Tom and Jerry ASCII Art

Copy & Paste Tom and Jerry ASCII Art Emojis & Symbols

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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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