Random Dot Art

⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠓⠒⠀⡇⡿⠀⠁⢸⡿⡇⠈⣿⣿⣛⠨⣝ ⢻⢿⣿⣿⣿⣿⣿⡿⠟⢩⣟⡟⠈⢀⣀⣀⣴⣷⠷⠒⠒⠛⠒⢻⠤⣿⢹⣿⣷⣮ ⣸⢸⢈⣻⠙⣿⣍⣴⠶⢿⣿⡟⠉⠉⠁⠀⠜⢁⠀⣀⣤⡴⣶⢿⠀⡟⣆⣿⣿⣿ ⣿⡜⠾⠛⠋⠉⠁⠀⣀⠀⠈⠃⠀⠀⠀⠀⠰⠷⣟⣇⣠⠤⢻⣾⠀⣧⢹⣞⢿⣿ ⡿⠆⣀⣲⣴⠶⠶⠶⣶⡖⠻⠄⠀⠀⠀⣀⠔⠚⠻⠗⠃⠀⢾⣿⢠⣿⣼⣿⣮⣻ ⠜⠎⠹⣅⠠⠤⠶⠾⠿⣯⠅⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠸⡿⢸⣿⣿⣿⣿⣿ ⠞⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⣿⣿⣿ ⠉⣡⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡿⡀⣿⣿⣿⣿⣿⣿ ⣿⡏⠙⢷⡽⢦⡀⠀⠠⡤⣀⡤⣤⣤⠴⡶⡯⠋⠀⠀⣴⣿⣱⢹⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠑⡜⡇⠀⠀⠈⠁⠛⠚⠛⠓⠁⠀⠀⣠⣾⣿⣷⡇⣼⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⡇⢹⣦⣄⣀⠀⠀⠀⠀⠀⡀⠔⠛⠛⠻⠿⢿⢃⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢰⢠⡇⠈⠻⣿⡿⡷⠒⠒⠪⢀⠀⠀⠀⠁⠀⡞⠌⠉⠛⢿⣿⣿⣿⣿ ⣿⣆⠀⠀⡘⣸⠣⢀⠀⢀⠝⠀⠀⠀⠀⠀⠑⢄⠀⠀⢰⡙⠀⠀⡐⠀⠙⢿⣿⣿ ⠘⢿⡄⢀⢣⡏⠀⠀⠈⠍⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⡞⠀⠀⠀⠃⠀⠀⠀⠙⣿ ⠀⠘⣿⠮⠋⠀⠀⠀⠈⠀⠘⡀⠀⡐⠀⠀⠶⠲⠒⡞⠓⠀⠀⠀⠀⠀⠀⢀⢠⣼

⢉⠡⠸⢾⣿⣿⣿⣷⣾⣏⠛⠒⠿⡍⠒⠤⢄⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⡠⡺⠁⡃⠀⢿⣧⠀⠀⠋⠀⠀⠉⠙⣫⣍⢍⠉⠒⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⣠⠊⢰⠁⠀⠱⢄⣀⡽⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢍⠢⡀⠀⠀⠀⠀⠀⠀ ⠄⡴⠁⠀⠸⠀⡀⠀⠀⡰⠡⠀⠀⣀⢴⠚⠹⣿⣿⣶⢦⣀⠑⣌⢢⠀⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⢱⠉⠐⠚⠒⠁⢀⠜⠁⠈⠢⡀⠀⠉⠀⠀⡨⠷⣿⣾⡶⠶⠶⠄⠀ ⢺⠀⠀⣸⣷⢄⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⢀⡼⡏⡻⣿⣛⠳⠶⠦ ⢼⠀⠀⣿⣧⡀⠉⠢⢄⡀⠀⠑⠠⣀⠀⠀⠀⠀⠀⢀⡴⠋⡰⢀⠃⠀⠙⠻⠷⠀ ⠀⡆⠀⣿⣿⣿⣷⣦⣀⠀⠁⠒⠂⠤⠬⠡⢤⠖⠈⠁⠀⡴⢁⠌⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⢿⣿⡿⠿⠿⠿⠿⣷⣶⣤⣄⣀⠔⠁⠀⢀⡠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠘⡅⠀⠀⠀⠀⠀⠀⠈⡹⠛⢁⣀⠤⠖⠉⣀⠔⠁⠀⠀⠀⢀⠀⠀⠀⢠ ⠀⠀⠘⡄⠈⠒⠤⠀⠠⠔⠒⠯⣍⠭⠥⠤⠄⠒⠉⠀⠀⠀⠀⠤⠒⠁⠀⠀⡰⢻ ⠀⠀⠀⠘⢄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⣢⣤⡤⠴⠒⣒⣉⣀⣀⠤⠴⠊⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢏⠉⠉⣀⣷⣿⣿⣀⡀⠱⢄⣀⠀⠀⠀⠀⠀⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣶⣿⣿⣿⣿⠏⠀⠈⠣⡤⠬⠝⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠝⠉⠻⣿⣿⣿⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⣸⡿⠉⣿⣿⣿⣿⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠁⠀⠈⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣟⣻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠹⣮⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠈⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠀⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠂⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡷⠀⠀⠐⠒⠒⠀⠐⠂⢀⣤⣐⣀⣀⣀⣀⣀⡤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣝⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢻⡾⣆⡀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⢀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠙⣮⠳⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣾⣿⠰⠀⠀⠀⠀⠀⠘⢧⡐⠀⠀⠀⠀⠀⠀⠌⢻⣧⣿⡇⠀⠀⠀⠀⠀ ⠘⢻⣿⣿⣷⣷⡄⠀⠀⠀⠀⠈⠁⢘⢠⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠩⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⠻⠛⠁⠀⠀⠀⠀⠀⠀⡘⠻⠋⠉⠙⠉⠛⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣴⠏⠀⠀⠼⣧⡀⣀⡀⠀⠀⠐⠋⠀⠀⣀⣀⡀⢐⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⢠⣷⢰⢹⡄⠙⠿⣶⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠅⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⣻⣇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠘⡟⣾⣬⠀⣤⠀⠈⠿⠇⢠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠙⣯⣿⠀⣈⣠⣤⣴⣷⣼⣆⣀⠠⠤⠀⠐⠚⠉⠁⢀⣠⣧⣤⣤⣤⠤⢤⣤⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣿⠟⠻⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡿⣿⡿⠿⠿⠋⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠰⠀⡞⠀⠀⠀⠀⠀⠀⠀⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⣤⠖⢀⣴⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⠻⣦⣀⣀⠀⢀⡀⠀⢉⣹⣬⣤⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣷⡀⠈⠉⠉⠉⠉⢉⣭⣭⣷⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣾⡅⠀⠀⠀⠘⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⡷⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡧⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⣀⡤⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⢶⣤⣀⠀⠀ ⠀⠀⢀⣀⣴⢟⢁⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢠⣤⠀⠴⠛⣛⡷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⠀⣀⣤⣴⡧⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⣠⣴⠟⠋⣉⣅⢀⣠⡀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢃⣴⡿⠋⠀⣠⡞⠁⣼⣯⣉⠹⡆⠀⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⢰⣷⡿⠟⠚⠛⢻⡟⠀⢸⠷⠦⠬⢭⣿⣀⣠⡤⠿⠃⠀⠹⣄⣀⣀⡠⠤⠤⠖⠚⠉⠁⠈⢳ ⠀⡿⠋⠀⠀⠀⢠⣿⡅⢀⡏⠀⢠⡴⠚⢻⡏⠙⠓⠦⣄⡀⠀⠹⡶⠶⠤⠤⣀⠀⠀⠀⠀⠀⡾ ⣸⠃⠀⠀⠀⠀⣾⣿⣷⡾⠀⢠⡏⠀⠀⡞⠀⠀⠀⠀⠀⠙⠳⣤⣻⠀⠀⠀⠈⠙⢦⠀⢀⡼⠁ ⡧⠤⠤⢤⣄⢸⣿⣿⡿⠁⠀⣸⣷⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⡟⠉⠀⠀ ⡇⢠⣄⣀⣨⠛⣿⠟⠁⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⢹⣆⠀⠀⠀⠀⠀⠸⣆⡴⠃⠻⠟⢁⡐⠊⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀ ⠀⣿⣷⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠤⠤⠄⠠⠴⠃⣲⡤⠤⠶⠶⢯⡁⠀⠀⠀⠀⠀⠀ ⠀⢹⡈⠛⢯⣗⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠈⣧⠀⠀⠈⠙⠓⠺⠭⣽⣶⣒⣲⠶⢶⣶⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⣤⣀⣀⣀⣁⣼⠇⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠛⠓⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣡⣼⡆⠀⠀ ⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⢸⡁⢿⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⠞⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠇⠀⠀⠀⠀ ⠀⠀⠀⢷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢀⠏⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⡼⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠈⠑⠂⠤⠤⠤⠀⠒⠉⠀⠀⠀⠀⣠⠎⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⡠⢸⡧⠤⠒⠤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠤⠀⠤⠔⠁⠀⠀⠀⠀⠀⢀⠔⠀⠘⣧⠀⠀⠀⠈⠑ ⠀⠀⣠⠔⠚⠉⠉⠉⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠘⢦⠀⠀⠀⠠ ⣠⠾⠥⠤⣀⠀⠀⠀⣸⠟⡇⢄⣀⠀⣀⠠⠄⠊⡐⢀⡄⠀⠀⠀⠀⠀⠙⠢⣄⠀ ⠁⠀⠀⠀⠈⢧⡠⠚⠁⠀⢧⠀⠀⠀⠀⠀⠀⡰⢀⠎⠀⠀⠀⠀⠀⠀⣀⠤⠜⠃ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡀⠀⠀⠀⠀⡔⢠⠊⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⢣⠀⠀⠀⣜⡠⠁⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡒⠠⢄⣀⡀⠀⠀⠈⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⣇⠁⠒⠠⠤⠤⠤⠤⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠀⠀⠀⠀⠀⢹⡆⠄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠙⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⢠⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋

⠀⠀⡠⠊⣀⠴⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣐⣴⢋⡔⢹⡭⡆⠀⣈⢀⠀⠀⢀⡀⠤⡀ ⠐⠋⠀⣸⣇⢂⠐⡹⠉⠂⢄⢛⠃⠠⡀⢀⠃ ⠐⠀⠠⠿⠃⢸⡦⠁⣀⠀⠀⠈⠀⠀⠨⠀⠀ ⠸⢦⣀⠀⠃⠈⠑⠠⠄⠠⢤⠤⠤⣂⠀⠀⠀ ⠀⠂⠁⠋⠶⠆⡠⠤⣤⠒⠁⠀⠀⠀⠑⠀⠀ ⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠀⠀⠔⠀ ⠀⠀⠈⢆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠚⠉⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⢀⣠⡴⠞⠛⠋⠉⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⣡⡶⠋⢁⡴⢋⣷⡋⢳⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⣸⡿⠛⠉⢉⡿⠁⡼⠛⠒⢫⣧⣤⡔⠛⠀⠙⣦⠤⠤⠔⠒⠈⠉⠀⢘⡄ ⢀⠏⠀⠀⠀⣼⣷⣰⠃⢠⠊⠁⡟⠀⠈⠙⠢⢄⡘⡏⠉⠑⠢⣄⠀⢀⡜⠀ ⡼⠠⠤⣀⢰⣿⣿⠃⠀⣿⡀⡸⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠈⡗⠋⠀⠀ ⢣⠰⠤⠬⠛⠟⡃⠀⡸⣿⡿⢁⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠈⣷⣄⠀⠀⠀⠙⠊⠀⠉⠐⢦⣀⡀⠀⠈⡣⣀⣀⣀⣀⡤⠊⠁⠀⠀⠀⠀ ⠀⢹⠙⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠲⣄⠀⠀⠀⠀ ⠀⠈⣇⠀⠈⠉⠓⠻⠭⠶⣶⠶⠶⣶⣛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠒⠢⠤⣄⣀⡀⠀⠀⠀⣹⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣀⣤⣤⣶⣶⣿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠉⢉⣉⣉⣉⠉⠛⢶⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⡾⠟⢋⣉⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣽⣿⣿⣿⣷⡌⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣽⣦⣾⣿⣿⣿⡿⢿⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡿⠻⣿⣿⣿⣿⣿⢿⣧⠰⡇⠀⠀⣀⠀ ⠀⠀⠀⢻⣷⣿⣿⣿⣿⣥⣿⠇⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣻⣿⣿⣿⡟⣸⠀⢣⢀⣽⣿⠇ ⢠⣶⠀⢸⣿⣝⠿⢿⣿⣿⣧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠁⠀⠀⠁⠀⣾⠀ ⠸⡆⠉⠛⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡠⢷⡀⠀ ⠀⠀⢀⡿⣙⡄⠀⠀⠀⢠⣤⣤⡀⢀⡤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣶⠞⠋⠁⠀⠀⠀⠀⣾⠉⠀⣸⡇⠀ ⠀⠀⢸⡇⠈⠉⢇⠀⠀⠀⠀⠈⠙⠛⡷⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⢀⣽⠇⠀ ⠀⠀⠘⣇⠢⠀⢾⢦⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠛⣻⣍⣉⠁⣀⣀⣙⡻⠦⠿⣻⡛⠛⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⣀⡤⠤⠾⠿⣿⣿⣿⣿⣿⡿⠃⠀⠸⣿⣿⣶⣤⣀⣀⣀⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠳⢦⣄⡀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢸⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢿⡜⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⠀⠀⠙⠈⠻⢦⣄⡀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⡿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠛⠛⢻⣟⣛⡛⣛⣿⣿⠟⠒⠿⠷⣄⣀⠀⠀⠀⠀⢀⣠⡶⠋⣰⠟⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠷⣤⣄⣀⣈⣽⣋⣉⣁⣠⡤⢶⡶⠛⠉⣿⡛⠛⠛⠛⠋⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠒⠒⠶⠦⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣀⠀⠀⠀⣤⣀⡀⣀⡤⠖⠛⣿⠀⠀⠀⠰⣷⣄⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠖⠛⠋⠉⠁⠀⠀⠀⠉⠳⣦⡀⠀⠀⠈⠁⠀⠀⣠⠾⠀⠀⠀⠀⠈⠛⢷⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡴⣤⣄⠀⢹⠟⠉⠙⢧⠀⠋⠁⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣬⣿⣿⣷⣦⣤⣄⣀⣲⣄⠀⠈⣹⣷⠤⢤⣤⣿⠃⠀⠀⠙⣧⡟⠀⠀⠀⠸⡆⠀⢀⣀⣠⡤⠶⠛⠉⣿⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠳⣾⠋⠀⠀⠀⢻⣾⠆⡀⠀⠀⠸⣧⠀⠀⠀⠀⣿⠛⠋⠉⠁⠀⠀⠀⢸⣿⠻⣿⣿⢻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢻⡇⢠⡀⢠⣼⣇⢰⣗⣤⡟⠀⠘⣧⣠⣤⣴⣿⡆⠀⠀⠀⠀⠀⢠⣿⡿⠀⣿⣿⢸⡿⠿⣿⣿⣿⣿⣿⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⠃⠘⣧⢸⡇⣸⡿⠉⠛⠛⢿⡀⠀⠀⠙⣿⣿⣾⣿⣇⡀⠀⠀⣀⣴⣿⡷⣇⠀⣿⣿⢸⠇⠀⣿⡟⣿⣿⣿⣿⡏⢿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠟⠀⠀⢹⡟⠛⠋⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⡀⠀⠻⠇⣿⣿⣿⣿⢠⡆ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⣿⣿⣿⣿⠈⠃ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠚⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛

⠀⢠⠔⠒⠉⢡⠟⠁⠀⠀⠀⠀⣠⠖⢡⡡⢁⠞⠁⠀⢸⠱⡀⠀⢣⠀⠀⢠⢱⡀ ⠀⠈⠀⠀⡴⠃⠀⠀⠀⢀⡤⠊⠁⣠⢞⣴⠃⠀⠀⡀⡇⠀⠹⡴⠈⣦⡀⠀⢣⢃ ⠀⣇⡤⠮⠤⣒⣲⠶⠚⠹⠤⡤⠞⢻⢡⠃⠀⠀⢰⣱⠄⠒⠒⠛⢖⠺⣞⠤⠀⠫ ⣋⡡⠤⡔⢋⠕⠁⠀⠀⠀⠀⠀⠀⢇⠇⠀⢀⢀⣏⠇⠀⠀⠀⠀⠈⢣⡘⢆⠀⠀ ⠀⣧⡪⠔⠁⠀⠀⠀⠀⢸⡐⠀⣸⡞⠀⣰⢣⢺⠏⠀⠀⠀⠀⠀⠀⠀⠙⢮⢫⢢ ⡇⡇⠀⠀⠀⠀⠀⠀⢀⡼⡇⡰⠣⡡⡺⠗⣡⠋⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠁⡷ ⠸⣗⠦⣤⣤⣀⣉⣭⣥⣶⠽⠵⠋⠉⠀⠀⠁⠀⠀⠼⠿⣶⣦⣤⣤⣤⣤⣶⢖⠇ ⠀⠹⡈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢈⠏⡀ ⢇⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡾⢀ ⢸⢳⣄⠱⡑⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡫⢃⠇⡜ ⢫⡄⢯⢳⠪⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⢀⡞⢰⠃ ⠀⠻⡸⡤⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⢇⠎⠀ ⣆⠈⢷⣷⡀⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡎⡜⠀⣼ ⡾⣄⠀⢿⣷⣔⡄⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⣜⡜⢀⣼⠧ ⣿⣞⢦⡀⠻⣯⣽⣶⣶⣿⣿⠑⠢⠄⣀⠀⣀⡠⠔⠊⢹⣿⣿⣿⡿⠊⣠⣾⣾⣄