⡠⠞⡱⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣙⣿⠟⡀⠀⠈⣙⣶⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⡿⣽⣿⣾⣯⡤⣿⣿⡷⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⣵⣿⣝⣃⣼⢃⣜⣌⣳⡇⡀⠔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡓⠙⠤⣶⡟⢁⢄⡻⣄⡹⡗⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠙⠛⠛⠂⠀⠋⠛⠉⠛⠀⢁⠀⠈⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⠀⠀ ⠀⢠⠤⣴⣶⣎⣴⠁⢀⣴⡱⠶⡓⢄⠀⡀⠀⠀⢀⡴⢠⢺⠟⢶⢣⠀ ⣰⠅⢠⣚⡦⢙⣿⣄⠙⢒⠁⠀⢧⢎⡄⠙⡧⠴⠏⢠⢂⢎⡀⡜⠛⠀ ⠛⠻⢿⣿⣿⣿⠿⣿⠮⢢⠧⣣⡻⠴⣉⣈⣃⡮⠏⠀⠙⠶⠎⠀⠀⠀ ⠀⠉⠉⠋⠉⠈⠙⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢓⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣏⡷⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⡊⠳⣄⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢷⣨⠈⢷⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⡾⢿⣧⡄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢎⣧⠛⢧⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠛⣧⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⢿⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠙⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡄⢹⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣈⠻⣦⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡈⢿⣆⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡽⢷⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⡻⣷⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣷⣄⠀⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⣙⢦⡀⠀⠀⠀⢰⣿⢻⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣁⠂⣙⣤⣀⣠⣾⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣛⣹⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡹⠿⢛⣻⡿⠋⠉⢿⣷⣄⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣉⡥⠟⠋⠀⠀⠀⠀⠙⢿⣷⡀⠀⠈⠧⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣀⡤⢻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣿⢟
⠀⠈⠢⡙⢷⡄⠀⠈⢦⡰⠀⠐⠂⠈⠑⠂⠀⠀⢣⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀ ⡀⠀⠀⠈⠪⡻⣦⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣠⣴⠁⢀⣄⠂⠀⠀⠀ ⠈⠢⡀⠀⠀⠘⢼⣷⣄⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⠓⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢼⠟⢁⣴⠟⠁⠀⠀⠀⠀ ⡀⠀⠈⢑⣤⡔⠊⠑⣝⣦⣿⡿⠞⠉⠉⠐⠢⣔⠚⢁⣾⠏⠀⠀⠀⠀⢨⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⠀⠀⠠⠃⣼⢧⠀⠈⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠐⠉⠈⠣⠀⠀⣀⣄⠀⠀⣠⠀⠀⠀⢀⣠⠾⣿⠀⢠⣇⣰⠃⢀⠉⠢⣌⢿⣷⡄⠀⠀⠀⠀⠀⠈⣑⠦⡀⢸⠁⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⢱⡾⣫⠀⠀⡰⡻⠁⢀⣴⠟⠁⠀⢹⣆⡞⣿⠁⠀⠀⠀⢀⠀⠙⠿⣿⡄⠀⢄⡀⠀⠀⠈⠑⢾⣇⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⢞⣿⠃⢠⣷⠃⣴⠟⠁⠀⠀⠀⠈⠹⡇⠀⠀⠀⡴⠟⠉⠉⠉⠀⠈⠳⡀⠈⣷⠀⠀⢰⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⢁⢎⡎⠀⢸⡇⣸⠗⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⢸⣧⠀⠀⢰⠃⠀⣀⠄⠀⠁ ⠀⠀⠀⠀⠀⠙⠢⣾⡼⠀⠀⢸⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡤⠄⠀⠘⣼⡇⠀⣾⡿⣆⢠⣃⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠁⡜⠀⡼⡇⠀⠀⢀⣀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢀⡶⠟⠋⠁⠀⠀⠀⠀⠈⠸⢧⢀⣿⡇⢸⣾⣥⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡎⠀⠀⡇⢰⠇⣁⡤⠶⠶⠦⢤⣄⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡗⢸⢿⡿⢿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⣰⢣⢸⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⢀⠃⣾⡸⣷⣽⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡇⢸⡟⢰⡏⣧⢹⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣘⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠤⠴⠒⠚⠉⢉⣿⣿⣿⡆⠀⢱⣸⢁⡿⠀⣿⡆⢿⣿⠃⠀⠀⠀ ⢠⣴⠖⠛⠿⠦⢤⣀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠁⠀⠀⠀⢀⣠⣶⣿⣿⢸⣿⠃⠀⠘⣿⣾⣷⣶⣿⣷⠘⠃⠀⠀⠀⠀ ⠘⣧⣤⢤⣤⣴⣾⣿⣿⣿⣿⡽⡆⠀⠀⣀⣤⣖⠉⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⡾⡿⠀⠀⢠⢿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠞⠉⠠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⡟⢿⣿⢠⠃⠀⢠⡏⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣧⣠⠀⠈⢿⣿⣿⣿⢿⣿⣿⡄⠀⠈⢿⣿⠻⣸⡟⠙⡇⠉⠉⠉⠀⠀⠀⡷⠀⢹⠃⠀⣠⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣦⡀⠀⠉⠻⣿⠘⣿⣿⣿⣄⠀⠀⠹⣶⡟⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇⡰⠃⢀⣴⣿⡟⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⡆⢀⠀⠀⠐⢿⡍⣿⣿⣷⣤⠀⠈⠳⣄⠀⠙⠢⠤⠤⠒⠊⣁⠞⢀⣴⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⡧⠄⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⢿⣿⣿⣷⠀⢤⡄⢻⠼⣷⣽⣿⣿⣿⣿⣦⣀⠈⠑⠢⠄⣀⣀⡤⠚⣁⣴⣿⡏⠀⠘⠀⠇⠀⣸⣿⣿⣿⣿⣿⣷⣧⣶⣤⣼⣷ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⠻⣖⠢⠤⠤⠤⠴⣾⡏⣿⣽⣷⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠑⢤⢀⣀⠀⢳⢻⡜⠙⣻⣃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠉⠑⠢⣯⡇⠀⠱⡃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠏⠀⣴
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡤⣄⠀⠀⠀⠀⠀⢸⠋⣰⣿⣷⡄⠀⢻⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣄⡀⣀⡤⠔⠒⠀⠘⠓⠴⢿⣷⡌⢧⡀⠀⠀⠀⠘⢆⣸⡿⠋⠉⠒⠉⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀ ⢠⡞⣋⣀⣌⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡜⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀ ⢸⡐⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡉⠲⣄⠀ ⠀⠓⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⡀⢰⡇⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⢘⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠘⣼⠀⠀⢀⡀⠀⠀⠰⣦⡄⠀⣠⡄⠀⠀⠀⠀⢀⣾⠿⠃⣠⠃ ⠀⠀⢸⠀⠀⠀⠀⠀⠐⠿⠂⠀⠿⡗⠀⠀⠀⠀⠀⠀⡟⢇⠀⠈⢣⣀⣀⠞⠉⠁⠀⠉⠁⠀⠀⠀⠀⣸⠆⠐⠒⠁⠀ ⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⡀⠀⣱⠀⠸⠁⠀⢀⡜⠀⠈⢦⠀⠀⠈⠙⢄⣀⡠⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠉⠙⢦⡀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣴⠋⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠀⣀⡟⠒⠦⢤⡤⠤⠤⠤⠔⠊⠙⠢⡀⠀⠀⣰⠟⠉⠐⠒⠤⠤⢀⣀⣀⡤⠴⢯⡀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠙⠢⢤⡀⠀⠀⠀⠀⠈⢢⡴⠁⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀⠀⠀ ⠸⡀⠀⠀⠀⢤⡜⠁⠀⠀⠀⠀⠀⠈⠉⠉⠓⠂⠤⠄⠠⢷⣄⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀ ⠀⠱⠤⢄⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠉⠉⠒⠒⠤⠤⡤⣀⣀⠀⠀⠀⠀⠀⢦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠢⠤⢀⠤⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣱⠃⠊⣰⣾⣿⣿⣷⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠐⣄⠀⠀⢰⣿⣿⣿⣴⠏⠘⢠⢻⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⣶⣄⡈⣿⣿⣿⡟⠀⠆⠃⢸⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠘⣦⡄⢸⠻⠿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⡇⢧⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⢻⢿⣿⠏⢀⡼⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣿⡿⠁⠀⣾⣞⡏⠀⣾⠁⠀⠀⠀⠀⠐⠛⠉⠾⠿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⣿⡁⠀⠀⣿⣼⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡏⢹⡆⠀⣟⣹⢠⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣧⣌⣿⡀⢸⣻⣾⡟⠀⠈⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢻⡟⠁⣠⣴⠾⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠘⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⠻⡇⠀⠀⠧⠀⢀⣴⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠉⢇⣠⠇⠈⡆⠀⠀⢸⡿⠻⣿⠷⠆⠀⠨⠍⣷⢀⠄⠀⠀⠀⢹⣿⣿⠟⢁⣠⠄⣻⣿⣿⣿⣟ ⠀⠀⠀⢀⣾⠀⡠⠎⠀⠀⠉⠀⠀⠈⠳⡀⠙⠃⠀⠀⣠⣾⡿⠊⠀⠀⠀⢀⣿⡿⢁⣴⡟⠁⢀⣿⣿⠿⣿⠋ ⠀⠀⡰⠋⢹⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⣼⡟⠁⢈⣿⡅⢀⣼⡿⡟⠧⣿⠀ ⠀⡼⠁⠀⠸⡇⠈⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢀⡠⠿⠁⡠⠚⣿⣿⠇⠀⣿⠀ ⢸⡇⠀⠀⠀⢻⡄⢤⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠋⣀⡴⠋⠀⢰⣿⡿⠀⢠⡏⠀ ⠀⢿⡄⠀⠀⠀⠳⡀⠙⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠉⣹⠁⠀⣠⣿⣿⠃⠀⣸⠁⠀ ⠀⠘⣿⣄⠀⠀⠀⠹⡀⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠁⠀⠀⠰⠃⢀⣴⣿⣿⡏⠀⢠⡟⠀⠀ ⠀⠀⢱⠈⢣⡀⠀⠀⢣⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⡟⢠⢀⣿⠁⠀⠀ ⠀⠀⠈⣇⠀⠹⣦⡀⠀⠈⠉⠉⠙⢿⡟⡽⠃⢹⣿⣟⠦⢄⠀⠀⢀⣠⣴⣾⠿⠻⢿⣿⡟⠀⠀⣼⠇⠀⠀⠀ ⠀⠀⠘⡍⢧⠀⠙⢿⣦⣀⠀⠀⢀⡞⣿⣄⠀⠀⠙⠿⣿⣦⣤⣶⡿⠟⠉⠀⠀⠀⠘⡎⢳⠐⠚⠛⠀⠀⠀⠀ ⠀⠀⠀⠘⣦⠃⠀⠀⠙⢿⣿⣶⣾⣈⡈⢿⣧⡀⠀⠀⠈⠛⠋⠁⠀⢀⣠⣴⣤⠀⠀⠹⣄⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⠑⢦⣤⣀⡀⢨⣿⣿⣿⠟⠲⢿⣿⣷⣦⣤⣀⣀⠠⠚⠉⠀⢻⣿⣷⠀⠀⠈⠳⣌⠳⣤⠀⠀⠀ ⠀⠀⠀⠀⣿⣧⡈⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠻⣿⣿⡉⠉⠉⠙⢦⣤⣀⣋⣙⠀⠀⠀⠀⢿⣷⣌⢷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡆⠀⠀⠀⣀⡤⠔⠒⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡔⠋⠀⠠⣧⡤⠞⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠉⠛⠶⣄⣰⠋⠀⢠⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠈⠉⠀⠀⣺⡐⠀⠤⠒⠉⠉⠒⠢⣄⡀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⢀⡴⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⡠⠄⣼⠃ ⠀⠀⠀⣀⡼⠇⠀⣰⠋⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⢱⡀⠀⠰⣅⢀⡾⠁⠀ ⠀⡴⠟⠉⠀⠀⣰⡏⠀⠀⠀⠀⣠⣾⠟⣻⣆⠀⠀⠀⠀⢸⠄⠀⠀⠀⢷⣀⠀⠈⢣⡀⠀⠀ ⠀⢳⡀⠀⢰⠋⣽⠀⠀⠀⢀⣴⠋⢠⢋⣭⡹⣆⠀⠀⠀⢸⡀⡀⠀⠀⢸⡍⢹⡆⠀⢳⡀⠀ ⠀⠀⠻⣄⢸⣀⡇⠀⠀⢀⡾⠇⢠⣟⣦⡤⠃⠙⣧⡀⠀⣼⣇⢱⠀⠀⠀⡇⡼⠀⠀⠀⢳⡀ ⠀⠀⠀⠈⠿⣿⠁⠀⢠⣟⣡⠤⡤⠖⠒⢒⣒⣒⢻⣇⢀⡿⠿⣆⢣⠀⠀⣷⠗⠦⠤⠤⠾⠇ ⠀⠀⠀⠀⠀⡿⠀⢠⣿⣷⣾⣟⠋⠉⠉⢉⡉⣉⣽⣿⣿⣏⡙⢿⡆⠀⠀⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⢀⡿⣿⣾⣿⣿⡓⠆⠀⠀⠙⢻⣿⣿⣿⣽⢹⠟⢻⡆⠀⣿⢭⣳⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⡼⢧⣳⣽⣿⣛⡇⠀⠀⠀⠀⠛⠓⠿⠛⠓⢋⣀⠤⢻⡀⢸⢼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⡀⣩⠭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⢀⣀⠈⣷⣧⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣾⡇⠀⡠⠄⠀⠀⠐⠦⠠⠄⠀⠀⠀⢠⡀⠀⠀⠀⣤⣸⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⢀⡠⠤⠖⠒⠉⠉⠉⠁⠀⠀⡼⠁⠈⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠉⠉⠙⠓⣲⡄⠀⠀⠀ ⠀⠀⠀⠀⣠⡔⠒⠋⠉⢩⠙⠿⣷⣄⠀⠀⠀⠀⠀⢀⣠⢾⠋⡜⠀⠀⠀⠀⡼⣵⠃⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡄⠀⠀⢸⡀⠀⢻⠙⠲⠤⠤⠴⠒⠋⠀⣾⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢇⠀⢸⡀⠀⠀⠀⠐⠉⠀⠀⠹⣆⡇⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠘⢶⣟⠃⠀⠀⠀⠀⠀⠀⠀⣠⢽⡇⢀⣯⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣷⡀⠀⢸⡏⠑⠢⢄⣀⣀⠠⠖⠋⠀⣰⡇⣎⡞⠙⠳⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠋⠁⢻⣷⠀⢸⣧⡀⠀⠀⢸⡧⠀⠀⠀⣠⢿⣿⣿⠁⠀⠀⠀⠈⠓⢦⡀⠀ ⠀⢀⡤⠞⠉⠀⠀⠀⠀⢻⡆⠈⣧⡙⢦⡀⢸⡇⠀⡤⢊⡤⠾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⢠⡞⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠃⠉⠢⠈⢳⠴⢋⡴⠋⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢰⠁⠀⠀⢔⣼⣽⢟⠘⢄⠀⢸⣿⡌⡷⣾⡿⢺⣿⣿⡻⣷⣂⠈⢂⠀⠀⠀⠀⠀ ⢻⡀⢀⣾⣯⣾⠋⣼⠀⣼⡀⠈⣿⢿⡑⠛⠂⠐⠉⣉⣵⢤⣷⣧⠀⠢⠀⠀⠀⠀ ⣀⣷⣞⣵⡿⢹⡆⢺⡆⢸⣷⠄⣿⠌⠀⠀⢤⢢⣾⣿⣷⣿⣿⣿⣧⠀⠱⡀⠀⠀ ⣯⣛⣻⣿⡀⢸⣿⢸⢿⡜⡏⠇⠛⠀⢀⠺⣴⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠐⠀⠀ ⢿⡼⠛⡅⠸⠈⣿⢻⠈⠁⠃⢘⢰⠀⠈⠄⠻⠻⣽⣿⣿⣿⠿⠿⠇⢣⠰⠀⠀⠀ ⡿⡷⣄⣷⠀⠀⢿⠃⠀⠠⢕⣢⣨⠀⠀⠀⠐⠢⠬⠉⠁⠀⠀⠀⠀⢠⢆⢡⠀⠀ ⣧⡇⠀⢹⢠⡗⣽⣾⣿⣿⣿⣶⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠸⡀⢃⠀ ⡏⡧⡀⢸⢉⣾⣿⣿⣿⣿⣿⢿⡸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠐⡇⠀⠄ ⣷⣀⠀⠀⡏⠿⣿⣿⡿⠭⠊⠋⠃⡇⠀⠀⠀⠀⠀⠀⣀⡤⢞⣿⠟⡤⢂⢣⢳⠸ ⣯⠹⠤⢄⠉⠀⠏⠇⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣠⡾⠋⠈⠻⠏⢈⠀⣸⠆⢻⡄ ⣿⣷⡀⠀⠈⡧⠀⢵⠠⢀⠀⠀⠀⠁⣠⡴⣟⡫⠄⠈⠀⠀⠀⣭⢕⢻⣿⡘⠈⡇ ⡏⡏⠉⠂⠈⢠⠀⡾⣦⣄⠈⠛⠻⣿⢷⣿⡁⠂⡀⢀⠤⢐⡸⠽⣿⣾⣿⣿⡡⠀ ⡇⠁⠀⠀⠀⠞⠀⠁⣿⣿⢿⣶⣦⣿⣐⣬⡆⢠⠍⠵⡾⠟⠂⠀⣼⣿⣿⡿⣧⠆ ⡇⠀⠀⠀⠀⠀⡇⢸⢹⣿⣸⣿⡏⢻⣿⣿⣰⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣧⠻⡞ ⠳⠀⠀⠀⠀⠀⢹⠀⡌⣯⣿⢹⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⢻⠓⢱ ⠀⠀⠀⠀⡀⠀⠘⡀⠁⠛⠋⡩⢿⢸⣿⡾⠛⠉⠛⢿⣿⣿⣿⣿⠏⠀⡌⡞⠆⠈ ⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⢸⡃⠀⠃⢐⠃⠀⠀⠀⠀⠉⠙⡓⠁⠀⡀⢀⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⡟⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢠⡇⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢸⡇⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⡴⠋⠉⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣿⣤⣴⣦⡴⠿⣷⣶⣶⣦⠀⠀⠀⠀⣾⠋⢀⣈⠉⠁⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣟⣛⠛⠁⠀⠈⠉⢻⣿⣿⣦⣄⣼⠃⠀⢸⠉⢳⣶⠾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠉⣧⡴⠋⠙⢳⣼⣿⡟⢀⡽⠃⠀⠀⡿⠀⠀⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠤⢤⣤⣤⣾⡟⢀⣴⣄⡼⡟⠀⠀⠀⠀⣏⠉⠀⠈⠀⠀⠀⢠⡇⠀⣀⣼⠟⠀⠀ ⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣶⣄⠀⠈⠙⠓⠒⠛⠛⠃⢣⠀⣶⡶⢠⠇⠀⠀⠀⠀⠀⠀⠈⢤⡞⠋⠁⠀⠀⠀ ⠀⢠⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠓⠿⠧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀ ⢠⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⣾⡃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⠈⠿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡿⠀⢀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠹⣆⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢙⡟⠁⠀⢸⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠘⢷⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠁⠀⠀⣼⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡟⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⣀⣀⣠⡼⣛⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢛⣾⠁⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⣾⠋⢿⡀⠉⠙⠓⠶⠦⠤⠤⠶⠞⠋⢁⣼⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠉⠳⣦⣄⡀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣤⣀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣷⡀⠁⠀⢠⣾⣿⣄⣀⣤⣤⣤⣼⣿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣺⣿⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⣻⣷⣀⣀⣼⣿⣿⡿⣿⣿⣿⣿⡿⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠴⢿⣿⣿⡿⢝⣹⡿⠿⠿⠏⣛⣡⣾⣟⣛⣥⡎⠀⠀⠠⡀⠀⠀⠀⠀ ⣴⣾⣯⣾⣿⡟⠙⣿⣿⣄⣟⠐⢿⣿⣿⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡈⠁⠚⠉⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡇⠀⠀⠀⠀ ⠋⢸⣿⣿⣿⣧⠀⠻⢁⡀⣀⣺⣿⡿⠋⠀⣴⣿⢿⣿⣿⣛⡫⠭⠶⠶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⡇⠀⠀⠀⠀ ⠀⢨⣿⣿⣿⣿⣷⣶⣄⣀⣉⣿⠟⠁⢂⣾⣿⣷⠟⢉⠁⠄⠰⢦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⠋⢹⡇⠀⡄⡀⠀⠀⢄⢷⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠉⡿⠟⢋⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣼⣿⣿⡆⠸⣧⣤⣇⣱⠄⠀⠀⢸⡇⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⡟⠈⢧⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣷⠀⢯⠀⠹⢦⣄⣀⡀⠈⠃⢠⢿⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⣉⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⡟⠁⠀⣰⡿⠁⠳⣌⠛⣿⡇⢸⣼⠀⠀⠘⠧⠀⠀⣷⣾⣼⣼⠿⠿⠛⠛⣿⡏⢠⢿⡦⢿⣿⣿⣿⣿⣿⣧⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⢿⠀⠀⠀ ⠀⠀⠀⢀⣿⡟⠀⢀⣼⠟⠀⠀⠀⠘⣆⠘⡇⠘⠏⣷⡄⢀⣼⣿⣟⣁⣀⣠⠤⣴⣶⠟⣫⣿⣇⠸⣧⡿⢰⣿⣿⣿⠿⢏⣣⣤⣤⣤⣾⣿⡿⢿⣿⠟⠁⠈⢻⣿⠟⠃⠀⢸⣷⠀⠀ ⢀⣤⠀⣾⡏⠀⠀⣾⡏⠀⠀⠀⠀⣼⠁⠀⣿⣠⡴⢛⣵⢿⣿⢿⣯⣭⣵⡿⠛⢉⣠⣼⣿⣿⣿⣶⣤⣶⣿⣿⣟⣁⣴⣿⣿⣿⣿⣿⣿⣿⣤⡞⠁⠀⠀⡀⠀⠹⣦⣤⣤⣾⣿⡃⠀ ⣿⣇⣾⠏⠀⠀⣾⣿⡀⠀⠀⢀⣼⣯⡤⠾⢋⣠⠞⢉⣀⣤⣾⣿⠿⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣦⠀⠘⣿⣿⣿⣿⠁⠀ ⣿⠿⠃⠀⢀⣼⢿⣿⣿⣧⣿⠟⠛⢁⣤⠾⣫⣥⣶⣿⡿⠟⠋⣀⣤⣶⡿⢛⡻⠿⢾⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣇⣽⣿⣿⣿⡟⠀⠀⣼⡿⣏⠀⢻⣆⠀⠙⣿⣿⣿⠀⠀ ⡏⠀⠀⠀⣼⠏⠀⣿⠿⠋⣀⡴⢾⣻⣿⣿⣿⡿⠟⠁⣀⣴⣿⠿⠋⠁⢠⡾⠁⣠⣿⣿⣿⠿⠋⠀⠀⠉⢙⡤⠀⠙⣿⣿⡿⣿⣿⣿⣿⠁⠀⣼⣿⡀⠹⣆⠀⢿⠀⠀⢹⣿⣿⡇⠀ ⡇⠀⠀⣸⡟⠀⢠⣿⡴⠛⣫⣶⣿⣿⡿⠛⠁⣠⣴⡿⣿⡏⠀⠀⠀⢠⣿⣷⣿⣿⡿⠋⣁⣤⡴⠶⠴⡾⠿⠃⠀⠀⠙⣿⣿⣿⣿⣿⡏⠀⠀⠉⠻⣇⠀⢿⡄⠘⡇⠀⢸⣿⣿⢷⡄ ⣧⠀⠀⣿⠃⠀⢸⡿⣶⣿⣽⠿⠋⣁⣠⣶⡿⠟⠉⠀⠟⠀⠀⢀⣴⣿⣿⣿⡿⠿⣖⣻⣽⣾⣿⣿⣿⡷⠆⠀⠀⢀⡴⠃⠈⠛⠿⠋⠀⠀⠀⠀⠀⣹⠀⣸⠇⢠⠇⠀⣸⣿⣁⣸⣿ ⢻⣄⣸⡇⠀⠀⢀⣿⠟⠋⢀⣤⣾⡿⠛⢿⡇⠀⠀⢠⠀⢀⣴⣿⣿⡿⣻⣷⣶⣿⣿⡟⣻⡿⢧⣽⡾⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⡴⠋⢠⡾⠀⣰⣿⣿⣿⣿⣿ ⠈⢻⣿⠀⣠⠾⠛⠁⣠⣼⣿⠟⠉⠀⠀⢸⢿⣦⣤⣾⣾⣿⣿⣿⣿⠿⣿⣁⣀⣀⣛⣁⣤⠿⢋⣀⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣰⠟⠁⢠⠎⠀⣰⣿⣿⡟⣿⣿⣿ ⠀⢀⣭⠟⠁⢀⣴⣿⣿⣿⣿⠀⠀⠀⢄⢘⡞⣿⡿⣿⣿⣿⣿⢏⣥⣤⣭⣥⣤⣤⣬⣵⣶⡾⠟⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡤⠖⠁⢀⣴⡿⣿⣿⣷⠹⣿⣿ ⠴⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣼⣿⣿⡿⠿⠛⢉⡥⠤⠭⢿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⣀⣴⣿⣿⣿⡹⣿⣿⣷⣜⣿ ⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣭⣿⣿⣿⠉⡇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣴⣾⣿⣾⡿⠿⣿⣷⣦⣍⢙⣿⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠁⠀⢘⠈⠉⢿⣿⣿⣋⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠘⣿⡟⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⢸⠀⣠⡿⢿⣿⡿⣿ ⣿⣿⡿⠿⠟⠛⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠗⢻⡀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠈⡀⠀⠰⠾⣿⣿⣽ ⠁⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣧⣤⣶⣺⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠒⠒⠢⢤⣀⠁⠀⠀⠀⠛⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣤⣿⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠈⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠻⣿⣿⠁⠀⣠⡤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⣶⣿⠛⠒⠦⣄⠀⠀⠘⢿⣄⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣿⣶⣾⣿⠟⠛⠒⠛⠛⠛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣾⣿⣿⡇⠀⠀⠀⠈⣷⣄⠀⠈⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠻⠟⠋⠁⠀⠀⠀⠀⠀⢀⣠⡾⠃⢀⣀⣀⣀⣀⣀⣀⣤⣤⣿⣤⣴⣿⣿⣷⣯⣤⣤⣤⣤⣤⣷⣽⠀⠀⢸⣧⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢠⡄⣀⣀⣀⣀⣠⣶⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⢻⢿⠉⠀⠉⣽⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⣯⣿⠟⠀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠆⠀⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣠⣤⡾⠟⠃⠀⠀⢀⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣴⠋⠉⠉⠁⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣼⣤⣤⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣰⣿⣿⣄⣀⣀⣀⣤⣶⣿⣷⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠛⠛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢸⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⢸⡇⠀⠀⠀⣿⠛⠉⢿⣿⣿⣿⣿⡿⢁⣀⣠⣿⣿⡿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⢸⣿⣿⣧⣬⣭⡶⠀⠈⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⣀⣤⣿⡇⠀⠀⠀⢷⡀⢀⣸⣿⠿⠛⠋⢉⣉⣭⣥⣤⣴⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⣿⠟⠁⠀⠀⣠⣾⣿⣿⣿⠿⣧⡀⣀⣴⢞⣯⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⢠⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣸⠃⠀⠀⣠⣾⣿⠛⣋⣥⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣇⣘⣻⣄⣀⡀⠛⠛⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⣠⣾⡇⠀⠀⣰⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣶⣶⣶⣶⡶⠚⠉⣼⠃⠀⠀⣿⡇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠉⠒⠊⠛⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⡄⠀⠀⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣷⣄⣴⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣧⠘⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣿⣿⣧⣤⣀⣩⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠾⠛⠋⠉⠉⣿⡟⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⣿⣿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣤⠞⠁⠀⠀⠀⢠⡴⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣀⣴⡟⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣴⣿⣿⡇⠀⢀⡴⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⠏⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠒⠒⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⢳⠶⡄⢀⠠⠔⠒⠀⠉⠉⠁⠐⠂⠤⣀⠐⠖⠀⠑⢦⠀⠀⠀⠀ ⠀⠀⢀⠜⠀⠀⠉⡠⠚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠓⠢⡀⠀⠀⠱⡄⠀⠀ ⠀⢀⠎⠀⠀⢠⠊⠀⠀⢻⣽⢵⣤⡀⠀⠀⢀⣤⢞⢿⡏⠀⠀⠙⢄⠀⠀⠘⡄⠀ ⠀⡜⠀⠀⢠⠃⠀⠀⠀⠈⡌⢏⠫⣙⣶⣮⣿⠕⡱⢱⠁⠀⠀⠀⠈⡆⠀⠀⢱⠀ ⠀⠁⠀⠀⡌⠀⠀⠀⠀⠀⠐⡨⡖⡑⢈⠩⠋⢶⢄⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄ ⢸⠀⠀⠀⡇⠀⠀⠀⢀⣔⡨⢷⠁⣌⣢⢧⣊⡆⡿⠅⣢⣀⠀⠀⠀⠈⠀⠀⠀⡇ ⠈⡄⠀⠀⢃⢀⣄⣾⣋⣲⠬⠟⢧⠙⠏⢘⠟⣽⠻⠭⢭⣽⣷⣢⡀⢸⢀⡀⠀⠇ ⠀⢣⠈⡇⠘⡍⠉⠉⠉⠉⠉⠉⠹⣏⠏⠹⣹⠏⠉⠉⠉⠉⠉⠉⢉⠇⠈⡇⠰⠀ ⠀⠈⢆⠃⠀⠘⢄⠀⠀⠀⠀⠀⠀⢻⣧⣴⡟⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠃⠀ ⠀⠀⠈⢦⠀⠀⠈⠳⢄⠀⠀⠀⠀⠈⣧⣼⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠃⠀⠀ ⠀⠀⠀⠀⠑⢄⠀⠀⠀⠉⠒⠤⢀⣀⣰⣆⣀⡀⠤⠔⠊⠁⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⣶⢤⠄⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠤⠤⠬⠤⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠋⠀⠀⠉⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠈⣿⣇⣀⠀⠀ ⢀⣴⣿⠿⠿⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠛⠛⢿⣷⡄ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⣻⣷ ⠘⣿⣧⡀⠀⢀⣀⠀⠀⠀⠙⢿⣷⣄⠀⢀⣴⣾⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣦⣀⠀⣠⣿⡟⠁⠀⠀⠀⣠⣀⠀⠀⣠⣿⡏ ⠀⠈⠻⢿⡿⠿⢿⣷⣄⠀⠀⠀⠙⣿⣷⣿⣿⠟⠋⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠉⠻⢿⣿⣿⣿⠋⠀⠀⠀⣠⣾⡿⠿⢿⣿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣠⣾⣿⡿⠋⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⠿⣿⣿⣦⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠋⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⣴⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⢠⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⣠⣿⣿⣿⣿⣿⣃⣀⣀⣤⣤⣤⣤⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢠⣿⣿⣿⣿⡿⠛⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣆⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡏⠀⢠⣿⣿⣿⣿⣿⠷⠶⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠾⠿⠿⣿⣿⣿⣆⡀⠘⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡷⠾⠛⠋⠉⠁⠀⢀⣠⣤⣶⡶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠷⠶⢶⣤⠀⠀⠀⠉⠉⠛⠻⠿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣥⣤⣤⣀⣀⣀⣀⣰⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣤⣤⣤⣤⠴⢶⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣀⡀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠉⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⡏⠉⢻⡟⠛⢻⡋⠉⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠈⣿⠛⠓⣿⠷⠶⢾⡷⠚⢻⡏⠁⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣴⣿⣿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣷⣶⣴⣿⠟⠁⠈⠻⣿⣿⣶⣄⠀⠀⠙⠻⢿⣿⣿⡷⣴⣯⣀⣀⣿⠀⠀⢘⣇⣀⣀⣿⡴⣿⣿⣿⠿⠋⠁⠀⣀⣴⣿⣿⡿⠁⠀⠈⠻⣿⣶⡿⢿⣶⣄⠀ ⢰⣿⠋⠁⠀⠈⠛⠁⠀⠀⢀⣴⣿⠟⢿⣿⣿⣶⣄⡀⠀⠈⠛⢿⡀⠀⠉⠉⠉⠛⠛⠋⠉⠉⠁⠀⢠⡿⠉⠀⠀⣀⣴⣾⣿⣿⠟⠻⣿⣦⡀⠀⠀⠈⠁⠀⠀⠙⣿⡆ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣀⣻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣏⣠⣴⣶⣿⣿⡿⠟⠋⠀⠀⠀⠈⢻⣿⠆⠀⠀⠀⠀⠀⠀⣽⡿ ⠈⢿⣷⣦⣤⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⣶⣶⣾⠿⠃ ⠀⠀⠈⠙⣿⣇⠀⠀⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⣠⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀