⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⢄⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢢⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⢀⡾⠁⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢣⠈⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⡞⠁⠀⠀⢠⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⢳⡈⡆⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢀⠎⠀⠀⠀⢠⢿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⡜⡄⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⠋⠀⠀⠀⡰⠁⢸⡆⡘⠀⠀⠀⢧⡦⣄⠀⠀⠀⢰⠁⠀⠸⡕⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠐⠒⢤⡤⠴⣾⠋⠀⠀⠀⠐⠁⠀⠀⢀⡜⣀⠴⡛⡱⠁⠀⠀⠀⠈⠉⠀⠉⠓⢲⠧⠤⠤⠤⢼⣤⠄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠟⠀⠀⡏⠀⠀⠀⠀⠀⠈⢉⠟⠉⠁⠀⡼⠡⠃⠀⡄⠀⠀⠀⡌⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⢦⡀⠀⢣⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⢀⠏⠀⠀⠀⡇⢀⠀⠀⠀⣀⠔⠁⠀⠀⠀⡰⠁⠀⣠⣴⠇⠀⠀⣰⠀⠀⢀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⡄⣇⢸⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⣳⠁⢀⡴⠊⠀⠀⠀⠀⠀⡴⠁⣀⠾⠋⢰⡆⠀⢠⠃⠀⢠⠎⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣷⣿⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⢹⣴⣟⣦⣀⠲⣄⠀⠤⠮⠖⠋⠀⠀⠀⣼⠁⡰⠁⠀⡔⠁⠀⢀⣯⣭⣥⣤⣤⣴⣿⣶⣶⣿⣾⣧⣌⡇⠀⠀⠀⠀⠀ ⠀⣦⣧⠀⠀⠀⠀⠈⣿⡿⠛⢿⡟⢿⣿⣿⣿⣟⣿⠿⠆⢠⠃⠜⢀⡠⠊⠀⠀⠀⠘⠋⠉⠉⣿⣽⣿⣿⣿⣿⣧⡏⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⠀⠀⠰⠀⠀⢹⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢠⠊⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⣿⡟⠛⡇⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⢧⠀⠀⢃⠀⠀⢻⠄⠀⢀⣨⡀⠀⠛⣀⡝⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣷⡄⠀⢀⣄⠁⢡⠁⠀⠀⠀⠀⠀⡀ ⠀⠀⢳⠈⢦⠀⠈⢧⡀⠈⢣⠀⠀⠽⠿⠥⠤⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠋⠁⡴⠁⠀⠀⠀⠀⢀⡜⠱ ⡄⠀⠀⠳⡈⢣⠀⠈⠻⡢⣀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⡀⠀⠀⣀⡴⠋⠀⠀ ⡹⣦⡀⠀⠈⠢⢵⣄⠀⠉⢌⢳⡒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⠊⢁⣀⡤⠚⠻⠁⠀⠀⠀ ⠙⢮⣯⠒⠦⢤⡌⠛⠑⣦⣀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠈⠉⠀⡜⠀⣠⢀⡐⠒⠀ ⠀⠀⠃⣱⣄⣀⠱⡄⠀⠹⣼⣏⠓⠒⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⢚⠋⠁⢤⠆⠀ ⢀⣠⣶⣿⡧⢿⣷⣌⡀⠀⢻⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢿⠀⡘⠀⢠⡼⠀⠀ ⠿⣿⣿⠋⠁⠸⣿⠀⢸⠙⡟⢛⣿⠟⠓⠤⣀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠣⡀⠀⠀⠀⠀⠀⢀⣤⡾⢻⣿⢃⡆⢀⠇⢀⣞⡇⠀⠀ ⣾⠟⠳⠂⡤⢀⣿⠀⢸⠀⡅⠈⠃⠀⠀⠀⠀⠉⠒⠤⣀⢠⠖⠁⢀⣄⣠⠚⡄⠀⡱⠀⢀⣠⣴⡾⠟⠁⢀⣾⢃⡜⠀⠀⢀⣎⣿⠀⠀⠀ ⠀⠀⠀⠀⠄⠈⡿⠀⢸⢀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⣨⠃⢀⠄⠀⠀⠀⠉⠓⠒⠷⣾⣿⠟⠋⠀⠀⣠⡿⢻⡟⠀⠀⠀⢀⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⢀⡈⢸⠇⢸⡇⠀⠀⠀⠀⠀⠀⣴⡁⠀⠀⠀⠀⠙⠦⠄⣀⡀⠀⣸⠁⠀⢀⣤⡾⠋⠀⡸⠀⠀⠀⢀⡞⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢸⠀⢸⡇⠾⠰⠀⢿⠃⠀⠀⠀⢀⣼⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡤⣶⠟⠁⠀⠀⢠⡇⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀

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⣽⡿⢿⣧⣼⣦⠀⡐⢿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣽⣿⡇⠉⠁⠀⠉⠀⠀⠈⠀⠀⠀⠀⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢹⣿⣿⣿⣿⣷⠯⣿⢷⣶⣶⠶⢶⠿⣽⣿⡟⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠐⣿⣿⣿⣭⠉⠃⣀⠙⠛⠋⠀⢠⣿⣿⡿⠁⠤⠄⠶⠖⠒⠤⠤⣤⣖⠾⠥⢄⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⢸⣿⠟⠛⠁⠀⡞⠀⣀⠤⢄⠀⣾⠿⢽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢴⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣮⡉⢸⡿⢀⠔⠀⠀⢘⡜⠀⠀⣠⠟⠁⠀⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠙⢿⣟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠛⠛⠒⠓⢋⡀⠰⣼⠋⢀⣀⡜⠁⠀⠀⠀⡥⠤⠤⣀⣀⠔⠁⠀⠀⠀⠀⠀⡘⢆⠀⠈⠑⢄⠀⠀⠈⢻⠒⠛⠛⠒⠒⠒⠒⠂⠀⠀⠚⠛ ⣀⣀⣀⡴⠋⠈⠹⣿⡟⠉⠈⢇⣀⡀⢠⠊⠀⠀⠀⠀⢈⡷⠂⠀⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠳⡀⠀⠀⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⢸⠀⠀⢀⣎⠟⠀⠀⣰⣺⣿⣶⡇⠀⠀⢀⣠⡖⠁⡠⠂⠀⠀⢀⣇⠀⠀⠀⢰⠰⠀⠀⠀⡐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀ ⠀⠀⠘⡄⠀⢸⠦⣀⢠⠞⠁⠘⣻⡟⠉⠉⠉⣿⡿⢁⠜⠁⠀⠀⢀⡜⡘⠀⠀⠀⠘⠀⡆⠀⠀⠱⡄⠀⠀⠸⠀⢠⠀⠀⢀⡜⠁⠀⠀⠀ ⠀⠀⠀⡇⢀⡼⡄⡸⠃⠀⠀⠀⡇⠸⡀⠀⠀⣸⢃⠎⠀⠀⠀⢀⣾⢁⠃⠀⠀⠀⠀⠀⡧⠀⠀⢆⢹⠀⡄⠀⢃⠀⣧⠀⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣯⣠⠞⠁⠀⠀⠀⠀⣧⡀⠁⠀⢠⣟⠎⠀⠀⠀⣠⠏⣹⠜⠀⢀⠃⠀⠀⣠⣿⡀⠀⠸⡀⠁⡇⠀⠘⡄⠸⣆⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⡤⠤⠄⠤⠤⢺⠋⠉⠢⣠⢻⡟⠀⠀⢉⠝⠉⢺⠗⠄⣠⡟⠀⠀⣴⡿⠛⢻⠀⠀⠣⠀⣷⠀⠀⢱⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⠁⣠⣖⣁⣀⣤⣎⡤⢚⡟⠀⠀⣰⠟⣀⣀⠀⢣⡀⠀⢠⢃⠀⠀⡄⢃⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠎⠀⠀⡰⠀⠀⡀⢆⠀⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⠻⣠⣊⡠⠤⠚⠁⣼⣿⣿⣿⣶⡷⣤⠎⠸⠀⠀⢹⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⢲⠒⢺⡇⠀⢠⡇⠘⡄⠀⠀⠀⠉⢿⡎⣁⡿⡿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⢩⢛⠏⣠⡇⠀⡀⡸⣴⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡾⡇⡀⠈⢷⠀⠹⣄⣀⠀⠀⠈⢇⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⢀⣤⣼⠛⠁⢀⢣⣧⠏⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣤⠁⠹⣵⡀⢦⠕⠊⢻⢿⣗⡀⠀⠈⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡋⠀⢀⣾⠏⠀⠀⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠃⠀⠙⠧⣸⣄⡀⠈⡞⡄⠉⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⠇⣠⡾⠛⢄⠀⠀⠀⠀⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⢀⠇⡇⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠋⢿⡐⡀⢈⢦⠀⠀⠀⠠⠾⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢻⠀⠀⠀⢹⣿⣿⠑⢤⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋⠸⠀⠀⠀⢸⠑⠜⠦⡙⢣⡀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⠀⢃⢤⣧⡹⣄⡀⠹⣍⠓⢦⣤⣶⣿⠟⢟⡀⠀⢸⡇⠀⠀⠈⡇⠈⢦⡀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡀⠈⢿⣿⠦⢀⠈⠓⠬⣷⣄⠈⣿⠉⣷⡄⣁⣀⢸⠀⠆⢀⠀⠸⠦⣴⡙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢠⣷⡀⠀⠉⠳⢄⣀⡀⠤⠀⢉⡿⠃⢀⣟⠥⠿⢯⢿⡟⣠⢻⠀⠀⠇⠈⢧⡀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⡇⠀⠀⠸⠉⣷⢦⣀⣀⡀⠜⢀⣠⢾⣭⡶⢖⣿⠁⢀⠴⠳⠾⠚⢁⠘⠀⢰⢠⠀⠀⠙⢦⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⢨⡇⠀⠀⠈⠉⠒⠚⠧⣌⣈⣀⣀⣹⣶⡉⠀⠀⠀⠀⢸⠀⠀⢐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⢠⠔⠈⠁⢀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢐⠔⢡⣷⠁⠀⢀⠔⠁⠀⠀⠁⢀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠘⠲⠃⡎⢀⢀⠊⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠄⠀⠀⠀ ⠀⠀⢘⢆⡄⠐⢁⠂⠀⢀⡞⠀⠀⢠⡀⠀⢰⠀⠀⠈⡄⠀⠀ ⠀⠀⡸⡎⠑⠂⡌⠀⡸⠏⠇⠀⠀⡙⠱⡀⢠⠀⠀⡀⠈⢆⡀ ⠀⡰⢁⢀⠀⠇⡗⡾⠒⢻⢀⡴⡡⢓⠀⠺⢾⡆⠀⢸⠉⠉⠀ ⠘⠂⢹⢸⠀⠈⢭⠀⠀⡎⠁⠉⠁⢸⡆⠀⡜⢀⠃⣀⠂⢄⠀ ⠀⠀⠸⣸⠢⣦⠤⡑⠂⠁⠀⠀⠀⠀⠀⠓⠒⢮⡰⠻⢗⠪⢦ ⠀⠀⠀⠈⠁⡄⠀⣷⢄⣀⣀⡀⠀⣀⡠⣔⡅⢸⠀⢆⡀⠳⡄ ⠀⠀⠀⠀⠀⡇⠠⠿⣽⣿⡷⠀⠀⣯⢉⡁⡇⢸⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⣱⣆⣾⠿⠧⡌⣲⠞⠁⠀⢨⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡹⣛⢽⣮⡠⠋⠀⠀⢀⡔⠓⠊⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣰⠀⠑⡞⠯⣒⠤⢂⠹⠛⠑⢄⣀⢱⣤⠀⠀⠀ ⠀⠀⠀⢠⠁⢰⠉⠉⡇⠀⠀⠈⠑⢄⠀⠀⢸⠉⠈⡆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠋⠉⠉⠉⠉⠀⠀⠈⠉⠉⠙⠒⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⢀⡴⠛⣹⠇⡴⠋⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠛⢷⡟⠀⣠⢏⣞⡁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⡘⠃⢠⡶⠟⢹⡇⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠛⢷⣴⡟⠀⢠⡟⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⠙⠁⠀⠿⠞⠛⣻⠇⢠⠟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⠄⠀⠀⢀⣤⠾⠋⠀⡞⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⢀⣿⠀⠀⢹⠀⠀⡼⠀⠀⠀⠀⠀⣰⢻⡇⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣴⡏⠘⢧⣀⡾⠀⢰⠃⠀⢀⡤⢶⣾⡷⢻⠃⠀⠀⠀⠀⠀⢶⡗⢷⣦⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⠀⢹⡼⠀⠀⢀⣴⡿⠋⢀⡟⠀⠀⠀⠀⠀⠀⡼⠁⠀⠳⣄⠀⠀⢰⠁⠀⠀⠀⢠⣀⠀⠀⠀⠹⢦⣄⠀⠀ ⠀⠀⠀⣠⡟⠀⡇⠀⠀⠀⢰⠀⢸⠃⢀⣴⢿⣫⣤⣶⣶⡇⠀⠀⢀⡾⠁⢠⣇⣤⣤⣄⣈⡳⣤⣸⠀⡆⠀⠀⠀⢻⡟⠶⠤⠤⠴⠛⠀⠀ ⠀⠀⣠⠋⠀⢸⠁⢀⠀⠀⠸⡆⢸⡖⢋⣷⠟⠋⠉⡆⢹⠁⠀⣠⣾⠁⢠⠏⠉⢸⠀⠀⠉⠻⣦⢹⣰⠃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⣠⠞⠁⢀⣠⣿⠀⣼⠀⠀⠀⢹⡈⣇⠟⠁⠀⠀⠀⡇⢸⠴⠞⠡⣿⡴⠃⠀⠀⣾⡄⠀⠀⠀⠈⣼⡟⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⢠⣟⠀⣿⠀⠀⠀⠀⠻⡾⣄⠀⠀⠀⢀⣧⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣇⠀⠀⠀⢀⡟⠀⠀⢸⠁⠀⠀⢸⠗⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⡀⠀⠀⠘⢷⣀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⢀⣀⡴⠋⠀⠀⢠⡏⠀⢸⣧⣾⣆⠀⠈⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⣿⠹⣆⢻⡦⣄⣀⠀⠙⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⡿⢻⣿⠀⢠⣾⠻⣿⡛⠓⢦⣄⡹⣆⠀ ⠀⠀⠀⠀⠀⠈⣧⡸⣇⠈⠻⣿⠀⠉⢻⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡴⠋⢻⠀⠈⠹⣦⡀⠈⠙⠛⠂ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡟⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡇⠀⢸⡇⠀⠸⣄⠀⠀⠈⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣓⠶⢤⣄⣀⣀⣀⣀⠀⠀⣤⡤⢴⣶⠻⣟⠶⠿⡇⠀⢸⡇⠀⠀⠙⢦⣀⡀⠀⠙⢿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣟⣙⣟⣒⣿⡿⢏⣤⣿⠀⠀⠀⠀⣟⠺⠟⠓⠛⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠞⠛⢛⣿⣿⣿⣿⣿⡋⠋⠀⠀⠀⠀⣻⣳⡤⣄⣀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡼⠀⢸⢋⡭⢟⣽⠏⠉⠛⢦⡀⠀⣠⣾⠿⠋⠀⠈⠉⢳⡟⠀⣐⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡇⠀⣿⣋⣴⠿⠷⠶⢦⠀⢀⣩⡿⠟⠁⠀⠀⠀⠀⠀⣸⠁⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⣿⡿⣿⢷⣯⡀⠤⠖⠒⣾⣰⠟⠉⠀⠀⠀⠀⠀⠀⢀⣰⠇⢀⣴⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⢿⣄⣯⣿⣦⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⡏⠿⠶⠋⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡿⠒⠦⣍⠛⠲⣾⣯⣀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⣠⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡇⠀⠀⠈⠳⣴⡿⣿⡏⠛⠲⢦⣀⡠⠞⠉⠈⣻⠿⠋⠁⠙⣦⠀⠀⠀⠀⢻⣆⣠⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠶⠶⣧⡀⠀⠀⠀⢻⠀⠀⠉⠛⠶⣤⣉⣀⡠⠖⠋⠁⠀⠀⠀⠀⠘⣷⣶⣶⣖⡼⣿⠶⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡏⠉⠉⠉⠁⡞⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀

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⣝⣿⣿⣿⣧⣤⣷⣄⠁⠠⢿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣘⣽⣬⣽⠈⠉⠀⠀⠙⠂⠐⠂⠈⠁⠀⠀⠀⠀⠐⠃⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠋⠁⠈⠻⣿⣿⣿⣮⣷⣦⣘⡻⣿⣭⣍⣉⣁⣀⣀⣐⡶⢶⣿⣿⣿⠃⠀⠀⠀⠴⠔⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠀⠀⣴⣾⣻⡿⡿⣿⣿⠛⠙⢾⣝⣿⡿⠟⠋⢉⣟⣙⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣧⠀⠘⣿⣿⣿⣿⡶⠤⠄⢀⡠⠜⠋⠈⠀⠀⢀⣾⣿⣿⡿⠧⠤⠒⠚⠛⠛⠛⠛⠓⠒⠦⠶⠿⠭⠤⠤⠤⢄⣀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣿⡀⢸⣿⣿⠿⢿⠀⠀⢶⠏⠀⢀⣀⣀⡀⠀⣸⣿⡯⢭⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣤⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⠛⠃⣿⣿⠀⠀⡜⠀⠀⠘⡇⡴⠋⠀⠀⠉⡶⠟⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⣄⠙⡏⢠⠞⠀⡀⠀⣆⡼⠃⠀⠀⣰⠏⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡴⠃⠉⠀⠀⠀⠀⠰⣄⠉⠙⠳⣄⡀⠀⠀⠀⠀⠹⣿⣌⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴ ⠉⠉⠉⠉⠉⠙⣀⣀⠙⢷⡏⠀⣀⣀⣴⠁⠀⠀⠀⠀⢀⡿⠖⠲⠦⢄⣀⠔⠉⠀⠀⠀⠀⠀⢀⠀⢰⠘⢆⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣀⣀⣀⣀⣠⠞⠁⠈⠹⣿⣿⠟⠁⠀⢹⡀⠀⡀⠀⡴⠋⠀⠀⠀⠀⠀⠈⣹⠶⠀⠀⠀⠀⠀⡸⠀⠀⠂⠘⡆⠀⠀⠀⠀⠱⣄⠀⠀⠀⠸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠉⠉⠉⢹⠁⠀⠀⢀⡖⢹⠃⠀⠀⠀⣤⣿⣿⣠⣾⠁⠀⠀⠀⠀⢀⡤⠊⠁⣠⠂⠀⠀⠀⢠⡇⠀⠀⠀⠀⢻⠈⣆⠀⠀⠀⠈⢆⠀⠀⠀⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠭⠛⠉ ⠀⠀⠀⢸⠀⠀⠀⣼⠒⠋⠀⠀⣠⡼⠳⣽⣿⣿⣯⠤⠤⣤⣠⣶⢫⠆⢀⡜⠁⠀⠀⠀⠀⡞⣿⠀⠀⠀⠀⠘⡆⠸⠀⠀⠀⢰⡀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⢹⠓⢤⣀⡞⠁⠀⠀⢨⡿⡏⠀⠀⠀⠀⢽⣿⠏⢀⠎⠀⠀⠀⠀⢀⣴⠃⡏⠀⠀⠀⠀⠀⠃⠀⡇⠀⠐⡀⠹⣄⠀⡇⠀⠸⡄⠈⢇⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣀⣾⡀⢀⡏⠀⠀⠀⠀⢸⠁⢸⡄⠀⠀⠀⢸⡟⢠⠋⠀⠀⠀⠀⠀⣼⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⡀⢸⠀⢁⠀⠀⢳⠀⠸⣆⠀⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡴⠃⢀⣹⠎⠀⠀⠀⠀⠀⢸⡇⠀⠙⠀⠀⢀⡿⢠⠏⠀⠀⠀⠀⢀⡾⢻⡆⡏⠀⠀⢠⠀⠀⠀⠀⢠⣇⠀⠀⠀⢧⠀⡇⢸⡄⠀⠈⡆⠀⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣗⡋⠁⠀⠀⠀⠀⠀⢀⣴⣿⢦⡀⠀⠀⣼⣷⠏⠀⠠⠤⠤⣴⢟⣀⣼⠊⠀⠀⣠⡏⠀⠀⠀⣜⣿⣸⣤⠄⠀⠘⡇⠀⢸⡇⠀⠀⢹⡀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠒⠂⠒⠚⠉⠽⠀⠀⠙⢦⡼⠈⡏⠀⠀⠀⣠⠞⠁⠀⢉⡏⠙⢀⣴⡟⠀⠀⢠⣾⡽⠁⠀⠻⡄⠀⠀⢹⠀⢸⡇⠀⠀⠈⢧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡇⢀⡠⠞⠁⠀⢀⣠⢟⣠⠖⢫⡟⠁⠀⠀⣴⠟⠁⠀⠀⠀⠱⣄⠀⠀⢀⡞⡇⠀⠀⢠⠘⡆⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⠄⠀⠀⡆⢰⠀⠀⠀⠀⠀⢸⠀⡷⣻⣽⣿⣿⣿⣛⡟⢿⡇⣠⠏⠀⣀⡤⠞⠁⣲⣾⣿⣿⢿⣦⣽⣆⣀⣸⠁⡇⠀⠀⢸⡆⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢉⣁⣀⣀⡠⣾⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠠⠤⢿⡟⢹⠛⣻⣿⣿⣻⠀⠛⠓⠛⠋⠁⠀⠀⠀⢻⣿⣿⣿⣿⡟⢿⣌⡿⠃⢸⠁⠀⠀⢸⣧⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢩⡏⠉⢰⣿⠀⠀⢰⡇⠀⠹⡄⠀⠀⠀⠀⠀⢸⣿⠀⢦⡎⣓⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⠟⣿⠠⠏⡸⠃⣴⣸⠀⠀⣴⢸⢿⡜⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⢀⡿⢸⢠⠀⠈⢷⡆⠀⠻⡄⢄⠀⠀⠀⠀⠳⡀⠘⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⡴⣠⣾⠏⠇⠀⢠⠏⣎⡼⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⠀⠘⡞⡆⠀⣆⣙⡢⠆⣿⢿⣕⠶⠀⠀⠀⠱⢤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠏⠀⠀⠀⡞⡼⠉⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠹⣾⡄⢸⡄⠀⠀⠸⡟⡏⠛⠶⣤⠤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡗⠀⢀⣾⣽⠁⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⢮⣿⣤⠄⠀⡇⢹⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡼⣃⣰⠿⠋⠀⠳⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢀⡇⠸⡆⠀⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣴⠛⠋⠉⡏⢿⡆⢳⡀⢠⠹⡄⠀⠀⠐⠒⠒⠚⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠇⠀⠀⠀⠹⣿⣽⣯⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⢸⠀⠀⠀⠁⢸⡟⢆⠱⣄⠙⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠐⡀⢀⢿⠹⣿⠀⠀⠻⣗⠦⣄⣀⠀⠀⣀⣴⣶⣿⣿⡏⠂⠀⠀⡇⠀⠀⠀⠈⢇⠀⠳⣄⠑⠲⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⡀⠀⢻⡸⣮⢧⠚⠳⠤⣄⠘⢦⣀⠙⠻⢿⢿⡿⣟⠀⠻⢤⠀⠀⠀⡇⢀⠀⠀⠀⠸⡄⠀⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⢧⠀⠀⠳⣻⣟⠦⢤⣤⡈⠑⠢⣝⣦⡈⠀⣼⡇⠸⣷⠦⣤⣀⣀⢠⠃⣸⠀⢸⠀⠀⣿⠢⣸⡆⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⣸⣆⠀⠀⠉⠊⢧⡀⠀⠀⠠⣄⠀⠉⢛⣾⠏⠀⢀⡏⣒⣺⣿⣍⣿⣷⠃⢠⢿⠀⠀⠸⡄⠈⢣⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢺⠁⠀⠀⠀⡿⠻⣦⣀⠀⠀⠀⠉⢑⡞⠁⠈⢁⡴⢎⣁⣀⣴⣿⠏⠀⠀⣠⢏⡵⣃⠴⡃⢸⠀⠀⡀⡇⠀⠀⠙⣦⡈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡾⠀⠀⠀⠀⠇⢠⣿⠛⠳⠤⣤⣒⣋⠀⢙⡶⢏⠽⡽⠚⠛⢾⣧⠀⣠⠞⠁⠋⠉⠀⠀⡆⠀⠃⠀⣇⢹⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣄⣃⣀⣀⢀⣾⣿⣁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⡱⠑⠈⠁⠀⠀⠐⠒⠉⠀⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⡩⠚⢫⠤⠒⠊⠁⠀⠀⠒⠦⣄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡡⠭⢒⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⢆⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⠀⠀⠤⠄⡀⢠⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣧⣤⣤ ⠀⠀⠀⠀⢠⢀⠀⠀⢸⡤⣶⡔⡙⠀⠀⠠⠉⠖⠤⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⠀ ⢄⠀⠀⠐⠋⣼⠀⠀⣿⠀⢻⣯⢴⠃⡠⢟⣿⣾⣆⡄⠀⠀⠀⠀⡇⠐⠀⣿⠁⠀ ⡀⢕⠠⡀⠀⠘⠀⢄⠹⡄⠃⠙⠒⠈⠀⠸⡘⢋⠹⡗⠀⠀⠀⣸⠀⢀⠀⣿⡧⠤ ⣿⠈⠫⡐⢁⠀⢡⠸⡑⢇⠀⠀⠀⠀⠀⠀⠀⣀⠌⢀⠀⢠⢱⡇⠀⠸⡄⠘⡁⠀ ⠿⠀⠂⠀⠀⠑⢜⠑⠱⣤⠖⢄⠀⠀⠀⠀⠋⡀⡶⠃⢠⢷⣽⡇⢠⡗⠿⡗⠨⠦ ⣤⡀⠢⣀⡀⠀⠈⢧⠀⠴⡈⠙⣷⠲⠒⡮⠋⣔⠡⠐⢁⠎⠻⢶⣧⠈⢦⠄⣍⡒ ⠃⡇⠀⢰⡼⣄⠀⠑⠬⣑⢯⣤⣁⢠⢴⣓⠝⠁⠀⢠⠁⠀⠀⠀⢹⣦⡀⡡⡀⠀ ⣠⡇⠀⡜⡇⠀⠈⢀⡁⠀⢸⠺⠒⠒⢏⠏⠀⠀⢀⡆⠀⠀⠀⠀⠀⢻⡟⠧⠈⠠ ⣿⢃⡔⠗⠴⡤⠥⠤⠢⠈⢺⡄⡆⠘⡌⡠⠀⡠⠊⠃⠀⠀⠀⢀⠀⠀⡇⠀⠈⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢄⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠈⠐⢄⠀⠀⡞⠀⢀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢂⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠂⢀⠜⠀⢀⠎⢀⠀⠀⠀⠀⠀⠀⠷⣃⠀⠀⠀⢪⡄⠀⠀⠀ ⠀⠀⡀⢀⣠⠔⠀⠀⠊⠀⡠⢂⡴⠄⠀⠘⠴⠤⣀⡐⠀⠱⡀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⡜⠁⠈⠀⠐⠒⢂⠖⠉⠱⠙⢀⠀⠀⡄⠀⠠⠁⠀⠀⠑⢄⠐⢀⢸⠀⠀⠀ ⠀⠘⠀⠀⠠⠂⡠⠊⠁⠀⡠⢁⡴⢺⠀⡰⠀⡐⠓⠀⠀⠀⠀⠀⢱⣿⣞⠀⠀⠀ ⢀⠇⠀⠀⢰⣮⣦⣴⣤⣶⣦⣥⡀⡜⡐⢁⠌⠀⠸⠿⢶⢶⣿⣶⣳⢷⡝⠀⠀⠀ ⠸⣿⠀⢀⠀⢇⠀⠷⡿⢿⡿⡇⠐⡠⠂⠁⠀⠀⠀⠀⠘⢟⠛⠟⢻⣸⠃⠀⠀⠀ ⠀⢃⢂⠈⢆⠘⠄⠐⢷⣈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠥⠤⢂⠄⠀⠀⢀⠤ ⢄⠀⠢⡢⡈⠳⠬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⠁⠄⣀⡴⠉⠀ ⠘⡧⠂⢤⠙⢢⣅⡳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⢩⠂⣄⠐⠂ ⢀⣤⣟⣦⣑⠈⢞⣄⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⢀⣰⠟⢨⠀⡹⠀ ⣻⢟⢁⢹⠀⡏⠏⠟⠉⠂⠄⡀⠀⡀⠔⠁⢠⠐⡄⠀⢀⣠⠔⢫⠏⠆⠄⣸⡇⠀ ⠁⠀⠀⢸⠀⡇⡀⡆⠀⠀⠀⠀⡑⠀⠈⡉⠐⠂⠷⡾⠛⠁⣠⠏⠎⠀⢀⠟⠀⠀ ⠀⠀⠀⡜⢰⢸⠃⢧⠀⠀⢀⡼⡆⠀⠀⠈⠁⠐⠰⣁⡴⠋⠁⣸⠀⢀⡎⠀⠀⠀

⠒⠒⠒⠒⠒⠒⠒⠒⣒⣶⣶⣶⣶⣶⣤⣤⣤⣤⣴⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠈⠁⣈⣩⣽⣻⢿⡏⢀⡽⠋⢉⣠⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⢉⣯⡼⠃⣞⠀⡜⠁⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢰⡏⠙⠶⣃⣀⣀⣀⡤⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣁⡤⢾⡧⠂⣰⠀⠀⠈⡇⠀⢠⠻⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⠀⣿⠀⣠⣯⠀⠀⢸⠃⠀⠋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣉⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⡄⠀⢹⡄⡟⢹⡄⠀⣿⠀⠀⠀⠀⢠⡟⠃⠀⠀⢀⠀⠀⠀⣿⠃⣿⢉⣉⠳⣄⠀⠀⠀⠀⠀⠀⢶⣠⡀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢃⡀⠀⠀⢷⣇⠀⣷⡀⣇⠀⣀⣠⣴⡿⠦⠄⠀⢠⡾⠀⠀⢰⣿⣰⣿⣿⣿⡷⣿⣶⡖⠂⠀⠀⠀⠘⣧⢣⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⣯⠞⠀⠀⠀⠀⠙⠲⣷⡟⠯⢴⣏⣴⣿⣶⣶⣀⡴⠋⡰⠀⢠⡟⣿⣿⣿⣏⡙⢳⡄⠉⣿⡦⠄⠀⠀⠀⢸⠈⢦⣧⠘⡇⠀⠀⠀ ⠀⠀⢠⡏⠀⣤⠄⠀⠀⠀⠸⢿⠀⢀⣸⣿⡿⣿⡿⠿⢿⡧⢤⣃⡴⠏⠀⠀⠸⣯⠙⠃⣸⠇⠀⢿⠃⣠⠀⡟⠀⠘⣀⡾⠻⡇⣿⠀⠀⠀ ⣠⠔⢋⣠⣾⠃⠀⠀⠀⠀⢠⢸⡇⢀⣼⣿⠀⢷⡄⢦⠄⢻⠚⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢠⡏⡼⡁⣠⠷⠋⢠⡟⠁⠀⣿⡏⠀⠀⠀ ⠓⠊⠉⠀⡟⠀⠀⣰⡇⠀⣼⠀⢧⣿⠉⢻⠆⠈⠓⠂⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠸⡏⣯⠀⠀⡴⠻⣄⠀⠠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣼⠟⣧⠀⣿⠀⠈⠻⣾⣻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣹⢾⣷⠞⣿⣄⠈⠛⢦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢰⠏⠀⠈⠳⣿⠀⣄⠀⠘⣿⡟⠹⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠚⠛⢛⡾⢋⣠⠞⠁⣾⣻⡀⠸⣟⢷⡀⠀⠈⠓⠦⣄⠀ ⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⢹⡄⢻⠀⠀⠹⣿⡀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢚⣿⣿⠋⠀⠀⣼⡿⠋⣇⠀⡙⣆⠙⠦⢄⣐⣄⡀⠙ ⠀⠀⡀⠀⢹⡏⠀⠀⠀⠀⡜⢻⢾⡄⣆⣶⣼⣷⣤⣴⣿⣿⠷⣶⡦⣤⣄⣀⣠⣶⣿⡿⠁⠀⠀⣰⠟⠁⠀⠘⣦⢹⡈⢧⡀⠀⠀⠉⠉⠑ ⠀⣸⠁⠀⠀⠹⠤⠀⢀⣾⡵⠃⠀⢧⢸⡇⠉⢳⣾⣯⣿⡟⢿⣿⡷⢯⣉⡛⣉⡽⠟⠀⠀⠀⢠⠿⢤⣀⠀⠀⠈⠳⣷⡌⠳⣄⠀⠀⠀⠀ ⠀⣿⣆⠀⠀⠀⢀⡴⢋⠞⠀⢀⣠⠞⠻⢷⣄⠀⣻⣿⣿⠔⠋⠉⢧⡈⠛⢿⣥⣶⠃⠀⡟⢠⠏⠀⣠⣾⠟⠒⠒⣶⣬⣻⣄⠈⢷⡄⠀⠀ ⠀⠹⡝⠷⢶⣖⠉⠀⠊⣠⠴⠋⠁⠀⢀⣠⣬⡶⠛⠉⣿⡆⠀⠀⠀⢈⡿⠋⢠⡇⠀⠀⣧⠿⢭⠉⡟⠁⠀⣠⡾⠋⠀⠀⠉⠙⠲⡌⠢⡀ ⠀⠀⠉⢓⡾⠁⢠⡾⠋⠀⠀⢀⡴⠞⠉⠀⠀⢷⡀⠀⠹⣿⣄⠀⠴⠋⠀⠀⣾⠀⡄⠀⣿⣀⡼⡾⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠂⢄ ⠀⠀⢀⡟⠀⢀⡟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢳⡀⠀⣨⠟⠁⣀⣠⡤⠴⡇⢰⣷⠀⠹⡏⠐⠋⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⣼⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⠀⠀⠀⢿⠋⠁⣴⡿⠁⠀⠒⢤⣿⠘⡏⢧⡀⠹⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⢠⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡆⠀⠀⢈⣽⣶⣯⣀⡀⠀⠀⣸⣿⣆⢷⣀⣼⣷⣾⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣏⡇⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⣿⡴⠳⢾⣿⣿⣿⣿⡿⠉⠉⠉⠉⠻⣿⣿⣿⣿⠟⠉⠓⢦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣧⠀⢀⡟⠀⠀⢀⣀⣀⣀⣠⣟⣀⡀⠀⠉⢻⣿⠋⠀⠀⠀⠀⡀⢀⣼⠟⠉⠀⣀⣤⣄⠀⠙⠳⣄⣿⣷⣄⠀⠀⠀⠀⠀⠀

⡟⠛⢾⣦⣬⡻⣿⣛⣀⣠⢤⣷⠋⠁⠈⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⢐⣿⣯⠝⡁⠓⠋⢡⣷⠿⠁⠀⠀⠀⠤⠴⠮⠄⣀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢸⢏⠅⠀⢦⠂⢐⠜⢩⠁⠀⠀⢀⠀⠀⠀⠀⣀⠀⠙⢻⡦⣀⠀⠀⠀⠀⠀⠀ ⠉⠁⡨⠤⣾⡡⢴⠁⠀⡸⠒⠂⢔⡁⠀⠀⠀⠡⠀⠑⢄⠀⠹⡈⠉⠀⠀⠀⠀⠉ ⠉⢹⠀⡰⠝⢀⡐⣿⣞⣀⣀⡔⢉⠂⠀⡰⠀⠀⠇⠄⠀⡂⠀⢩⠉⠉⠉⢉⠝⠉ ⠀⠈⠀⣈⢰⠃⠀⡊⠅⠀⢸⡡⠁⠀⣰⠱⠀⠀⠀⠀⠀⡐⠀⠀⡄⣆⠠⠁⠀⠀ ⠀⠀⠻⢐⠁⠀⣀⡥⢄⢠⡷⠁⢤⠔⣹⠂⡰⠀⣠⠶⠀⢠⠀⡀⠰⠘⡄⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⠀⠃⣇⣔⣁⣤⡥⡺⠁⡠⢋⣀⡡⡀⠰⡁⢠⢂⠃⠀⠀⠀ ⠀⠀⢥⠤⡆⠀⠈⡄⠀⠀⢻⢛⣿⡷⠑⠂⠈⠀⣻⣿⣟⠿⢃⠁⡀⡬⡆⠀⠀⠀ ⠀⠀⢸⠰⢣⡀⡣⡰⣤⠀⠈⢄⣉⠁⠀⠀⠀⠀⠈⠋⠀⣶⠋⢀⡹⠃⢡⠀⠀⠀ ⠀⠀⠀⠑⠀⠓⢡⡀⠉⡉⣶⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣻⡠⠟⠄⠀⠀⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠃⢻⣷⠄⡀⠀⠀⠀⢀⣠⠖⠇⠈⢹⠕⠘⢆⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢸⠈⣸⣞⠢⢕⢅⠒⢾⢏⠣⠀⡇⠀⠈⡄⡢⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢠⠃⠈⣇⠈⠓⠅⡀⠌⡱⠃⡸⠜⡧⡗⠐⠀⢀⠙⡈⠄⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠘⠀⢸⢸⠁⠒⠨⠴⣛⣛⡑⣧⠊⠉⠁⡆⠀⣿⠀⠈⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⣩⠞⢉⣠⠴⠖⠚⠉⠉⠉⠀⠀⠀⠈⠉⣉⣲⣶⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠀⢠⡿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣠⣤⣤⣖⠋⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡼⠟⠋⠉⣹⣠⠴⠚⠋⠉⠉⠉⠉⠀⠀⠀⠀⠐⠛⠉⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣧⣠⡾⠁⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣰⠶⠶⢶⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠖⠋⠘⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡟⢦⣤⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣰⠷⠶⠶⠤⣀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀⠀⠀⢹⠞⣹⠀⠀⠀⠀⠀⠠⣴⠯⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⣿⣾⣿⠎⠘⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⠀⣸⣷⣶⣿⣯⣭⡖⠁⢰⠇⠀⠀⠀⠀⠀⢠⠏⠀⠈⢏⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⣿⣗⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣹⠀⣾⠀⠀⠀⠀⢀⣿⡿⠋⣰⣟⣿⣷⣴⠃⠀⣠⠀⠀⠀⢠⣿⣖⣒⣒⠌⢣⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⢸⣯⣿⠃⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡆⣿⠀⠀⠀⠀⢸⣿⡇⠀⣿⠉⣿⣟⣁⡤⢶⡏⠀⠀⢠⣿⠿⣿⡿⣿⣿⣷⣷⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠃⠀⢸⣿⡿⠀⠀⠀⠀ ⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⡙⠀⠀⠀⠀⢸⣿⡇⠀⢿⣀⠿⡏⡇⢀⡜⠀⣀⠴⠋⠀⢀⡿⠾⣿⣿⣿⣻⣿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⠀⠀⣸⣷⣧⣀⠀⠀⠀ ⠀⠀⣄⠙⠢⣄⠀⠀⠀⠀⠀⠀⢻⡀⠀⢠⡀⠀⢹⣽⡀⠈⠻⠤⠼⠃⠚⠒⠋⠁⠀⠀⠀⠸⡇⠀⠿⠏⢀⡇⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢘⠀⠀⢹⣿⣿⣿⣄⣀⡀ ⣦⡀⠈⢷⣄⠈⠓⢦⣄⠀⠀⠀⠀⡇⠀⠈⣷⡀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣠⠞⠀⠋⡿⠀⠀⠀⠀⠀⠀⣼⠀⣼⡏⠀⠀⠀⢼⡇⠀⠈⣿⣿⠏⠉⠉⠉ ⣮⣿⡆⠀⢻⡍⠒⠲⠾⠟⠒⠂⠀⠸⡄⠀⢻⡟⠶⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⣰⠃⣴⡿⠀⠀⠀⢀⢸⡇⠀⠀⠸⡿⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠙⣳⠴⠶⠶⢦⡀⠀⠀⢹⡄⠀⢧⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⡠⠀⠀⠀⣰⠏⣸⡟⣼⠀⠀⠀⢘⡟⢿⣆⡀⠀⠹⣆⠀⠀⠀ ⢿⡇⠀⠀⢠⡏⠁⠀⠀⠀⠀⠙⣦⠀⣸⢙⠦⣈⢧⡀⠘⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣛⣉⣀⣀⣀⣤⣾⠃⠀⠀⣠⣏⡼⠛⣟⣿⠀⠀⢀⣼⢧⡘⣿⣿⣦⣀⠈⠳⣄⠀ ⠞⠷⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠷⣏⢸⠀⠈⠙⠓⣶⠿⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠭⢻⡿⠃⠀⠀⣰⠟⢹⣿⣶⣿⡇⠀⢀⣼⢿⡀⠙⠻⣷⣿⠈⠙⠒⠚⠓ ⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⡆⢹⣀⣬⠷⣖⡛⢦⡀⠀⠀⣀⣀⣠⡤⢶⡶⠞⠁⢀⡞⠁⠀⢠⠴⠁⠀⡾⠿⣿⣿⣀⣠⣾⡁⠈⢻⣦⡀⠀⠉⠓⠶⣤⣀⡀ ⣶⣶⡆⠀⠈⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⣿⡎⣯⠀⠀⠀⠙⢾⡿⢛⠽⠋⠈⢻⣠⠟⠀⣀⣴⣏⡤⠶⠚⠁⠀⠀⣰⠗⠒⠛⠻⣿⣙⣿⣧⠀⠀⠙⣿⢶⣍⣳⡦⣀⣀⣉ ⡇⠈⢿⠀⠀⠀⠈⢻⡉⠳⡤⠀⠀⠀⠀⢸⡛⠓⠲⠷⢮⣺⠧⣄⠀⠀⡾⠙⠀⠀⠀⠀⣸⠃⣀⡠⠖⡻⠃⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠻⣾⣿⣇⠀⠀⠈⢳⡀⠀⠉⠉⠀⠀ ⠇⠀⣿⠀⠀⠀⠀⠸⢷⣴⣳⣄⠀⠀⠀⠀⠙⡶⣄⣀⠀⢻⣷⡌⡇⣼⠃⠀⢀⣀⣤⣖⡿⠿⣗⡤⠞⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠙⣄⠀⠀⠀⠀ ⠀⢰⡿⡄⠀⠀⠀⢰⣾⣧⠈⠛⠷⢤⣤⣤⣤⣤⣤⠬⠓⠋⠘⡇⠇⣿⠴⠚⠉⠽⣭⣥⣖⣾⡽⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⣶⣆⠈⢷⡀⠀⠸ ⠀⢸⡇⡇⠀⠀⠀⣸⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣟⠗⠒⠒⠒⠚⣩⢶⡾⠁⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⢿⣿⡀⠀⠙⢦⡀ ⣴⣏⣿⡇⠀⠀⢰⣇⠀⢻⠀⠀⠀⠀⠀⠀⠴⠶⠤⢤⡀⠀⢨⣷⠀⢹⡀⠀⠉⢦⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⠳⣄⠀⠀⠙ ⣿⣿⣿⠀⠀⣀⠏⡟⣆⢸⡀⠀⠀⠘⠢⠤⠤⠤⢤⡀⠈⠓⢼⣿⡄⠀⡇⠀⠀⢸⠀⡟⠀⢀⠀⠀⠀⠀⠀⣴⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠓⠦⢤ ⣿⣿⠃⢀⠔⡏⠀⠳⠈⢻⡁⢻⡛⠛⠛⠛⠋⠉⠚⠳⠦⠀⠀⣿⣇⣀⣿⣄⡀⢋⣰⡃⢀⣾⠀⠀⢠⣠⠞⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀

⠀⠀⠠⢤⣤⠼⣶⠶⢶⠶⠶⠮⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠐⠋⣹⠝⣰⢠⠊⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀ ⠀⠀⢠⢃⢼⡀⡉⠒⢂⠀⠆⠀⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀ ⠀⠀⢸⠃⢨⢰⡇⠀⡇⠈⠀⢠⠇⠀⠀⠀⢰⢸⠼⢄⠀⠀⠀⠀⡀⠈⢿⠀⠀⠀ ⠀⢀⣏⠅⠈⢾⢸⣄⡅⡄⡴⠧⠀⡠⠇⢀⣿⣾⣿⡶⢧⡀⠀⠀⠹⢃⠈⢆⠀⠀ ⠀⢸⠂⡀⠀⠀⠹⡏⢁⣿⣿⡿⣾⣠⣡⠞⠚⢿⠲⣸⠀⡿⢁⢰⠀⢈⠾⣼⠀⠀ ⠐⠥⢺⠁⢀⠀⡀⡇⡼⣇⠰⣐⣪⠎⠁⠀⠀⠈⠉⠁⣠⢳⡥⠒⣡⠋⠀⡿⠀⠀ ⠀⠀⢀⢠⠞⡄⡇⠘⢿⣲⡄⠀⠀⠀⠀⠀⠀⢀⣀⢔⡁⢈⢾⡔⣧⡉⠢⣀⠀⠀ ⠀⠀⢸⡌⠀⠈⢃⢢⠀⢻⡈⢦⡀⠀⠀⠀⠐⠠⢤⡮⠒⢁⡯⢣⢘⡝⠤⣀⣁⠢ ⠀⡄⠘⡇⠀⢀⡫⠻⣰⡷⣗⣶⣿⣟⣶⡶⠤⢾⡟⠁⠀⣞⠀⠈⢮⣌⢆⠀⠀⠈ ⢸⢇⠀⢀⠴⡑⢁⡠⠓⠧⢈⣿⡯⠊⠣⣙⣣⢵⠀⡄⣜⣠⡵⠒⢢⠽⢢⡑⢄⠀ ⠀⠃⡭⠃⡤⠒⠁⣠⠔⠊⢏⠀⢻⡀⠠⠚⠁⡇⡀⣟⣱⡜⢀⡴⠁⠀⠀⠈⠣⢁ ⠀⢰⠁⡼⠁⠀⡜⠁⠀⠀⠈⢧⠠⢋⡄⠐⡺⡄⢧⠘⡍⡡⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠇⠀⢰⠁⠀⠀⢠⠀⢈⣶⣭⣀⣀⣸⣧⣇⣵⣮⣆⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⡄⢀⠇⠀⢀⣀⣸⣃⠉⠻⣿⠋⠀⠀⠈⡻⠟⢉⣀⠙⠦⣰⣦⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠦⠄⠀⠠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠀⡴⠋⣹⣡⠊⠁⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢻⠁⢰⣷⣷⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣦⣴⠋⢠⠏⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠈⠋⠀⠺⠒⣰⠆⣰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⠗⢠⡀⠀⡞⠁⢠⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣠⠛⢧⣀⡇⢀⠏⠀⢀⣠⣴⡷⡇⠀⠀⠀⠀⢴⢿⣄⠀⠀⠀⡇⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⢀⡾⡟⠀⠀⠉⠀⣾⠀⠀⣠⡾⠋⢰⠃⠀⠀⠀⠀⡎⠀⠹⣄⠀⢸⠁⠀⠀⠠⣀⠀⠀⠻⢤⡀⠀ ⠀⠀⢀⠞⢠⠇⠀⠀⢸⠀⣏⣤⣞⣵⠶⡿⣿⠀⠀⣴⠁⡸⠶⡖⠲⢬⣗⢼⢰⠇⠀⠀⢹⠉⠓⠒⠉⠀⠀ ⢀⡴⠋⢀⣸⠀⡆⠀⠀⢆⢋⡴⠋⠀⠀⡇⣇⡴⢞⣏⡴⠁⢀⡇⠀⠀⠘⢸⡟⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⠈⠛⠉⠉⣾⠀⡇⠀⠀⠘⢾⡆⠀⠀⢠⣇⠀⠀⠈⠉⠀⠀⠸⣿⠀⠀⠀⡾⠁⠀⡇⢀⠀⡷⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⢿⢸⣿⡀⢀⡀⠀⠑⢤⡀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠛⢠⣴⣊⣀⣀⡜⠀⣸⣷⣷⣄⡈⢳⡀⠀ ⠀⠀⠀⠀⠘⣆⣧⠙⢾⡟⠒⢦⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠘⣇⡰⢿⠘⠻⣄⠉⠓⠿⠄ ⠀⠀⠀⠀⠀⠈⠛⠀⠀⡇⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣿⠀⢸⠀⠸⡄⠀⠈⢳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣯⣕⣲⣦⠤⡤⠄⠀⠰⣖⣾⣉⣟⠛⡏⠀⢸⠀⠀⠙⠢⢤⣀⣹⡗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠷⢾⣿⣿⣯⡾⠇⠀⠀⠀⣯⣍⡀⠀⢠⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣸⠀⣴⣫⢟⡿⠉⠓⢦⡀⢀⣴⠟⠁⠈⠙⢾⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣀⣿⠵⠛⢒⣒⡆⣠⡽⠋⠀⠀⠀⠀⢀⠇⠀⡼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⡿⣿⣹⣷⣌⠁⣸⠟⠁⠀⠀⠀⠀⢀⡴⣾⡤⠞⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠧⠬⡛⠻⣽⣞⡁⠀⠀⠀⠀⢀⣴⣿⣇⣀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡁⢸⠀⠀⠈⢳⠟⠿⣍⡛⢲⡤⠚⢁⡨⠟⠋⠀⠱⡄⠀⠀⠘⣦⢤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⠉⢹⠦⠤⠤⢸⠀⠀⠀⠉⠓⠲⣖⠉⠀⠀⠀⠀⠀⢻⠛⠛⠚⢻⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⡜⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⠶⠀⣀⡠⠤⠤⠖⠒⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⢰⡧⠒⠉⠀⠀⠀⠀⠀⠀⠔⠒⠊⠉⠉⠉⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⣴⣶⣶⠁⠀⣠⣤⣤⣤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡴⠊⠉⢀⡾⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣉⡩⠤⢤⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠉⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⠖⠒⠀⠤⣀⢠⡿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣿⣿⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣸⣀⣠⣤⣀⡼⢡⠇⠀⠀⠀⠀⡺⠛⢦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⡇⢠⠀⠀⠀⢀⣿⠟⢻⣿⣿⣀⠎⠀⡀⠀⠀⣰⣧⣤⠈⢦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⣿⠄⠀⠀ ⢄⠀⠀⠀⠀⠀⠋⠉⢣⢸⠀⠀⠀⢸⣿⠀⠘⠩⣿⣯⠤⣾⠁⠀⣴⡿⢿⣿⣿⣾⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠃⠀⣿⡿⠀⠀⠀ ⠀⠙⢦⡀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠸⣿⡀⠸⡄⠻⣇⣰⣃⠤⠊⠀⠀⡟⢻⣿⠿⡿⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣿⣷⣄⠀⠀ ⡄⠈⢦⡈⠳⢄⡀⠀⠀⠈⡆⠀⢣⡀⢹⣇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢣⡈⠉⡠⠡⢿⠋⠀⠀⠀⠀⡀⢀⡿⠀⠀⠀⡄⠀⢿⣿⡟⠒⠒ ⣿⣦⠈⠻⡒⠀⠽⠒⠂⠀⢱⠀⠸⡗⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⠊⠀⠀⠀⠀⣰⢁⣾⠁⠀⠀⢠⡇⠀⠘⣿⠀⠀⠀ ⣿⡇⠀⠀⡨⠗⠒⠒⢢⡀⠀⣷⡀⢳⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⢀⡴⠀⠀⢰⢃⣾⣿⠇⠀⠀⡿⢻⣦⡀⠈⢆⠀⠀ ⣽⡇⠀⡞⠀⠀⠀⠀⠀⠙⣤⠃⠈⠒⠷⣄⣼⡑⢄⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢲⣶⡿⠁⠀⣰⢿⣯⣼⣿⠀⠀⣼⡛⠺⣿⣿⠒⠤⠵⠤ ⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⣷⡆⠀⠀⢸⣃⡽⢶⡓⢄⣀⣀⣀⣀⡠⢤⡶⠊⢀⠞⠀⢀⠔⠁⢸⠿⣿⣏⣠⣾⠁⠳⣄⠀⠉⠒⠤⣄⣀ ⡷⢶⠀⠈⠣⢤⣀⡀⠀⠀⠀⠈⣿⣄⢸⣧⣣⡀⠀⠈⣺⡟⠙⠁⠈⣧⠋⠀⣴⡯⠔⠊⠁⠀⡠⠟⠉⠉⠻⣿⣿⣆⠀⠘⢿⠮⠵⠦⠤⠤ ⡇⢸⡄⠀⠀⠈⣦⣹⡁⠀⠀⠀⠳⣄⠈⠙⢿⣝⣆⢠⠇⠀⠀⣀⣠⣧⣖⣉⠜⠁⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠻⣿⣆⠀⠈⠳⡀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⣾⡏⠛⠦⢄⡀⠀⣉⡉⠷⠚⢹⡟⣼⠤⠒⠻⣿⣭⢴⡾⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣠⣤⠙⢆⠀⠀ ⢀⣼⡇⠀⠀⢰⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⠒⢉⡑⠩⠔⡟⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠿⡄⠀⠱⣄ ⣿⣿⡇⠀⢀⢿⡀⢣⠀⠀⢠⡀⠈⣉⡉⠒⢄⣸⡇⠘⡄⠀⢘⠀⡞⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠢⢀⡈ ⣿⡟⠀⠴⠇⠸⠘⣾⠰⡖⠒⠒⠒⠀⠻⠦⠀⠘⣿⣀⣧⡀⠘⣸⠀⣰⠂⠀⣄⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠉