Steam Profile Emojis & Text

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⡿⠟⢛⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣩⠉⠉⢿⠀⢞⠉⠈⠳⠌⢿⣿⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢠⠋⢀⣤⢤⣄⠀⡞⠛⢶⡀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⢀⣿⣿⣿⡇⠀⢰⠏⠀⠀⢹⣾⡇⠀⠀⢷⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠸⣇⢠⣦⣤⡇⢷⣿⣷⣺⡇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠙⢯⣿⣿⣿⣼⣿⡿⠿⢧⣄⠋⠉⠉⠻⢿⣆⠀⠀⢀⡞⠉⠙⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠛⠻⡄⢠⡜⠋⢰⣿⣿⣿⣿⡇⠀⣬⣥⣤⣤⠀⠀⢹⡆⠀⣸⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢀⡴⠋⠀⠀⢻⣿⣿⣿⣿⠇⠀⢠⠞⠀⠀⠀⢀⡾⠁⠀⡏⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠰⠟⠷⣤⣀⠀⠀⠈⠉⠉⣀⣠⣴⠋⠀⠀⣀⡴⠋⠀⠀⠀⢹⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠉⠻⣿⣻⣿⣭⣭⣴⠏⣠⡴⠟⠁⣠⠴⢶⡟⠉⠹⣇⠀⢸⡗⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡬⣽⠛⢛⣷⠦⣌⣙⣛⣛⣋⣥⠞⢯⠀⢀⡞⢡⣤⠀⠹⠆⢠⠋⠀⠀⠁⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠉⢁⣠⣾⣃⣰⡿⠁⠀⠀⠀⠀⣹⡟⠀⠀⠈⢷⡾⣷⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡴⢋⣄⠉⠉⠉⠉⠓⠲⢤⣀⣼⠟⠀⠀⠀⠀⠈⢿⡞⠁⠀⠀⠀⢰⠄⢰⠀⡄⢠⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠎⣠⣾⣿⡇⠀⣠⣾⣿⡄⠀⠈⠙⢦⣸⠻⣆⠀⠀⡾⢷⡀⠀⠀⠠⣾⣠⢏⡼⣡⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⣿⣿⣿⠃⢰⣿⣿⣿⣿⠀⠀⠀⠀⠙⡆⢹⡀⠐⣧⠀⠙⢷⣤⡀⢀⣃⣯⠶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠁⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣹⠀⢧⠀⠈⠳⢦⣤⠼⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠈⠳⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣴⣋⣀⣀⣀⣀⣀⠀⠀⣀⣀⣠⣀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣈⠉⠉⠙⣟⠉⠀⠀⠀⡇⠉⠉⠉⠑⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡄⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⡇⠀⠀⣷⡀⠀⢀⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⢏⠙⢦⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢱⡀⠈⢦⠘⡄⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⣀⣠⣤⣶⣦⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣤⣼⣿⡄⢀⣿⣷⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⠤⠒⠉⠉⠀⡠⠞⠿⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡠⠿⠷⠍⠛⣄⣯⠙⡏⠑⠒⠓⠴⢲⠷⠾⠿⠃⠀⠀⣠⣴⣏⣀⡀⠀⠘⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⣤⡿⠃⠀⠀⠀⠀⢻⡆⢇⠀⠀⠀⢠⡎⡀⠀⡀⠀⡠⠊⠡⠒⠿⣷⡄⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣄⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠀⠀⠀⣿⢠⢁⠜⠁⠈⠀⠀⠀⠀⠘⢦⣽⠦⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⡠⢔⣿⣿⣿⣷⣌⠛⠀⠀⢠⡇⢣⣊⣀⣀⡀⠀⠀⠀⠀⠀⢩⣿⠄⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⣜⣛⣷⠦⣉⣉⣉⡉⠉⠉⠉⢶⣤⣤⣤⠴⣏⣡⣾⣿⣿⣷⣦⡀⠀⠀⠀⠙⠳⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠧⡤⠔⠊⢉⡀⠤⠜⢳⣀⣀⡤⠀⠀⠀⠀⢀⣠⣿⠁⠀⠀⠀⢈⡉⠙⠛⠛⠻⠗⠀⠤⡀⠀⠀⠴⢾⣇⠀⠀⠀⠀⠀ ⠀⢀⡶⠋⠀⠀⠀⠀⠉⠀⣠⠔⠂⡩⠜⠋⠓⠒⠒⠒⠉⠁⠀⠈⠑⢦⡀⠀⠀⠑⢤⡉⠒⠲⢵⣶⠄⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⣀⣼⡁⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠚⠻⡒⢇⠛⢬⡑⠢⢄⠀⠀⠀⠈⠹⣟⠂⠀⠀ ⠉⠉⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠙⢦⡈⠑⠀⠉⠢⢄⠀⠠⣿⠁⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢾⡄⠀ ⠀⠀⣄⠀⠐⣦⡀⠀⠀⠀⠙⠦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠆⠀⠀⠀⢨⣷⠀ ⠀⠀⢻⣼⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣀⣤⣴⠿⠛⠁⠀⠀⠀⠀⢸⣿⡆ ⠀⠀⠈⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠁⠀⠀⠀⢉⡀⠀⠀⠀⣀⡤⠤⠿⣿⠃ ⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⢘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⠶⠶⠶⠦⠤⠤⠤⠤⢤⣤⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⢤⠄⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠠⠴⠚⣻⠧⠤⠤⠤⠤⠴⠚⢋⣩⠷⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣤⠶⠒⠚⠉⠉⠀⠀⠀⣸⣋⣻⣿⣿⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⣤⡤⣤⣤⣔⣂⠀⠀⠀⠀⣤⢤⠘⠳⣖⢮⣀⡉⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠾⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣿⡿⠿⠿⡇⠀⡄⣠⣙⣂⣀⣺⣣⣴⣷⠏⠧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⣤⠞⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠘⠁⠙⡟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣄⣀⣤⡴⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⠘⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣴⠟⢻⣴⠟⢻⣆⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠞⠉⣇⡞⠁⢀⡿⠁⢠⠟⢹⡇⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⡞⠀⢀⡞⢠⣿⡆⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⡀⣀⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠏⠀⢠⠋⣀⣾⣼⠃⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢻⡄⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⣷⢞⣍⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣤⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠈⢿⣀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀ ⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⢀⣠⣤⠶⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⡶⠤⠤⠴⠖⠒⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⢲⡿⠶⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠉⠉⠁⠈⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⠛⣷⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣶⠶⣦⠀⢀⡀⠀⣼⣿⣿⣿⡏⠀⢸⡇⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⠂⢸⣷⠟⠁⠀⠿⣿⣛⢛⣀⣴⠟⢁⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠐⣿⣿⡿⣋⣤⣾⠏⣠⣤⣤⠀⠈⠙⠛⢉⣠⡴⠿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠈⣿⠋⠉⠁⠻⣦⣴⡶⠛⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠄⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⢀⣀⣀⣤⡶⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⢓⣾⠀⣀⣄⠀⠀⠀ ⠀⠀⢸⡟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣄⠀⠀⠹⣧⡀⠀⠀⠀⢀⣠⣤⡶⠶⢶⣿⠁⠀⠀⢠⣾⣧⠾⣛⣿⡇⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⢿⡆⠀⠀⠸⣧⡀⣠⡶⠛⠉⠀⠀⢀⣼⣃⣀⣀⣰⣉⠈⠁⠶⠶⠾⠷⢶⣄ ⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣷⠀⠀⠀⢻⣷⠟⠀⠘⠛⣶⡾⠛⠋⠉⠉⠉⠉⠙⠛⢶⣄⠀⠀⢀⣀⣿ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⠹⣆⡈⢁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣧⡼⠿⠃ ⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣬⣌⣉⣹⡦⠀⠀⠀⠀⠀⣤⡖⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣷⣸⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠛⠁⣀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣷⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣤⣤⣤⣤⣤⣶⠶⠿⠛⠉⠀⢸⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢰⣶⠒⠲⠶⣿⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣄⡀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣈⣙⠿⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠦⣀⢀⣀⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣫⣶⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⣿⣿⣮⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⣱⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣹⣿⣿⣿⣧⡈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⡇⠀⣿⢿⣿⣿⣿⣿⡄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢿⣿⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣿⣿⣿⢸⣿⣼⣿⣿⣿⣿⣯⢆⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⣿⡈⢿⣿⡼⣿⣿⣿⣿⣿⣿⢿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣯⢣⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⣿⣿⣧⣿⣧⢹⡙⣿⣿⣿⣿⣿⣎⣻⣷⡈⢻⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣇⢧⠸⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢿⣿⣿⢿⣿⣇⠻⣌⠻⡟⠉⢄⣠⣭⠈⠙⠀⠉⠻⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢸⣿⣿⡞⠿⠟⠃⠉⠀⠀⠠⢺⡯⣮⣽⡛⠦⣤⡤⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⢛⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣮⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠘⣧⢿⣷⣄⡀⠀⠀⠀⠀⠀⠋⠀⣿⡟⢷⠀⠈⢹⠂⠀⣿⣿⣿⣿⣿⣿⣿⣧⣍⠑⠄⠈⢿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠸⡌⢻⠾⣿⣦⠀⠀⠀⠀⠀⠀⠹⣷⣸⡇⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠈⢳⠀⡀⠘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡷⠀⠹⣾⠀⠸⣿⣣⠀⠀⠀⠀⠀⠀⠹⣾⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡼⠁⣸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡆⠀⢸⣷⡄⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⣿⣿⣿⣿⡧⠴⠃⣰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⢾⣿⣿⣦⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⢀⣇⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀ ⣧⣤⣄⡀⠀⠀⠀⠘⣇⡏⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣯⣿⣺⣿⣿⣿⣿⣼⡿⠁⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠀⠀ ⣿⣿⣯⣭⡉⠙⠲⠀⠘⣿⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡏⣿⠀⢿⣿⣿⣧⣿⠇⡄⣿⠃⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⡀⠀ ⣿⣿⣿⣿⣿⣿⣆⠀⠀⢻⢹⣿⣿⣿⡻⡀⢀⣴⡶⠒⡆⠀⠀⠀⠀⠀⠀⢸⣯⠀⣿⣿⣿⣿⣧⣿⡇⢸⣟⣾⣿⣇⠀⣧⣿⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡌⡇⠀ ⣿⣿⣿⣿⣿⣿⣽⡆⠀⢸⠈⣿⣿⣿⣿⠙⢦⠻⣄⣠⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⣻⣿⣿⣿⣿⢸⡇⢼⣇⣸⣿⡏⠀⠸⣿⠀⠀⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀ ⣿⣭⣛⠻⠟⢿⣿⡇⠀⢸⡴⠋⠉⠻⢿⣆⠈⠳⣌⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⠟⣿⣿⢸⢸⡇⢸⣮⣿⣿⠃⠀⠀⢿⣶⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡀⠀ ⣿⠿⢿⣷⣄⠀⠹⢇⡴⠋⠀⣀⣤⣄⣀⢹⣆⠀⠙⣆⠀⠀⢀⣠⡴⠚⣯⣽⣿⠏⣿⠀⣿⣿⠈⢸⡇⠀⢿⣿⣿⣷⡶⣄⢸⣯⠀⠀⢸⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀ ⣿⡆⠀⠈⠻⡄⠀⢸⠀⠉⠉⠁⢀⣀⣈⣿⠉⡇⠀⠈⠉⢉⣡⣶⣿⣿⣿⣿⡇⡇⡿⢸⣿⣿⠀⢸⡇⠀⠸⣿⣿⣿⣿⣿⡄⢻⡇⠀⣸⡅⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⠀ ⣿⢿⣆⠀⠀⠁⠀⡏⠠⠖⠒⠉⠉⠀⠀⡏⠀⣇⣀⣤⣾⣿⣿⣿⣿⣿⡿⢻⡇⠀⠁⢸⣿⡏⢀⢸⡇⠀⠀⣽⣿⣿⣿⡟⣿⣿⢿⣆⣿⠥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⠀ ⣿⣿⣿⡀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠤⢤⢹⣾⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⢸⡇⠰⠀⣿⣿⡇⢸⢸⠀⣠⣾⣯⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀ ⠈⣿⣯⠇⠀⢀⣴⡇⠀⠐⠉⠉⠀⢀⢸⣽⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⣰⠏⢠⠀⣷⣿⣿⡇⢸⣿⣾⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⠀⠈⣿⡄ ⠐⠛⠁⠀⢠⣿⣿⡇⠀⠀⠠⠖⠚⡏⢀⣿⣿⣿⣿⣿⣿⣇⠈⠙⠒⠒⠁⠀⢼⡶⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⠀⠀⢽⡇ ⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⡷⣿⣻⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⠀⠀⢸⡇ ⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢧⠿⢻⣿⣿⢻⡟⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠛⠻⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⠀⠀⠂⡇ ⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⠏⠀⢾⡟⡿⢾⡇⠀⠀⠀⢀⣴⠟⠛⠏⠛⠩⣿⣿⣿⣿⠃⠀⠀⠀⠹⣷⣮⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣠⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⡷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣎⢣⡀⠀⠀⠀ ⠀⠀⢰⣿⢿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣧⣿⣿⣿⣦⡳⠀⠀⠀ ⠀⠀⡿⣿⣿⡭⡻⠟⣛⠓⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣃⠀⠀ ⠀⠀⡇⢿⡯⡉⠀⠀⠻⡿⡁⠂⢹⣿⣿⣿⢕⠍⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⡀⠀ ⠀⠀⢹⡈⢎⢻⡆⠀⠀⠹⠇⠀⢸⣿⣿⣿⡄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀ ⣀⠀⠀⢣⣺⣷⠇⠀⠀⠀⠀⠀⢸⡟⣿⣿⣇⣼⣿⣽⢻⢻⣿⣿⣿⣿⣿⣿⣷⠀ ⣿⣯⣅⠀⠷⣿⣦⢀⡀⡀⠀⠀⢸⡇⣿⣿⡇⢻⣿⠇⣸⢸⣿⣿⣿⣿⣿⣿⣏⠀ ⣿⡿⢿⡇⢠⠟⠿⡑⠕⠃⠀⠀⣸⣧⣿⣿⡐⢳⣿⠀⢻⠀⢿⣿⣿⣿⣿⣿⣿⡇ ⣏⠙⠆⠑⠑⣒⢒⡗⠈⢂⣲⣿⣿⠁⢸⡏⡎⠘⣿⣿⣞⡇⡸⣹⣿⣿⣿⣿⣿⡇ ⢿⡆⠀⡇⠀⠠⢠⣶⣾⣿⠟⠋⠹⡤⣸⡇⣇⣴⣿⣿⣿⣾⣿⣯⡻⣿⣿⣿⠈⡇ ⠘⠁⣾⡇⠀⠒⣪⣿⣿⣿⣁⠒⠁⢓⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡆⢇ ⠀⢸⣿⡇⠀⢀⠞⣿⢿⠙⠛⡻⠿⢿⣿⡿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⣀⡄⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⣠⡞⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡼⠋⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣤⠶⠶⠤⢤⣀⣀⠀⠀⣠⡾⠋⠀⠀⢀⣀⣀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠎⠀⣠⠟⠀⠀⠀⠀⠀⣴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠘⣇⠀⠀⡇⠀⠀⠀⠀⠀⠉⠳⡞⠉⠙⠛⠦⣖⣛⣭⣥⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⣠⣾⠏⠀⠀⠀⠀⠀⣴⡟⣾⢀⣆⡀⠀⠀⠀⠀⠀⠀⣰⠀⠻⣦⣜⣧⡀⣧⠀⢀⣠⢴⣾⣻⠯⠷⢶⡄⠀⠀⠙⢧⡤⠴⠶⠾⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡞⣹⠃⠀⠀⠀⠀⠀⢸⣿⠀⡇⢸⢯⠙⠦⠀⠀⠀⠀⢠⡏⠀⢠⡏⠈⡟⠉⢿⣖⣿⠞⣩⡵⠖⠊⠉⢻⣽⠀⠀⠀⠈⢧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣼⠃⠀⠀⠀⠀⠀⢠⣿⢿⣷⣧⡀⠸⡆⠀⠀⠀⠀⠀⢸⠀⣠⠟⠠⠤⢽⣄⠘⣯⡞⠋⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠘⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⠹⣴⠃⠀⠀⠀⠀⡀⠀⢸⠁⣸⣿⣿⣷⣶⠿⣆⠀⠀⠀⠀⣸⠞⠁⠀⠀⠀⢸⣏⡉⠺⠷⣄⡀⠀⠀⢀⡴⠃⢻⠀⠀⠀⠀⠀⢹⡉⠉⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣧⠀⢸⡀⡿⢻⣯⣿⡟⠀⠙⢧⡀⠀⠀⢸⡖⣲⣤⣤⣤⡞⢻⣷⠀⠀⠈⠳⣦⠴⠋⠀⠀⢸⡀⠀⠀⠀⠀⠈⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⢰⠆⠀⠀⠀⠘⣇⣸⠁⠻⠄⠉⠸⠁⠀⠀⠀⠉⠳⢦⣘⣯⡁⣰⣿⣿⣿⣷⣿⣇⠀⠀⠀⢿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡏⢷⡀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⣿⡀⠀⠀⠀⠀⠘⡟⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡿⢿⣿⣿⣯⣳⡄⠀⠘⡆⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⡀⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢿⢣⡀⠀⠀⣆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⠛⣿⣿⡏⠀⠙⠂⠀⠻⡄⠀⠀⢰⠇⢻⡀⠀⠀⠀⣿⡝⣶⣤⣝⣷⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠈⠻⣏⠳⣄⠀⠘⢆⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣤⣈⡉⢹⠇⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⢷⡀⠀⠀⣿⠹⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢣⠈⣿⠒⠬⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⢠⠀⢣⡀⠀⠸⡀⠙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣱⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⡿⠀⠀⢳⡀⠀⣧⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⠀⠀⠀⡸⠁⠹⡄⠀⠀⠀⠈⠉⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣿⠀⡇⠀⠀⠀⠻⡄⠘⣦⣄⠀⠈⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀⠀⠀⡼⠃⠀⠀⠻⣄⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⡿⡄⠈⢿⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠋⠀⢠⡞⠁⠀⡾⠁⠀⠀⠀⠀⢹⣶⣶⣤⣤⣤⣤⣤⣤⡴⠶⠶⠚⣩⠟⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⠀⠀⢹⠀⡇⠀⠀⠀⢸⠃⢹⡀⠀⠙⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⠞⠁⠀⠀⠀⠀⢀⣿⣿⣿⣶⣾⣿⣿⣿⣧⠀⠀⣀⣴⠋⠀⢠⠀⠀⠀⠀⠀⢀⡾⠀⣿⠀⠀⢸⡄⢿⠀⠀⣰⡟⠀⢸⣧⠀⠀⠀⠈⢳⠀⠀ ⠀⠀⠀⢀⡶⠋⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠞⠉⠁⠀⠀⣸⠀⠀⠀⠀⠀⣼⠁⠀⠘⣇⠀⠀⢻⡈⢷⣰⡿⠁⠀⣿⣿⠀⠀⠀⠀⠀⠑⡀ ⠀⡠⠚⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠔⠒⠀⠀⢠⡇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠹⡄⠀⠀⠙⣦⣽⡗⠀⣼⢃⠇⠀⠀⠀⠀⠀⠀⠁ ⠈⠀⠀⠀⠀⠀⣴⠃⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡼⠙⣇⠀⠀⠀⠀⠹⣦⠀⢀⣿⣿⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠃⢀⡞⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣴⢿⣀⠀⠸⣆⠀⠀⠀⠀⠈⠓⣼⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⢀⡏⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠾⠛⠋⠉⠉⠉⠛⢳⡴⠟⠁⠀⠈⠳⣄⠹⡄⠀⠀⢀⣀⡰⠟⠁⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⣄⠘⢦⢸⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠛⠒⠒⠒⠶⢦⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣷⠀⠀⠈⠉⣹⣶⣶⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⣹⣄⠀⢸⣿⣄⠀⠀⠀⠀⢿⣿⣿⡙⢿⣿⣿⠙⠳⣤⡀⠀⠀⠀⠀⠙⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⣴⣿⠿⣆⠈⢻⣿⣶⣤⣀⣀⣀⣙⣿⣿⣯⣿⢿⡇⠀⠈⠻⣶⣄⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⣿⣿⣷⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⣿⣷ ⠀⠀⡼⣹⣿⠀⢻⣷⣤⣙⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⠀⢻⡄⠀⠀⠈⠻⣷⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢹⣿⣿⣿⣷⣄⠀⠀⣧⠀⠀⠀⠀⠀⣿⣿ ⠀⢸⠇⣿⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⢁⡿⢃⡏⠀⠀⠻⠤⣄⣀⣤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢿⣿⣿⣿⣿⣷⠄⠸⡇⠀⠀⠀⠀⣿⣿ ⠀⢸⠀⣿⣷⠀⠀⠘⣿⣯⠛⢿⣿⣿⡿⠁⣾⠃⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣶⠀⠈⢻⣦⠀⠈⢿⣿⣿⣿⣿⣧⠀⡇⠀⠀⠀⢰⣿⣿ ⠀⠈⠀⠘⣿⣦⠀⠀⢻⣿⡄⠀⠙⣿⡇⣰⣿⠀⢸⡇⠀⠀⠀⣸⡟⢧⡀⠀⠀⠰⢲⠀⠀⠀⠀⠀⠀⠘⢧⣤⠟⠀⠀⢀⣿⣿⣦⣤⣉⣻⣿⣿⣿⣆⡇⠀⠀⣠⣿⣿⡿

⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⢶⣶⡖⠖⠒⢲⡶⢐⣀⣀⡀⠀⠀⠀⠈⢧ ⡾⠁⠀⠀⠀⠀⠐⠞⢻⣿⠿⠿⠻⢿⣿⡛⠁⠀⡄⠘⣿⣿⡿⠟⠿⢿⠒⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⢲⣿⣵⡴⠀⠀⠠⣿⠁⠀⢸⡇⠀⣿⡣⠀⠀⢴⢆⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠈⠹⣿⣿⣶⣤⣦⣶⢯⠀⠀⢸⣇⠀⠘⢿⣦⣤⣶⡿⠳⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡯⢛⢡⡖⣠⣾⣿⣧⣤⣸⠿⠽⠿⠋⡀⡀⠀⡆ ⡇⠀⡴⠋⠉⠉⠑⠀⣀⣀⣁⣤⣴⣿⡾⠿⣿⣿⣯⣿⣿⣯⣦⣄⣀⡀⡀⠈⢠⡇ ⢱⡸⡁⠀⣠⣶⡾⠽⠷⠒⠚⠻⢿⣿⣟⣛⣷⣒⣶⣖⣒⣲⣾⠿⠛⠻⣷⣶⢸⠇

⠀⠀⠀⢀⠔⣸⠸⠠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢓⠀⠀⠀⠀ ⠀⠀⡠⠊⡰⢻⢠⡆⢣⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠰⡂⠀⠆⠀⠀⠀ ⢀⡼⠔⠊⢳⠀⠈⢸⢄⠡⡀⠑⢄⠀⠀⠀⠀⠀⠐⢄⠀⠐⠤⠒⠉⠢⢾⡀⠀⠀ ⠉⠀⠀⢀⠜⢰⡰⣃⠄⢢⢌⠢⣄⡀⠀⠀⠀⠀⠀⠱⣦⡀⠑⠨⣦⢴⡈⢇⠀⠀ ⠀⠀⠸⡁⠀⠈⣇⢫⣮⣏⠀⠈⠐⠟⠲⣦⣐⣄⠀⠀⠙⠪⣑⣢⠄⠘⢍⠉⡄⠀ ⢄⠀⣠⠖⠊⣈⣈⣮⣞⢟⣕⠄⠀⠸⣶⢌⣁⣶⣽⡒⢄⠀⢝⣟⠫⢁⢒⠸⣿⠀ ⠀⡏⠀⡴⠚⠉⣩⡍⠛⠐⢝⢕⠳⣤⢽⡏⣉⣮⡉⠻⡕⠳⠎⠮⢏⠀⠈⠆⢹⠄ ⠀⢃⠰⠁⠀⣿⠿⠿⠀⠀⠀⠀⠁⠒⠁⢾⠿⢿⠇⠀⠡⢠⡤⠜⡘⠀⠀⢸⠀⠂ ⠀⢘⡀⢄⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣖⡝⠂⡌⢧⡆⠀⠀⡇⠀ ⣄⠚⢷⠟⠁⠀⠀⠀⠀⠀⣀⠤⠠⣄⠀⠀⠀⠄⠚⠉⢪⠿⡓⣥⠃⡆⠀⠀⡇⠀ ⠰⡍⠚⢆⠀⠀⠀⠀⠀⣔⡩⠿⠃⠠⠵⡀⠀⠀⢀⢀⢾⡁⠀⢻⢇⡇⠀⠀⠇⠀ ⢠⣌⠛⢶⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⢀⣴⡁⢸⠇⠀⢸⠈⠏⠀⣸⡄⠀ ⡀⠲⢮⣵⡏⠘⡗⠢⣀⠈⢢⢤⡠⡠⣊⡤⠒⡻⠁⢻⡮⣀⢀⣿⣿⠆⣴⠟⢀⠂ ⡉⠣⠀⢹⠀⠀⠈⠢⢈⣾⢏⠤⢝⠙⢿⠦⠊⠀⠀⠀⡄⠀⠙⠻⠮⡉⠈⢖⢦⡀ ⠀⠀⠀⢸⠀⠀⠀⢀⢼⡷⣁⠔⠊⡌⢲⢵⡆⠀⠀⠀⡇⠀⠀⠀⠀⠈⣦⠀⠁⠂ ⠀⠀⠀⠸⠀⠀⠀⣼⠀⠈⠀⢰⣉⠛⠉⠁⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⠀⠀

⠀⢡⣿⣿⣿⡿⣣⣾⣿⣿⡟⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⡟⣧⠸⡇⠀⠀ ⠀⢸⣿⡿⡿⢱⢿⡿⢻⣿⠁⠟⠹⣾⣹⣿⢹⣿⣿⣿⡹⠙⣇⠡⠀⠈⢻⠁⠀⠀ ⠄⡟⠛⢸⢡⠁⠈⠀⢣⣿⡀⠀⡑⣀⠈⡏⠘⠸⡽⠃⡃⣧⢀⠲⠀⠀⡜⠀⠀⠀ ⡇⡐⡤⢇⣇⡔⡇⣠⡼⣿⣧⣰⣽⣿⡴⣡⠀⠀⠀⢀⣧⡿⣿⡆⡆⣶⡇⠀⠀⠀ ⡇⢿⠁⣼⣿⣿⣿⣿⢳⣿⣿⣿⣿⡇⣧⣿⣿⣿⢁⣾⢿⡇⢿⣿⣧⣿⡇⠀⠀⠀ ⢀⢸⡀⢹⣿⣿⣿⣏⠈⢻⠘⣿⠿⢄⣿⣿⣿⣿⣾⣟⣸⠧⢺⣿⣿⣿⡇⠀⠀⠀ ⣾⣼⣎⣰⢿⣿⣿⣷⣳⣾⣦⣬⢆⣀⡏⣿⣿⣿⡟⢄⣒⡤⢼⣿⣿⡟⡇⠀⠀⠀ ⣿⣿⡿⢧⢞⣿⣿⣧⠹⢍⣁⣐⠀⢀⠸⠛⠉⠨⡾⠋⡓⣠⠎⣿⡿⣁⣧⠀⠀⠀ ⠛⠉⠀⠀⢻⡯⡟⠿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣼⣿⡿⠧⠻⡀⠀⠀ ⠀⠀⠀⠀⠈⡅⠹⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣹⡿⡏⢀⠁⠀⢧⠀⠀ ⠑⢄⠀⠀⠀⢃⠀⠑⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡇⣧⢸⠘⢦⠘⡆⠀ ⠀⠈⢆⠀⠀⠈⡄⠀⡈⢿⠳⣄⡀⠀⢀⢲⣌⡠⠒⠁⠀⢻⣿⣾⢸⡷⣼⡇⠘⡄ ⠀⠀⠈⢆⠀⠀⢡⣀⠐⡀⠜⠁⠙⣶⡞⡡⠛⢇⠀⠀⠀⠀⣿⣽⣿⡇⠘⣆⡀⠘ ⠀⠀⠀⠘⡄⠀⠈⡌⠙⠓⠠⠤⠽⡟⠌⠠⠡⠈⠳⡀⢀⢮⢺⣿⣿⣿⠀⠙⡅⠂ ⠀⠀⠀⠀⢡⡀⠀⠘⠄⠀⠀⠠⡙⡘⢀⠇⡔⠐⢠⣿⡕⢁⣾⣿⣹⡟⠀⠀⢹⠀

⣀⡀⠠⢤⠤⡒⠒⠉⡏⠀⠀⠀⠀⢠⡀⠀⠀⢣⠆⢀⠀⠀⢢⠈⢆⠀⠀⡇⠀⠀ ⠀⠀⠀⢸⠀⠃⠀⢠⣧⠀⣾⠀⠀⠸⣧⠀⠀⢱⣿⠀⣧⠀⠰⣇⠈⠆⠀⠓⢄⠀ ⠀⠀⠀⣼⠀⠀⠀⢸⠘⡄⢻⡇⠀⢀⣯⣦⠤⠤⣿⣀⠛⠦⢦⡿⡄⠘⡀⠀⠈⡠ ⠀⠀⢀⠷⣇⡆⠀⢸⠤⠸⣼⢳⠴⠲⠛⠠⡤⢖⣚⣯⣀⡀⠘⡀⠃⠀⢣⠀⠀⠀ ⠀⠀⣾⡚⠙⠳⠒⠚⠄⠀⣧⠑⠂⠀⢑⣯⡾⠿⡹⠀⠉⠙⡷⡇⡀⠀⠈⡆⠀⠀ ⠔⢲⣿⣁⣴⠾⣿⣿⣷⠄⠘⠀⠀⠀⠀⠋⠉⣉⣤⣤⣤⢔⣁⠃⡇⠀⠀⢻⡀⠀ ⠀⣸⡿⣿⡅⠀⣁⣒⣂⢀⠰⠀⠀⠀⠀⣠⡿⣫⢆⢔⠕⣭⢯⠏⢧⠇⠀⢸⢳⡀ ⠀⠇⣧⠨⣓⢏⣝⣔⠯⡃⠀⠁⠀⠠⠞⠋⠐⢕⠕⣑⠝⠁⡷⠀⡘⢰⠀⢸⠈⣷ ⠀⢰⣾⡦⣲⢫⠪⠟⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⡠⠁⠀⠀⣀⡴⠔⣿⠀⢸⡀⢿ ⡇⠘⣿⡟⠣⠁⠈⠀⠠⣀⣔⣥⣶⣿⣿⣶⣿⣿⠁⠀⠈⠉⠀⠀⢈⡿⠀⢸⢉⠀ ⢸⠢⡘⢿⡄⠀⣸⠀⠀⠘⣿⡟⠻⣿⠟⠉⢹⠏⠀⠀⠀⢈⠀⢀⣼⣷⡄⢸⠀⢄ ⡿⠀⣰⣷⣾⣶⡒⠁⠀⠀⢸⠀⠀⡇⠀⣠⢾⠀⠀⠀⠀⢀⣴⣿⣿⣏⣧⣼⡀⠈ ⠁⠛⠾⣿⣯⡿⢈⣷⣄⡀⠸⠀⠰⠄⠀⡠⠓⠃⠀⣠⣴⣿⣿⣽⣿⣿⢣⣿⣜⠦ ⠀⠀⠀⠈⠙⠷⡾⣿⣿⣿⣶⣇⠀⢠⠊⠀⣀⢤⣚⡻⠿⠛⠋⠉⠉⠀⣾⠗⠙⢆ ⠀⠠⡀⠀⠀⠀⠈⠠⡈⠉⠉⠉⢡⠘⡖⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠦⠤⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡏⠉⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣡⢢ ⠀⠀⡼⣰⣳⣦⡑⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⣸⠁⣿⣿⣿⣿⡎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀ ⠾⠛⣆⢿⣿⣿⣿⣿⢸⠆⠀⠀⠀⠐⣟⡒⢤⡤⢄⣀⣤⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠘⠧⣿⣿⣟⣫⠞⠑⠒⠢⢄⡀⠀⠉⠁⡽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡤⠴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡄⠀⠀⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⡧⠀⠀⢹⡄⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡄⣒⡪⠽⠿⣼⣦⣇⣴⠜⠃⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⢲⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠚⠀⠀⠀⠈⠉⠒⠒⡒⠯⣍⠓⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⢤⣀⣀⣀⣀⣀⣀⣰⣀⣈⠦⠜⠒⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣒⣛⠓⠒⠒⠠⣴⢿⣿⣖⢯⠲⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢋⡾⡞⠀⠘⣧⠀⠀⡸⢿⠟⠛⠭⢮⣆⠀⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⢀⡾⠋⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⣿⣄⠀⠀⠀⠀ ⠀⠀⢠⣞⠃⠺⢋⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⡠⠒⠋⢿⣶⣝⠓⠌⢾⡤⢤⠀⠀ ⠀⠰⢁⠸⠀⡔⠁⠀⠀⠉⢳⠀⠀⠀⠀⢀⣎⣀⣀⣀⣀⡀⠘⡆⠀⠀⠀⡆⠃⠀ ⢀⠇⡎⠀⣰⠖⠉⠩⠭⠉⠙⡇⠀⠀⠀⠘⠁⠀⠐⠒⠠⠄⠉⠛⠀⠀⠀⠀⢸⠀ ⣸⠀⠁⠀⠣⣤⣀⣀⣤⡤⠎⠀⠀⠀⠀⠀⠢⠤⣤⣤⣤⣤⠤⠂⠀⠀⢀⠃⢸⠀ ⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢨⡆ ⣿⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠿⠄⠀⠀⠘⡇ ⣿⠀⠀⠐⠛⢳⠒⠠⡤⡤⠤⢤⠤⠤⢤⡤⠖⠶⢖⠊⣉⠟⠉⢆⠀⠀⠀⠀⠀⡇ ⠏⡆⠀⠀⠀⠀⡹⠋⠀⡱⠠⠜⢤⠔⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢰⢱⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⢸⡈⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⡤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⠀⡠⢊⡤⢒⣛⡿⠹⣿⣷⡜⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⡴⢻⠀⠀⠀⠀⠰⢱⡴⠯⢄⣭⣴⣶⠾⠞⠃⢿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⢐⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡷⡇⠀⠀⠀⠘⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣸⠀⠀⡇⠀⠀⠀⢨⡻⠄⠠⣶⣶⡶⠃⢰⡾⠿⠻⢿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠃⢸⠀⠀⢋⣈⢢⢀⣸⠋⣃⠀⠀⠀⠁⠐⠸⣢⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⡜⡇⢨⡀⠀⠙⠀⠙⡉⠳⠙⠴⠡⠀⢠⡎⠲⢤⣷⣧⡀⢠⠇⠀⠀⠀⠀⠀⠀ ⡞⠀⡇⡄⠠⡀⠀⠀⠨⠈⢹⠀⣠⣧⠈⠎⠳⣬⣭⣥⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⢡⠐⠃⠀⠀⢃⠀⠀⠀⠀⠘⣾⣿⣇⠑⢄⠀⠘⠫⠷⠋⢰⠃⠂⡀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⠉⠂⠤⠤⣔⣡⣴⣤⣘⣶⣤⡀⠀⠀ ⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣏⢧⡀⣠⠾⣴⣛⣛⡇⠁⠹⣿⣿⣧⠀ ⠀⠀⠀⠈⠐⡖⠀⠀⢐⠴⢋⣿⣿⣿⣿⣿⣧⡛⠁⠀⠈⠓⣭⠧⠀⠀⢻⣿⣿⣇ ⠀⠀⠀⢀⡴⠷⠒⠈⣁⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣱⠞⣳⠀⠘⣿⡿⠟ ⠀⠀⠀⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠐⠒⠈⠙⠺⠫⠥⠀⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠛⢗⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣦⠐⣴⠀⠀⠀⠀⡜⠀⣀⠤⠐⢒⢾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⢤⡓⠉⠣⡏⠇⠐⠒⠲⠚⠛⠀⡠⣾⡥⠀⠊⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⠘⠉⠀⠀⠀⠸⣰⠀⢰⠣⡠⠀⠂⠈⠈⢽⡦⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⢀⢤⣀⠆⠿⠿⠷⣈⣀⢘⡱⢠⣤⣄⠀⠀⠘⢇⠀⡇⠀⠀⠀ ⠀⠀⡤⠥⠐⡂⠭⠙⣇⣠⠈⠀⢀⠨⣏⠁⠈⠍⣛⠛⠓⠠⠄⠀⠴⣇⠀⠀⠀ ⣀⡏⠀⠀⢀⠄⠊⠁⠈⠀⠉⠁⠀⠀⠀⠑⠠⠬⠷⠬⡽⡋⢄⠀⠀⠀⢧⠄⠀ ⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠢⡑⠈⠂⠄⢺⠁⠀ ⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡆⠀ ⠀⡀⠀⡀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠀⠀⢳⠀ ⠀⢹⣆⣿⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠴⠤⠴⠛⠁⠀⠀⣸⡆ ⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠉⠙⡇

⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⢀⣉⣙⡛⠿⢷⣶⣿⣀⠀⣾⡟⠀⠀⣴⡿⠛⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⢠⣾⣷⠀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣶⠿⡋⠙⣿⡆⠀⠸⡟⠻⣿⣿⣥⡀⣼⡟⠁⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠃⠈⠛⠛⠀⣿⣿⡇⠀⣿⡏⠀⠀⠀⠀⣿⡏⣿⣿⠇⣸⡟⠀⠀⠀⠀⠛⠉⠙⢿⣿⣤⡀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠉⠀⣼⡿⠀⠀⠀⠀⠀⠻⣷⣌⣥⣴⡿⠃⠀⣴⣾⣿⣦⣄⠀⠈⠉⣻⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣇⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⣾⠏⣴⣶⡝⣿⡆⠀⠀⠙⠋⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣷⣶⣤⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠛⢛⣵⣿⠃⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠛⠛⠶⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠘⢷⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢻⣧⡀⠀⠀⢀⣠⣶⠄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠙⠿⠿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣀⡴⠏⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣷⣦⣀⣠⣤⣴⣶⣾⣿⠁⠀⠈⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠛⠁⠀⣀⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣿⣿⡿⠿⠛⠛⠉⢹⡿⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣿⣾⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠛⠿⢿⣿⣶⣤⣄⣀⣠⣶⣶⠀ ⠀⠁⣿⡿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠻⢿⣿⣿⣤⡄ ⠀⠀⠛⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⡟⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢀⣠⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⣀⣴⣿⣿⣇⠀⠀⣿⠟⣻⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣶⣿⠿⠛⠁⠘⢿⣷⣦⣿⣷⣿⢃⣠⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣈⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣶⡟⣻⣿⣿⣿⣿⡬⡝⢿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢁⣤⡧⠈⡏⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡟⣿⣿⣿⣿⣿⣿⣛⣫⣤⣾⣴⣟⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⣿⣿⠻⡟⣿⢿⣿⠟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠥⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠈⠻⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣴⣯⣤⠀⠀⠀⠀⠀⣀⣠⣤⡄⢠⡤⠖⠒⠉⢁⡤⠖⡂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⣺⣿⣿⣿⡋⠀⠀⠀⡾⠉⢀⣤⠤⠖⠓⢶⣖⣒⣩⠵⠖⠋⢁⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⣠⠋⢀⣀⣀⣀⣈⡀⣀⠀⠀⠀⠀⣈⠛⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⢛⣽⣿⣾⡗⠀⠀⠀⠀⠀⠁⣴⣿⡿⠿⠿⠿⠿⠗⠀⠀⠀⢰⣿⣶⣶⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣿⣥⣯⣾⣿⣿⠟⠂⠀⠀⠀⠀⣼⡿⠋⠀⠀⣀⣤⣴⣆⠀⠀⠀⠘⣿⢉⣙⡯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⠁⢀⠴⡿⠋⢷⢿⡦⢰⣾⡄⠀⠹⣦⡐⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣽⠧⣍⠙⠛⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠟⠓⠒⣛⣽⠗⠀⠉⠁⠀⠀⠘⢿⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠉⠀⠹⠿⣶⡄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠚⠻⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡷⢶⠀⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠆⠀⠀⠀⢠⡿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣜⣇⠙⢮⣛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⠛⠒⢻⣽⣶⠋⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴ ⠀⠀⠀⠀⠻⣾⣳⣜⠉⠉⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢤⣠⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠋⣠⠆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠈⠛⢾⡅⠀⣰⡇⠀⠀⠀⠀⠀⠱⡄⠀⠘⣟⢿⡏⣦⣄⣀⣀⣤⡴⠶⠶⠞⠻⣶⡷⠶⠶⣶⣶⣶⣶⣿⣿⣷⣷⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢸⣄⠀⠀⠀⠀⠀⠹⣆⠀⠉⠃⠃⠀⠀⠀⠘⠿⠧⢀⣠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠶⠦⠤⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠠⠤⠤⢤⣤⣤⣄⣀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠒⢹⣿⡟⠀⠉⠀⠒⠄⠓⠢⢅⣿⡷⡦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠉⢀⢔⢿⠿⠃⣠⡀⣀⠀⠀⢀⠀⣸⣿⣇⠈⠪⡳⣄⠀⠀⠀⠀ ⠀⠀⡴⠃⠀⡐⠁⠀⠀⣨⠕⢀⠈⢎⢝⠢⡀⠱⣙⢿⡇⢂⠀⠐⡌⢣⡀⠀⠀ ⠀⡜⠀⠀⠐⠔⡠⠀⡰⠁⠀⡀⠀⠈⠇⢱⢌⠀⢣⠩⠇⠀⡀⠀⢸⡄⢱⡀⠀ ⢰⠁⠀⢠⡛⢰⠁⣰⡆⠀⠀⠃⠀⠀⠘⠀⡄⡢⠀⡀⢳⠀⠀⠀⠀⣷⠀⢣⠀ ⡇⠀⠀⣼⠁⡇⡜⢹⣇⠀⠀⢸⠀⣇⠀⠀⢀⠐⡐⡇⠀⢣⠀⠀⠀⡇⡄⠸⠀ ⡇⠀⢠⢹⢀⣏⣀⣢⣟⡀⠀⠈⡄⠈⢧⠀⢸⠀⠰⠘⡄⠈⣌⠀⠀⠁⠀⠀⠀ ⡇⠀⠈⠀⠘⢪⡰⣿⣧⢡⠀⠀⢣⡄⠤⠑⢄⢧⡀⢳⡘⡄⣿⡆⠀⠉⢰⢠⠀ ⢸⡀⡇⠀⠀⠀⠉⠀⠀⣆⠁⠀⠘⡗⠋⡿⢾⣷⡿⠠⢵⡟⠳⣰⠀⡇⢆⡜⠀ ⠀⠣⣇⢠⠀⡆⠀⠀⠜⠀⠣⠄⠀⢁⠐⠩⠭⠒⠈⠒⠩⠫⢓⡏⢠⡇⣸⡇⠀ ⠀⠀⡿⣾⠀⡗⡀⢀⡀⠀⠀⠹⡄⢸⠀⠀⠀⠀⣰⡟⡥⣾⢿⠁⢸⠆⠈⡇⠀ ⠀⠀⡞⢺⠀⡏⢙⡄⡏⠅⢲⡠⣇⡼⠀⢀⣤⡞⠃⣷⡇⣸⢟⠀⣼⡄⡀⢹⠀ ⠀⠀⠇⠀⡄⡄⢸⡍⢗⠐⣁⣀⡬⠐⣞⡥⠏⠀⠀⡿⠁⡿⢸⠀⡿⠺⡇⠈⡆ ⠀⠀⠈⠆⠁⠇⠘⠘⡀⣠⡉⡗⢄⡜⠥⡀⠀⠀⠰⡇⣸⡧⠊⢠⠁⠢⡸⠢⡠

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣷⣞⠛⠿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣋⣭⣿⣯⣶⣿⣿⣿⣿⣿⣛⣫⣯⣬⣿⠻⠿⣿⠟⢷⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣠⣶⣽⠂⢨⡇⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣀⣴⣟⣠⣿⢟⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣉⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣛⣿⣿⣿⣿⣬⣟⣸⣿⣼⣛⡉⠀⠀⠀⠀⠀⠿⢿⣿⡟⢛⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠁⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⡂⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠂⠉⣁⣠⡴⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⢟⡟⠀⠀⠀⠀⣠⣤⠖⠒⠛⠛⠛⢠⡞⢋⣁⢀⣠⣤⠴⢚⣋⣥⠆⠀⣀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⣽⣿⣿⣿⣏⡁⠀⠀⠀⠘⠿⠁⠀⣠⠾⠛⠛⠉⠉⢛⣙⣥⠤⠴⠾⠛⠉⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢠⡞⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠛⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣭⣶⡄⠀⠀⠀⠀⠀⠀⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣇⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⢊⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣻⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⡼⣿⣾⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⢀⣠⣴⣿⣶⡿⠄⠀⠀⠀⠀⠈⣿⡃⣤⡬⠿⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡴⣫⡿⠋⢷⡿⣿⡦⢰⣾⡇⠀⠀⠘⣷⣆⠐⠋⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⡿⣻⣏⡉⠛⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣤⣤⠾⠛⣿⡄⠀⠙⠃⠀⠀⠀⠘⢿⣧⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣶⢿⠀⠹⣷⣤⣀⠀⠉⠹⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣧⡀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠉⢛⡿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡷⢾⡆⠀⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠄⠀⠀⠀⠀⢀⣿⠃⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⣌⢿⡄⢻⣄⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣿⣧⣴⡶⣖⣦⣶⡾⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠ ⠀⠀⠀⠀⠙⢿⣟⣷⣄⠘⠟⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠛⢻⡏⠀⢀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⢿⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢲⣴⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣧⡀⠀⣐⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿⡼⣿⡇⣶⣤⣄⣀⣀⣠⣤⡶⠿⠿⠿⠟⠻⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠉⣧⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠻⠜⠇⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⣀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣶⣤⣀⣀⠀⠀⠀⣀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣶⣶⣿⣇⠀⠀⣼⣿⠇⠀⠀⢀⣴⣿⠟⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠇⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣿⣷⣄⠀⠉⢻⣿⣿⣷⣶⣿⡇⠀⠀⢠⣿⡟⠁⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠏⠀⣿⣿⣿⠀⢀⣴⣶⡄⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣾⡿⣋⣴⣄⠀⢿⣿⠀⠀⠈⠛⠀⢩⣿⡿⣿⣷⣦⣿⠟⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⠈⠙⠉⠀⢸⣿⣿⡏⠀⣸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠃⣿⣿⡿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⢿⣿⣷⣤⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣧⣈⣉⣠⣼⣿⠟⠀⢀⣴⣾⣿⣷⣦⣄⠀⠀⠉⠉⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⢀⣾⡟⢉⣩⣙⢿⣿⡆⠀⠀⠀⠸⣿⠟⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣄⡀⠀⠀⠀⢀⣤⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⣿⣿⠂⣿⡿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⢉⣡⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⣤⡀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠈⠛⢿⣦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠻⣿⣦⡀⠀⠀⣀⣤⣾⡿⠃⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠉⠻⠿⢿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⣀⣴⡿⠋⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠾⠛⠋⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣦⣄⣀⣠⣤⣤⣶⣶⣿⣿⡿⠀⠀⠀⠉⠻⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠁⠀⠀⣀⣀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣬⣿⣿⣿⣿⣿⣿⡿⠿⠛⢹⣿⡇⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⣀⣤⣶⡄ ⠘⠻⠟⣿⣿⡟⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⠛⠁ ⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠉⠉⠉⣿⣿⣿⣶⣶ ⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⢸⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⣤⣶⣿⣶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣄⠀⠀⢸⣿⠋⢙⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣤⣾⣿⣿⠟⠋⠀⠻⣿⣷⣤⣸⣿⣦⣿⡿⠃⢀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⣷⣶⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠶⣶⡶⠶⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠋⠁⠀⠀⢀⣾⡿⢿⣦⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠟⣿⣿⣦⡀⠀⠀⠀⣼⡏⠀⠀⢻⣇⠀⠀⠀⢀⣼⣿⡿⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠀⠈⠻⢿⣿⣿⣶⣶⣿⣦⣤⣤⣼⣿⣶⣶⣿⣿⠿⠛⠁⠀⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠙⢻⣿⠛⠛⠛⠛⣿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢿⣧⡀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⣀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⠾⠿⠿⠷⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⢿⣿⠿⠿⢀⣴⡿⠛⢿⣶⡀⢻⣷⡀⢠⣿⠋⣠⣾⠟⠻⢷⣦⠘⠿⢿⣿⠿⠿⠀⣰⣿⣷⡀⠀⠀ ⠀⠀⢸⣿⡆⠀⢸⣿⠀⠀⠀⣹⣷⠀⠹⣷⡿⠃⠀⣿⡇⠀⠀⠈⣿⡇⠀⢸⣿⠀⠀⢰⣿⡃⣻⣧⠀⠀ ⠀⠀⢸⣿⡇⠀⠘⢿⣦⣤⣴⡿⠃⠀⠀⣿⣧⠀⠀⠙⢿⣦⣤⣾⠟⠀⠀⢸⣿⠀⢠⣿⠟⠛⠛⢿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀

⠀⠀⢸⡟⢿⡀⢀⠀⠀⠀⠀⠀⠘⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⠀⠀⠉⠻⣿⣿⣿⣿⣆⢿⣿⣿ ⠀⠀⡾⠀⠀⢣⠈⣦⡀⠀⠀⠀⠀⠘⣏⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀⠀⠈⢿⣿⣿⡿⠟⠻⣿ ⠀⣰⠃⠀⠀⠀⢣⢹⣿⣶⣤⣄⡀⢦⠘⡄⠀⠀⠀⠉⠚⠿⣿⣶⣷⣶⣶⣶⣾⣿⣷⣄⠀⠀⠈⢦⣀⠀⠀⠀⣽⣦⡀⠀⣹⣏⠀⣠⠒⠙ ⣴⡏⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠠⣄⣉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣇⡠⠀ ⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣦⣄⠈⢻⣿⣿⣿⣿⣿⣷⣌⢻⠷⣀⣴ ⣿⠀⠀⠀⠀⠀⠀⣠⠖⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⣿⠀⠀⢀⡠⠔⠊⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⣠⣴⣷⠶⠶⠶⠶⢶⣦⣬⡙⢿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⠐⠊⠁⠀⠀⠀⠀⠠⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠉⠀⢀⣴⠞⠒⠒⠦⣄⠈⠻⠷⣿⣿⣍⢿⣷⠙⢿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⣠⣤⣶⡾⣧⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠙⣆⠀⠀⢸⣿⣿⣿⣿⡗⡦⢽⣿⣿⣿⣿⣿ ⣿⠀⢠⣿⡿⠛⠉⠤⠤⢄⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⠂⣧⣴⡿⠶⠖⠿⠀⠀⢸⡿⠻⣿⡟⣹⡀⠀⠙⣿⣿⣿⣿ ⣿⣷⡟⠁⠀⢺⡄⣀⡤⠄⢻⡄⠀⠀⠀⠀⠀⠙⢮⡛⢯⡙⣿⣧⡀⠀⠀⠀⣄⠀⠉⠀⠰⡄⠀⠀⠀⢸⡇⠀⢻⣿⡿⢹⠀⠒⠉⠹⣿⣿ ⣿⣿⠀⠀⠀⣿⠀⢧⣼⣿⠟⠻⠀⠀⠀⠀⠀⠀⠀⠉⠂⠙⠻⣼⣷⣄⠀⣀⣼⠿⠿⠿⠟⠋⡐⢃⣄⣼⡇⠀⠀⢿⠀⠀⡇⠀⡁⢀⣿⣿ ⠋⢻⡆⠀⠀⢿⡄⠀⠉⢀⣠⣤⠀⠀⠀⢀⠄⠔⠁⠀⠀⠀⠀⠈⠙⠻⣾⡦⣈⡳⣄⠀⠀⠀⢠⣿⠋⢸⣿⡀⠀⠈⢧⠀⠸⡔⠁⣼⣝⢿ ⣆⠰⣿⠹⣦⠀⠀⢶⡶⠟⠋⠁⢀⢔⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠓⢄⠀⠁⠁⠀⠘⢸⣷⠀⠀⠈⡆⠀⢣⣼⣿⣿⣷ ⢻⣷⡟⠀⡏⠻⡄⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠙⢢⡀⠀⠀⣾⣿⡇⠀⠀⢡⠀⠈⡿⣿⣿⣿ ⣧⣿⡇⠀⡇⠀⢹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠲⣄⠀⠀⠙⢄⠀⣿⠇⢹⠀⠀⠘⡀⠀⢣⣿⣿⣿ ⣿⣿⠃⠀⡇⠀⠀⡟⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠓⠢⢄⣀⠀⠀⠑⡀⠀⠀⠳⡏⠀⢠⡆⠀⠀⢳⠀⠘⣿⣿⣿ ⠟⢹⠀⠀⢸⠀⠀⠇⠀⠀⠀⠉⣠⠋⣷⠀⠀⠀⠀⠀⢀⣀⡠⠒⠈⠙⠳⣀⠀⠀⠈⠑⢄⠀⠱⡀⠀⠀⠈⠳⣿⣧⠀⠀⠀⢧⠀⢹⣿⣿ ⠀⡇⠀⠀⡏⠀⢀⠁⠀⠀⠀⢠⠃⠐⡿⢠⣶⠖⠂⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠁⢄⠹⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⡇⠀⠀⠃⠀⠀⡆⠀⠀⢠⠋⠀⢰⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡀⠀⠀⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⣰⠃⠀⢠⠇⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠁⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠢⠤⣀⠀⢀⣠⡴⣾⠿⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣿⣿⣿⣿⣿⣆⠀⠀⠉⣉⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣄⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⢡⣿⣿⣿⣿⡿⢿⡦⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣿⠼⠛⢉⡿⠋⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⢀⣾⠁⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⣄⡀⠀⢀⣶⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣷⣀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡠⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⠉⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⡌⣻ ⠂⠀⠀⠀⠀⣠⡿⢀⣶⣧⣄⡀⢲⣄⣀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠟⠋ ⡅⠀⠀⠀⢠⡿⠁⣾⣷⣾⣿⣿⣦⡘⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀ ⡇⠀⠀⢀⣾⠃⣼⣿⣿⣿⣿⣧⣿⣿⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸ ⡇⠀⣴⣿⣿⡄⢸⡟⣿⣿⣿⣽⣷⣹⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⢸ ⡇⠀⠿⠃⠸⣷⡈⢿⣿⣿⡿⣿⣿⣿⣹⠀⣾⠁⠀⠀⠀⠀⠀⠀⠘⢿⣄⡟⠹⠶⡶⠶⢦⣀⣠⣶⣶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠘⢿⣮⣹⣿⣿⣿⣿⠿⢃⣾⠟⠒⠶⢤⣤⣀⡀⠀⠀⠀⠈⠙⠓⠒⢛⣶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠉⠛⣶⣄⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣠⣴⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⠉⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣿⣆⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢲⣿⡄⢰⡏⠀⣴⠀⢤⠀⣸⡷⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣋⣉⡡⠴⠚⠛⠛⠻⢮⣿⣿⣭⣤⣾⡾⠋⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠀⠀⠀⠀⢰⡆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⣇⣀⡀⠹⠧⠤⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠶⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠒⠲⢦⣌⡉⠛⠷⣦⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠳⣄⠀⠈⣿⣀⣠⡿⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣽⣤⠤⠤⠼⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠘

⠀⠸⠙⡀⡄⠀⠀⠘⡶⢄⡀⠀⠀⠀⠙⠲⣄⠀⠈⠢⡀⠀⠠⡀⠉⢻⣿⣷⣽⣿ ⢀⠃⠀⠐⣸⣦⣤⣀⡜⡀⠈⠑⠲⢶⣶⣶⣬⣿⣦⡀⠈⢆⣀⣈⣦⡀⢙⣋⡠⠚ ⣾⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠒⠊⠽⠿⣿⣿⣿⣦⣀⠹⣿⣿⣿⣦⡻⣗⢀ ⡇⠀⠀⢀⡤⠚⢿⣿⣿⣿⣷⡀⠀⠀⠀⠤⣀⣀⡉⠚⠿⣿⣷⣜⢿⣿⣿⣿⣞⣿ ⡇⠄⠊⠀⠀⠄⠈⠻⣿⣿⣿⣷⡀⠀⠀⠚⢉⡭⠉⢍⡙⢪⣿⣟⣷⡻⣿⣿⣿⣿ ⡇⠀⣠⡴⠞⠛⠂⠀⠙⢿⣿⣿⣷⡀⠀⠀⣴⢀⢠⣄⣱⠀⢸⣿⣿⢯⠚⢿⣿⣿ ⣷⠞⠁⡢⠠⢌⣣⠀⠀⠀⠙⢝⢏⣻⣄⠀⠡⣈⣉⢠⡀⠀⢸⠀⢻⠎⠆⠘⢹⣿ ⠿⡄⠀⣇⠑⠛⢉⠀⠀⢀⡠⠀⠀⠉⠻⢦⣖⢫⠉⠉⠈⡼⢺⡄⠈⠄⠰⡐⢸⢿ ⣆⡏⠳⡀⠰⠚⠉⡠⠖⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠢⡈⠁⠈⣷⡀⠘⠀⢳⣿⣷ ⣾⡇⠀⠘⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⢄⠈⠢⠀⡟⠇⠀⠇⠸⣽⣿ ⡿⠇⢰⠀⡏⠓⠠⢀⢄⠀⠀⠀⠀⢀⠠⠦⠈⠐⠠⡀⠡⠀⠙⢄⣼⠀⠈⡀⢻⣿ ⢰⠀⠈⠀⡇⠀⢀⠆⠺⣰⠖⠂⠉⠁⠀⠀⠉⠢⡀⠈⠠⣡⠀⠀⠉⠁⠀⠀⢸⣿ ⠘⠀⠀⠀⠃⢀⠎⢠⠃⠋⠀⠀⠀⠀⠀⢀⡀⠔⠑⢄⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⢸⡎⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠈⠁⠀⣷⣦⣀⡀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⡾⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡍⠒⠠⢔⡪⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠀⢀ ⠀⠀⠀⠀⠀⠀⢸⣻⣼⣿⣿⢻⡆⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃ ⠀⠀⠀⠀⠀⢀⠛⠋⠁⡞⠁⢸⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣀⣤⠤⢤⣤⣤⠖⠊⠽⠛⠉⠀⠀⠈⠉⠳⢶⡋⠉⠛⠛⠓⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⣤⠞⠋⠁⣠⡴⠛⠁⠙⠁⠀⠀⠀⣀⣤⡤⠤⠤⠤⠀⠙⢶⣤⡀⠀⠀⠀⠈⢹⡟⢓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠷⠶⠿⠅⣀⡴⠟⠋⠁⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⠁⠈⠻⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⡇⠀⢀⡴⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢠⡟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⢿⡜⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠷⣶⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⣬⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠈⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠷⢤⠇⠀⠀⠀⠀⠀⡏⠉⢙⡗⠦⢸⣥⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣀⣾⡀⠀⠀⠀⠀⠀⢷⡰⢦⡙⠷⠀⠀⠀⠀⠀⠈⠻⣆⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⡅⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⡟⠃⠀⠀⠀⠀⠀⠈⢧⡛⠛⠛⠒⠀⠀⠀⠀⠀⠀⢸⡿⣅⠀⠲⣍⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⡬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠳⣄⡈⣿⣦⣀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠰⣶⠶⣦⣬⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣯⡉⠻⢦⣄⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⢁⡤⠀⠀⢰⡇⠀⠀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⠿⢿⣷⣄⡈⠻⢦⣄⡀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⢀⡴⠃⡰⣿⢀⠀⢠⣾⠇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⣴⣾⣿⡍⠃⠐⢿⡻⣶⣶⣽⣿⣷⣦⣀⡀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣤⢟⣡⠞⢹⠏⡾⢀⡞⠁⢀⣼⢿⣤⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⣀⡄⠹⣿⡀⠀⠀⠈⠳⣟⢮⣿⣽⣆⠉⢷⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠰⠞⠙⠉⠀⠀⡾⣸⠁⡾⠀⢀⣾⠏⣾⣽⠃⠀⠀⡈⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢿⡈⠛⢀⣿⣇⣀⣀⡀⠀⢘⣿⠻⣿⣿⣆⠀⣷⣄⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⣿⢠⠃⢀⡾⠃⠀⣿⣿⡀⠀⢠⡿⠛⢾⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⡾⠿⠟⠛⣿⠟⠛⣻⣿⣾⠛⢹⡇⢸⣿⣽⠀⡟⢸⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⡾⣥⠀⠀⠻⣼⡇⠀⠘⣷⠀⢾⡽⣿⠀⠀⠀⣰⡶⠟⠛⠙⣧⡀⠀⠀⢀⣴⠟⠀⢀⣿⠟⠀⠀⠈⡇⢸⣷⠟⣰⠃⣸⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣾⣼⠃⣿⠀⠀⠀⠙⢿⣆⣠⣼⣷⣶⣶⣿⣦⠀⠀⠌⢷⡄⠀⠀⠈⠉⠒⠒⢛⣡⣴⠶⠛⠁⠀⠀⠀⢠⡇⠀⢨⣵⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⢸⡀⠀⣠⠶⠿⠛⢯⣄⠀⠀⢸⡇⠸⣷⣠⣄⡈⡷⠼⣤⣤⣤⡶⠾⠛⠉⡞⠁⠀⠀⠀⠀⠀⠀⠹⠋⠉⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣇⢀⣿⣆⠀⠀⠀⠉⠛⠶⠋⢀⣠⡟⣯⠉⠉⣁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⣿⣦⣀⣀⣠⣤⠴⠞⠛⠁⠀⠈⠀⠀⠈⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢡⠀⠀⣿⠘⣇⠀⠀⠀⠀⠀⢀⡏⢠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⡇⡼⠀⠀⠙⠓⠘⢧⠀⠀⠀⠀⡼⢁⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠋⢀⡿⣿⠃⠀⠀⠀⠀⠀⠸⣧⠀⠀⣼⠃⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⢀⣠⣿⣱⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡏⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣛⡍⠀⠀⠀⢊⡿⡟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣼⠻⠛⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣒⣲⣶⣿⣿⣛⣻⡿⠉⠁⠀⠀⢀⡾⠑⠁⠀⡿⢹⣦⠀⠀⠀⠀⡴⠋⠙⣿⠀⠀⠸⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⣭⡟⢩⣿⡾⠛⠂⠀⣠⣾⡿⠂⠀⠀⠀⣼⠟⠲⣤⡀⠐⢷⣤⣴⠏⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⢹⣿⡟⠃⠀⠀⢈⡿⠹⠁⠀⠀⠠⣿⡇⠀⠀⠈⠙⢶⣿⢧⣀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠲⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠈⢿⣓⣩⣷⡄⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠈⢉⣉⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⡪⠐⣢⠔⠊⠀⡁⠀⠤⠙⠬⡉⠉⠲⢦⣀⠀⠀⠀⠳⡄⠀⠀⠀ ⠀⠀⠀⢠⠋⢁⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢙⣄⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⢰⣙⡖⠁⠀⠤⣀⢠⠓⣄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡈⠈⢢⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⢴⠄⠀⠀⢶⠮⠀⠀⠀⢳⡄⢂⢄⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠸⡀⠀ ⠀⠀⠀⡌⠀⢠⠄⣺⡆⠀⠀⠀⠀⠈⠑⢵⡢⢄⠀⠐⣄⠀⠀⠘⢧⠀⠀⠈⠇⠀ ⠀⢀⢌⡔⠀⠌⣠⠋⠀⠀⠀⠀⠀⢠⠎⢉⠽⣖⠙⢦⣬⣷⣄⡀⠘⡇⠀⠀⢸⠀ ⠐⠃⠁⡟⠌⡰⢻⡏⠉⣲⡀⠀⠀⠈⡄⢘⣗⣸⣆⣀⣹⡿⣧⢱⣄⡇⠀⠀⠀⠇ ⠀⠀⠀⡇⣴⡇⠘⣧⠘⣄⣹⡀⠰⡖⠙⠍⡠⢞⡠⠟⠀⡇⢿⣜⠇⠓⠀⠀⢀⠀ ⠀⠀⠀⠈⠇⢣⢰⠊⠛⠤⠝⣹⡄⠕⠒⠒⠊⡙⠀⠀⠀⣩⣍⡄⠀⠀⠀⠀⢾⠀ ⠀⠀⠀⠀⠀⠀⢻⠓⠒⠒⠉⠀⡀⠀⢀⠤⠊⠀⠀⠀⢀⡼⠈⡗⡀⠀⠀⡘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⢫⡷⠀⠈⠘⡀⠰⡙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢀⣀⣀⣀⣀⣤⡖⠁⢰⠟⣷⡀⠀⢀⣱⡗⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠩⢯⡿⠂⢠⠗⠀⣡⠓⠤⣸⡔⠁⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⠀⠀⠀⠀⠉⠀⠀⠘⡛⠂⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠊⣸⡄⡇⢠⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣂⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠜⠁⣰⣿⠀⢰⠀⢆⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠙⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⢀⣴⠏⡿⠈⡌⡆⠈⢆⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠹⡁⠀⠀⢱⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⢀⡠⠾⣧⠀⡇⠀⠇⢻⡀⠈⢣⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠈⠳⢄⠀⣀⣀⠷⠤⡀⣄⢧⠀⠀⠀⠀⠀ ⠀⣴⠟⠋⠁⠀⠀⢀⡇⡇⠀⢸⡸⡙⢄⠀⠱⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠘⢦⡙⢅⡀⠀⠀⠘⡌⢞⡆⠀⠀⠀⠀ ⠹⠁⠀⠀⠀⠀⠀⡼⠀⣇⠀⡄⠃⢣⠈⠳⣄⠈⠣⡀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣕⣄⠀⠀⠙⠦⣉⡲⣄⣠⠇⠈⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠔⠋⠀⠀⢸⣇⢸⣷⡀⢣⣠⠎⠑⠢⢌⡙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠓⢤⡀⠀⠈⠙⢿⡻⡷⠶⠼⡇⠀⠀⠀ ⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⢿⡄⣻⣼⣾⡳⡀⠀⠀⠀⠀⠙⣟⠛⠻⢷⣤⢌⣢⣀⠀⠀⠀⠀⠙⠑⢄⣬⡉⡒⠤⠀⠉⠻⣄⡀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⣼⣠⠶⠏⠐⠈⢳⡈⢧⢹⡿⣿⢄⠀⠀⠀⠀⢾⣦⣀⠈⠙⠲⢤⣍⢳⣦⣄⡀⠀⠀⢈⠻⣿⣿⣙⠒⠦⢤⡤⠭⢷⣷⠀⠀ ⠈⢢⣄⡤⠞⠁⠀⢐⣰⣤⣤⣦⣿⣿⣧⡙⢌⣷⣅⠠⡀⠀⠈⢿⣯⠓⣤⣤⣬⣿⣿⣟⠦⣉⠢⡀⠈⠳⡿⢧⣈⡛⠒⠤⣧⠀⠻⣿⡀⠀ ⠀⢸⡏⠀⠀⢠⣶⠟⠉⠀⢠⣌⡉⠛⠗⠙⠦⡙⢮⡑⠮⣦⣄⣀⣻⡟⠁⠈⢳⢄⡈⠙⢷⣮⠙⠿⢷⠦⣝⣦⣧⠀⠀⠀⠈⢆⠀⢻⠣⠀ ⠀⠀⡇⠀⢠⡟⠁⠀⣤⣴⣿⣿⣿⠀⠀⠀⠀⠈⠓⠙⠢⢌⣙⠻⢍⣹⣶⣿⣿⣿⣷⠀⠀⠹⡆⠀⢸⠀⠈⢇⠈⡇⠀⠀⠀⠈⡄⠈⢆⠀ ⠀⠀⢳⠀⢹⠁⠀⠠⣿⣿⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠛⠛⢿⠟⠀⠀⠀⠓⢀⣾⡶⠳⡌⡆⢡⠀⠀⠀⠀⣷⠀⠈⠈ ⠀⠀⠸⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⡶⢉⣿⠤⢃⠘⣾⡈⡀⠀⠀⠀⢹⡆⠀⠰ ⠀⠀⢀⣷⠈⢡⡔⡫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⢉⣨⡿⠗⣲⣯⣈⡀⢸⠀⢹⢣⠀⠀⠀⠀⠈⡇⠀⠀ ⣆⠒⠛⠿⣖⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠤⢄⡀⠀⠀⠀⠀⠠⠖⠉⠉⠀⠈⢡⠿⠿⢋⣡⣴⠃⠸⡇⠀⠀⠀⠀⡇⠀⠀ ⠹⡙⠢⠄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⣿⣛⠋⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠴⠊⠁⢹⢸⣆⠀⡇⠀⠀⠀⠀⡇⠀⠀ ⠀⠻⢆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⢶⠤⠒⠉⠉⠉⠉⠙⠻⡆⠀⠀⠀⠀⢀⠆⣠⠏⢸⣄⠀⠀⠀⣿⠛⡄⣇⠀⠀⠀⣀⠃⠀⠀ ⠀⣤⡤⠽⠿⣶⣼⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠁⠀⢸⣿⠀⠀⠀⣿⠀⢹⣿⠀⠀⠀⣟⡀⠀⠀ ⠉⢻⠳⠆⣤⠴⢛⣿⠛⣶⣄⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⣠⣶⡟⠻⣦⡀⡞⢹⠀⠀⢠⣿⣦⡜⡁⠀⢠⣿⡿⠀⠀⡇ ⡀⠈⠙⠿⣷⣖⣻⣇⠀⠘⣿⠉⠓⢤⣀⠀⠈⢓⡤⢦⡤⢤⡴⢊⣠⡴⠚⠉⢨⠟⠀⠀⢹⣿⡧⣼⡀⠀⣾⣟⣿⣿⠃⣠⣿⡝⠁⢀⡜⠀ ⠛⠲⣦⠤⠴⠛⡏⠀⠀⠀⠈⠳⣄⠀⠙⢏⣷⡛⠊⠉⣳⠶⠿⣿⣾⣆⣀⠖⠁⠀⠀⠀⠈⣏⠀⠀⠉⠛⡿⣿⣱⠷⠚⠋⠛⠴⣤⡀⠀⠀ ⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⢰⣾⠏⡠⠊⠉⠙⣤⢄⠈⠻⡏⢳⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⠉⠓⢤⡀⠀⠑⠪⡙⠷⡆ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⣿⣻⠞⠁⣠⠼⠋⢠⠀⠑⡿⣜⣾⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠈⠓⠄ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠙⠙⠶⠋⠀⢀⡤⢾⣷⠤⢼⠎⠁⢳⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣀⡜⠁⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⠀⠀⠀⠀

⠀⠉⠛⠃⠀⠀⠀⠀⠑⠀⠀⠀⢠⡤⣄⠀⠀⠈⠙⠒⠚⠉⠁⠀⠀⠀⢀⡠⠒⡞⠛⠣⣄⣀⣀⣤⡀⠀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡞⠀⢈⣳⣄⠀⣀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠘⠙⠫⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠞⠀⠀⠈⢯⡛⢿⢦⡁⠀⠀⠀⠀⡴⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⣠⡀⢀⣴⠗⠋⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠏⣤⢔⡒⠒⠀⠓⠀⠳⡈⠻⣆⣠⣎⣀⣀⣤⣀⣀⣀⠀⠲⣄⢀⣴⡀⠀⠀⡀⢀⣠⣴⣿⣏⣁⠀⠀⠀⠐⡄ ⠀⠀⠀⣤⠀⠀⠀⠀⢀⡟⠀⢀⡼⠏⠁⠀⢀⣠⠤⠷⠀⠈⢉⡅⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢤⣈⣀⡤⢚⡽⠋⠙⠉⣽⣀⠀⠀⠀⠀⢱ ⠀⠀⠀⠈⠑⠒⠤⠴⣾⡇⢠⠎⣤⢄⡴⠊⠁⠀⠀⢀⠄⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠁⣴⠋⠀⠀⠀⠀⠀⢀⡩⠇⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⢀⡴⢃⡿⠂⠀⠀⠀⡴⠁⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠄⠀⠀⠈⠳⣤⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣯⡴⠃⣠⠋⠀⠀⢠⠃⡘⢁⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠀⠀⠀⠠⡀⠳⣄⠀⠀⠀⣳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⡴⢁⠄⠀⢠⠃⠀⢀⡞⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⡇⢸⠀⠀⠀⠀⢳⠀⠀⠳⡀⣄⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⣠⡞⢀⡎⠀⢠⡟⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⡇⣾⠀⠀⢀⠀⢻⣇⠀⠀⠁⠈⢻⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⣰⠟⡹⠁⡼⠀⢠⠏⡇⢀⡼⠀⢀⣸⡆⠀⠀⠀⠀⠀⠀⠀⢰⡿⠳⢤⡀⢧⣿⡆⠀⠘⡄⠈⣿⡀⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⢠⣾⠗⣼⠃⢀⠇⢠⠇⢀⠏⠀⣱⣼⠗⠚⠉⠉⢇⠀⠀⠀⠀⠀⢀⢀⡎⠀⠀⠀⠈⢻⣯⢷⠀⠀⢧⠀⢽⡇⠀⠀⠀⠀⠀⠀⡀⠠ ⠀⣰⣳⠋⣼⡇⠀⢸⢀⣾⠀⡜⠂⠁⠈⠛⠆⠀⠐⠒⠼⣆⠀⠀⠀⠀⣼⡞⠀⠀⣀⡀⡀⠈⣿⡞⣧⠄⢸⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢽⠇⠀⣿⠆⠀⢸⡟⢸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣀⠀⢸⢿⠃⠀⣀⠀⠀⠀⠀⠸⣧⠸⡄⢸⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠐ ⠈⠀⠀⠀⣹⠀⠀⠘⠇⡞⠛⢤⣤⡾⠟⠒⠚⠛⠿⢿⠗⠀⠀⠈⠑⠓⠚⠀⢀⣠⣬⣿⣔⣂⡀⠹⡄⢱⣸⡆⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⢀⢰⠧⣿⡟⢻⡁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢤⡈⣉⣙⣷⣾⣾⡟⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⡌⣸⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢥⡄⠹⠟⠙⣷⣷⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⢸⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡞⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠏⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⡆⠀⠀⢸⣿⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⣶⣿⣷⣶⣦⣍⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⡇⠀⣠⣾⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⡜⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⡇⠀⠉⣿⣼⣧⠈⢧⠀⠀⠀⢀⡤⢤⡀⠀⣿⣿⡿⠟⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⠀⣠⠏⠠⠋⠰⠁⢑⠀⠀⡠⠀⣠⠎⠀⠀⠀⠀ ⡜⠀⢷⡇⠀⢹⠟⣿⠀⠈⣷⡀⠰⡁⠀⠀⠘⠀⢻⣏⠀⠀⠀⢀⣀⡼⠁⠀⠀⠀⠀⢀⠞⣡⠀⠀⠀⠀⢀⡌⠁⣠⣥⠞⠁⠀⠀⡰⠀⠀ ⡇⠀⠸⣿⣀⢸⠀⢸⣆⣸⠿⢿⣄⠈⠒⠒⠁⠀⠀⠘⠛⢿⡟⠛⠉⠁⠀⠀⠀⢀⠴⢁⡼⠃⠀⠀⠀⠀⠀⠀⣸⠟⡡⠀⠀⢀⣾⡇⠀⠀ ⠀⠀⠀⠹⣧⠈⡇⢸⣧⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣠⠖⢁⡴⣿⡷⠒⢪⣟⡅⠁⠀⣰⣏⡴⠁⠀⣀⣼⠟⢇⠀⠠ ⠀⠀⠀⠒⢻⣦⣻⣿⡁⠂⠀⠀⠀⠀⣾⣷⣄⡀⠀⠀⠀⠀⢰⡇⣀⣴⣊⠥⠚⢁⣠⡟⠁⢀⣚⡏⠀⠀⣰⣿⡾⠁⢀⣄⡾⣿⠀⢈⣆⠀ ⠀⠠⠀⠀⠀⠻⣿⣦⠈⠙⠦⣴⣶⣿⣿⣿⣿⣍⠦⣄⣀⡀⢈⠙⠿⠭⠒⠒⠉⠁⡿⠀⠀⠀⣿⣅⠀⣴⣿⣿⠇⢀⣾⣿⠀⣏⡠⠤⠾⠦ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢙⣿⣿⢻⣿⣿⣄⣤⣀⣀⣀⣤⣄⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠠⣿⠿⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⣾⣷⣾⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣾⣿⢃⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡿⣿⣆⠀⣿⣿⠁⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠘⢿⠟⠛⠈⢻⣆⢸⡏⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠟⣿⣿⡿⠀⢸⠛⢹⣟⣿⠇⣸⣿⡇⢿⣿⣿⣿⣿⣿⡇⢻⠉⢿⣇⠈⢇⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⠋⣼⠃⡰⠛⠉⠛⠋⢠⢫⣿⡇⠀⠀⠀⠞⡸⠉⡞⢻⣿⠇⢸⡟⣿⣿⣿⠇⢿⠀⣇⠀⠙⢆⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⡂⠀⡏⡏⠃⢠⠇⣰⠁⠀⠀⠀⠀⠁⢸⣿⡇⡆⠀⠀⡰⢁⣄⡇⠀⡿⠀⠀⡇⠹⠇⠫⠁⢈⠄⣿⣆⢠⠀⢰⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀ ⡇⠀⢀⣄⡀⡼⢀⡇⢀⣄⣼⢠⢀⢀⣿⣿⣇⣇⡀⢠⣇⣾⣿⣇⢰⠃⣀⠀⠀⠀⠀⠀⠀⣸⣆⣿⣿⣮⣧⠈⡆⢰⣤⣼⠁⠀⠀⠀⠀⠀ ⡇⠀⡃⣶⠈⡇⣿⣿⣼⣿⣿⣸⣼⣼⢻⣿⣿⣿⣿⣾⣿⣿⡟⣿⠊⣼⣿⣀⢠⣤⡀⠀⢠⣿⣿⣿⠘⣿⣿⣄⣷⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⡇⠀⣷⠁⢸⣱⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣇⣿⣿⣿⣿⣿⠃⣿⣴⣿⣿⣿⣾⣿⡇⢠⣿⡿⣿⣿⠀⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⠀ ⠇⠀⢻⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⡏⠹⣿⣿⡇⣿⠀⣿⣿⢻⣿⣿⣿⣿⣣⣿⣿⠃⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⣸⢸⣧⡈⡆⣿⣿⣿⣿⣿⣿⣯⡀⠀⠸⡇⠀⠹⣿⡟⠻⠦⣿⣟⣿⣿⣿⣿⣿⣿⣿⣇⡠⡿⠛⠊⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣼⣿⣾⣧⠙⡆⣼⣿⣿⣿⣿⣿⣷⣾⣶⣦⣥⣄⣂⠻⠧⠀⠀⢸⠏⣿⣿⣿⣿⣿⣿⠟⠀⡠⠥⠔⣒⣸⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣆⢣⢿⣿⣿⣿⣿⡛⢷⣼⣿⣿⡟⠛⠿⠛⠳⣆⠸⢰⣿⣿⣿⠟⣩⠏⣀⣵⣶⡿⠟⠛⢛⣿⣿⣿⣿⡟⢸⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⡜⣎⢿⣿⣿⣿⣷⡈⠿⢅⠈⠁⣀⠖⠀⣀⣈⣀⡾⠟⠋⠁⠈⢡⣾⠟⠁⠙⡒⠀⣤⡎⢸⣿⣿⡟⣠⣸⡇⠀⠀⠀⠀⠀ ⣿⣿⠟⠋⠁⠀⢱⣹⣮⡻⣿⣿⣿⣷⣄⠀⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠦⣴⠯⠔⠚⠉⢀⣿⣿⣿⣶⡟⣻⣿⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⢻⣿⠙⣿⡙⠻⣿⣿⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⣿⠋⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠘⣷⡀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣿⣿⣿⡏⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⡝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⣿⡏⢺⡇⠀⡆⢸⠀⠀⠸⣇⠀⠀⠀ ⠈⢳⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⢆⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣇⠀⣿⠘⠹⣦⠀⢹⡄⠀⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⢦⢻⡳⣤⠀⠀⠀⠀⠀⠀⠀⣐⡒⠒⠂⠀⢀⣤⠞⠉⠀⢿⣿⣿⣌⣿⢠⣿⠀⡀⢿⡆⠀⢻⡀⠀ ⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⡇⠀⠀⢂⠀⠹⣷⡙⢷⣦⣀⠀⠀⠀⢸⠉⣿⣤⢤⡖⠋⠀⠀⠀⠀⠈⣿⣿⢿⣿⢸⣿⡀⢿⣾⣧⠀⠀⢻⡄ ⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢸⡀⠀⠈⢢⠀⠀⣨⠟⠉⠙⣷⣦⣤⣾⠞⣱⣿⣯⡀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣿⣿⣿⡇⠀⢻⣄⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⣷⢦⣤⣀⣲⠈⠁⠀⠀⣀⣼⣿⡟⢁⠜⢀⡇⠘⢷⣄⠀⠀⠀⠀⠀⡰⢿⣿⣿⣿⣿⣧⡀⠀⣿⣦⡔⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⡄⠈⠉⠛⠳⠦⢤⣈⣤⡟⡝⢠⠋⠀⡞⠁⡄⠀⠹⣦⠀⠀⢀⡞⣱⢻⣿⣿⡿⣿⡿⡇⠀⡄⢿⡄⠘⠢ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡞⡞⢀⠃⠀⡼⡐⠀⠀⢀⠀⢸⣷⡴⢋⡼⠁⣸⣿⣿⣿⣿⣿⠀⠀⠁⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠜⡰⠁⡜⠀⣰⠇⢠⠎⠀⠀⠀⣾⣿⡵⠋⢀⡴⣿⣿⡿⣸⣿⡟⠀⠀⢀⠀⠘⡆⠀

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⣦⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠲⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠟⠉⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡃⢀⡉⠻⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣴⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡿ ⡁⠀⠀⠀⠀⠀⢀⣾⡟⠀⣾⡿⣷⣦⣄⠈⢻⣦⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠀ ⡅⠀⠀⠀⠀⢀⣼⡿⠀⣾⣿⣧⣾⣿⣿⣷⣤⡘⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⢸⣿⠁⣰⣿⣿⣼⣿⣿⣿⠙⣿⣷⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⣿⣇⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣾⡿⢿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣼⣿⣧⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠘⠿⠇⠀⣿⣷⠀⢿⣿⣿⢿⣿⣿⣿⣿⣿⢹⡟⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⣼⠉⢿⣶⣶⠶⠶⣤⣀⣀⣴⣶⣶⣾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠈⢻⣿⣄⠻⣿⣾⣿⣿⣿⣿⣿⡾⠁⣾⡿⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣄⣿⣦⣤⣤⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⡿⠟⠛⠛⣉⣤⣾⠟⠀⠀⠈⠉⠙⠛⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣀⣤⣴⣶⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡟⠛⠛⠋⠁⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣾⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⣿⡇⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⣿⠿⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⣻⣿⣧⠀⣾⣇⠀⢠⡆⠀⢠⡄⠀⣼⣿⠂⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡿⠛⠉⣁⣀⡤⠾⠿⠿⠿⣷⣝⣿⣷⣟⣁⣀⣼⣷⣿⠟⠁⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠓⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣿⡏⠉⠉⠉⠁⠀⢀⡀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⡀⠈⠿⠷⠶⠶⢶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛⠛⠛⠛⠳⠶⠶⠦⣤⣤⡈⠙⠛⠻⣶⣦⡀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠈⠉⠻⣷⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠻⡆⠀⢀⣼⣿⣤⡾⠟⠁⠀⠀⠀⠀⠀⢘ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠦⠤⢴⠷⠶⠶⠶⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨

⠀⠉⠀⠀⠀⠃⠀⠰⠲⡀⠈⠑⠉⠁⠀⢀⠴⠬⠙⠂⠀⠤⠠⡤⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⡹⠁⠐⢟⢷⢕⡀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⡤⠏⡀⣠⠖⠂⠀ ⠀⠀⡀⠀⠀⢸⠑⣺⠉⠈⢀⣡⠙⠚⠒⠒⠒⠒⠈⠤⣚⠂⣀⢤⠖⠟⡖⠀⠀⢁ ⠀⠀⠁⠒⢒⡏⠐⡓⡔⠈⠀⡠⢢⡎⠀⠀⠀⠀⠀⠀⠄⠉⢰⠁⠀⠀⢉⠝⠀⠈ ⠀⠀⠀⠀⢹⡣⢊⠜⠁⡠⡐⠡⡇⠀⠀⠀⠀⠀⠀⢡⢂⠀⠀⠉⢤⠀⠈⡇⠀⠀ ⠀⠀⠀⢀⠜⣡⢊⠂⢰⠀⡰⠁⠀⠀⠀⠀⠀⠀⡠⠋⢸⠀⠀⢸⡀⠱⠰⡇⠀⠀ ⠀⠀⣠⢁⠖⠇⡌⠠⢹⢠⢁⣠⠄⠀⠀⠀⠀⡼⠡⢄⣼⡄⠸⠈⣇⠀⠀⠘⠀⠀ ⠀⢼⢫⠏⢸⣰⢀⠇⠚⠯⠁⠀⣣⠀⠀⢀⡰⠀⢀⠀⢷⢡⡀⡆⢾⠀⠀⠀⠀⠀ ⠘⠃⢸⠀⢸⢃⡌⠀⣀⣀⣀⣀⡀⠓⢄⡜⠇⠠⢀⢀⠘⠏⠆⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⢀⡌⣾⢻⠁⠀⠀⠉⠁⠀⠀⠀⠀⠚⠫⡛⣓⣮⣾⢇⠘⠀⠀⠀⠀⠀ ⠀⢀⠃⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠚⠽⢻⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰⠀⠀⠄⠀⠀ ⠀⡀⠀⢸⡏⠀⠀⠀⠀⠀⢠⠎⣥⣬⣅⡢⡀⠀⠀⠀⠀⢀⠞⡐⠀⠀⠀⠀⠀⢰ ⢸⡇⠠⡾⡟⢇⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⠆⠀⠀⠀⢠⢊⢎⢀⠀⠀⠀⡀⠀⠀ ⡄⢷⠀⡿⢿⠈⣆⢰⠈⢉⠈⣟⠁⠀⣀⡝⠀⠀⢀⠔⠅⠀⠀⡐⢂⡢⠊⠀⡀⠀ ⠃⠘⣷⢡⢸⡐⠛⠣⡈⠁⠀⠀⠉⠋⠁⠀⢀⠀⣣⣎⠠⡤⠀⢀⢞⠄⠀⣸⡇⢀ ⠀⠀⠺⣼⡮⣁⠀⢀⣸⣦⢀⠀⠀⢸⣠⡴⢅⡊⡼⠁⢸⠃⢀⣾⡏⢠⡼⡇⠨⡄ ⠀⠀⠀⠙⠃⠀⠙⢻⣿⣿⣧⣑⣂⣀⣌⣁⣀⡀⠁⠀⠘⣡⣾⡟⢠⠿⠇⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡴⠒⠲⣄⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡗⠀⢀⡼⠀⠀⠀⠀⠀⠀⢿⠀⠀⠚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠐⠒⠒⠒⠒⠲⠶⠬⠑⠒⠚⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉⢀⣀⠈⠑⢿⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢾⡟⢷⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⢀⣠⡶⢏⡹⠃⠀⠀⠮⡁⢈⣳⠞⢻⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣼⣿⣶⣞⡙⢷⡀⠀⠀⠀⠀⠀⠀ ⡇⢀⣾⣿⣿⣶⣶⣤⠀⠀⢀⣠⢿⡏⣽⡤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⣿⡟⠛⠻⣿⣾⣷⡀⠀⠀⠀⠀⠀ ⡇⣼⢁⡾⠛⠻⣿⠛⣷⠚⠋⠀⢀⡴⠋⣴⠋⣠⣤⣀⠀⠀⠀⠀⠀⠀⣿⢷⣤⣀⠀⠀⠀⠀⢀⣸⣿⢻⡄⠀⠀⢸⡎⣿⡻⣦⡀⠀⠀⠀ ⡇⡏⢸⡇⠀⠀⣿⢠⡟⠀⣠⡶⠋⠀⣼⠿⣿⡉⣏⢉⣿⣶⣦⣄⣀⣀⣿⣀⣀⠉⠙⠛⢻⣿⡛⣿⣿⣎⣻⠶⠴⠟⠀⣿⣷⣿⠛⢷⣄⡀ ⣥⣿⡌⠻⠶⠾⣷⠟⣠⠞⢹⣇⣤⣼⠏⠀⠈⢿⢉⣙⣷⡖⠚⠉⠉⠉⠀⠉⠉⠙⢟⠳⣿⢋⣦⡟⠛⣯⠙⢷⡄⠀⠀⢸⡎⣿⠀⣸⠉⢻ ⣿⣿⠃⠀⢀⡾⠃⠀⣨⣴⡟⠋⢈⣟⠀⠀⢀⣾⢻⡟⢋⠙⠳⠦⢤⣄⣀⠀⠀⠀⡸⠀⣻⡄⠈⢿⢦⣽⣧⡀⢻⡄⠀⠈⣧⢸⡷⠋⢴⣿ ⣿⡟⠀⢀⡾⢁⣠⣞⣋⡉⠛⠓⠛⠻⣦⣴⡾⠁⢿⡀⠀⠑⢄⡀⠀⠀⠉⣳⣦⣴⠁⣠⡟⠀⣠⠟⢠⡽⠿⢷⡀⠻⠶⠾⠋⣸⠇⣠⡟⠁ ⡍⣿⣴⡾⠷⠿⢧⣤⣀⣀⡀⣀⣠⣴⣿⠀⢁⠰⡌⣷⠀⠤⠤⠙⠒⢂⡼⠃⣀⡿⢻⣿⡇⢀⠁⡀⢿⡐⠚⠋⠙⠳⠶⣴⣾⣯⠾⠋⢲⣤ ⣿⡇⠀⢶⣄⡀⠀⠀⣩⠉⠉⠉⠉⣴⡋⠊⢸⡄⠉⣿⠧⠤⠶⠖⠚⠋⣿⣉⣉⣀⣀⠙⢷⡼⠀⢇⢘⠷⢤⣤⡶⠶⠛⡟⠉⠁⢀⣴⢟⡁ ⣿⣷⣄⡀⠈⠛⠶⣤⣅⣠⣤⠴⢾⡟⣷⠀⢸⠁⢰⠏⠀⠀⠀⢀⣀⠤⠼⠋⠓⡿⠬⢝⣿⠇⢣⠈⠙⣇⠀⠀⢻⣦⣀⣨⣶⠾⠋⠀⠘⣤ ⡇⢸⠉⠙⠷⣤⣜⣀⣀⣀⣤⡴⠛⡄⢸⡇⢸⠀⣿⠀⠤⠒⣉⣡⣤⣴⡶⠿⠿⢯⣹⡾⠁⢀⡼⠀⠀⢹⠀⠀⠘⣄⠻⣆⠀⠑⣀⣤⠾⠋ ⣷⡘⠳⡶⠛⠉⣽⠉⠉⠉⡀⢠⢞⡧⣸⠇⠘⢰⡇⢀⣶⠿⠓⠋⠉⠀⠀⠀⡇⠀⢸⡄⠚⠋⠀⠀⢠⠏⠀⠀⠀⠸⡄⠈⢿⡛⠉⠀⠀⠀ ⡍⣧⠀⣧⠠⠞⣁⣠⡴⠞⡱⢣⢏⣴⠂⠀⢀⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⡇⠀⣀⡤⠀⠚⠀⢠⡀⠀⠀⠈⠢⡈⢷⣄⣀⡀⠀ ⡇⢻⣤⠈⠙⢛⠟⠛⠁⠀⠠⣿⠟⠁⣀⣴⣾⠃⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢠⡾⠀⣈⣉⠀⡼⢦⡀⠀⠙⠶⣄⠀⢀⠘⡌⠁⠉⢻⡄ ⡇⠈⢿⣅⡀⠈⠑⠒⠒⠒⢰⡏⠀⠈⣸⠁⡿⠀⠀⡞⠉⠉⠁⠀⠀⠈⢻⣄⡴⣿⠉⠁⣠⢋⡼⠁⠀⠙⣦⠀⠀⠈⠙⠘⡄⢹⡀⠀⢀⣿ ⡇⠀⠀⠉⠛⠳⠦⣤⣄⣀⣼⡇⠀⠀⣿⠁⡟⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⠋⡇⠘⢷⡄⢻⡘⠁⠀⠀⠀⠈⠳⣤⡀⠀⠀⠁⠀⢣⠀⣼⠋ ⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣼⠃⠀⠸⣄⡀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡟⢢⠁⢻⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣇⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⢿⣷⠀⠸⡄⠀⠀⠀⠀⢀⡞⠀⠀⣾⡟⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠉⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠆⠀ ⠀⠈⠉⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⡶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⠤⣴⣴⠾⠿⠧⢤⡙⠟⠙⢧⡀⠀⠀⠀⢠⠞⠀⣿⣿⠿⠿⠿⠶⢖⣒⡛⠋⠀⠀⠀⠀⠀⠀⡀⠀ ⡀⠀⠀⠀⠀⠀⠘⢄⠀⡴⠋⢱⣶⠀⢀⣤⣾⠏⠀⠀⠀⠑⠀⠀⠀⣏⠀⠀⢫⡀⠀⠰⡿⠆⠀⠀⠈⢳⠖⠀⠀⠀⠀⠀⠣⠀ ⠀⠀⠀⡘⠲⣤⠀⠀⢻⢤⣤⡤⠶⠞⢛⣥⠏⢠⠖⠒⠦⠀⠀⠀⠀⢻⡤⢤⡈⢯⡻⢶⣦⡤⠤⠤⠒⡏⠀⣠⠔⡂⠀⠀⠀⠀ ⡄⠀⠀⠙⠂⠈⠁⠀⠨⠤⠤⠤⢴⡺⠟⠁⠀⢸⠀⣠⣤⣦⡀⠀⠀⠘⣧⠀⣷⣀⠙⠶⢄⣉⡉⠉⠁⠀⠘⠁⠚⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⢡⣄⠠⣤⠀⠀⣀⣉⣿⣭⣳⡀⠀⠀⢸⣄⣀⠈⠛⠀⢶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⠄⠀⠈⣀⣤⠶⢾⣟⠉⠁⢹⣿⠿⠶⣦⣤⡿⠛⠻⣶⣤⣤⣀⡀⠙⠒⣶⡄⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⠀⠑⢀⣠⡾⠿⢿⣧⣀⣼⣿⣷⣶⣿⣿⣿⣶⣿⣿⣷⣶⣾⣿⣇⡀⢸⣿⠿⢷⣤⣉⠀⠈⢻⣧⠄⠀⠀ ⠀⠀⠀⠀⣀⡤⠞⠈⣠⡶⠿⢿⣤⣠⣾⡟⠛⢻⣿⣁⣨⣿⣏⣀⣹⣿⣯⣉⣹⣿⡟⠙⢿⣿⢿⣦⡤⢼⣿⣷⡀⠀⠈⣷⠀⠀ ⠀⠀⣶⡶⠉⠀⢠⣾⣿⣀⣠⣿⣟⢉⣽⡷⠖⠛⠛⠉⠉⠉⠀⠀⠀⠈⠈⠉⠉⠉⠙⠛⠛⠷⠼⣿⣧⣴⣿⣿⡇⠀⠀⣸⡆⠀ ⠀⠀⣸⠁⠀⠀⣿⣿⣯⣤⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⢀⣠⡿⠀⠀ ⠀⠀⢻⠀⠀⠀⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠛⠓⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡄⠀ ⠀⣆⠘⢷⣄⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠤⠞⠋⠀⠀ ⠀⠈⠉⠀⠉⠛⠛⠉⠀⢀⣠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠘⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⣛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⢇⡘⠷⠀⠀⠀⢀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠟⠛⢉⠀⠀⠀⠀⣀⠀⠀⢀⣠⠔⠀ ⠀⠀⠰⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⡤⠴⠒⠚⠁⠀⠀⣀⣀⡭⠔⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⠶⠀⠀⠒⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⢀⡠⢴⡶⠖⠒⠻⠯⣉⡭⠶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢋⡤⠖⠋⣩⠽⠋⠛⠀⠀⢀⣀⡀⠤⠤⠬⠳⢤⡀⠀⠀⠉⢻⡖⣤⣄⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠟⠒⠻⢄⡴⠛⠉⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠈⠁⠈⢯⣧⠀⠀⠀⠀⠀⠀⢻⡵⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣽⣦⡀⠀⠀⠀⠀⠀⢻⡽⡀⠀⠀ ⠀⠀⠀⠀⢰⠏⢧⡤⠊⠉⠀⢀⡀⠀⠀⠀⢐⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠈⠁⠈⠳⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⢸⠷⢶⠃⠀⠀⠀⢸⠉⠹⣳⠄⠧⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠘⠦⣾⠄⠀⠀⠀⠘⣎⣷⣼⣁⠀⠀⠀⠀⠙⣦⡔⠒⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣆⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣈⣆⠀⠀⠀⠀⠀⠀⠀⠻⠙⢦⡉⢦⣍⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢬⣿⠀⠀⠀⠀⠀⢼⡇⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠠⣶⠶⢤⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣯⣙⠲⣄⡀⠀⠀⢿⣆⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠈⣧⠀ ⠀⠀⠀⢀⠞⣠⠖⠀⢠⡇⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⢻⣷⡤⡙⣳⣤⣀⡹⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀ ⠀⢀⡴⢃⠔⡝⣴⢀⠟⠁⣰⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣞⢉⠛⣷⠀⠈⠓⢝⣯⣻⣻⡛⢲⡀⠀⠈⡇⠀⠀⠀⠀⠀⣇ ⠰⠋⠊⠁⢰⢷⠇⡎⠀⣼⠋⣯⠇⠀⢀⡙⢦⡀⠀⠀⠀⠀⠀⢧⠀⠀⢿⠘⠃⣸⣇⣀⡀⠀⣻⡽⢿⣷⡀⢷⢄⣰⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⢸⢰⠁⣼⠁⠈⡿⡄⠀⢸⠋⢙⣷⡀⠀⠀⢀⣠⣼⣶⠖⠚⠛⠉⣽⠉⢉⣿⠛⠉⡇⢸⣻⡇⡎⣸⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣼⣼⣸⢹⠀⠀⠹⣷⡄⢘⣧⣜⣸⣧⠀⢀⢻⡅⠀⠈⠳⠤⠤⢞⣃⣤⠾⠋⠀⠀⣸⠘⣻⣰⣧⠏⠀⠉⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠈⠹⡇⠸⡀⠀⡤⠾⠻⣯⡁⠉⢹⠙⢷⣠⣀⣻⠴⣤⣤⡴⠾⠋⡵⠀⠀⠀⠀⠀⠘⡛⠉⢩⡄⠀⠀⠀⠀⠀⠀⢠⡏⡆ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣰⢷⡀⠀⠀⠉⢛⣡⡴⠊⠇⠀⠡⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠰⡿⢿⣼⡁⠀⠀⠀⠀⠀⠀⡼⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠛⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⣼⢇⠀⢻⠱⡄⠀⠀⠀⠀⢰⢡⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡼⠀⠈⠓⠹⡄⠀⠀⢠⠇⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠁⣼⢻⠃⠀⠀⠀⠀⠹⡀⢀⡞⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠠⡾⡟⢿⡄⠀⠀⠀⠀⠀⢳⣸⡥⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣶⣖⣲⣶⣶⣛⣿⠟⠁⠀⠀⣼⠙⠀⢸⢳⡄⠀⠀⠀⡔⠚⣿⠀⠨⢇⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠩⣿⣹⣷⠋⠁⢠⡶⡗⠀⠀⢀⡼⠛⠲⣄⠈⡷⠤⠃⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠿⠁⠀⠀⠘⠃⠁⠀⢠⡽⠃⠀⠀⠀⠹⡿⠲⣄⢀⡤⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠔⡈⠆⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⣁⠚⠀⣠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⠀⠀⠀⠀ ⠀⠀⢀⢊⠔⠁⠀⣰⠃⠀⠀⠀⠐⠌⢆⢸⠈⢉⣐⣖⠓⠠⠶⢭⡆⠀⠀⠀ ⠀⠀⡞⠏⠀⠀⣰⣁⡸⡑⠀⠀⡄⡘⢹⠹⣞⠏⠓⠙⡇⠀⠹⡀⢸⠀⠀⠀ ⠀⠈⡏⠀⠀⡀⡇⢿⣷⠳⡀⠀⣏⣀⣨⢯⠛⠤⡠⠊⢃⠀⠀⢏⠹⠀⠀⠀ ⠀⠀⣠⠀⠀⠱⠧⠁⠀⠀⠈⠑⠓⡾⣿⣿⣧⠀⡄⠀⢸⡀⠀⢪⠢⡀⠀⠀ ⠀⠀⠙⡧⢀⢢⡇⠀⠀⠀⠀⠀⣠⣦⣌⣛⠇⠀⠘⠀⠈⠱⠀⢸⢽⠈⠁⠀ ⠀⠀⠀⢈⠎⠉⠱⠀⠀⠀⡀⠀⠈⠉⠙⡛⠀⠀⢠⠀⡆⠆⠑⡈⡌⠢⠀⠀ ⠀⠀⠠⢂⠀⡔⠀⠱⣀⡀⠋⠀⣀⡀⡔⠀⠀⠀⣸⠀⠇⡇⠀⡵⡘⢆⠀⠀ ⠀⢀⠔⠁⠜⠀⠀⣰⣿⣿⣿⣿⡠⠌⢀⠀⠀⢠⠁⡄⠰⢣⣰⠁⠇⠀⠐⠀ ⠀⠁⢀⠊⠀⠀⢠⣿⣿⣿⡿⠟⠂⠀⡌⠀⠠⢇⠀⠘⡄⢹⣟⠜⠂⠀⠀⠀ ⠀⠀⡎⡘⠀⠀⣾⣿⣿⣿⡦⠔⠒⠚⢠⠜⠑⢌⡄⠀⣀⠟⣁⠄⠀⠀⠀⠀ ⠀⢀⡆⢻⣀⠀⠻⣿⣿⡟⠢⡀⠉⠓⡎⠀⠀⠀⠳⠀⢰⣿⡄⠀⠀⠀⠀⣀ ⢠⢿⠈⣦⣽⣿⣿⢟⢿⠘⣄⠈⣣⠜⠁⠀⠀⠀⠀⢇⠈⣿⣷⣄⢡⠀⠀⣿ ⠀⢸⡀⢸⡏⠻⡟⡞⢸⠀⢀⢇⠀⠀⠀⠀⠀⢌⡀⠈⣦⣘⣿⣿⣼⠀⣠⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠤⢄⠀⠀⠀⠀⡠⢄⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⢸⠹⠄⠜⣀⣀⣀⣘⢄⣨⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠴⠚⡉⡁⢛⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡤⢶⡲⣞⡀⠀⠀⠀⠀ ⡀⣠⣶⣭⣌⠀⢈⣢⣺⣡⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⡇⣾⠿⢷⣽⡄⠀⠀⠀ ⣵⢱⠋⢹⣍⠎⢁⡴⢊⣎⢴⠦⣄⡀⠀⢸⠓⠦⠤⣀⣤⣿⡹⣄⣠⢿⣯⡦⣀⠀ ⣼⡞⠢⣾⠞⡔⣿⣤⡞⠈⢻⣙⣯⡚⠉⠉⠉⠑⠖⣞⠡⡟⢟⠳⡄⠀⣏⣇⣸⢱ ⣿⠁⢰⢃⣤⠛⠥⠼⢆⣠⠏⡏⠐⢌⠁⠒⣤⣠⢃⡜⢀⠍⣻⢧⡹⢤⠼⡸⣡⠟ ⣽⢒⡛⠛⠢⠤⠤⠴⡻⡈⡔⢽⣐⣒⣁⢴⠥⠜⠻⣇⡄⡜⣆⢉⣉⣒⡾⠟⢁⡶ ⡿⣤⡉⠓⡤⠥⠤⣺⢳⠀⡇⡜⠀⣀⠠⠌⣛⣹⡱⡾⢠⠁⢇⠉⠣⣤⠦⡖⠁⣣ ⡇⢧⠼⢓⠒⠒⠊⣵⣀⠇⢱⠃⣭⠶⠚⠋⠉⠉⣞⠤⠊⠀⡜⠀⠘⡈⢢⠔⠊⠁ ⢻⡈⠶⢯⡴⠊⢋⡧⠂⢀⡏⠉⠀⠀⠀⠀⠠⠀⡼⠠⠔⣀⠀⠢⡀⠈⠢⠳⠤⡀ ⡆⠫⣄⡑⠒⠐⢼⠁⢨⢹⠀⢰⠂⠉⠉⠑⣆⢼⡀⠩⡱⠁⠱⣄⠈⠃⢃⢃⠀⣹ ⠃⠀⠀⠉⠑⠒⢻⠀⢐⡸⠀⣇⠀⠀⠀⠀⡉⡄⢱⠘⠀⠀⠀⠈⠑⠂⠈⡤⡂⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣀⣀⣀⠀⠀⠀⠐⡆⠸⠀⠀⠀⠀⡜⠀⣴⠀⠀⢀⣀⣀⣤⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⡀⠁⠀⠀⠐⠀⣼⣧⣴⣾⣿⣿⣿⣿⣿⡤⠀ ⠈⠉⠉⢛⣛⣛⣛⣿⣿⢿⡷⡄⠀⠀⢀⡜⣿⣿⣿⣛⣛⡩⠉⠁⠀⠀⠀ ⠀⠀⠀⠢⣠⠚⠭⣀⣤⡟⠀⠈⠂⠀⢌⠀⢯⣀⠰⠀⠉⢰⠀⠀⠀⠐⠀ ⠀⠪⠑⠀⠋⠘⣩⡵⠊⢰⢉⣁⡀⠀⠸⡉⡎⠪⠙⡋⠉⠉⠐⠩⠀⠀⠄ ⠀⠀⠀⠀⠀⢉⠁⠆⢒⣀⡤⠿⣾⣄⣀⣧⣤⣉⡐⠀⢤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠘⣀⡴⠚⣯⣸⣷⢶⣿⢶⣿⣷⣶⣿⣉⣻⡖⢮⣁⠁⢦⡄⠀ ⣠⡔⠊⣡⣞⣉⣷⢺⡯⠼⠗⠚⠓⠒⠛⠒⠚⠳⠼⠏⣿⣹⣿⡆⠀⣧⠀ ⢸⠀⢰⣿⣷⠿⠋⠁⠀⠀⢀⣀⠤⠤⢤⣀⡀⠀⠀⠀⠀⠈⠉⠡⠴⠃⠀ ⣌⢦⣀⣉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠐⠋⠀ ⢀⠀⠀⠀⠀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⡠⠁⠁⠀⠀⠀⠀ ⢀⠰⠀⠀⠀⠈⠒⠤⠤⣄⣀⣀⣀⣀⣠⡤⠴⠒⢛⡩⠀⠀⠠⢀⡠⠒⠀ ⠀⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀

⠀⠠⠀⢂⢪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣰⢍⢳⡎⢆⠀⠀ ⠀⣠⠊⣾⡕⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⠎⠀⠀⣧⠁⠙⢌⡄⠀ ⣜⠼⣴⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠀⢀⣴⡟⣧⡀⠂⠿⡀ ⢀⣎⡿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢱⠄⠐⠄⡀⠁⢆⢀⢠⢾⣹⣷⡍⡟⣦⡀⠱ ⣷⢻⠁⠆⠀⠀⢀⠀⡟⡀⠀⠀⡆⠈⡎⠢⡀⢸⢢⠈⡄⠁⠀⢻⣿⣷⣿⡘⣷⡀ ⡇⡌⡘⢀⡄⢀⢸⠀⡅⣡⠀⠆⢰⠀⢨⠉⠑⡌⣆⣱⣴⠀⠀⡆⢃⠘⡳⣳⠑⣿ ⣡⣱⢁⡆⠀⢸⡄⠆⡄⠀⢣⠰⠈⣄⠈⣖⡵⠟⢿⠙⣿⡄⢀⢱⢌⠄⠐⡱⡡⠀ ⢩⠸⡘⡇⠠⢼⡟⢻⠛⢯⣔⡱⣴⠏⢂⠻⡉⠝⣼⠀⠉⡃⠈⢦⣂⠙⠒⠓⠊⠪ ⠗⢤⠇⡇⠄⢸⢷⡈⢧⡢⠽⠀⡏⠲⠀⠁⠉⠋⠁⠀⠀⡇⣦⢸⣉⣭⠷⢦⣄⠀ ⡄⠀⣴⣟⣽⢸⣈⡆⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⣰⡇⣿⣾⣿⣿⣿⡇⢩⡓ ⢠⡼⡏⢏⣿⡿⣿⠹⡀⠀⠀⢀⣀⡀⠠⡤⢒⠄⢀⣴⠻⡸⠫⢺⠛⡛⠭⠤⠂⠊ ⠍⠃⢱⠀⠹⣅⢸⠆⢸⢤⠤⣀⣁⠈⠁⠈⢘⡴⠋⢸⠀⢧⢃⢸⢣⠁⠀⠀⠀⠀ ⢈⠓⠴⣤⣀⣹⣍⠀⢸⢸⢰⡔⡻⣿⢶⣾⣿⣏⠢⣼⡄⢘⡌⢆⠆⠀⡀⠀⠀⠀

⠏⠀⠈⠄⠀⡀⠀⠀⠀⠀⠀⠈⢾⣟⠢⡀⠀⠀⠤⡀⠀⠀⠀⠉⠲⠇⢀⣐⡈⢃ ⠀⠀⠀⠈⣆⠐⡀⠀⠀⠀⠤⣀⠈⠯⠽⠿⢦⡀⠈⢶⢄⠀⠀⣀⠀⠀⣈⡛⠧⣀ ⠀⠀⢠⠀⠟⠣⢌⡂⠀⢠⡴⡙⠠⡀⠀⢒⠚⠳⠀⢈⠛⠢⠀⠈⠻⠋⡱⣾⡛⡟ ⠀⠀⠀⠆⠸⠀⠀⠹⡿⠃⠒⣠⣦⣤⣴⣧⡤⡴⠀⢸⠓⠤⡀⠀⠀⠸⡍⠂⣼⠈ ⡀⢀⠀⠘⢄⢂⢀⣾⣧⣠⣟⡾⠛⠻⠟⢹⣣⠯⠀⠈⠀⠀⢎⢦⠀⡏⠨⡆⢨⣸ ⡇⠘⣷⢧⡀⢗⢄⠙⠂⠈⢼⠁⢘⠤⠐⠛⠉⠀⠀⠀⠀⠀⠈⠀⣕⠇⠷⠜⢺⢸ ⢿⣤⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⣀⣠⠎⡀ ⡄⠈⠋⢿⠛⣟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢼⠂ ⡇⠀⠀⠈⣳⢲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷ ⠘⠌⢦⣄⡀⠙⠿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷ ⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⡀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⣿⣿⣿⢱⣄⠀⠈⠚⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠠⠂⠈⢍⣹⡘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠀⠀⠀⢀⣠⣤⣤⣶⣾ ⠀⠃⠀⡀⠀⠹⣷⣘⣛⣩⣿⣩⣐⣢⣄⠠⣴⣾⣏⡛⠿⢆⣤⣾⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⢷⣄⢠⡈⣻⡟⠛⠛⠙⠏⠒⢦⣤⠸⣿⣿⣿⣴⣿⣿⣿⣛⣉⣁⡀⠀⠀

⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠰⠶⢶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⠴⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠛⣿⣶⣿⣟⡋⠉⠋⠁⠀⠀⠀⢉⣷⡚⠉⣍⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗ ⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⠿⠛⠻⠋⠉⠋⠛⠛⠿⢿⣿⣿⡉⠁⠀⠀⠀⢀⡾⠀⠀⠀⠀⣿⣿⣿⠿⠟⠋⠉⠋⠙⠙⠟⢿⡏⠉⠁⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣤⣿⣿⢻⣶⠦⡄⠀⠀⠀⠀⠐⠂⣾⣿⡟⠃⠀⠀⠀⢀⣾⡧⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠿⠶⠏⠀⠀⠀⣀⠀⠒⢾⣿⣷⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⣿⣷⣿⣁⠀⠀⠀⠀⠘⠷⠿⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠟⢻⣿⣿⣿⣯⣧⣀⡄⠀⢠⣄⠈⣇⣠⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠹⣿⣿⣷⣄⠒⠀⢀⣀⣠⣶⣿⡷⣦⡄⠀⠀⠀⠀⠀⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⢛⣵⠃⠀⠀⠀⠀⢠⣿⣿⣧⢀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⡏⢀⠈⠓⠀⠀⠀⠀⢰⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠏⠀⣀⣠⡤⠀⠀⣠⣿⣿⣿⣿⣀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣟⣿⣿⠗⠉⠀⠀⠀⠀⠀⠀⣼⠏ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣶⣿⢟⡿⠛⠁⢀⡀⣼⣿⡛⢡⣶⣾⣿⣿⣿⣿⣿⣭⣭⣽⣥⣶⣿⠋⠉⠛⠟⠛⠉⠁⠀⢀⣀⣄⣀⠀⠀⠀⣿⠀ ⡇⠀⠀⠀⠀⢠⣶⠾⠛⠉⠋⠛⠛⠒⠦⠀⠀⠀⠀⠀⠀⠉⠻⠤⠌⠉⠀⣠⣴⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠋⣦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠻⡄⠀⣿⠀ ⣿⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣍⣳⣌⣢⣠⣿⣿⣾⣿⣿⣿⣷⣴⣤⣀⣀⣀⣀⠀⠀⠀⢀⡇⣼⣿⠀ ⢹⣷⠀⠀⣿⠀⠀⠀⠀⠀⣀⣄⣠⣶⣾⣟⣿⣿⣯⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⠷⠦⠶⠤⢤⡬⢭⢭⣤⣤⣤⣤⠤⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣤⡌⢸⣿⡇⠀ ⠀⢿⣧⡀⢿⠀⠀⠀⠀⣾⣿⣿⣾⣿⡯⠕⠚⠛⠋⠉⠉⠁⠈⠉⠉⠛⠿⢿⣿⣿⣿⣦⣴⣴⣦⣶⣷⣤⣴⣶⣶⣶⣤⣤⣤⣤⣶⣾⣿⡿⠿⠋⠉⠉⠁⠙⠻⣿⣷⢿⣷⢸⣿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢁⡤⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⢀⠔⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡴⠋⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠲⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⡰⠋⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⡀⠀⢣⠀⠀⡤⠒⠢⠤⠤⣀⠀⣠⣚⡁⠀⣀⣀⠼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⢀⡞⠁⠀⠀⠀⣴⢻⢁⠀⠀⠀⠀⠀⠀⡙⢦⡈⢣⡀⡇⠀⠀⢀⣠⣤⣯⣀⠀⠉⠻⡖⠒⣒⣻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢾⠟⠀⠀⠀⠀⣼⠏⠈⡹⡒⠤⠀⠀⠀⢠⠃⠀⡝⢱⡟⢻⢴⡮⢛⡫⠭⠛⢺⡶⠀⠀⠹⡍⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢃⠏⠀⠀⠀⠀⢠⠿⣶⣦⡇⢳⡀⠀⠀⠀⢸⣀⠞⠠⠬⣧⣈⢿⡊⠁⠀⠀⠀⡸⡇⠀⠀⠀⢹⣀⣀⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⡞⠀⠀⠀⢠⠀⢸⢰⣿⡿⣿⡝⢳⡄⠀⠀⢺⣁⡀⠀⢀⣿⣇⠙⠓⢤⡀⣠⠜⠁⣧⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⡄⠀⠀⠘⢦⢸⠸⣄⠛⠝⠀⠀⠙⠢⢄⡸⡖⢛⣿⣾⣦⣿⡄⠀⠀⢏⠁⠀⠀⢸⡀⠀⠀⠀⡟⣆⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⡇⠀⠀⠀⠈⡟⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⣿⣿⡿⢦⠀⢸⡀⠀⠀⠀⢧⠀⠀⠀⢹⣌⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣟⣄⠀⠸⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣀⠉⠹⠿⡇⠀⠉⠀⢻⠀⠀⢸⠈⢆⠀⠀⢸⢎⣷⠚⠙⠒⠒⠂ ⠀⠀⠀⠀⠀⠙⢎⢑⡤⣘⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣟⣿⣿⣶⣾⠁⠀⠀⠀⠀⠇⠀⣾⠀⠘⣆⠀⢸⠈⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢧⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠇⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠈⢇⠀⢧⠀⠱⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡜⠀⢷⠀⠀⠀⠀⡳⠄⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣾⠀⠀⡇⢸⠀⠀⠈⢦⠘⢷⡄⠀⠉⠀⠀ ⠀⠀⠀⠀⠔⠁⣠⠂⢠⠞⠀⠀⠀⢳⣄⣀⣀⣀⣀⣀⣀⣀⡤⢴⡞⠀⠀⠀⠀⠀⢰⢻⠀⠀⣧⢸⠀⠀⠀⡏⢧⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠁⢠⠏⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣿⠀⢀⣠⠊⠀⡄⠀⠀⠀⠀⡞⠈⡆⠀⢻⠸⡄⠀⣼⠁⢸⡇⠀⠀⠙⡆⠀ ⠀⢀⡠⠚⠁⠀⡠⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠞⢉⠁⠀⢠⡇⠀⠀⠀⡼⠁⠀⢱⠀⠀⢣⡱⢾⡇⢀⣟⡇⠀⠀⠀⠈⠄ ⠰⠃⠀⠀⠀⡴⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⡜⠀⠀⢀⡼⣇⠀⠀⠀⢣⡀⠀⣼⣿⢁⡞⠘⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⡴⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⣠⠎⠀⠀⣠⢮⡀⠘⡆⠀⠀⠀⠙⢢⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⡄⢠⠇⢠⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣚⣋⣉⠉⠉⠉⢳⠚⠁⠀⠈⢢⣹⡀⠀⠠⢤⣚⣁⣀⠤⠆⠀⠀⠀⠀⠀⠀⠀ ⠈⠂⠜⢸⡀⠸⣷⡀⠀⠀⠘⣿⣿⡿⣿⣿⡷⣄⠀⠀⠉⠙⠳⢤⡟⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⢷⡀⢻⣷⣦⣀⣀⣙⣿⣷⣿⡿⣇⠈⠙⢦⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣿⣿⣧⠀⠀⢢⠀⠀⠀⠀⢸⣦ ⠀⢠⢻⣿⠀⢿⣶⣽⣿⣿⣿⣿⡿⢡⢿⡇⠹⡄⠀⠀⠙⣧⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢿⣿⣿⣷⡄⠈⢇⠀⠀⠀⢸⣿ ⠀⡈⢸⣇⠀⠘⣿⡿⣿⣿⣿⡿⢠⡟⢸⠀⠀⠈⢱⡒⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠈⢷⡀⠘⣿⣿⣿⣿⡅⢸⠀⠀⠀⣸⣿ ⠀⠀⠘⣿⣄⠀⢻⣧⠀⠙⣿⠃⣿⠁⣿⠀⠀⠀⣾⢧⠀⠀⠀⢠⠀⠀⠀⠀⠀⠣⣤⠇⠀⢈⣿⣦⣬⣙⣻⣿⣿⣼⠀⠀⣰⣿⣿

⠀⠀⡘⠀⣼⣟⣦⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⣿⣿⣿⣿⣾⣿⡟⢠⣿⣿⣿⣿⡟⣼⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⣿⣿⡟⣿⣿⡄⠀⢾⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⢳⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⡿⡽⣿⡌⢻⣳⡀⠸⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣻⡟⣿⢇⣾⣿⢹⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⡻⡝⣿⣿⣿⡄⠘⣷⠁⠈⠀⠀⠳⢳⢰⣿⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⣿⣿⣿⣿⣿⢟⣿⠏⢀⣿⡿⣿⣿⣿⠏⢸⢟⣿⣿⠀⠀⡏⠋⢰⡿⣼⣿⠃⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢻⣧⠙⣆⠈⢻⣿⡀⠈⢇⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀ ⢠⠀⢰⣿⣿⣿⡟⠋⣼⠏⠀⡼⠟⠁⡻⠻⠃⢠⡟⣼⣿⠃⠀⠘⠀⠀⡸⢡⠏⠸⣸⢸⣿⣿⠁⠘⣿⢻⣿⣿⣿⣟⡎⣿⠀⢸⡄⠀⠛⢣⠀⡈⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀ ⢸⠀⢸⠟⡿⠿⠁⢰⡏⠀⡼⠁⠀⠀⠀⠀⠀⡞⢀⣿⣿⡄⢸⠀⠀⠀⢁⡜⠀⠀⣿⠀⣿⡟⠀⠀⢹⠈⣿⡇⢻⠙⠁⠘⡆⢸⣷⡀⠀⠀⠁⢧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⡌⠀⠸⠀⡇⠀⠀⣼⠀⢸⠁⠀⠀⢠⡆⠀⠀⠀⢸⣿⣿⠃⣾⠀⠀⠀⡞⢀⣾⣶⣿⠀⣿⠇⠀⠀⠘⠀⠈⠿⠈⠇⠀⢰⡅⢸⣿⣷⡈⣇⠀⢸⡀⠀⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣠⣦⣄⣰⡇⡀⣿⡀⣠⡇⣼⡇⡄⢠⢀⣾⢻⣿⣠⣿⣤⡀⡆⡇⣾⣿⡏⣿⢀⡟⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢸⡟⢿⣿⣾⡆⠈⣧⠀⣧⣶⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⠁⣾⡀⢹⠁⣿⣿⣧⣿⣣⣿⡇⡇⣿⣼⡏⣾⣿⡿⣿⣿⣿⣼⣿⣿⣿⡇⣿⠘⢀⣿⣿⠀⠀⢠⣠⡀⠀⠀⢠⣿⣿⣾⡇⠘⣿⣿⣿⡀⣿⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⢀⡇⠁⡟⢸⢻⣿⣿⣿⣿⣿⣧⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⣼⣿⣿⣇⣟⣿⣏⡏⠀⣰⣿⣿⣿⣿⡇⠀⣿⣿⣿⣇⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⣼⠀⠀⡇⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡏⣿⠷⣽⣿⣿⣿⣿⢸⡏⠀⣿⣶⣿⣹⣿⣿⣿⣿⣿⡇⢠⣿⣿⠏⣿⣿⡇⠀⢹⣿⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢀⡆⣿⡀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣿⠀⠈⣿⣿⣿⣇⢸⡇⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣡⣿⣿⡿⠀⢿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⣸⣧⠀⢳⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠁⢹⠀⠀⠈⢿⣿⡟⠻⠷⣦⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣼⠷⠓⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣾⡇⣿⣇⠑⣮⢠⢻⣿⣿⣿⣿⣿⡿⣿⣏⣳⣤⣀⣀⠧⠄⠤⠌⢿⣇⠀⠀⠀⢹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢁⡏⣀⡠⠤⠀⣿⣿⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⢰⣿⣿⣦⣸⡘⡞⣿⣿⣿⣿⣿⣿⡿⣿⣛⢻⣿⣿⣿⣿⣶⣶⣦⣭⣭⣀⡀⠈⡇⣸⣿⣿⣿⣿⣿⠟⣿⠏⠠⠔⣋⣩⣥⣴⣶⣾⣿⣿⣹⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣿⣿⣿⣿⣿⡇⢳⡸⣿⣿⣿⣿⣿⣧⡋⢻⣾⣿⡵⣿⡏⠉⠉⠓⠀⠉⠻⣍⠀⠃⣿⣿⣿⣿⠟⢁⡾⠁⣠⣶⣿⣿⡿⠛⠀⠀⠀⣽⢿⣿⣿⣿⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢿⡈⣇⢹⣿⣿⣿⣿⣿⣷⡀⠹⢷⡄⠀⠀⠀⡠⠞⠀⠀⠀⠈⠁⣸⠿⠟⠋⠁⠀⠉⢠⣾⡻⠏⠀⠙⡳⠃⠀⣴⣟⠁⣿⣿⣿⣿⠏⡀⣀⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠋⠀⠀⢷⡸⣷⡹⢿⣿⣿⣿⣿⣷⡄⠀⠙⠛⠒⠛⠛⠛⠋⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀⣙⠧⣀⣀⣚⣁⡴⠾⠟⠁⢸⣿⣿⣿⣧⡾⡵⠇⣿⡆⠀⠀⠀⠀⠀⠀ ⠿⠛⠋⠀⠀⠀⠀⠀⠘⣧⣿⡿⣬⣿⢿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⢿⣥⡾⣹⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⢿⣇⠉⠙⢿⣿⣮⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡿⠋⢈⡏⠀⠈⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠈⢿⣦⡀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣽⣿⣿⣿⠋⠀⠀⠁⡇⠀⠀⠸⣧⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⢯⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⢀⣼⣿⣿⠡⣿⠀⠀⢠⡀⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⢧⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⣿⡄⠀⢸⡇⢳⢠⢀⠀⠈⣷⡀⠀⠀⠀ ⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⢣⡀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⣿⣿⣿⣷⠀⢿⣧⠀⣾⡇⢸⠈⣿⡇⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠱⣌⢿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡉⠓⠒⠂⠀⢀⣠⡾⠛⠁⠀⠘⣿⣿⣿⣧⣹⣿⠀⣿⣿⢀⡀⢹⣿⠀⠀⠻⣇⠀⠀ ⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡄⠀⠙⢯⢶⡘⢿⣶⣄⠀⠀⠀⠀⠀⠀⡿⠹⣿⡄⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⣿⣿⠘⣷⣾⣿⣇⠀⠀⠹⣧⠀ ⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠸⣆⠀⠀⠙⠒⢶⡿⠿⠿⣦⣄⡀⠀⢰⠃⡴⠛⣿⣯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⢿⣿⣴⣿⣿⠀⠈⢿⡏⠉⠀⠀⠀⠹⣇ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠘⢆⠀⠀⡤⠋⠀⠀⠀⠹⣿⣿⣿⡿⠋⣠⠞⢺⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⡀⠀⠈⢻⣆⠀⠀⡀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢻⡟⢶⣦⣤⣘⡳⠈⠀⠀⠀⢀⣠⣴⣿⣿⡿⠁⡴⠃⢀⡎⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⣿⣿⣿⣿⣿⣇⡆⠀⢸⢿⣦⣾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣧⠀⠈⠙⠛⠿⢶⣤⣀⠐⠉⣁⣼⢟⡝⠁⡜⠁⢀⡞⠐⣀⠀⠈⠻⣧⡀⠀⠀⠀⢠⡞⣡⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠈⣷⡀⠈⠲⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⢩⣇⠞⠀⡾⠁⠀⡼⢀⡄⠹⠀⠰⠄⠙⣿⡄⢀⣴⠏⣴⠏⢀⣿⣿⣿⣿⣾⣿⣸⠁⠀⠼⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠀⢸⠁⠀⣰⠣⠊⢠⡄⠀⡶⠃⢀⣿⣿⠟⣡⡾⠃⠀⣼⣿⣿⣿⠇⣿⣿⣿⠀⠀⠄⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢠⠏⣰⢃⣠⢇⠀⢠⡿⠀⣠⠏⠀⠀⠐⠀⣸⣿⣿⡾⠋⣀⣠⡾⣹⣿⣻⡟⣸⣿⣿⡏⠀⠀⢀⡀⠀⠀⢷⡀⠀

⣀⣀⣠⣴⣶⣿⣿⠿⠟⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⣷⣄⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⢹⡏⠀⡀⢈⣉⣿⡿⠿⠷⢾⣭⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠚⠋⠉⠉⠙⢛⣾⠭⠤⠄⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠛⠛⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⣀⣤⠄⠒⠂⣀⠀⠀⠈⠙⠛⠒⠪⢤⣭⡙⠓⠶⣤⣄⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢀⡀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣠⣤⡤⠤⠔⠒⠠⡶⠞⠁⠀⠀⠀⠀⠈⠉⠓⠢⣄⠀⠀⠀⠀⠀⠉⠙⠦⣤⡈⠉⠛⢷⣶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠃⢄⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⢀⡠⠴⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⢿⡟⠛⠒⠶⣌⣑⢦⡀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⠖⠉⠀⢀⣀⣴⠶⠖⠓⠀⣀⠀⣀⡀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠸⠙ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⠁⠀⢀⣴⡿⠋⠀⠀⢀⣠⠞⡟⠀⡇⢱⡀⠀⠀⢹⡝⣦⠀⠀⠀⠀⠀⠀⠲⢄⡹⣆⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⣴⠋⠀⠀⠀⣰⡿⠋⠀⠀⢀⡴⠋⠀⠀⡇⠀⢸⠘⡇⠀⠀⠀⢷⢊⣷⠀⠀⠀⠀⠀⠀⠀⠑⢼⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⣆⠀⠠⠂⠀⠀ ⠀⠀⣠⡴⠋⠀⣠⠚⠀⠀⠀⠀⡰⣿⠃⠀⡀⣠⠋⠀⠀⠀⠀⣇⠀⢸⡆⡇⠀⠀⠀⠈⢿⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣷⡔⠀⠀⠀ ⠹⢿⠟⠁⠀⣴⠃⠀⠀⠀⠀⣰⢳⠇⠀⢰⡿⠁⠀⠀⠀⠀⠀⣽⠀⠈⡇⡇⠀⠀⠀⠀⠀⡇⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣄⠘⣇⠀⠀⠀ ⢀⠎⠀⢀⡾⠀⠀⠀⠀⠀⢰⣇⡎⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⢿⠀⠀⠇⡇⠀⠀⠀⠀⠀⡇⠀⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡄⢹⡄⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠞⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⣴⠃⢸⡆⠀⢀⡇⠀⠀⠀⠀⢰⠃⠀⢿⠄⠙⠷⣄⠀⠀⠀⠀⠀⠀⢻⣧⢸⡾⣆⠀⠀⠀⠀⠀⠀⠀⠘⣦⢻⠀⢣⠀⢀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡎⠀⠀⠀⠀⠀⡴⠁⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⢸⡄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣿⣦⢇⠘⣆⠀⠀⠀⠀⠀⠀⠀⣿⡆⢧⠘⣧⠊ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⣼⡇⠀⢾⠀⠀⠀⠀⠀⢺⠀⠀⣸⠛⢦⡀⠀⠀⠈⠣⠀⠀⠀⠀⠙⢿⣾⠀⠸⡆⠀⠀⠀⠀⠀⠀⢹⢹⢸⡆⢹⣧ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣰⠃⠀⠀⣼⠏⡇⠀⣞⠀⠀⠀⠀⣸⣿⠀⠀⣿⡄⠐⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠐⢻⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇⠀⢱⠸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡟⠀⠀⠀⢠⠏⠀⠀⣴⠋⠀⢸⢠⣿⠀⠀⠀⢠⠟⡟⠀⢴⡟⠁⠀⠀⠀⠀⠙⢶⣤⠀⠀⠀⣄⠀⠈⣷⡄⠀⢿⡄⠀⠀⠀⠀⠀⣧⢰⠈⡇⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡇⠀⠀⠀⡾⠀⠀⡼⠛⠁⢀⣸⡟⣿⠀⠀⠀⠈⠀⡧⢼⣿⣲⠤⣤⣄⣀⣀⣀⣀⣀⣹⣦⣄⡈⢳⡀⢸⣧⠀⠸⣿⡀⠀⠀⠀⠀⢿⠘⡆⢸⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⣸⠁⠀⣼⠗⠀⣴⠿⢻⣇⣿⡇⠀⠀⠀⢀⡧⠀⡟⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣿⡄⠀⢹⡇⠀⠀⠀⠀⢸⠀⡇⠈⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⢠⡏⢀⡼⠁⣀⠶⠁⠀⠈⣇⡿⡇⠀⠀⠀⣼⣿⣼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣿⡇⠀⠘⣿⠀⠀⠀⠀⠸⠀⣷⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⢀⣴⡟⢀⣾⠶⠚⠉⠀⠀⠀⠀⣿⡇⡇⠀⠀⢀⡟⡿⡟⠀⠀⠈⠁⠀⠀⣠⣀⡴⣶⣶⣶⠿⣶⣶⣶⣦⣹⣾⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣟⣽⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⠁⢱⠀⠀⣸⠁⣿⠁⠀⠀⠀⠀⠀⢸⠟⣡⡾⢋⣁⣀⣀⠀⠀⠉⠛⢿⣿⣇⣀⢸⡇⠀⠀⠀⠀⠀⠈⡆⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢇⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡀⢠⡿⠀⣿⠀⠀⠀⠀⠀⠀⢋⣼⡟⠁⡿⠛⢉⠛⣷⠀⠀⠀⠘⣿⡇⠉⢸⢿⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠟⠀⠀⠀⠀⠀⠀⠤⠤⢴⣶⡀⠀⠸⡇⣾⠇⠀⣿⠀⠀⠀⠀⠀⠰⠛⣸⡇⠘⡇⣾⣿⣿⣿⣧⠀⠀⠀⠙⢷⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢀⣠⣾⠟⠛⠛⠛⠻⢿⣶⣬⣗⠀⣧⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢿⡛⠉⡤⠀⣿⠀⣠⣤⣶⢾⡀⢈⠈⠀⠀⠀⠀⢨⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣰⣿⠟⠀⠀⣴⡿⠿⢦⣄⠈⠳⢤⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣞⣡⠼⠟⣫⠤⠿⡇⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠃⠀⠀⠀⣿⣀⣠⣴⣿⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⡂⠃⠀ ⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢿⣿⡟⠛⡁⢹⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⡄⠀⠀⠀⢹⣻⡟⢦⣀⠀⠀⠈⠳⣍⣉⡱⠎⢀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⠀⠀⠀⠀⠀⣀⡇⠀⠀ ⠀⢸⣧⡀⠀⠀⣿⢳⢳⠀⠀⠀⢸⠃⢧⠀⢨⠷⣾⣿⣦⣤⣤⢀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠀⠀⠀⠀⠀⡿⠁⠐⠀ ⠀⠀⢯⣇⠀⠀⣿⣯⣿⠀⠀⠀⠘⡇⢸⣧⠀⠀⠀⠔⢋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣸⢹⡇⠀⠀⠀⢸⠈⠁⠀⠀ ⠀⢠⣾⡿⡄⠀⢸⢹⣎⣇⠀⠀⠀⡇⠘⣯⣧⡀⠀⣰⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢖⣛⣻⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢁⣿⡇⠀⠀⠀⣿⠀⢂⠀⢠ ⡀⢸⠇⢻⣻⠀⠀⠇⣿⣿⡀⠀⠀⢠⠀⢻⣿⢿⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⣿⠀⠈⡇⠈ ⡇⢸⠀⠀⣷⢤⠀⠀⢹⡼⣧⠀⠀⠀⠀⠸⣿⣆⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠋⠋⠻⣄⠀⠀⠀⠀⠀⠀⢀⣼⡇⣿⡇⠀⠀⡿⣿⠀⠀⠘⢆ ⡳⠿⣄⠀⠘⣯⠀⠀⠀⣷⣿⣧⠀⠀⠀⠀⢿⣏⠳⣄⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⣾⠛⡇⢻⣇⠀⢰⠛⢿⠀⠀⡰⠛ ⠉⠲⣎⡳⣄⠘⣆⠀⠀⢹⣇⠹⣇⠀⠀⠀⠈⣿⣳⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣿⣧⠀⢠⠐⢿⠀⣾⠀⢘⢠⣾⣷⣦ ⠀⠀⠈⠃⠙⣆⠘⣧⠀⠀⢿⡄⢹⣆⠀⠀⠀⠘⣧⡇⠈⣿⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⣿⡿⡿⣿⠀⢸⡀⢾⡀⣿⡇⠼⢻⣿⣿⡿ ⠀⠀⠀⠈⢣⠙⡄⠈⣷⡀⠸⣿⣦⣿⣆⠀⠀⠀⠹⡇⠀⠋⠈⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡤⠤⠖⠚⠛⠉⠁⠀⠀⣠⣼⣿⣿⣧⣻⢽⡆⠘⣇⠘⣇⣿⡟⠀⣾⡛⠋⠐ ⠀⠀⠀⠀⠀⠀⢻⡀⠈⣷⡄⢻⡄⠘⠻⣦⠀⠀⠀⢿⠀⢱⠀⠀⠀⠘⡏⠻⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣟⠈⠉⠛⠻⢦⣿⣄⣻⡛⡄⠀⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡟⢞⢷⠀⠀⠈⠣⣀⠀⠘⣆⢸⡀⠀⠀⠀⠀⢀⣻⣿⣿⣿⡿⠿⣿⣷⣶⣶⣤⣄⣀⣀⣤⣾⣿⣿⣿⢿⠃⢹⣷⡄⠀⠀⠀⠈⠙⢯⣇⠹⡄⢻⣿⣿⡗ ⠀⠀⠀⠈⠀⠀⠀⠙⡄⠀⢹⡜⢯⣧⠀⠀⠀⠉⠶⣀⣹⣾⣧⠀⠀⡼⠞⠉⠉⠀⢀⡄⣻⡄⠀⠉⠙⢿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠙⢧⡙⡄⢹⣿⣟

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⣤⣠⣴⣾⣿⠿⠛⠉⠉⠹⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⠿⠾⣷⣤⣄⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣀⠤⠤⠷⣀⡠⠤⠟⠛⠛⠛⠚⠿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠟⠛⠛⠒⠒⠒⠒⠒⠉⠉⣁⠀⠄⠀⠀⠐⠢⠤⠽⣛⣒⠦⢤⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣠⠤⠤⠔⠒⠠⠖⠋⠀⠀⠀⣈⣙⠒⢄⡀⠀⠀⠈⠉⠲⢤⡉⠑⠲⣖⠋⠁⠀⠀⠀⠀⠈⠠⡸ ⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡤⠒⠉⠉⣀⡀⠀⠀⠀⠀⠀⠠⣤⠒⠻⠏⠉⠑⠢⢝⢦⡀⠀⠀⠀⠀⠈⠑⠦⡈⠳⣄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣠⠞⠁⡠⠚⠁⢀⣠⠶⠛⠉⢀⣴⡆⣖⣆⠀⠀⢿⢧⠀⠀⠀⠀⠀⣄⠳⡝⢆⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⡄⠀⠀⠀⠀⠁ ⠀⠀⠀⢀⡴⠁⣠⠊⠀⠀⣠⡟⠁⠀⢀⠔⠉⢸⡇⢹⢸⡀⠀⠘⣯⣳⠀⠀⠀⠀⠀⠑⢼⣆⠳⡀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢦⠀⠠⠀⠀ ⣀⣀⡴⠋⢀⠞⠁⠀⠀⣰⡿⠀⣠⡴⠁⠀⠀⠸⡇⠸⣾⡇⠀⠀⠘⣷⡅⠀⠀⠀⠀⠀⠀⠻⡄⠹⡄⠀⠀⠀⠀⠀⠀⢀⠱⡌⢷⡆⠀⠀ ⢙⡟⠀⣠⠋⠀⠀⠀⣰⣻⠁⢠⡟⠁⠀⠀⠀⢰⡇⠀⣿⠇⠀⠀⠀⣿⢹⣦⡀⠀⠀⠀⠀⠀⠘⣆⢹⣄⠀⠀⠀⠀⠀⠀⢳⢱⡘⣇⠀⠀ ⠈⠀⣰⠃⠀⠀⠀⢠⢏⡏⠀⣼⠁⠀⠀⠀⣠⠏⣧⠀⢷⠇⠀⠀⠀⡟⠀⣯⠙⢦⡀⠀⠀⠀⠀⢸⣆⢿⢧⠀⠀⠀⠀⠀⠈⣧⢧⠸⡆⠀ ⠀⠰⠁⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⣰⠃⠀⣿⠀⣿⠀⠀⠀⠀⡇⠀⣿⡀⠀⠙⢦⡀⠀⠀⠀⣿⡾⡎⢧⠀⠀⠀⠀⠀⢹⣏⣆⢳⡞ ⠀⠂⠀⠀⠀⠀⠀⠀⠸⠀⣸⠁⠀⠀⢰⠃⠀⣰⣿⠀⣿⠰⠀⠀⣸⡇⠀⣿⢙⢦⡀⠀⠙⠀⠀⠀⠈⢻⣇⠘⣆⠀⠀⠀⠀⠘⣿⠸⡜⣷ ⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⢀⡟⠀⢠⡟⢸⡀⣇⠀⠀⢀⣿⡇⢠⡿⠀⠁⠙⠢⣄⠀⠀⠀⠀⠀⢿⡀⢹⡄⠀⠀⠀⠀⡏⡀⢇⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⡼⠀⢠⠟⠈⢈⡿⣿⠀⠀⠘⢸⣀⣾⡥⢄⣀⣀⣀⣀⣙⣢⣄⡑⣄⠸⣷⠀⢿⡄⠀⠀⠀⢿⢹⠸⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⢰⠃⢠⠟⠀⡴⠟⣧⣿⠀⠀⠀⣸⠄⡟⠈⠉⠉⠀⠀⠀⠀⠀⠀⠑⢮⡻⣿⡄⠘⣿⠀⠀⠀⢸⢸⡄⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⣠⡏⣠⣋⡤⠊⠀⠀⣿⣿⡆⠀⢀⣿⣿⠃⠀⠤⠀⠀⠀⠀⣀⣀⣠⣀⣀⡘⢿⣇⠀⢿⡆⠀⠀⢨⢘⡇⠸ ⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡴⣿⣴⠋⠁⠀⠀⠀⠀⣿⠛⡇⠀⢸⢹⡟⠀⠀⠀⠀⣰⠗⣫⠟⠛⠉⠛⠛⠿⣿⣿⡀⢸⡇⠀⠀⠀⠘⢣⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣱⠃⠀⠀⠀⠀⠀⠀⣸⠀⣇⢀⡿⢸⡇⠀⠀⠀⠀⢫⣾⠃⡾⠛⡛⢦⠀⠀⠘⣿⡉⢹⣷⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⢀⣀⣀⣒⣒⡶⢶⡀⢻⣼⡇⠘⡇⠀⠀⠀⠐⢩⠿⠈⣷⣿⡿⠿⣇⠀⠀⠙⡇⠀⠻⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣠⣾⠟⠉⣠⣬⣉⠛⢷⡓⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣐⡡⢃⣴⠾⢫⣷⢰⡀⠀⠀⠀⡇⣼⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡿⠁⠀⢸⣏⣁⣹⣦⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⢸⢸⠁⠀⠀⠀⠃⢿⠀ ⠀⠀⠀⠀⢠⡄⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣟⣋⢹⡆⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡆⠀⠀⠀⢘⠘⠀ ⠀⣄⠀⠀⢸⣧⣆⠀⠀⢸⣿⡙⠢⣀⣀⡙⠲⠤⠚⢰⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⡾⠀⠀ ⠀⢻⣇⠀⢸⣿⣿⠀⠀⠸⡍⣧⡀⠉⠉⠿⢋⡩⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⣿⡧⠀⠀⢸⠡⠀⠀ ⠀⣸⣿⡄⠀⡿⣿⡆⠀⠀⡇⢻⣷⡀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣒⣲⣤⡀⠀⠀⠀⠀⠀⠀⠐⠋⠈⣼⡷⠀⠀⣾⠀⡂⢸ ⡄⡟⠹⣿⠀⠟⣿⣷⠀⠀⠧⠘⣿⡿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢠⣿⠀⢸⡀ ⣧⡇⠀⢻⡆⠀⠸⣾⣧⠀⠀⠀⢻⡷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠟⠋⠁⠀⠙⣆⠀⠀⠀⠀⣴⢿⢹⡇⠀⣾⣿⠀⠀⣡ ⠣⢭⡳⡄⢳⡀⠀⢻⡟⣇⠀⠀⠈⣿⣮⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣼⣏⢸⡈⣷⢠⡇⢿⢠⣾⣄ ⠀⠈⠓⡹⡌⢷⡀⠸⣧⢹⣆⠀⠀⠹⣿⠈⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⣀⡤⠋⠀⣰⣿⣿⣿⠸⡇⢿⣸⣷⠸⣻⣿⡿ ⠀⠀⠀⠁⢹⡀⢳⡀⢻⡷⢿⣆⠀⠀⢻⡀⢁⠀⠉⢳⣦⣄⣀⠀⠀⠀⠑⠒⠒⠒⠋⠉⠁⠀⠀⣠⣾⣿⡿⢿⣻⡄⢿⢸⣿⡟⠀⣿⣭⡤ ⠀⠀⠀⠀⠀⣧⠈⢿⢌⣧⠀⠙⢦⠀⠈⣇⢸⠀⠀⠀⠃⢹⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⢀⣠⣾⣿⣿⠝⣧⡀⠀⠉⠛⢿⣿⢹⡀⣿⣿⣇ ⠀⠀⠀⠀⠀⠘⡆⠈⣏⢿⣆⠀⠀⠑⢄⢸⣾⡇⠀⣰⠖⠊⠉⢉⡙⣆⠉⠙⠻⣿⣿⣿⣿⣿⣿⠟⠉⠀⣿⣿⣆⠀⠀⠀⠈⠳⡱⡙⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡇⠉⢉⣉⠤⠤⠤⠄⠺⢟⡛⠿⢶⣶⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢁⣾⣿⣿⡗⠈⠁⠀⠀⠀⠒⢦⡈⠙⠟⠢⠤⣈⣽⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠳⢍⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⠞⢱⣿⡻⠟⠋⠉⣉⣂⡀⢤⣉⡉⠁⠀⠤⣀⠀⠀⣿⣿⣿⡿⡄⠀⠀⠱⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡴⠁⢀⠔⠁⠠⠒⢉⠅⠀⠀⠈⢧⡉⡛⢶⣄⠀⠀⠱⣌⠻⣿⣿⡇⠘⡄⠀⠀⠘⢆⠈⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⠁⠀⠀⠀⡜⢀⠔⠁⠀⠀⢠⡾⠁⠀⢠⠂⠀⠈⢷⡌⠢⡈⠳⡄⠀⢱⡑⣌⢿⡇⠀⠘⠄⠀⠀⠈⢧⠀⠹⣦⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⡜⡐⠁⣠⠀⠀⢠⡟⠀⠀⠀⢸⠀⠀⠀⠈⢿⠀⢛⠢⡈⠀⠘⢧⠈⢦⡃⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣧⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⣰⠱⠀⣸⠃⠀⢠⡛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆⠈⡆⢘⢆⠀⠟⡆⠀⢿⡄⠀⠨⠀⠀⠀⠀⢿⡄⠀⠹⣆⠀⠀ ⠀⣸⠁⠀⠀⠀⢠⣏⠇⢠⡏⠀⢠⣿⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⢱⠀⢫⠂⠀⢡⠀⠘⣷⠀⠀⡆⠀⠀⠀⢸⢧⠀⠀⢻⡀⠀ ⠀⡏⠀⠀⠀⠀⣾⡟⠀⣼⠀⣰⠏⢹⣿⠀⠀⠀⠀⠈⡆⠀⣳⡀⠀⠀⠀⠀⡄⠈⠆⢱⠸⠀⠀⢹⣇⠀⢁⠀⠀⠀⢨⠈⡆⠀⠘⡇⠀ ⠀⠇⠀⠀⠀⢰⢻⡇⠀⣇⣼⠃⡀⢸⡟⡆⠀⠀⠀⠀⣷⠀⠺⣷⡀⠀⠀⠀⢇⠀⠘⡤⠘⣆⠀⠀⠸⡀⢈⠀⠀⠀⢸⠀⢣⠀⠀⡇⠀ ⢸⠀⠀⠀⠀⡜⢸⠁⢰⡿⢁⣀⡘⢾⣿⣣⠀⠀⠀⠀⢹⡀⠀⠈⢿⡄⠀⠀⢼⠀⠀⠹⡄⠛⡆⠀⠀⣧⡄⠁⠀⠀⠈⠀⢸⠀⠀⡇⠀ ⠀⡆⠀⠀⢀⡇⠘⠀⢸⣿⠋⢉⣿⣿⣿⢫⢇⠀⠀⠀⠈⡇⠀⠀⠀⠙⢄⠀⠈⣆⠀⠀⣧⡇⠙⡄⠀⢹⣷⡀⠀⠀⠠⡇⠈⠀⠀⡇⠀ ⠀⣇⠀⠀⢸⠀⢠⠀⢸⢻⢧⠈⢿⣿⣿⣆⢪⠆⠀⠀⠀⢙⣶⠄⠐⠂⠀⠷⢄⢹⣧⡀⡏⢿⡆⠘⣆⢸⣿⡇⠀⠀⠀⢱⠀⡇⢀⡇⠀ ⠀⢻⡀⠀⢸⠀⠘⠀⠘⠀⠀⠓⠂⠁⠀⠘⣄⠛⡄⠀⠀⠘⣿⡼⠟⢻⣿⣶⢾⣿⣮⣿⡇⣀⠑⣤⣿⢿⣷⠘⡄⠀⢸⢸⡇⢢⣸⠀⠀ ⠀⠈⣧⠀⣼⠀⢰⠀⠀⠆⠀⠀⠀⠀⠀⣰⠛⣆⠀⠀⠀⠀⢹⠀⠀⠹⡧⣏⣿⡟⠻⣯⡁⠉⣹⣿⣇⢀⠙⣧⡇⠀⢸⢸⢣⣾⠇⠀⠀ ⠀⠀⠘⣧⣿⡀⢸⠀⠀⡇⠀⠀⠀⠀⠼⠃⠀⠘⢄⡄⠀⠀⠀⡇⠈⠒⢬⣉⡭⠖⠂⠀⠉⠉⠁⠔⠊⠼⢛⡟⠀⠀⣿⠈⡈⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⣧⣸⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⠐⠂⣠⣶⣿⡇⠀⢠⣏⠀⠙⢿⡆⠀⠀ ⠀⠀⠀⠀⢻⣛⣿⡇⠀⡏⠱⡄⠀⢀⡀⠀⠀⠀⠀⠈⢿⡀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣾⢿⠤⢶⢿⣼⡿⣿⡇⠀⢸⡟⠉⠀⠸⣇⠀⠀ ⠀⠀⠀⠀⢸⠿⣾⡇⠀⡇⠉⠙⣆⠀⣿⠉⣒⠢⣤⣄⣸⣧⢀⣾⠀⠀⠀⠀⣀⣴⡿⠇⢸⣠⡇⠀⢹⣿⣿⡀⠀⣾⣇⠀⡃⠀⢿⠀⠀ ⠀⠀⠀⠀⡇⠀⠘⡇⠀⠇⠀⢰⣿⣆⡇⠀⠁⣀⠾⠚⠉⣿⠾⠃⢀⣀⡤⣾⣿⠏⠀⠀⢸⣿⡇⠀⣿⡇⢸⠀⠀⣿⠙⡄⡆⠀⠸⡇⠀ ⠀⠀⠀⠀⢣⠀⠀⢱⠀⡀⠀⢸⣏⡏⣏⠢⠚⠁⠀⢀⣠⡥⠶⠎⢹⣉⣤⠿⠁⠀⠀⠀⢸⠟⠁⢸⣿⠇⣼⠀⠀⣿⠷⣿⡇⠀⠀⢳⠀ ⠀⠀⠀⠀⠈⢆⠀⠸⠀⡇⠀⢸⠉⢇⠈⠑⠒⢺⢿⣿⡟⠀⠀⢠⣼⠋⠀⠐⠀⠆⠄⠀⣼⠀⠀⣾⡏⢀⡇⠀⢸⠟⢆⠈⢻⣄⠀⠈⠆ ⠀⠀⠀⠀⠀⠈⠇⠀⠀⠷⠀⢾⠀⠘⡄⠀⣰⣇⢈⡟⢸⢀⣖⣉⠚⠣⠄⠀⠀⠀⠀⡼⢹⠀⣠⣿⠟⠉⡇⢠⡏⠀⠀⠑⣌⠎⠓⣄⠰

⡀⠀⣀⡄⠀⡆⢀⠞⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣿⡍⣤⡙⠻⣶⣤⡙⣆⠀⠀⠀⠀ ⠀⠀⠀⡇⡠⢃⣎⡜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢣⡼⠟⠓⠾⣟⠧⡘⠻⡄⠘⡆⠀⠀⠀ ⠀⠀⣠⡟⠒⣺⣏⡴⠁⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⢲⠎⠀⠀⠀⠀⣹⡄⠀⠀⠘⢦⠸⡄⠀⠀ ⢀⡞⢹⡇⢠⣿⣟⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡞⠀⠀⠀⠀⣰⡟⣿⣆⠀⠀⣀⠻⣷⡀⠀ ⡩⠞⠋⡽⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⢀⣾⡟⣧⢹⣿⣷⣄⠀⠉⠛⢧⠀ ⠀⢀⣾⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣆⠀⠀⢳⣄⠀⠀⢢⡀⠀⠀⠐⠘⡄⠀⠇⠀⣰⣿⡏⣷⢸⣇⡿⣿⢿⣷⡄⠀⠀⢧ ⣠⣋⣽⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⢹⣄⠀⢸⡏⠣⡀⠀⠉⠘⣦⡀⠀⠘⡄⠘⠴⠃⠘⢿⣿⣾⣿⡇⣿⣆⠹⣿⣆⠀⠈ ⢹⡟⢸⡇⠀⡆⠀⠀⠂⠀⠀⡴⠀⢸⠸⡄⠀⠀⠀⠀⢯⠀⠀⢹⠀⠘⢆⠀⠀⢹⠹⣆⠀⢱⠀⠀⠀⠀⠈⣿⣻⣿⣿⣿⣿⡄⠹⣿⣦⡀ ⣿⠁⣸⠀⣸⠀⠀⡰⠀⠀⠐⡇⠀⠈⠀⢳⠀⠀⢀⠀⠘⡄⠀⠀⡟⠒⠒⠻⡉⠹⡇⠈⢷⡀⢇⠀⠀⠀⢀⠈⡇⠈⠹⡻⣟⢿⡄⠯⣽⣿ ⡇⢀⡇⢠⠃⢀⢦⠃⠀⢰⢸⢷⠀⠟⠒⠒⢧⠀⠘⡆⠀⡇⠀⠀⢳⠀⠀⣀⢙⣆⣷⣶⣿⣿⣼⠀⠀⠀⢸⡄⠘⡄⠀⠱⡘⣦⠛⡢⠿⠟ ⢃⡞⣰⡇⢀⡿⠈⠀⠀⢸⡸⠘⡆⢀⠀⠀⠀⢧⠀⢁⠀⢹⡄⠀⠸⡖⣫⣶⡿⠿⣿⡍⠉⢿⣿⡇⠀⣄⠈⣷⣄⠸⡄⠀⠡⠈⢆⡀⠄⠐ ⡾⢿⠁⡇⡸⠁⠀⠀⠀⢸⣿⣷⣿⣿⣶⣒⠦⢤⠳⣘⡄⣼⡙⣆⠀⣿⡟⢗⠔⣺⠚⣷⠀⠸⠿⢷⠀⠸⣄⠘⡄⠑⢿⣄⣀⢳⣈⠿⣄⠳ ⡀⠇⠀⣧⡇⠀⠀⠐⠒⢸⣟⠉⢻⡏⠉⢛⢿⣶⡤⠹⣧⡏⣇⠈⢦⡏⢳⣌⣉⣁⣼⠇⠀⠀⠀⣸⠀⠀⠘⣷⣜⣆⡀⠈⠉⠈⠁⠀⠈⠳ ⡿⠤⣀⣿⠀⡄⠀⣄⠀⣾⣿⣆⠀⢿⣔⢬⣰⣹⡇⠀⣸⠓⢾⡄⠀⠃⠀⠉⠛⠛⠋⠀⠀⠀⠀⣿⠀⣧⠀⢻⠉⢙⣛⣻⣶⣦⣄⠀⠀⠀ ⠃⠀⠈⡇⢀⣧⣼⣽⠀⣇⠘⣎⠀⠀⠙⠳⠦⠊⠀⠠⠃⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢐⣿⢰⠽⡆⢸⣶⣶⣶⣤⣤⣬⠻⣿⣄⡀ ⡄⠀⠀⢱⣾⣿⣡⣾⠀⣿⣤⠸⡆⠀⠀⠤⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣼⣿⢸⠾⣿⣾⣿⣿⣿⣿⣿⣿⠀⢹⡈⠙ ⣣⣤⣶⣿⠋⢹⢻⣿⣼⣿⣿⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡄⠀⠀⣠⣾⣿⠘⣿⡖⢯⣿⣿⣿⣿⣿⠟⠁⣀⡞⠌⡑ ⣀⣿⡿⢩⡇⠘⢌⣿⣿⡭⠽⡇⢸⢷⣄⠀⠀⠀⠀⢶⣦⠀⠐⢒⡰⠽⢁⣠⡞⠁⢀⡶⢿⠅⡟⣇⢳⠙⠀⢸⣽⢁⠇⠉⠉⠉⠉⠀⠀⠈ ⠤⠔⠋⠈⢳⡀⠀⠸⣎⡆⠀⣧⡇⠀⢻⢦⣤⣀⣀⠀⠈⠉⠉⠉⠉⠉⠁⠘⣧⣶⠋⠀⢸⠀⡇⢻⡄⢇⠀⢸⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⢤⠀⢘⠁⠀⠀⢹⣿⢤⠟⠀⠀⠘⠀⣿⠀⡟⢩⣷⢶⣦⣤⡀⣠⣴⣾⣿⣥⡀⠀⣿⠀⠇⠘⣧⠘⣄⡌⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠉⠙⢺⣶⣤⣄⣠⣿⣧⡀⠀⠀⡄⠀⣿⢠⣷⢋⣩⠿⣿⣿⢧⣿⣿⣿⣯⣄⠉⠳⣿⣾⠀⠀⣸⡄⠹⣄⠃⠀⠀⣀⠀⠀⣀⠀⠀⠀

⠀⠀⠀⣸⡟⢿⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣷⣆⢿⣿⣿⣿ ⠀⠀⠀⣿⠁⠀⢻⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠛⢷⡀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣿⣿⣿ ⠀⠀⣸⠁⠀⠀⠀⠻⡀⢹⣷⣄⡀⠀⠀⠀⠀⡀⢹⡆⠀⠀⠉⠛⠶⢄⣠⣤⣀⣀⡀⣀⣀⣀⣀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢿⣿⡿⠏⠁⠀⣹⣿ ⠀⣰⡏⠀⠀⠀⠀⠀⢳⡘⣿⣿⣿⣷⣶⣤⣄⣳⣄⢱⡀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⢳⣤⣄⣀⣀⡀⣮⣿⣦⡀⠀⣤⠻⣄⢀⣴⠏⠁⠈ ⣰⣿⠀⠀⠀⠀⠀⠀⠀⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡀⠀⠀⠀⠀⠀⠀⢤⣀⣈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣾⣻⣇⣡⠔⠂ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⢿⣄⠀⣠ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣽⣻⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢣⣽⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣉⣀⣀⣀⣀⡀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣦⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿ ⣿⡇⠀⠀⣀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠿⠛⠛⠒⠛⠿⠿⢷⣶⣦⡙⠻⣿⣿⢿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻ ⣿⡧⠴⠋⠁⠀⠀⠀⠀⣀⣤⢤⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠒⠋⠁⠀⠀⣠⣶⠿⠓⠛⠶⣤⡀⠀⠙⢿⡳⣿⣿⣷⡙⣿⣿⡆⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⣆⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣻⠁⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⢸⣿⣿⣿⣮⣻⣿⠦⣄⡙⢷⣮⣿⡿⣿⣿⣿ ⣿⡇⠀⠀⣄⣤⣶⣿⡿⠟⠛⠉⠛⠋⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣏⢠⡤⠀⣧⠖⣀⠀⢹⡇⠀⠀⠈⣿⣿⣿⣿⣿⡿⣴⠋⠉⠳⣽⣿⣿⣿⣿⣿ ⣿⣇⢀⣴⡿⠿⠋⣀⠀⡒⠚⢓⢶⣄⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⢾⣿⣿⢿⣿⣧⡀⠀⠀⠀⠀⢿⠇⠸⠷⣿⡿⠋⡿⠋⠙⠃⠀⠀⠀⣿⡇⠘⣿⣿⢠⡿⣄⠀⠀⠈⣯⢿⣿⣿⣿ ⣿⣿⣿⠋⠀⠀⠘⢻⠄⣁⣤⠤⠄⢻⣧⡀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠙⢿⣄⢹⣿⣷⡄⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠳⢤⠀⠀⠀⠀⠀⡟⠃⠀⠙⣿⡜⡇⠘⡏⠐⠊⠉⠈⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⣼⡿⠠⣯⣠⣞⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠈⠻⣧⡘⣿⣦⠀⠀⠀⢈⣿⣿⣿⣿⣶⡿⠿⢠⠜⢀⡄⢠⣿⠀⠀⠀⢻⡇⠀⠀⣷⠈⠉⢓⠀⣿⣿⣿ ⡿⢻⣷⠀⠀⠀⢻⣿⠀⠘⠛⠛⠁⠅⢀⡀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣴⡏⠉⠳⣄⠀⠀⠀⠀⠀⠞⢠⣞⠞⠁⣿⡇⠀⠀⠈⢳⡀⠀⠘⡆⡠⠏⢠⣟⢿⡻ ⡀⠀⢻⣦⣤⡀⠈⠛⠂⠀⠀⣀⣤⣶⡿⠃⠀⠀⡀⢠⠖⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⡒⠒⠊⠳⣄⠀⠀⠀⢰⢫⠏⠀⢰⡏⣿⡄⠀⠀⠈⢧⠀⠀⢻⡁⢀⣿⣿⣦⡙ ⣿⡀⢻⣿⠘⣟⣆⠀⠀⠚⣿⠟⠋⠁⠀⠀⡠⢏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠘⠀⣿⣿⡀⠀⠀⠘⡇⠀⠈⢷⣾⣿⣿⣿⣿ ⠻⣿⣾⡇⠀⡏⠉⠳⡄⠀⠀⠀⠀⠀⡠⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⣿⠀⠀⢸⡟⣿⣿⣿⣿ ⣇⢹⡙⡇⠀⣇⢠⠁⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢧⡀⠀⢸⣿⠇⢻⠀⠀⠀⠘⡄⠀⠀⣧⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⢻⠀⠀⠘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠳⢄⣀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠙⢦⣸⠏⠀⠘⡇⠀⠀⠀⢻⡀⠀⢸⣿⣿⣿⣿ ⣿⡿⣿⠀⠀⢸⡄⠀⠀⡇⠉⠙⠳⠶⢤⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣦⣀⣀⠈⠉⠓⠦⣄⠀⠀⠀⢣⡀⠀⠀⠀⠻⣄⠀⣰⣿⠀⠀⠀⠀⢧⠀⠀⢿⣿⣿⣿ ⠟⢁⡏⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁⢹⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠁⠀⠈⠳⣤⡀⠀⠀⠀⠈⠱⣄⠀⠈⢧⡀⠀⠀⠀⠈⠻⣿⣿⣤⠀⠀⠀⠘⢧⠀⠘⣿⣿⣿ ⠀⣼⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠁⠀⠀⣸⠃⠴⢻⠇⣰⣶⡶⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠓⣄⡈⢳⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⣿⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⡰⠃⠀⢀⡟⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠙⢮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠻⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⡼⠃⠀⢀⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠹⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣆⠀⣾⠁⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠚⠉⠁⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠃⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⢸⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠓⠶⢤⣀⣀⣀⣠⡴⢟⣹⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⢉⣁⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠦⣀⣀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⡿⢀⣿⣿⠿⣿⣿⠟⠁⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠼⠗⠚⠁⠀⣼⡟⠁⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀