Neko ASCII Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⡉⠒⢲⣤⣀⣀⣤⣴⣶⣶⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⡠⠄⠂⠈⢈⡉⠉⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⡠⠀⠀⠀⣠⠔⠀⡠⠚⠀⡄⠀⠀⠉⠻⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⠟⠃⠀⢀⠞⠀⠀⢠⠞⠁⣠⠊⠀⢀⣼⠁⣾⡀⠀⡄⠘⣿⡏⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣶⠏⠂⢠⢀⠎⠀⠀⡰⠃⢀⣼⠃⠀⡠⢋⠇⣰⠁⢿⡄⢸⡆⢹⣇⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⡎⣞⠀⣠⡾⢁⣾⢻⠃⣠⡞⠁⡜⡰⠃⠀⢸⡗⢒⡇⠈⣿⠀⠀⠀⠀ ⢰⣿⣿⣿⡏⠀⠀⠀⠀⢀⡠⠞⣿⠁⣄⣰⣼⢁⡝⢳⣷⡟⠁⣼⡴⠙⠀⣼⠟⠁⠀⠀⠸⢸⠀⡇⠀⠿⠀⠀⠀⠀ ⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⡏⢿⡟⢻⡿⢲⣿⡿⣿⣦⣤⣾⣿⣆⣁⣉⣀⡀⣸⢰⠀⠀⣾⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠘⣰⠈⠃⣾⡟⢡⡘⣿⡏⢸⡏⢩⣭⣽⡟⣿⣿⢻⣿⣼⣏⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⡼⣏⣿⣿⣿⣿⣴⣿⣦⣼⣟⣠⣦⣄⣻⡇⣼⠇⣶⣬⣿⠁⣿⡇⢸⡿⢻⣿⡄⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣷⣦⡞⢸⣿⡟⢿⣾⡿⣿⢦⡀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⢶⣬⣥⣿⣇⣾⠹⡗⠄⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣿⣿⡅⡿⠀⢧⠘⣇⣷⣝⣆⠉⠒⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡿⣁⣼⣿⣿⣠⢸⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⡙⢷⡀⠈⠳⣿⡁⢻⣿⣷⡒⠀⠀⣿⠉⠉⣻⡏⠀⠀⠤⣴⣿⣟⡿⠋⣾⠛⣿⡜⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠶⣯⣀⡞⣁⡙⢻⣿⣿⣿⣦⣄⡀⠒⠒⠚⢀⣠⣴⣿⣯⣽⣋⣤⡾⠳⣴⣿⠿⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠭⡉⡿⠋⢹⣌⣿⣏⠻⣿⣷⣶⣿⣿⠋⢙⣿⡀⠀⢙⡏⠀⢠⠞⠙⣗⠢⡉⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢇⠀⠃⠀⠸⡀⠈⢇⠀⡇⠙⣿⣽⠤⡉⣛⣟⢋⡇⡴⢫⡾⢿⠀⢸⠀⡔⠁⡠⠀⠀⠇⠘⡆ ⠀⠀⠀⠀⠀⠀⢰⡇⠈⠂⢸⠶⡀⠑⣄⠘⡄⠘⣶⠟⠻⣦⣆⣠⣀⣀⣻⣷⠏⠀⢸⠀⠘⠴⢥⣎⣀⠔⣁⡴⠘⡏ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠄⠜⠢⣈⡦⠗⠀⠸⢴⡶⡇⠈⠀⠙⠁⠠⢿⣦⠀⠈⠳⠄⣀⠀⠉⠉⠉⠀⣄⡜⠁
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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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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