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╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

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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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⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀ ⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⣤⣴⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⢀⠴⡄⣸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿ ⢹⣿⣷⠀⠀⠀⠁⡤⢶⣿⣿⣁⠀⢠⠀⠀⠀⣿⣿⡏ ⠈⢿⣿⣇⠀⠀⠀⢳⠀⢙⣿⣿⣷⠾⠀⠀⣸⣿⡿⠀ ⠀⠘⣿⣿⣆⠀⠀⠠⠤⠾⢹⡏⠀⠀⠀⣰⣿⣿⠃⠀ ⠀⠀⠘⢿⣿⣷⡀⠀⠀⠰⠟⠀⠀⢀⣾⣿⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⡤⠖⠛⠉⠛⠶⣤⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⣿⣿⣿⣿⣿⣿⣿⡿ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⠶⣄⣀⣤⠖⠋⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣶⠖⠀⠀⢀⣶⣶⡖⠀⠀⠀⣶⣶⡶⠂⠀⠀ ⠀⢸⣿⣯⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀ ⠀⠈⢿⣿⣷⣄⠀⠀⠻⣿⣿⣆⠀⠀⠻⣿⣿⣦⡀⠀ ⠀⠀⠀⢹⣿⣿⠀⠀⠀⠙⣿⣿⡆⠀⠀⠈⢿⣿⡇⠀ ⠀⠀⢀⣼⣿⣿⠀⠀⠀⣰⣿⣿⠃⠀⠀⣠⣾⣿⡇⠀ ⠀⢠⣿⣿⠟⠁⠀⢀⣾⣿⡿⠃⠀⠀⣾⣿⡿⠋⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⠒⠢⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣲⣨⣽⢲⣎⣦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣷⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠷⡿⣉⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢀⡀⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠬⠍⣠⡉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⢋⣽⣿⣿⣶⣿⣿⣷⢶⣴⠊⣾⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⡿⢻⣿⡹⣟⠿⣾⣾⣿⣿⣿⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⡠⠈⢺⠇⠉⠹⡏⠉⠉⠙⣵⡹⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣸⣿⠁⠈⢿⠀⠀⢠⡇⠀⠀⠀⣠⣃⣨⣿⣿⣿⣏⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⣔⣊⣻⣿⣷⣦⣮⣇⣤⣼⣿⣦⣤⣾⣿⡻⣿⣿⣿⢻⣿⣆⠑⢦⠀⠀ ⠀⠀⠀⠜⢀⣩⣿⡟⢟⣿⣿⠛⠉⣮⣟⣿⣿⠁⠈⠿⣿⣿⣿⠀⠻⣿⣆⠤⠁⠀ ⠀⠀⠈⣴⢟⣿⠟⠀⠀⠻⣧⣤⢰⢇⣨⠀⣽⠦⢉⣿⣿⣿⡿⠀⠀⡿⠁⢠⢀⡖ ⢀⠈⢀⣷⣿⠋⠀⠀⠀⠀⠹⣧⣾⣿⡻⣎⣀⣴⣾⣿⣿⣿⠃⠀⠰⠁⣠⢎⡾⠁ ⠛⢿⣦⡀⠈⠠⣀⠀⠀⠀⠀⢨⡛⢩⣿⣿⣿⣧⣾⡟⣵⡟⠀⠀⣀⡾⢋⡾⠁⠀ ⠀⠀⠙⠿⢷⣦⣌⡑⠄⠀⡔⢺⣝⣾⣿⣿⢿⣿⣯⣾⣿⣇⠀⣸⣿⣵⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣶⣡⣿⣿⣿⣿⣿⠻⣿⣿⡿⣿⢿⣿⠾⣾⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⡙⣧⣿⣿⣿⣿⡿⣁⣀⣶⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⡟⢀⡇⢳⢸⣿⣿⣿⣿⣧⡿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠿⡿⣠⠞⠀⠸⢘⣿⣿⢿⣿⣿⣷⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⣀⡀⢠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⣠⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠿⣿⣿⣿⣿⣿⠘⣿⣿⣷⣶⣾⣿⡿⠛⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⠁⠀⠰⠀⠀⠀⠀

⢹⣿⠛⢛⣛⣛⣛⣛⢿⣷⣤⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⣿⣿⠛⠛⠓⢹⣿⣷⠱⣶⣄⠀ ⢸⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠂⢻⣿⣇ ⢸⣿⠀⠀⣿⣿⠀⠀⠀⣼⣿⡿⠀⢸⣿⣿ ⢸⣿⠀⠀⣿⠿⢀⣠⣾⣿⠟⠀⢀⣾⣿⡏ ⢸⣿⣶⣶⣶⡿⠿⠿⣿⡅⣀⣴⣿⡿⠋⠀ ⢸⣿⠀⠀⣶⣶⣶⣶⡽⣿⡜⢿⣯⡀⠀⠀ ⢸⣿⠀⠀⣿⣿⠀⠀⠀⢹⣿⡀⢻⣷⡀⠀ ⢸⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿⣧⠀⢿⣷⠀ ⣼⣿⡀⠀⣿⣿⠀⠀⠀⣸⣿⣿⡀⢸⣿⡇ ⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠛⢿⣿⣿⣿⠿⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⢠⡄⢹⡟⢠⡄⠀⠹⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣾⣷⣄⠀⠀⣰⡿⠿⣿⣿⣿⣿⣆⠀⠀ ⠀⢰⣿⣿⣿⠿⠿⢯⣀⡙⠷⢶⣿⠀⠀⣿⡶⠾⢿⠴⠒⠉⠻⣿⣿⣿⡆⠀ ⠀⣿⣿⣿⠠⠤⠤⠤⠤⠬⠅⠀⠙⢿⡿⠋⠀⠀⣽⣛⡛⠛⠛⠛⣿⣿⣿⠀ ⢰⣿⣿⣿⡄⠠⠶⠒⠋⠉⠁⠀⠀⣸⣇⣀⣀⣀⠀⠀⠈⠉⠃⢀⣿⣿⣿⡆ ⠈⣿⣿⣿⡿⠷⣶⣤⣤⣤⣶⠶⠟⠛⠛⠛⠛⠛⠛⠛⢻⡿⠛⢻⣿⣿⣿⠁ ⠀⢹⣿⣿⣇⠀⢸⣇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣸⣿⣿⡏⠀ ⠀⠀⢻⣿⣿⡆⠀⠻⣧⣰⡿⠋⠙⢿⣴⠟⠛⢿⣤⡾⠃⠀⢰⣿⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣿⣦⡀⠈⠛⠷⣶⣤⣤⣤⣴⡶⠟⠋⠀⢀⣴⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⢙⣿⣿⣦⣤⣄⣀⣀⣈⣁⣀⣀⣠⣤⣴⣿⣿⡋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣄⣈⣉⣉⣽⡟⠋⠙⢻⣯⣉⣉⣁⣠⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣇⠀⠀⣸⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⣿⠀⢸⣿⠿⢿⠀⢸⣿⠿⠿⠿⣷⣦⡀⠀⢸⠿⠿⠿⣿⣿⠁⣿⡿⠿⡇⠀⣿⡿⠿⠿⢿⣆⠀⣿⡿⠿⠿⢷⡆⢸⣿⠿⢿⠀⠀⣿⡇⠀⣿⡏⠀⢹⣿⡇⠀⣿⡏ ⢸⣿⠀⢸⣿⣶⣶⣦⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⠇⠀⣿⣷⣶⣶⡆⣿⣷⣶⣶⣾⠏⠀⣿⣷⣶⣶⡾⠃⢸⣿⣶⣶⣶⠀⣿⡇⠀⣿⡇⠀⢸⣿⡇⠀⣿⡇ ⢸⣿⠀⢸⣿⠉⠉⠉⢸⣿⠀⠀⠀⢠⣿⠇⠀⠀⠀⢀⣿⡏⠀⠀⣿⡏⠉⠉⠁⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠉⠉⠉⠀⣿⡇⠀⣿⡇⠀⢸⣿⣧⠀⣿⡇ ⢸⣿⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⣾⡿⠀⠀⠀⠀⣼⡿⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⣿⣇⣿⡇ ⢸⣿⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⢰⣿⠃⣤⣤⡄⣸⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠸⣿⣿⡇ ⢸⣿⠀⢸⣿⠀⠀⠀⢸⣿⠀⢀⣿⡏⠐⠛⠛⢠⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⢻⣿⡇ ⢸⣿⠀⢸⣿⣤⣤⠀⢸⣿⠀⣸⣿⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⣿⣧⣤⡄⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠈⣿⡇ ⢸⣿⠀⠘⠛⠛⠛⠀⢸⣿⣰⣿⠇⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠉⠁⠀⢸⣿⠀⠀⣿⡇ ⢸⣿⣶⣶⣶⣶⣶⠀⢸⣿⡿⠋⠀⠀⠀⢰⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣶⣶⣶⠀⣿⣷⣶⣶⣶⠀⢸⣿⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀ ⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠉⠁ ⠴⠿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀ ⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠛⠉⠉⠛⢶⣦⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣿⠀⠀⠀⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠐⠷⠀⠀⠀⢀⣿⣶⣾⣿⡆⠀⠀⠀⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣷⣤⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣤⣤⡤⠶⠟⠋⣿⣋⡭⢹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⢀⣧⠼⠷⠤⢄⣉⣭⣽⣿⣿⣿⣿⣿⣿⡿⠿⠶⠶⠶⠖⠛⠛⠛⠛⠳⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⣀⣤⠆⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣧⠀⠈⠙⡷⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠿⣿⠁⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⢧⡀⢀⣽⠉⠉⠙⣿⠛⠛⢻⡟⠉⢉⣷⣤⠾⠃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣆⠙⣿⣿⣶⣶⣿⣿⣦⣤⣾⣿⣿⣿⣿⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⢿⡁⠀⠈⠋⠀⠀⢀⡟⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠙⠷⠦⠶⠶⠚⢉⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠶⢤⣤⣤⣴⣶⣿⡟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠐⠒⢚⣿⣿⣿⣯⣉⡛⠒⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡶⠞⠋⠁⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⢠⣶⣶⠀⠀⠀⠀⠀⠀⠈⢢⠔⠁⠀⠀⠅⠀⠀⢀⠔⠁⠀⠄⠑⠄ ⠀⠠⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠅⡆⠈⠀⠀⠀⠌⠣⢸ ⢠⠁⢠⣄⠀⠀⠀⠀⠀⠀⢾⣷⡄⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠘⢄⠀⠀⠀⣀⠀ ⡆⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠑⢲⠒⠹⠀⠀⠀⠀⢸⠉⡏⠀⠀ ⡇⣠⣄⠀⣰⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⡄⠀⠀⠀⢘⠀⠇⠀⠀ ⡇⠙⠋⢀⣿⠋⠉⠙⣿⣿⡄⠀⠀⢻⣷⠀⠀⠀⢸⠀⠆⢃⠀⠀⠀⢸⢠⠀⠀⠀ ⢰⠀⠀⠘⣿⠀⠀⠀⠸⣿⣷⠀⠀⠀⠉⠀⠀⠀⢸⠀⢰⠸⠀⠀⠀⢸⢸⠀⠀⠀ ⠀⢆⠀⠀⢻⣦⣾⡀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⡌⠀⠀⡀⡇⠀⠀⠈⠘⠀⠀⠀ ⠀⠈⡆⠀⠀⠙⠛⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⢰⠀⠀⡄⡄⠀⠀⠀ ⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠰⢀⠀⠀⡇⠀⠄⠀⡇⡇⠀⠀⠀ ⠀⠀⠀⠈⡢⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⢀⠤⠤⠵⠤⠇⠀⠐⠠⢀⣁⠀⠀⠀ ⠀⠀⡠⠄⠰⣀⣈⣉⡉⠙⠛⢂⣀⣀⠐⠈⠀⢀⣀⠠⠤⠄⠤⠀⣀⡀⠠⠓⠤⠀ ⠀⠀⠈⠉⠑⠤⠀⠠⢤⣀⣀⠠⠤⠤⠤⠤⠄⠤⣀⣀⠀⠤⠤⠄⠤⠐⠒⠂⠂⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜ ⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜ ⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩 ⬜🟩🟩⬛⬛🟩🟩🟩🟩⬛⬛🟩🟩 ⬜🟩🟩🏻🟩🟩🟩🟩🟩🟩🏻🟩🟩 ⬜🟩🟩🟩🟩🟩⬛⬛⬛🟩🟩🟩🟩 ⬜🟩🟩🟩🟩🟩🟩🟥🟩🟩🟩🟩🟩 ⬜🟩⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜ ⬜🟩⬜⬜🟩⬜⬜🟩⬜⬜⬜🟩⬜ 🟩🟩⬜🟩🟩🟩⬜🟩🟩⬜🟩🟩🟩

⬜⬜⬜⬜⬜⬜⬜⬜🏼🏼🏿🏿🏿🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏼🏼🏻🏻🟫🟫🟫🏻🏻🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏼🏻🏻🏻🏻🟫🟫🟫🏻🏻🏻🏻🏼⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬜⬜🏼🏻🏻🏻🏻🏻🟫🟫🟫🏻🏻🏻🏻🏻🏼⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬛⬛⬜🏼🏻🏻🏻🏻🟫🟫🟫🟫🟫🟫🟫🏻🏻🏻🏻🏼⬜⬛⬛⬜⬜⬜⬜⬜ ⬛🏽⬛🏼🏻🏻🏻🏻🏻🟫🟫🟫🟫🟫🏻🏻🏻🏻🏻🏼⬛🏽⬛⬜⬜⬜⬜⬜ ⬛🏽🏽⬛🏻🏻🏻🏻🏻🏻🟫🟫🟫🏻🏻🏻🏻🏻🏻⬛🏽🏽⬛⬜⬜⬜⬜⬜ ⬜⬛🏽🏼🏻🏻🏻🏻🏻🏻🏻🟫🏻🏻🏻🏻🏻🏻🏻🏼🏽⬛⬜⬜⬜⬜⬜⬜ ⬜🟫⬛🏼🏼🏻🏼🏻🏻🏻🏻🏻🏻🏻🏻🏼🏼🏻🏼🏼⬛🟫⬜⬜⬜⬜⬜⬜ ⬜⬜🟫🟫🏼🏼🏼🏼🏼🏻🏻🏼🏼🏻🏼🏻🏼🏼🏼🟫🟫⬜⬜⬜⬜⬜⬜⬜ ⬜🏼🏻🏼🟫🟫🟫🏼🏼🏼🏼🏼🏼🏼🏼🏼🟫🟫🟫🏼🏻🏼⬜⬜⬜⬜⬜⬜ ⬜🏼🏻🏼🟫⬛⬜🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜⬛🟫🏼🏻🏼⬜⬜⬜⬜⬜⬜ ⬜🏼🏼🟫🟫⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛⬛🟫🟫🏼🏼⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🏿🏿🟫🟫⬛⬛⬛⬛⬛⬛⬛🟫🟫🏿🏿🟫⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏼🟫🏼🏿🏿⬛🏿🏿🏿🏿🏿⬛🏿🏿🏼🟫🏼🏿⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏼🏻🏻🟫🟫🏼🏼⬛⬛⬛⬛⬛🏼🏼🟫🟫🏻🏻🏿🏿⬜⬜⬜⬜⬜⬜ ⬜⬜🏼🏻🏻🏻🏻🟫🟫🏼🏼🏼🏼🏼🟫🟫🏻🏻🏻🏻🏿🏿🏿🏿🏿⬜⬜⬜ ⬜⬜🏼🏻🏻🏻🏻🏻🏻🟫🟫🟫🟫🟫🏻🏻🏻🏻🏻🏻🏻🏻🏿🏿🏿🏿🏿⬜ ⬜🏼🏻🏻🏻🏻🏻🏻🏻🏻🏼🏿🏼🏻🏻🏻🏻🏻🏻🏻🏼🏻🏻🏿🏿🏿🏿🏿 ⬜🏼🏻🏻🏻🏻🏻🏻🏻🏼🏿🏿🏿🏻🏻🏻🏻🏻🏻🏻🏼🏻🏻🏻🏻🏿🏿🏿 ⬜🏼🏻🏻🏻🏻🏻🏻🏻🏼⬛⬛⬛🏻🏻🏻🏻🏻🏻🏻🏼🟫🟫🟫🟫🏿🏿⬜ ⬜⬜🏼🏼🏼🏼🏼🏼🏼⬜⬜⬜⬜🏼🏼🏼🏼🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬛🟫🟫🟫🟫🟫🟫⬛⬜ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫⬜🟫🟫🟫🟫🟫🟫⬛ ⬛🟫⬜🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛ ⬛🟫⬜🟫⬜🟫🟫⬜🟫⬛ ⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬛⬛🏼🏼⬛⬛⬜⬜ ⬜⬜⬜⬛🏼🏼⬛⬜⬜⬜ ⬜⬜⬜⬛🏼🏼⬛⬜⬜⬜ ⬜⬜⬜⬛🏼🏼⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬛🏿⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏿⬛⬜⬜ ⬜⬛🏿⬛⬛🏿⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏿⬛⬜ ⬜⬛🏿⬛🏿⬛🏿⬛🏿⬛⬛⬛⬛🏿⬛🏿⬛🏿⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🏻⬛⬛⬛⬛⬛⬛🏻⬛⬛⬛🏻⬛⬛⬛⬛⬛🏻⬛ ⬛🏻⬛⬛⬛⬛🏻🏻🏻⬛⬛🏻🏻🏻⬛⬛⬛⬛🏻⬛ ⬛🏻🏻⬛⬛🏻⬛🏻🏻⬛🏻🏻🏻⬛🏻⬛⬛🏻🏻⬛ ⬛⬛🏻⬛🏻🏻⬛🏻🏻🏻🏻🏻🏻⬛🏻🏻⬛🏻⬛⬛ ⬛⬛⬛⬛🏻🏻⬛🏻🏻🏻🏻🏻🏻⬛🏻🏻⬛⬛⬛⬛ ⬛⬛⬛⬛⬛🏼🏼🏻🏻🏻🏻🏻🏻🏼🏼⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛🏼🏻🏻🏻🏻🏻🏻🏼⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛🟪🟪🟪🏻🏻🟪🟪🟪⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛🟪🟪🟪🟪🌫️🌫️🟪🟪🟪🟪⬛⬛⬛⬛⬛ ⬛⬛⬛⬛🟪🟪⬛🟪🟪⬜⬜🟪🟪⬛🟪🟪⬛⬛⬛⬛ ⬜⬛⬛⬛🟪🟪⬛🟪🟪⬛⬛🟪🟪⬛🟪🟪⬛⬛⬛⬜ ⬜⬛⬛🏻🏻⬛🟪🟪🟪🌫️⬜🟪🟪🟪⬛🏻🏻⬛⬛⬜ ⬜⬜⬛🏻🏻⬛🟪🟪🟪⬜🌫️🟪🟪🟪⬛🏻🏻⬛⬜⬜ ⬜⬜⬛🏻🏻⬛⬜🟪🟪🌫️⬜🟪🟪🌫️⬛🏻🏻⬛⬜⬜ ⬜⬜⬜⬛⬛⬛🌫️⬜🌫️⬜🌫️⬜🌫️⬜⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏻🏻⬛⬛⬛⬛🏻🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟪🟪⬛⬜⬜⬛🟪🟪⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜🟪⬛⬜⬜⬛🟪⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪🟪⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟪🟪🟪🏿🏿🏿🏿🟪🟪⬛⬛⬜⬜⬜⬜⬛⬛ ⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪🏿🏿🏿🏿🏿🏿🏿🏿🏿🟪🟪⬛⬛⬜⬛⬛⬛ ⬜⬜⬛⬛⬛🟪🏿🏿🏿🏿🏿🏿🏿🟩🏿🏿🏿🏿🏿🏿🏿🟪⬛⬛⬛⬛⬜ ⬜⬛⬛⬛🟪🏿🏿🏿🏿🏿🏿🏿🟩🟩🟩🏿🏿🏿🏿🏿🏿🏿🟪⬛🟪⬜⬜ ⬜⬛🟪🟪🏿🏿🏿🏿🏿🟩⬛⬛🟩🟩🟩⬛⬛🟩🏿🏿🏿🏿🏿🟪⬜⬜⬜ ⬛🟪⬜⬜🏿🏿🏿🏿🟩⬛🏿⬜🟩🟩🟩⬜🏿⬛🟩🏿🏿🏿🏿⬜⬜⬜⬜ 🟪⬜⬜⬜🏿🏿🏿🏿🟩🏻🏿🏿🟩🟩🟩🏿🏿🏻🟩🏿🏿🏿🏿⬜⬜⬜⬜ ⬜⬜⬜🏿🏿🏿🏿🏿🟩🏻🏻🟩🟩🟩🟩🟩🏻🏻🟩🏿🏿🏿🏿🏿⬜⬜⬜ ⬜⬜⬜⬜🏿🏿🏿🏿🏿🟩🟩🟩🟩🟩🟩🟩🟩🟩🏿🏿🏿🏿🏿⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏿🏿🏿🏿🏿🟩🟩🟩🟩🟩🟩🟩🏿🏿🏿🏿🏿⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏿🏿🏿🏿🏿🏿🏿🟩🟩🟩🏿🏿🏿🏿🏿🏿🏿⬜⬜⬜⬜⬜ ⬜⬜⬜🏿🏿🏿🏿🏿🏿⬛⬛🟪🟩🟩🟩🟪⬛⬛🏿🏿🏿🏿🏿⬜⬜⬜⬜ ⬜⬜⬜⬜🏿🏿🏿⬛⬛⬛⬛⬛🟪🟩🟪⬛⬛⬛⬛⬛🏿🏿🏿🏿⬜⬜⬜ ⬜⬜⬜⬜⬜🏿⬛⬛⬛⬛⬛⬛⬛🟪⬛⬛⬛⬛⬛⬛⬛🏿🏿⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛🏿⬛⬛⬛⬛⬛⬛⬛⬛⬛🏿⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛🏿🏿🏿⬛⬛⬛⬛⬛⬛⬛🏿🏿🏿⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛🏿⬜🏿⬛⬛⬛⬛⬛⬜🏿⬜⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🟪⬜⬜⬛⬛⬛⬛⬛⬜⬜🟪🟪⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟪🟩🟩🟩⬛⬛⬛⬛⬛⬛⬛🟩🟩🟩🟪⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩⬛⬛⬛⬛⬛⬛⬛🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬛⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬜⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬜⬜⬛⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛ ⬛⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬛⬜⬜⬛⬛ ⬛⬛⬜⬛⬜⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬛⬛⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬜⬛⬛⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛ ⬛⬛⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬜⬜⬛⬛ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬛⬛

⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🌫️🌫️🌫️🌫️🌫️🟪⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️⬛⬜⬜⬜ ⬜⬜⬛🌫️⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜🌫️⬛⬜⬜ ⬜⬛🌫️⬜⬜🟨🟨⬜⬜⬜⬜⬜⬜⬜🟨🟨⬜⬜🌫️⬛⬜ ⬛🌫️⬜⬜🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨⬜⬜🌫️⬛ ⬛🌫️⬜🟨🟨⬜⬜🌫️⬜⬜⬜⬜⬜🌫️⬜⬜🟨🟨⬜🌫️⬛ ⬛🌫️⬜🟨⬜⬜🌫️⬛⬜⬜⬜⬜⬜⬛🌫️⬜⬜🟨⬜🌫️⬛ ⬛🌫️⬜🟨⬜⬜⬛🌫️⬛⬜⬜⬜⬛🌫️⬛⬜⬜🟨⬜🌫️⬛ ⬛🌫️⬜🟨⬜⬛⬛⬛🌫️⬛⬜⬛🌫️⬛⬛⬛⬜🟨⬜🌫️⬛ ⬛🌫️⬜🟨⬜⬛🌫️🌫️⬛🌫️🟪🌫️⬛🌫️🌫️⬛⬜🟨⬜🌫️⬛ ⬛🌫️⬜🟨⬜⬛⬛⬛🌫️⬜🌫️⬜🌫️⬛⬛⬛⬜🟨⬜🌫️⬛ ⬛🌫️⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜🌫️⬛ ⬜⬛⬜⬛⬜⬛⬜⬛⬜⬜🌫️⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜ ⬜⬛🌫️⬜⬛⬛🌫️🌫️⬜⬜🌫️⬜⬜🌫️🌫️⬛⬛⬜🌫️⬛⬜ ⬜⬜⬛⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬜⬜ ⬜⬜⬛🌫️⬜⬛🌫️⬜⬜⬛⬛⬛⬜⬜🌫️⬛⬜🌫️⬛⬜⬜ ⬜⬜⬜⬛🌫️🌫️⬛🌫️⬜🌫️🌫️🌫️⬜🌫️⬛🌫️🌫️⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛🟪🌫️🌫️🌫️🟪⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟥🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟨🟨🟥🟥🟥🟥🟥🟥🟥🟨🟨🟧⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧⬜⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟧⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟧⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟧⬜⬜⬜ ⬜⬜⬜⬛🟧🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟧🟧🟧🟧🟨🟨🟨🟧🟧🟧🟧⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬛⬜⬜⬜ ⬜⬜⬜⬛🌫️🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🌫️⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦⬜⬜🟦⬜⬜⬜🟦⬜⬜🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦⬜⬜⬜⬜⬜🟦🟦⬜⬜⬜⬜⬜⬜