Two Gay Roblox Noobs Fucking Emojis & Text

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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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⠀⢀⣠⣴⣶⣦⣄⡀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡿⣷⢿⣿⠹⡹⣆⠀⢻⡟⠛⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣛⡄⢿⣿⠙⠃⠀⣿⡄⠈⠉⠣⣀⡍⠀⢄⢀⣴⣄⠀⠀⠀⠀⠀⠀ ⢻⣿⣷⣿⢿⡄⠀⠠⠼⠃⡤⠴⠌⡀⢈⠔⠈⠀⠀⠀⠙⢄⠀⠀⠀⠀ ⠸⢿⣷⣭⠟⠎⠂⠀⣠⣮⢂⡀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⢸⢿⣿⣦⡀⠀⠈⠻⡅⠈⠀⢀⠠⠤⠀⡀⠀⠀⠀⠀⡰⡄⠀⠀⢀ ⠀⠀⠠⠛⣉⡍⡠⠄⠊⠁⠒⠈⣠⣄⡀⠀⠀⠰⠒⠐⠬⢖⡁⠀⠀⣸ ⠀⢰⡖⠊⠉⠁⠀⠀⠀⠁⠀⠀⣿⣿⠇⠀⠀⠀⢁⠀⠒⠀⠈⠒⠤⡟ ⠀⠀⠇⠀⠀⠀⠀⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢄⠀⠀⠀⠜⡀⠠⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠑⠄⠀⠀⠈⠃⠘⠒⠂⠤⠤⢐⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀

⣧⣿⣾⣿⣿⣿⣿⢿⡿⡋⢣⢩⣷⢧⣿⣹⣈⢮⡄⣹⡆⠹⣷⢿⣿⣿⣿⣿⡀⠀ ⣿⣿⣿⣿⢿⢻⣥⠩⠳⡱⠀⣆⣿⠀⠞⠓⣩⣽⠷⢶⣷⣶⣿⣼⡞⢻⣿⣿⣿⡄ ⣿⣿⠟⠁⠈⣿⡟⢴⡀⠕⠋⠁⠀⠀⠀⠀⠘⢠⣤⣶⣦⡀⠙⢻⣷⣿⣿⣿⣿⣿ ⣿⢿⡂⢀⡰⣻⡌⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⢀⡽⠿⠀⢸⢎⣿⣿⣿⣿⣿ ⣟⡆⢹⠾⣫⣶⡴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠂⢩⠛⡭⠥⠷⠽⢿⣿⣷⣿ ⣞⢞⢋⣾⣟⣍⣴⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠶⡶⠒⢋⣻⣿ ⣟⣮⣿⡏⣞⡟⠃⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠟⣩⣷ ⣇⢴⣿⠀⠻⡿⡮⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣦⣄⠀⠀⠀⠀⣶⣷⣾⣿⣿ ⣯⣿⡛⠓⡄⡎⠐⠀⠀⠀⠀⠀⠀⠀⣠⣂⣠⣴⠞⠒⠿⡇⠀⠀⠀⠰⠙⡟⢒⣰ ⣿⣿⣏⠓⠈⠈⢀⡀⠀⠀⠀⠀⠀⢰⣯⠊⠁⠀⠀⠀⠠⠁⠀⠀⢠⣧⣤⣟⡽⠁ ⣈⠻⣟⣯⣦⠴⣷⠏⠀⣠⢶⡄⠀⠀⠣⠄⠀⣀⡀⠔⠁⠀⠀⢠⠛⠛⠻⠿⠀⠀ ⣿⣿⣿⣿⣀⣴⣿⣢⠔⠉⣹⣯⡆⠀⠀⠀⠀⠀⠈⠃⠀⠀⡐⣹⣵⣤⡄⠃⠀⠀ ⡿⠟⣿⣿⣟⠀⣰⣷⣥⢾⠁⢸⢳⣦⠤⠤⠄⠀⠀⢠⣤⣾⣽⠟⡠⣵⢩⠂⠀⠀ ⠀⠀⢹⣿⠫⠎⠹⡿⢣⣿⣶⠮⠞⠛⠒⠒⠂⠒⠚⠛⠛⠻⠿⠮⠥⠴⠶⠜⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠦⠐⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠎⠀⠀⠀⣀⢰⡌⢻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⢠⠇⣸⡿⣂⣴⣌⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢰⣶⣟⠉⠈⠀⣱⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠠⠤⣤⡇⣽⡝⡿⢷⠀⠀⣅⠉⠋⣞⡧⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⠤⠒⠈⠁⠀⠀⠰⠃⣇⣫⡌⠙⠀⢩⣶⡆⠀⢀⡿⡇⠀⠈⠁⠢⡀⠀⠀⠀⠀ ⠂⠀⠁⠢⢀⠀⠈⠆⡘⢿⠁⠈⢦⣀⠐⠹⢀⠴⢹⠁⣧⠀⡠⠂⡩⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠄⣼⢈⠞⣷⠲⠯⠥⢈⢉⠯⠦⠼⡀⢸⢏⢀⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢹⣿⠇⠻⡀⢠⣴⣶⣶⡶⠀⠒⠽⣼⡇⠃⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢠⢃⣾⠁⡀⠀⠑⣸⣘⢨⡷⣿⡧⣀⠀⠿⣿⠜⡄⠀⠀⠀⠂⠀⠀ ⠠⠦⠤⣤⢠⠃⡮⠉⠀⠀⣴⠞⣩⠶⣿⡯⠰⣌⣸⡅⠀⠈⡇⠘⢄⠀⠤⠤⣦⣤ ⠀⠀⠀⠀⡏⠠⠧⢀⠀⣠⣏⠈⢐⣟⣓⣧⡰⠦⠈⢃⢀⣠⡁⠤⠬⢆⠀⠀⠀⠀ ⠄⢀⡀⡰⠋⠀⠀⠀⠉⠃⠀⢠⠞⠉⠉⠣⠴⢆⠀⠈⠉⠁⠀⠀⠀⠈⢆⠀⠀⠀ ⠉⠉⠉⠓⣤⣤⣄⣀⣠⠔⠂⠁⢀⣀⠀⠀⠀⠀⢁⠰⢢⠄⣀⣀⣀⣄⡴⠷⠄⢀ ⠲⣤⢀⡀⠀⠀⢀⠬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠀⠀⢀⠤⢒⠾⠁ ⠀⠘⡀⠈⠁⠲⢅⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⠠⠕⠈⠀⠀⡌⠀⠀ ⠀⠀⢁⠈⠢⠀⠀⠈⠀⠀⠞⠁⠀⢰⡄⠀⠈⢅⠀⠈⠁⠀⠀⠀⠐⠁⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠐⢄⠈⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠐⣿⡇⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣿⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⢢⡀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⣿⣾⣷⣀⣠⠄⣠⠄⠚⠀⠀⠀⠂⠸⠀⠀⠀⢀⠤⣤⣀⣀⠠⠄⠐⠒⠓⠀⠀⠀ ⣼⣷⣿⡿⠓⠂⠁⠒⢄⠀⡀⠁⠀⡄⠀⢀⢌⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⢻⣿⣿⣃⢤⢲⡸⠆⢀⢁⠀⠀⠔⣀⠤⠊⠀⠀⠂⡀⣠⠲⠳⡒⠒⠒⣒⡒⠁⣀ ⣼⣿⡏⠈⣉⠤⢐⢖⡾⠓⠺⡉⠁⠀⠀⠠⣂⣈⢼⣾⢃⢠⡐⡒⠈⡀⡐⠁⢌⢀ ⠋⠙⣗⠰⠁⡀⠈⠘⠁⠀⠀⠁⢀⡠⠚⠈⠀⠀⠀⠘⣬⢦⡪⡚⠻⢁⣀⠚⠢⠏ ⢀⢔⠌⠀⠀⠠⣀⠀⠀⣀⣤⠛⢣⡀⠀⠀⠀⠀⠀⠀⠐⠓⡀⢀⠂⡌⡐⠠⠙⠴ ⠑⠁⠀⠀⣀⡤⣄⡟⠉⠀⠈⠔⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣉⣄⢀⠂⠀⢀ ⠀⠀⠀⠀⠀⠉⢻⡇⠠⠀⠀⠀⢀⡛⠀⠀⢀⠄⠀⠀⠀⠀⠀⢩⠉⣭⢄⠠⢂⠕ ⠛⠀⠀⠀⠀⠀⠀⠳⠀⡠⠀⢠⠞⣠⣪⡖⠁⠀⠀⠀⠀⠀⠀⠀⡭⣯⡕⠙⠇⠀ ⡀⢀⡄⠀⠀⠀⠀⢘⠛⠒⢺⣿⣿⣿⣿⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⣲⣇⠛⠀⠠ ⠈⢁⠀⠀⠀⠀⡀⠂⠀⠀⢈⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⣲⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠉⠹⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡰⣸⠟⣧⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡜⠀⠀⢀⠀⣤⣼⣿ ⠀⠀⣆⠀⠀⠀⣠⡇⡏⢷⣿⣤⣤⣤⣤⣤⣼⣇⣀⣀⣀⣐⣏⣦⣤⡾⣿⠁⠈⣹ ⠀⢰⠋⠁⠀⠊⢠⢰⡀⠀⠙⣶⣾⣿⣿⣿⣿⡏⠉⢉⠽⢋⡯⢧⠏⠁⠂⠀⢐⣽ ⢀⠊⠀⠀⠀⠀⢹⢸⣿⣤⡀⠈⣿⣿⣿⣿⣿⣿⣴⠇⣴⠏⠀⠀⠁⠀⠶⣀⣞⢋ ⠺⢄⠀⠀⠀⡂⠸⠘⡿⠋⠉⠉⠉⠙⠭⣿⣿⠟⠘⣿⡏⠀⠀⠀⠀⠀⠀⠉⠙⠚ ⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⠆⠀⠀⠁⣴⣶⣦⣤⣄ ⠀⠀⡀⠀⠀⡀⠄⡢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠀⡴⠿⠿⠿⣿⣿ ⠀⠀⠈⢗⠂⢄⠀⠀⠈⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠈⢀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⣏⠂⠴⠀⠼⠁⠀⠒⢀⡀⠄⠒⠂⠈⠀⠈⠲⡶⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠑⠈⠹⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⠤⠠⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠌⠀⠀⠀⠀⠀⠉⡂⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠐⡀⠡⠀⠀ ⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠒⡆ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣂⠁⠀⠀⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠹⡠⣀⠀⢢⠀⢠⢺⢫⣽⡿⡿⠃⢀⡼⠇⠀ ⠀⠀⠀⠀⠀⢀⠔⢱⠆⠉⠒⠓⠁⠀⠈⠛⠃⠀⠀⢈⡖⠀⠀ ⠀⠀⠀⡠⠐⠁⠀⠀⢋⢃⢄⡀⠄⠀⠔⢀⣠⠴⠌⠔⢡⠀⠀ ⢀⡔⠉⠀⠀⠀⠐⡄⡀⡗⠢⡞⠛⠖⠞⠯⠤⠖⡁⢀⠄⠀⠀ ⠘⡆⠀⢔⠂⠉⠀⠠⠁⠃⠀⠀⠸⡿⠀⠀⠀⠆⡇⠆⠀⠀⠀ ⠀⠈⢄⠈⡄⠀⡀⢣⠀⠆⠀⠀⢀⠁⠤⠤⠤⠂⡏⠀⠀⠀⠀ ⠀⠀⠀⠑⢼⣹⢿⢿⠱⣢⠤⣤⡞⣦⣀⣀⠠⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠙⠀⠀⠁⢄⠀⣿⣽⠑⢺⢸⢀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡰⠛⠁⠀⢸⡿⢌⢒⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡿⠁⢠⡞⢡⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠋⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠃⢠⣿⠃⠈⠀⠀⠀ ⣿⡿⠋⠁⠈⢃⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⠄⠚⠿⡆⡾⠀⠀⠀ ⡿⠁⡜⢰⠀⢨⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣽⣿⢏⡴⣭⠟⠀⠀⠀⢹⠃⠀⠀⠀ ⣧⡘⠳⣯⣣⢾⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢁⣿⠋⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⢻⡀⠀⠛⠙⣈⡈⠀⠀⠩⡟⠿⣿⠟⠻⠋⠀⠀⣯⠀⠠⠀⠀⠀⣧⡄⠀⠀⠀⠀ ⣾⣷⣶⣿⢰⠁⠀⠀⢄⡀⠘⡀⠀⠀⢠⠀⠀⠀⣉⠉⠁⠒⢿⣶⠘⠛⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣄⡀⢠⣿⡫⠓⠕⠂⢰⠒⠅⠀⡐⠒⠠⢽⣲⣤⠙⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠉⠩⡟⠿⡁⠀⠀⠀⠀⠀⠈⣾⡆⢐⣶⠌⣨⡿⢦⣄⣀⣴⠛⠁⢀ ⡿⠿⠿⡧⠧⠀⣠⠀⠀⣀⣁⣀⣀⣀⣘⠁⠙⢀⠈⠇⠀⠁⠀⡆⡌⠀⡏⡇⠐⠏ ⣅⡀⠀⠀⠀⠀⠈⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠲⢷⣒⠒⠓⠃⠘⠒

⠀⠀⠰⠀⣀⡀⠠⠤⠀⠀⠀⠀⠈⡄⠀⠀⠀⣼⣀⠁⢀⣘⣀⠀⣠⠄⠼⠗⢤⠀ ⠀⠀⠧⢊⠕⠀⠀⠀⠑⢆⠑⢄⢀⠳⢄⠀⡰⠋⠁⠀⣎⠀⠙⠀⠘⠒⡆⠀⠀⠇ ⠀⡐⠁⠀⠈⠀⠀⠀⢈⡠⠓⡘⠃⠉⠈⠛⢤⠔⠂⠀⠈⠐⡦⢀⠀⠀⡐⠧⢰⡄ ⠀⠀⠀⠀⡀⣤⠾⢑⠏⠀⠊⠀⠀⠀⠀⠀⠀⢵⡀⠀⢀⠎⠀⠀⠈⠢⣜⣀⠈⠏ ⠀⠀⡠⠐⠩⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡔⠉⢄⠀⠀⢀⠀⢠⠈⠒⣀ ⠀⠀⠀⢀⠀⢈⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡤⠥⠶⠵⡈⢁⠐⢦⠈ ⠀⢠⡒⠅⠒⠙⡘⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣂⠁⠤⠬⠶⠑⠄⠀ ⢺⣿⣆⠀⢀⡐⠀⠀⠱⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⠇⠁⠀⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡒⢤⠤⡤⢤⠽⢍⣩⣳⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡒⢖⠒⡈⡘⠦⢘⣎⢶⠁⢻⣠⣄⡉⡡⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢄⢣⢸⢌⠳⠒⡀⡸⢦⠚⠫⠳⢿⢿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣤⠌⢒⠻⣿⣏⣀⣀⣠⢺⣦⠹⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠐⡫⠋⢈⠫⣊⣽⡫⠖⠁⠀⠀⠀⠀⠀⠀ ⣠⡔⠂⣨⢩⠝⠁⠂⢄⠀⠀⠀⢀⡞⢲⠀⠀⠀⠹⡀⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠺⡏⠀⠀⢄⡶⠁⢂⠄⠒⡓⠚⠶⡂⠀⠀⠓⠄⠈⢾⣷⡀⢠⠀⠀⠀⠀ ⢘⢟⡠⠄⠚⠂⠀⣳⣡⡔⠁⠀⠃⠀⠀⠀⠈⠔⠢⢤⠘⢦⡞⣻⣤⡪⡇⣀⠀⠀ ⢸⣾⡇⠁⠀⢀⠌⠀⠀⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠖⣡⠆⠀⣰⡄⠀⠀⠀ ⠈⢿⣇⡄⠀⣎⠀⠀⠀⢩⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⣆⠀⢩⣡⠀⠀⠀ ⠀⠐⠛⢇⠀⡇⠀⠀⠀⢼⠹⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠢⡀⠀ ⠀⠀⠀⢀⢆⢧⡀⠀⠀⠀⠁⠝⣷⠤⡏⠐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀ ⠀⣀⡼⢋⠜⢋⠁⠀⠀⠀⠀⠀⡈⠰⡷⠀⠀⠀⠈⠁⠐⠠⠄⣠⣀⣠⠏⠙⡇⠀ ⠒⠂⠎⠁⡀⠘⡦⠀⠀⠀⠀⢀⢧⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢸⣇⠀ ⠓⠈⠁⠀⠀⢻⡅⠂⠄⠀⠀⠌⠈⡄⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠼⡀ ⠀⠀⠀⢀⣀⣘⡁⠀⠀⢀⠎⠀⠀⢰⠀⠹⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀

⠈⢂⠀⠀⠀⡤⢄⠤⢄⡀⣇⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⢄⠀⠑⡈⠣⡀⠈⠙⠷⢤⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠈⠲⢮⢶⠶⣾⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠀⠀⡟⢄⡀⠀⣧⡇⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢋⡀⠒⡄⠙⢿⠯⠐⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⢀⠈⢰⡗⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡀⡀⠙⣽⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢣⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣧⡤⣼⡇⠀⠀⠀⠀⠀⠀⢀⢴⠋⠀ ⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠘⣿⢾⠷⠓⠒⠀⠄⣀⣠⠔⡕⠁⠀⠀ ⠀⠑⠤⣉⠐⠀⠀⠀⠀⠒⠉⠀⢀⢿⠁⠀⠀⠀⠀⠀⠀⠈⠛⢌⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠒⠻⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠢⡁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⢈⢢⣄⡈⢦⣀⠉⠿⠋⠉⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⠁⠀⠀⣹⢲⠓⠉⠀⠀⠠⣤⢪⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠓⠘⠂⠀⠘⠛⠪⡦⢄⡀⠀⠙⢿⠋⠀⠀⠀⠀ ⠀⠀⢀⡀⠴⠆⢀⠄⠁⠀⠀⢀⣾⠀⠀⠀⠀⠈⠲⢬⢆⡶⠜⠀⠀⠀⠀⠀ ⠀⢀⡀⢠⠀⠠⠣⠀⣀⣤⣶⢋⢹⣄⠀⠀⠀⠀⠀⠈⢋⠀⠀⣰⣖⣂⣒⡀ ⠀⠀⠀⠀⠀⢧⠊⠉⣯⠛⣧⡎⠀⣏⣷⡖⢤⡀⠤⠒⠪⡆⠀⠱⠦⠡⠬⠁ ⣀⠀⠀⠀⡠⠃⢀⡴⠀⢀⡇⠀⢾⣻⣟⠇⡈⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠑⠪⠭⣇⠀⡁⠁⡀⠉⣿⠻⢰⠱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠲⢿⣇⡄⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠀⣉⠆⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡐⡉⠉⠁⠺⡹⢢⣀⠀⠀⠀⢀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠇⠀⣧⡦⣦⣠⡐⠒⠲⡥⠀⠀⠀⠈⠁⠂⠀⠀⠙⠲⢂⠀⠀⠀⠀ ⠀⠀⠘⢃⠂⠁⠠⠊⠀⠀⠉⠃⢌⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⢸⡆⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⠦⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⠃⠀⠀⠀ ⠀⠀⢸⢠⣺⠎⠲⠵⣶⠔⢠⠐⠤⠎⠀⠀⠀⡠⡰⠂⢉⢇⠠⠐⠚⣒⠢⢄⠀ ⠀⢠⠂⣿⣳⠀⢀⣾⠛⡷⠸⠇⠀⢌⣄⠀⢌⡞⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠡ ⠀⡇⠀⢸⠟⠗⠈⢛⠓⠁⡏⠀⢆⠈⣿⣰⠊⢄⡀⠀⢀⡠⠪⠁⠀⠀⠀⠀⠀ ⡄⢻⡀⡏⣲⣆⣂⡉⢱⢰⠄⠂⠨⢠⠃⠤⡙⠂⠒⠬⡀⠀⠃⠀⢰⠂⠀⠀⠀ ⠻⡂⠈⢩⠁⠈⠉⣽⣷⠖⢣⠠⢥⠗⠀⠀⠀⠁⠀⠀⠐⠄⡠⣔⠁⠀⠀⠀⠀ ⠢⡘⠦⡘⠀⣠⣾⠋⢙⡎⠃⠈⡆⠀⠀⠀⠀⠀⢀⡠⠂⠃⠀⡇⠉⠁⠀⠀⠀ ⠀⠈⢑⠒⠊⠉⢨⡆⠀⠀⢂⠀⠀⠀⠀⠀⢰⠔⠁⠀⢸⣀⡀⠅⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠀⢀⢧⠀⠀⠀⠈⠀⡄⠀⠀⠠⠛⠂⠄⡄⠓⠠⠄⣸⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⡘⠌⢄⣀⡀⣰⢀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠐⠀⠺⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢕⠠⣀⠑⣯⣡⡏⠀⠀⠀⣦⣀⠉⠑⠦⡀⠀⠀⠀⠈⠁⠀⠀⠀

⠀⠀⠀⠠⠂⠀⠀⠙⠉⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⣀⠣⡀⠀⣸⡀⠀⠀⠀⠀⠀ ⠀⢀⣀⠠⣴⢄⣀⣀⠀⢀⣴⡞⠙⣑⠔⠀⠀⠀⠌⡰⠁⣸⣢⣍⡎⢘⠈⠁⠀⠀ ⠀⠀⢀⣼⢁⡾⠋⠉⣹⢻⢯⡇⠸⡟⠀⠀⠤⡎⡔⠁⠀⢻⣷⢻⣷⠀⣱⢁⠀⠀ ⠀⠀⢹⣁⡞⠁⠀⢠⠃⡜⢸⠘⣠⡇⠀⠀⡼⢸⠀⠒⡄⡎⠻⣿⠹⢸⠭⠉⠀⠊ ⣰⢅⢸⣝⡡⠠⢠⣿⢖⠁⣾⡀⠘⣝⠀⠃⣧⠛⡄⠀⢱⡱⡀⢻⠶⡁⠀⠁⠃⠁ ⢡⠸⢌⣇⡀⡗⢯⢻⡜⠀⡇⢇⡤⠋⠀⠀⢻⣢⢛⢼⡀⢻⣽⣌⡇⠑⠦⡄⠀⠀ ⡄⠀⠀⠈⡆⠀⢸⢸⣇⢧⡗⠈⢒⡀⠀⠀⠄⢇⠙⢄⠙⠣⣣⡙⡇⠀⠀⡹⠂⠀ ⣧⠈⠰⠤⣇⠀⠸⠙⣡⣾⢿⣿⣿⡿⣄⠀⠀⠈⢆⡴⣤⠷⠾⠿⣧⠀⣸⠁⢠⣀ ⣷⣿⡍⢿⣷⡈⠒⠧⣟⠱⠞⠻⠙⠄⡆⢱⠤⠄⣈⠣⡀⠀⠀⢠⡉⣱⣡⣤⡾⣿ ⣿⣻⣿⣾⢷⢫⠁⠐⠌⡫⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⠂⣠⠹⠧⠻⠋⠀ ⣿⣿⣿⣿⣄⣉⣣⣄⡀⠈⢌⠂⡀⠀⠀⠀⠀⠀⠀⢀⠀⣰⢉⠅⠋⣀⡴⠋⠀⠀ ⠹⣿⡻⣷⣾⡉⠂⠐⠯⡟⠶⢧⢹⡀⠀⡾⠓⠚⠙⠛⡟⡧⠁⡰⠚⢁⢴⡆⠀⠀ ⣶⡵⠉⠀⣠⣞⣄⠀⠀⢺⠷⣦⡷⡽⣄⠁⠀⠀⡀⢠⠀⡑⠝⠮⡏⠀⡼⣷⣴⣷ ⢛⡀⠀⢰⢿⡿⡟⢤⣦⢌⢪⠀⢀⣽⣄⠻⡓⣲⠖⢁⣸⣀⢤⡄⣧⠀⣇⡉⡿⠻ ⢄⠠⠔⡡⣫⡊⡄⣠⣞⣗⣩⢟⠟⡿⡽⣔⢼⡟⣰⣟⣿⣿⣷⣿⣾⡀⣿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⣷⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢟⠛⢻⠏⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣸⢶⣴⣷⣏⡤⠁⣿⣇⡀ ⠠⢠⣤⣶⣟⣷⠖⢲⣥⠖⣵⠀⢢⡆⠙⠿⣿⣧⣰⣿⣿⠁ ⠀⢰⣿⡟⣉⣕⣦⣽⠁⡈⠁⠀⠀⠀⠀⠁⠬⣿⣿⣿⡟⠀ ⠀⠘⣿⣿⣿⠛⠛⠁⠀⠀⢀⡀⢀⣤⠀⠁⣴⣿⣿⡿⠀⠀ ⠀⠠⣿⣿⣷⣄⡀⠀⠱⡟⠒⠚⠋⠀⢀⣾⣿⣿⡿⠃⠀⠀ ⠀⠀⢹⣿⣿⣮⡳⣦⢀⠈⢑⠂⠂⣰⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⠲⣼⡷⡦⢾⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠉⠉⠁⠈⠃⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠤⠤⠤⠄⡔⣀⠀⣢⠖⠒⠲⠓⠒⠢⠄⠁⠀⠉⠉⠉⢉⣙⡉⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠀⣇⢿⣰⡏⢠⣉⣛⡄⠀⠀⠀⠠⠤⢄⣠⡂⠆⠀⠉⠘⠢⢀⠀⠀⠀⠀ ⠀⠀⣿⣆⡏⢘⡿⢀⣧⣬⣆⣙⣁⣀⣀⣤⣴⣶⢯⢺⣭⡈⠙⠂⡀⠀⠁⠀⠀⠀ ⢤⠴⢗⠹⠇⢸⠋⠘⠖⡺⣋⢴⢾⡿⢮⣵⣿⢻⡿⡷⢘⣿⢳⣄⠘⠅⠀⠀⠀⠀ ⣹⡂⢺⣆⣾⠋⣴⢰⣰⡟⡊⢣⠫⠼⢝⢁⡿⣈⣽⢳⣻⡟⣿⣾⣇⡀⠀⠀⠀⠀ ⢹⢷⣸⢹⣇⣸⣿⢘⣾⣧⣷⠪⢀⠿⠇⠙⢷⣿⣷⠻⢓⡒⠪⣿⢀⠃⠀⠀⠀⠐ ⠸⠀⢛⢹⣿⠏⢻⡁⣿⠏⠈⠀⠀⠀⠀⠀⠘⠆⠀⠀⠽⠟⠀⣸⡻⠀⠀⠀⠀⠀ ⠀⢧⡟⢸⣿⠀⢶⠛⣼⠀⡇⠀⠀⠀⡀⠀⠀⠀⠈⠂⠈⠀⠐⢧⡇⠀⠀⠀⠀⠀ ⠀⢸⠏⠝⡹⠀⡄⣤⢼⣠⠑⡀⠀⢰⠟⠛⠻⢶⡄⠀⠀⢀⠜⠁⢱⠀⠀⠀⠀⠀ ⠀⢌⣷⢰⣷⢸⣷⢸⣮⣯⡄⠑⠣⡈⠢⣀⡀⠜⠀⠀⡰⢁⠀⠀⠊⠄⠀⠀⠀⠀ ⠀⣸⢿⣼⢾⡾⠻⡙⡅⠐⡑⢇⠀⠘⠶⠤⠤⠴⠮⡎⢠⢃⠄⣠⠏⢀⠀⠀⠀⠀ ⠀⠈⠀⣃⣀⡃⠀⡁⢛⡀⠰⣸⠀⠀⠀⠀⠀⠀⠘⣆⡖⠁⠰⠊⡠⠃⠀⠀⠀⠀ ⠐⢈⠉⠉⢛⠁⠐⠊⣉⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀