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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⢀⣀⣤⡤⠶⠖⠛⠛⠋⠉⠉⠙⠛⠛⠓⠶⢦⣤⣀⣀⡴⠞⠛⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⣤⣤⣤⡙⢷⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣾⣿⣿⣶⡈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⣿⣿⣿⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢐⣾⣿⣿⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⡿⠏⠀⠀⠀⠀⣿⠷⣾⠀⠀⠀⠀⠙⠿⠟⠃⠀⠐⠉⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⢀⡟⠀⡟⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⣸⠃⢸⠇⠀⠀⠀⠀⠀⢀⣀⣸⠄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣠⡶⠛⠛⠛⢶⣼⠀⢀⣤⣠⣀⣀⣿⡉⢹⣴⣤⡀⢀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣾⣧⣾⣷⠦⣤⣶⣤⣤⠰⠊⠀⠀⢠⡾⠋⠀⠀⠀⠀⠘⣿⣤⡼⣧⠀⢻⡏⣙⣷⣿⡏⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠉⠻⣶⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⠀⢸⣆⡼⠟⠉⠉⠉⠙⣶⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⢸⣦⡾⠋⠀⠀⠀⠀⠀⣼⠋⠉⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⣏⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠀⠻⣦⡤⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⣁⣠⣤⣤⠴⢶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠁⠤⠄⠈⠉⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⡑⠀⡇⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠐⠒⠒⠁⠒⠋⠁⢠ ⢀⢻⣾⢳⠀⢀⡧⢀⢸⡄⠀⣀⠔⠚⠉⠘⠒⠺⡁⢀⣙⣂⣀⣙⣉⣁⠍⠉⠉⢹ ⢖⣯⣥⢾⠀⠀⡇⣼⡼⠝⣟⣗⠀⢀⡀⠀⠀⠀⠘⢉⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⡾⢺⠍⢸⠀⠀⣷⣿⠡⣄⡈⠉⠀⠈⠀⠀⠀⠀⠀⠀⢣⢀⣀⣀⣀⡀⠀⣀⠀⠀ ⠃⠀⠀⢀⠀⢠⠋⠀⠀⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⣄⠀⠀⠀⠀ ⡆⢀⢸⣸⣤⣦⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢤⡇⡀⣇⡆⠀⡤⠤ ⣧⣼⡿⠟⣽⡿⢷⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠄⠀⠉⠓⠚⠉⠉⠁⠀ ⣿⡿⠛⢻⡿⠷⠒⡙⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡷⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⡷⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣰⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠭⢽⡿⣿⠿⠯⢭⣧⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠁⠀⢠⣿⣷⣾⣿⣿⣿⣷⣾⣶ ⠀⠛⠛⠛⠛⠛⠛⠻⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠋⠉⠙⠋⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠂⢤⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠤⢼⣄⣄⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡄⠀⢰⡏⠀⠀⠀⠀⠀⣠⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠿⢧⡄⢀⣤⣤⣤⣤⣠⡼⠀⢠⣤⣼⡿⠳⠖⠀⠀⢀ ⠀⠀⠀⠀⢀⠄⡀⠀⠈⣱⠂⠀⢸⣿⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⢀⣴⢶⠏⣾⣥⡆⡐⠃⠀⠀⢸⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣟⣛⣶⣀⡀⢀⣴⠖⠒⠛⠙⠒⠒⠒⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠐⠶⠶⠶⠶⠶⠶⠾⢿ ⠄⢈⠚⣾⣺⢃⣏⠌⡇⠀⠀⠀⢸⣿⡦⡄⣤⠀⢘⣿⡄⠀⠀⠀⢀⣠⡼⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⢅⡀⠀⠀⣀⣀⣈⣁⣉⣀⣀⣀⣀⣉⣀⣀⣀⣀⣴⡶⠀⠀⠀⠀⠀⠀⣸ ⠠⠞⣰⡷⣧⣟⠄⣸⡀⠀⠀⠀⢸⣯⡃⡀⢻⠔⣮⡿⣿⣤⢤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡤⠬⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠤⠤⠶⠤⠞⠩ ⣩⢉⣼⢰⣷⣶⣰⠏⡇⠀⠀⠀⢸⣿⡇⣷⣿⣤⣿⣶⡾⠻⣟⣁⣾⠗⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒ ⠁⣼⡷⢿⣿⣿⡏⢀⡇⠀⠀⠀⢸⣿⠃⢿⣿⣿⠟⠁⠀⠸⣿⣿⣷⣶⠆⠀⠀⢸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠷⣿⢋⣿⠁⠀⡇⠀⠀⠀⠸⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⣿⠸⣿⠀⠀⢧⠀⠀⠀⢠⣿⣿⡿⠿⠛⠉⠩⠽⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠻⠯⠭⠭⠽⠿⠿⠿⠿⠛⠀⠠⠬⠥⠄⠀⠀⠀⠀ ⢿⠀⠀⣿⠀⣿⠀⠀⡌⠀⠀⠀⢘⡿⠋⠁⠀⠀⠀⠀⠀⠶⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠉⠀⢨⠀⠀⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠂⠀⠀⠀⡄⠀⠒⠒⢶⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⣀⠀⣹⠀⠀⣧⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣿⠀⣿⣀⣼⣿⣾⣷⣿⣧⡀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠴⠶⣶⣾⡇⠀⡆⠀⢸⣤⣸⠀⠀⠀⢠⡶⠶⠶⠶ ⣿⠀⠀⣿⣶⣿⣿⣟⣿⢾⣷⣿⣿⣷⣄⡀⠀⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡀⠀⠀⠀⠈⠛⢧⣷⣄⡌⣿⠛⡿⠛⠒⠛⠋⠀⠀⠀ ⣿⣿⣶⣿⣿⣿⡿⠿⠁⣼⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢿⡇⠆⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣭⣶⣶⣶⣾⣿⣿⣿⡅⠀⢉⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣿⡟⠋⠛⠿⣿⣿⣿⡿⠿⠞⠋⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣤⣥⣤⣤⣤⣿⠧⠠⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢣⡏⠈⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣷⣿⣿⣯⣿⣿⣿⣯⣭⣩⣩⣉⣫⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢢⣦⠀⣴⣮⡟⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠻⠻⣿⣿⣿⣿⣿⡿⡿⡟⠛⠛⠻⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣽⣴⠿⠋⠀⠀⠀⠀⠀⣼⡿⡿⠷⠾⠿⠿⠿⠿⠿⠿⠿⢿⢾⠿⠶⠿⠿⠷⠶ ⠛⠻⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣿⠿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠤⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⡼⠿⠶⠶⠶⠶⠷⠶⠿⠿⠿⠿⠾⠾⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣷⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡞⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠈⠉⠓⢶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⣀⠀⠀⠀⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣴⣏⣀⣀⣀⣼⣫⠄⢀⡄⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠿⠓⠞⠷⠲⠶⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠶⠀⢰⡇⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠚⠻⠄⠠⠤⠤⠤⠴⠂⠠⠴⠿⠛⠂⠀⢠ ⠀⠀⣀⡴⣤⣀⠀⠊⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣄⠀⠀⢀⡠⠤⠤⢀⣀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣾ ⠀⠘⢻⣴⢻⠋⡆⠀⠀⢸⣿⣀⢀⠀⢻⡄⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠉⠓⠲⢏⠀⠀⠀⠀⠒⠂⠀⠀⠀⠒⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸ ⣐⡣⡿⠿⠇⢰⡇⠀⠀⢸⣿⢠⢸⠂⣿⢿⣦⣴⢞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡶⠒⢭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠤⠖⠒⠉ ⠖⣼⣿⣿⣧⠏⡇⠀⠀⢸⣿⢹⣿⣷⡿⠛⢩⣯⣾⣋⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⢼⠟⡟⠀⡇⠀⠀⠸⣿⣎⣿⡏⠀⠀⠀⠉⠛⠛⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠈⡇⠀⠇⠀⠀⢠⣿⣿⠟⠋⠉⠽⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠿⠥⠴⠶⠶⠶⠆⠀⠠⠦⠄⠀⠀⠀ ⢹⠀⠘⠀⠇⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡇⠀⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⠀⡄⠀⡇⢣⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠀⣧⣴⣿⣶⣾⣧⡀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠶⠶⣾⠀⡄⠀⣧⣼⠀⠀⢠⡖⠒⠲ ⣿⣀⣸⣿⣿⣿⠟⣿⣿⣿⣿⣦⣄⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣯⡀⠀⠀⠈⠻⠷⠶⠿⠙⠋⠉⠙⠁⠀⠀ ⣿⣿⣿⣿⣭⣍⣴⣿⣿⡟⠛⢛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠛⠻⣿⣿⠿⠿⠚⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣶⣶⣿⣧⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣻⣿⣿⣟⡛⡛⠻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⣀⣴⡏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⡛⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠧⠿⠋⠀⠀⠀⢠⣿⣶⡶⡶⠶⠶⢷⢶⣶⣶⣶⣶⠶⠶⠶ ⠉⢉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣻⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣟⣻⣛⣻ ⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠾⠿⠿⠏⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠙⢺⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⡔⠀⠀⢈⣇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠦⠧⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠤⢤⡀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠒⠦⢄⣠⢖⣒⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣴⣿⣷⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⡄⡀⠀⠀⣾⣷⠄⢀⠀⢸⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⡉⠉⠀⠀⢐⠏⡇⠀⠀⠈⠉⡐⠁⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠄⠀⢀⡠⢼⣰⠀⠀⠀⢠⠤⣇⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⣀⠤⠧⢿⡢⢴⣤⠐⠊⠀⠞⠁⠀⠈⢻⡤⢯⢹⣋⣧⣟⢹⠊⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⢀⡴⠋⣧⡼⠊⠁⠀⢠⠟⠢⡀⠀⠀⠀ ⠀⠀⢹⠉⠉⠩⡉⠉⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⢸⠀⠀⠀⢸⡀⣰⠃⠀⠀⠀ ⣀⣀⣸⠀⠀⠀⠁⢰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣼⣤⣤⣤⣴⣋⣀⣀⣀⣀⣀ ⠀⠀⠀⣇⣀⣀⣀⣸⠀⠀⠀⠀⠀⢀⣀⠤⠒⠒⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⠶⠶⣤⡤⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣼⠿⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⢻⠶⠴⡟⡛⠟⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠉⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⣠⣾⡶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡄⢸⣟⡈⠁⣹⣷⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡐⣿⠁⠀⢸⡇⠀⠀⠉⠙⠉⣻⣆ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣄⣀⣤⡶⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⡀⣴⢿⠉⠉⠉⠉⠛⢿⣆⠀⠈⣿⣤⣈⣡⣤⡶⠟⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠠⠍⢹⡿⠅⠀⠀⠀⠀⠀⢿⠛⠀⠀⢠⣿⣷⡄⠀⠛⢛⣫⣿⡿⠇⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠈⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠏⠻⣷⡄⢸⡷⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢠⡾⣿⠻⠷⠀⠀⣻⣧⠈⠻⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⡀⠀⠀⠀⢀⣿⠉⠀⠀⠈⢛⣷⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⣀⢀⡀⣀⣀⣴⡿⠟⠛⢷⣦⣄⣀⣤⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠄⠒⢠⠄⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣠⡐⡐⡂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡐⠈⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠈⢁⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⠊⠃⠀⠀⠀⠀⠀⠀⠂⠐⠀⠿⡍⠈⠈⠉⠁⠉⠉⠁⠉⠁⠑⠒⠠⢴⡋⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠡⠏⠀⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠀⠀⠀⠀⠀⠀⠀ ⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀Cute!⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠄⠀⠀⠀⠀⠀⠀⠁⠐⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡽⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠟⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⢀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡕⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠃⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⡁⠀⠁⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁⠈⠀⠁⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠛⠋⣉⣉⠛⢛⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⠃⣀⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⡄⣉⣋⢠⢤⣠⡈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣦⣶⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣿⠟⠁⢉⠙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢻⡇⠠⢷⣾⠆⠈⠛⠿⣿ ⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⢯⠀⣾⣿⡇⢸⣿⣿⣶⣦⣶⠄⠹ ⣿⣿⣿⣿⣿⣿⣷⣦⡄⠉⠻⠿⠛⢉⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⠋⡀⣶⣶⣶⣶⣤⡀⠹⣿⣷⠀⠛⠷⠞⠛⢉⣠⣿ ⣿⣿⣿⣿⣿⠿⠿⠿⣟⣲⡆⢀⣺⣿⣿⣿⣿⣿⣀⣤⣿⣿⣿⣿⣿⣿⣿⣤⣤⡼⠁⢀⣸⣿⣿⣿⣿⣿⣿⠀⣺⣿⣿⣿⣷⣾⣾⣿⣿⣿ ⣿⣿⣿⣿⠇⢠⣰⣄⠈⢻⡇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⡟⢁⠀⣄⣈⣿⣿⠄⠘⣷⣄⠉⢻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⠘⢿⣿⣿⣿⡿⠀⣶⣿⣿⣷⡤⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣤⣤⣤⣤⣤⣼⣿⣿⣿⡿⠃⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠛⣿⣿⣿⡿⠟⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢉⢉⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠙⠿⠿⡿⢿⠿⠿⠋⢀⣠⣤⡈⠙⠻⠿⠛⠟⠛⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣧⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠙⠷⠞⠛⠲⠾⠋⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡄⠀⠀⢿⠗⢀⣀⡀⢿⡿⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⡰⠋⢩⣶⡉⢳⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⡇⢀⠈⣍⠀⡀⡇⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠙⣷⣀⠹⣌⡉⠈⣉⡴⢁⣠⡟⢁⣀⣤⣀⡀⠀ ⠀⣰⡟⠋⠉⠉⠻⡏⠈⠑⠲⠭⠭⠴⠒⠉⠈⣻⠛⠉⠀⠉⠻⣦ ⠠⣿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿ ⠀⢻⣆⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣴⠟ ⠀⠀⠉⠛⣿⡭⠥⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣩⡟⠋⠁⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠉⠳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢹⠀⠀⡼⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⣼⡦⠤⣷⡀⠀⠀⠀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠳⠶⠛⠉⠀⠀⠈⠛⠶⠶⠛⠋⠀⠀⠀⠀⠀

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⠀⠀⠀⣰⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣦⠤⠶⠶⠶⣿⠿⠛⠛⠓⠒⠲⠤⠴⠃⠀⣼⣿⣿⠄⠀⠀ ⠀⠀⠀⢿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀ ⠀⠀⢀⣼⠟⠁⠀⠀⡀⠀⠀⠀⢀⣲⣦⣀⣤⠖⣂⣀⣀⠀⠀⢙⣿⣿⣷⡄⠀⠀ ⠀⠀⣾⠏⠀⠀⠀⠀⠉⠛⢿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣴⣿⡿⢿⣿⡄⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⣀⣨⣽⣿⣿⠛⠉⠉⠉⣿⣿⣿⣿⣿⠛⠉⠀⠀⠻⣿⣿⡄ ⢰⣿⠀⠀⠀⠀⠀⠛⣻⣿⣿⡟⠙⠇⠀⠀⠀⠟⠛⢧⣝⣿⣷⣤⡑⢦⣀⠹⣿⣧ ⣼⣿⠃⣷⠀⠀⠀⣰⣿⣿⣿⠀⠀⣤⣶⣶⣦⡄⠀⠀⣿⣿⣿⣿⡛⢷⣽⣿⣿⡟ ⣿⣿⢠⡸⣷⡀⠀⣿⣿⣿⣿⠀⠀⠰⠿⠿⠆⠁⠀⢀⣿⣿⣿⡝⣿⣌⢿⣿⡟⠀ ⢻⣿⠀⢳⣿⡻⣄⠸⡿⣿⢻⣷⣶⠀⣀⣀⡀⣶⣶⣿⣯⣿⣾⣿⣞⣿⣾⠏⠀⠀ ⠘⣿⠀⠈⢿⣷⣌⡁⠀⠹⠈⠋⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠹⣧⠰⡄⢪⡙⠿⣿⣿⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⢧⠹⣦⡙⢶⣤⣽⣿⣿⠟⡟⣿⣿⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠳⢦⣿⣦⣌⢻⣿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠦⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢊⠠⠤⢄⢹⠁⠀⠀⠀⠉⠰⣂⣉⠉⣁⢢⠀⠀⠀⠀ ⠀⠀⠀⠰⢠⠁⠐⠆⠘⠁⠀⠀⠀⠀⠀⠀⠑⠂⢀⠀⢡⠇⠀⠀⠀ ⠀⠀⠀⠰⠘⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡊⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣠⡄⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠋⢁⢤⡄⠈⢃⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢇⠀⠤⣉⡡⠀⡜⠀⠀⣠⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⠁⠂⠤⡴⡽⠋⠉⠉⠙⢿⡯⠤⠐⠈⠀⠑⢄⠀⠀⠀ ⠀⠀⢀⠆⠀⠀⠀⠀⠷⠁⠀⡦⣤⣆⠀⢳⠲⣄⠆⠀⠀⠈⡄⠀⠀ ⠀⠀⡘⠀⠀⠀⠀⠄⠘⣄⠀⢣⡿⠓⠉⠁⠈⠁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠈⠒⠒⠛⢧⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⣀⢀⣀⢴⡒⡒⠯⠤⠤⢄⠀ ⠀⠀⠀⢸⠢⢀⣀⠀⣄⠀⠀⠀⢰⣨⡾⡈⢰⣹⠇⠀⢀⠤⢄⠀⢡ ⡠⠊⠁⠀⠉⠂⠀⠀⠀⠈⢋⠉⢙⢍⡁⠈⠐⠁⠀⡔⠁⠀⠀⡇⠸ ⠃⠰⠂⠀⠂⢄⠀⠀⠀⠀⠈⢄⣑⠾⢅⠀⠀⠀⢸⠀⠀⢀⠜⡠⠃ ⢆⠐⢄⠀⠀⠀⢣⠀⠀⠀⢠⠎⠀⠀⠈⠑⠤⡀⠀⠉⢉⡠⠊⠀⠀ ⠀⠑⠄⡁⠒⠐⠊⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠑⠂⠤⠜⠁⠀⠀⠀⢀⣀⣀⣴⠋⣉⠑⡶⠚⠋⠉⠙⠓⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠯⢤⣤⡉⢿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀ ⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⡳⣄ ⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⡀⢯⡽⠐⣐⠢⠀⠀⠀⣷⢸ ⣠⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡔⠁⡆⠘⡇⢀⡇⠀⠁⠀⡼⠀⣾⣹⠀⢸⠞ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠏⡜⠀⠀⠀⢸⠇⠈⠀⠀⠀⠺⠇⡰⠀⠀⠀⢸⠀ ⣄⡀⠀⠀⠀⣀⡤⠤⠀⡽⠊⣆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⣾⠀ ⠈⢳⡀⠀⠀⠁⠀⢠⠀⣄⢀⡞⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣰⠏⠀ ⠀⠀⠳⡀⠀⠀⠀⠜⠀⠀⠉⣀⡤⠖⠒⠳⣦⡴⠛⠛⠛⣥⣤⡤⠶⠞⠋⠁⠀⠀ ⠀⠀⠀⠙⢦⣄⣀⣀⣀⡠⠚⠁⠀⠀⠀⣀⡿⢧⣀⣀⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣩⠇⢠⠤⠴⠒⢚⠋⠉⠀⠀⠉⠉⢹⠀⠹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⢻⣤⣀⡴⠋⠀⠀⠀⠀⠀⠀⣸⣄⣀⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠞⠉⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⠠⣄ ⠀⠀⠀⠐⠿⣿⠃⠀⣸⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡰⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⣤⣿⡑⠶⠄⢴⠦⠀⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⢰⠂⣠⠔⠉⠉⠉⠈⠉⠑⠺⡤⢽⣀⢀⣀⣴⡟⠁⠀ ⢰⡙⡆⢀⣘⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣩⠙⢻⡍⠀⠀⠀ ⠀⠑⡽⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⡵⠛⠀⠛⢄⠀⠀ ⠀⡰⠁⣀⣇⠀⠀⠀⠀⠛⠀⠖⠒⠘⠃⠀⠀⣇⣀⡢⣮⡩⠇⠀ ⠀⠓⠒⠃⠨⠗⠠⠤⠄⠀⠀⠀⠀⠠⠤⠤⠚⠁⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣿⣿⣿⣦⣾⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣋⣽⡟⢉⣷⠞⠉⠀⠺⠛⠛⣻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣯⣵⠖⠛⢉⡠⠤⣾⡟⢀⠀⠀⠀⠙⣧⡻⢟⣿⡿⣶⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⡿⠛⠉⠉⠋⠁⠀⢰⣿⠁⢀⣿⠁⣿⡄⠀⠺⣿⣤⠉⣁⣀⠀⠀⣹⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣾⡟⠀⠀⠀⠀⠀⣸⡇⢸⣿⡀⠈⠿⣧⣌⠙⠳⠀⠈⠁⣼⡟⣿⠟⠿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢑⣿⡿⠁⠀⠀⠀⠀⠀⢻⣇⠈⠹⣷⣄⠀⠈⠛⠣⣀⣀⢀⣄⣋⣑⡛⠛⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠏⢉⣁⣠⡤⠤⢤⣀⡠⣿⡿⠀⠀⣦⣍⣷⣦⣶⣾⡿⠿⠟⠀⠀⠁⠈⠙⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣷⡀⢾⣤⡀⠉⠀⠀⠀⠀⢍⡛⢧⡀⠀⠈⢡⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠻⣷⣄⣉⣛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠻⢿⣿⡟⠃⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢿⣏⣿⣦⣍⡛⢻⣛⠛⡛⠛⠉⠀⠀⠀⠀⠀⢀⣴⠾⢚⡿⠷⠤⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⢸⣏⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠲⠷⣄⠀⣡⠾⠋⢡⡘⣦⣧⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠗⠁⠀⠈⢿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣨⡷⢦⣴⣽⣶⣿⠟⠋⠻⣦⡝⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣫⠄⠀⠀⠀⠈⠻⣦⠸⡿⢿⣿⣿⣿⣿⣿⠙⠻⠿⣿⠟⢳⣾⣿⣿⣿⣶⣒⡀⠀⠀⠛⢧⡀⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⣽⣡⠂⠀⠀⠀⠀⠀⢻⣄⠘⣄⠉⠛⠻⣿⡟⠀⠀⠀⡀⠀⣸⡅⠀⠙⠿⣿⣿⣿⣧⣤⠀⠈⢻⣆⢸⣄⠀⠀⠀ ⠀⠀⠀⢹⢇⠀⠀⠀⠀⠀⠛⢿⣿⠳⢼⣶⣤⡶⠀⠀⠀⠀⣰⡿⠐⢿⡇⠀⠀⠀⠈⠉⠻⢿⣿⣿⣧⣄⠉⠀⠉⠳⡄⠀ ⠀⠀⠀⢸⠸⣷⡀⠀⠀⠀⠀⠀⠙⣦⡈⣿⡋⠀⠀⠀⢀⣠⡿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄⡀⢧⠀ ⠀⠀⠀⢸⡄⠙⢿⣄⠀⠀⠀⠀⠀⠈⢻⣽⣷⣤⡀⠀⠞⠋⢀⢀⣀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡇⣸⠀ ⠀⠀⠀⢠⣧⡀⠀⢙⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄⣼⣿⡟⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠛⠁⠀ ⠀⠀⠀⠈⣿⠇⠀⢾⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⡤⠀⢸⡟⠀⠀⠀⠀⢠⣾⢻⣿⣿⣿⣿⡿⠟⠠⠤⣤⣀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣽⠁⣠⠏⠀⢾⣧⣤⣾⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣥⣄⣠⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⢁⣼⡏⠀⠀⠀⠀⠀⣼⡿⠋⠛⢿⣿⢿⡯⠤⠤⠖⠚⠉⠉⠙⠛⠃⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠁⠸⠿⢟⣠⣄⣠⣴⣿⢧⡀⠀⠀⠀⢀⡞⠀⠐⠀⢀⣴⡤⠤⠤⢴⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠈⠹⠽⠻⣉⢻⡓⣾⣦⠀⠀⠘⠧⣄⣀⣀⣈⠀⣀⣀⠀⠀⠉⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠦⠤⠖⠒⠒⠲⠦⠤⣾⣾⣽⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣞⠉⢡⠐⠒⠈⠀⠒⠒⢎⠐⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠥⠃⠀⣟⠊⠀⠸⠀⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⡄⡆⠀⠀ ⠀⢰⠸⠀⠀⠀⠀⠠⠤⠤⢄⠀⠀⠀⠀⠀⢀⠃⠧⡀⠀ ⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠄⡀⢨⠁⠀⠀⠈⡄ ⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⢀⠇ ⠸⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡎⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠒⠂⠉⠀⠃⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⢸⢸⠀⠀⠀⠀⠀⢲⠤⠤⡔⠒⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⣰⢠⠀⡀⠀⠀⠀⡦⠀⠀⢇⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠈⠉⠉⠈⠈⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⠶⠶⠦⣄⠀⠀⠀ ⠀⣀⣤⣄⡀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠈⠉⠺⠁⣤⣀⠀⠈⡇⠀⠀ ⡼⠉⠀⡀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢀⣰⠇⠀⠀ ⡇⠀⢸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀ ⠙⠦⣤⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡶⢀⣠⣴⡄⠀⠀⢧⠀⠀⠀ ⠀⠀⣼⠀⠀⠠⢤⣤⣄⣈⠉⢁⡤⢦⡄⠛⠛⠤⠄⠀⠀⠘⣿⡄⠀ ⠀⠀⢹⠀⠀⠐⢈⡭⠛⠁⠀⢀⡹⠞⠓⠃⢶⠖⡄⠀⠀⠠⣾⠃⠀ ⠀⠸⣟⡃⠀⠀⠈⠀⠀⣠⠒⢉⣠⠤⢤⠀⠀⠀⢧⠀⢀⡞⠁⠀⠀ ⠀⠀⠻⢥⠄⠀⠀⢠⠎⠙⢠⠋⠰⢾⡁⠀⢀⠀⡸⢀⣾⠴⠒⣲⠄ ⠀⠀⠀⠈⠉⠲⣄⠘⠦⢴⣽⣀⣀⣀⡱⠤⠞⣫⠕⠋⢀⡠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⡶⠤⠄⠀⠀⠀⠀⠀⠈⠁⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⣠⠔⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡤⠤⠿⠛⠚⠋⠉⠙⣆⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠥⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ฅʕ • ᴥ • ʔฅ

⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠦⠤⠤⢤⣤⣀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⣀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠉⠉⠙⠻⣍⠛⠒⠶⣤⡀⠀⠈⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣶⣦⣝⣧⣀⣠⡄⢿⣆⡀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢠⠏⡴⠋⠀⠀⠈⠻⡿⠒⠚⠛⠻⢿⣆⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⢀⣴⣏⡾⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢻⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢿⣿⣽⡟⠛⢛⣾⣷⣖⠒⢶⡷⠶⠤⢤⣀⣾⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢧⣰⣿⣿⣿⣿⣷⡞⠙⢿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣅⣬⣿⣽⣿⣯⣼⡟⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠀⠀⠀⠀⡀⠀⠉⣽⠇⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣴⣦⡤⠖⠛⠋⠉⠉⠉⠉⢉⣿⠀⠀⠀⠀⠀⠀⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣍⣀⣤⠴⠶⢾⡟⠓⢲⡟⢻⡇⠀⠀⠀⠀⠀⢰⣧⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡟⠀⠸⣇⠀⠀⠀⠀⣠⡿⠿⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡟⠀⠀⠀⠙⠲⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡉⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢸⣷⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢶⡶⢴⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⡾⠕⡛⣼⠏⠀⠈⢅⡯⢷⢤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣒⡼⠉⠉⠉⡄⣾⠀⣾⠸⢄⠘⠷⣩⣤⣀⡽⠁ ⠀⠀⠀⠀⠀⠀⢠⢪⡿⠀⠀⠀⢐⡇⠙⢦⡈⠛⢆⣀⣀⣛⣛⢢⠀⠀ ⠀⠀⠀⠀⠀⢠⡖⣥⡒⠒⠀⠒⡸⣇⠀⠓⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢷⡻⣮⣭⣀⣀⠀⠈⠉⠁⢈⣻⣟⠉⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⢹⡛⣿⣶⣶⣶⣶⣶⡦⠦⡀⡫⠖⠕⣼⡡⡀⠀⠀⠀⠀⠀ ⠀⢐⡋⠀⠀⢳⡘⣿⣿⣿⣿⡿⣧⣤⢾⣵⣿⣟⠉⠙⠲⡕⠠⠀⠀⠀ ⠀⢸⠄⠀⠀⢀⣣⡐⡌⠛⠿⠃⠀⡄⢨⡄⠙⠻⢿⣧⣄⡙⠆⠧⡀⠀ ⠀⢸⢦⡀⠀⠀⠙⣌⣛⠋⠀⢀⣰⠇⢸⡇⠀⠀⠀⠉⠛⠻⣦⣀⡸⠀ ⠀⢸⠈⠳⠄⠀⠀⠈⢻⣷⣦⡈⣡⡤⠞⢤⠀⠀⠀⠀⠀⠀⠙⢿⠵⠀ ⠀⠨⡇⠐⡦⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⡏⡠⠣⣄⣠⣞⣿⣿⣿⣯⣥⣽⢓⣀⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⣼⡅⠀⢀⣴⠛⠉⠛⡻⠒⠒⢉⠀⢉⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠉⠿⢫⢳⣵⡄⠀⠣⠄⠠⠭⠄⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠒⠀⠉⠀⡾⢷⣄⠀⠉⠀⠀⠐⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠜⠀⠀⠀⠀⠀⠁⠀⢙⣷⡔⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⢶⢍⠙⣧⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡏⠀⠀⣙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠈⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠈⠫⠖⣨⣟⠻⣦⠀⠀⠀⠀⠀⠂ ⠡⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢍⠀⠤⠇⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀ ⠀⠈⠄⠀⠀⡐⠂⠢⠄⣘⣬⣐⡊⠄⢀⣀⣀⣉⡠⢲⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⠀⢃⠀⠀⢸⠀⠈⠑⠚⠭⠥⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⡜⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠈⠐⠤⢀⡀⢀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⢤⣠⡤⠀⢒⣲⣬⣭⣭⣭⣶⣤⣤⡤⠤⠒⣼⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠲⡟⣉⣙⣲⠔⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣌⡳⣴⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣘⠟⠀⠀⠀⢠⡾⠛⢉⠛⡿⡟⡳⢬⣭⣴⡌⠻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢞⣭⠀⠀⠀⠀⢸⣇⠫⠉⢓⡶⠃⢉⢶⣭⡽⢀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣇⣾⡿⠀⠀⠀⠀⠹⢿⣿⣿⡏⠀⠁⠀⠀⠹⡀⠈⠉⡟⠀⠀ ⠀⠀⠀⠀⣠⣶⠞⣽⣿⡕⣡⠀⠀⠀⢀⣠⣭⣿⠇⠀⡴⣶⢾⣶⡽⡄⠀⡇⠀⠀ ⠀⠀⣴⣿⣿⠇⣸⣿⣿⠞⣡⠞⡄⠀⠞⠻⠿⢿⣧⣀⢻⡏⣾⡿⠇⣷⣾⡇⠀⠀ ⢠⣾⣿⡟⠁⠀⢼⣿⣿⡟⣡⡾⠃⣠⢶⣶⣦⣜⠿⣿⡦⠥⠿⢋⣰⣿⣿⣿⡄⠀ ⢸⣿⠏⣠⡀⠀⣿⣿⣿⣿⣿⡤⣐⡁⢻⣿⣿⣿⡿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢹⣟⣼⣷⣿⡀⣻⣿⣿⣿⣿⣿⡿⢠⣄⡄⡁⠈⠘⢁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠨⠿⡿⢿⣿⣷⣿⣿⠿⣿⣿⣟⣴⣼⣿⣇⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀ ⠀⠀⠀⠈⠹⠉⠀⠀⠀⠘⠙⢻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠿⡿⠇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠟⢻⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠂⠀⣐⣾⣿⣄⣠⡿⢺⣮⣵⣤⣤⣄⠀⠻⣿⣄⠀⠹⢿⣷⣾⣽⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠥⠀⢀⣤⡴⠞⠿⠋⠉⠉⠀⠀⠀⠀⠀⠉⠁⣿⡄⠀⠹⣷⣀⠀⠈⠁⠉⠛⢿⣿⣿⣦⡀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⡷⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠙⣿⣷⣀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⣹⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠔⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷⡄⠀⢹⣿⣾⣿⣶⣄⣴⣿⣿⣿⢏⠇⠀⣿⣷⣍⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⡤⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣷⠀⢸⡏⢉⡩⢿⣿⣿⣿⣿⡏⣸⠀⠀⡇⢿⣿⣦⡙⢷⡄⠀ ⠀⠀⠀⢀⣤⣴⡾⢻⠟⠋⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣆⣼⠃⠀⢧⠙⠋⣹⣿⣿⠁⡏⠀⠀⡇⢸⣿⣿⣷⠈⢿⡀ ⠀⢀⢞⣫⡟⡽⠁⡏⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢻⣿⠀⠀⠸⡀⠰⣻⣿⣿⣶⣥⣄⣸⣷⣼⣿⡇⢿⡇⠸⣇ ⠀⢀⡾⠋⣰⠃⢰⢃⣾⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⣧⠀⠀⠀⣧⠀⢩⣿⣿⣿⠟⠿⣿⣿⠋⠉⠀⠀⣿⠀⣿ ⢰⡿⠁⢰⠃⢀⣾⣼⣿⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⢾⣿⡏⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠩ ⠸⣷⣔⡋⠀⢸⢘⣿⡿⢸⡇⢀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠐⠿⠛⣿⡟⣿⣻⣟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣻⣿⣿⣦⡼⣿⣿⠀⠀⠀⠀⠘⠇⠀ ⠀⠈⠩⢹⡗⠻⣼⣿⡇⠀⠀⢾⠿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣝⣛⣡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠚⠉⠿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢹⣿⣇⠀⠀⠀⠀⠛⣿⡿⡇⣠⣾⡄⠀⠀⠀⠀⠀⠒⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣚⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠸⡿⡄⠀⠀⠀⠀⠀⠀⠛⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣽⡿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⡀⠀⠀⢑⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣰⠋⠀⢀⡴⢛⣿⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⢸⡇⠁⢀⠀⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠁⢀⡾⠋⠀⠀⣿⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⢨⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢻⡄⠀⠀⣠⣿⠀⠀⠀⢠⣆⡟⠀ ⠀⠀⠀⢘⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⣶⣖⣒⣖⣲⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢠⠟⠀⢀⣴⠏⣿⠀⠀⠀⣿⣹⠇⠀ ⠀⠀⠀⢸⣹⡆⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢀⢀⣠⣤⡴⠋⠁⠐⣿⠀⠀⢰⣿⡟⠀⠀ ⠀⠀⠀⠀⢿⣇⠀⢸⣿⣟⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣵⣿⡟⠉⠀⠀⠀⢰⣿⢀⠀⣸⣿⡇⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠀⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣴⠛⠑⠀⠁⠀⠀⠀⠀⢸⣿⣽⡿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⣿⣿⣿⡇⠈⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢿⠀⣻⡿⣷⡷⠀⠀⠀⠈⠉⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⢻⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠶⣾⣿⢿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣼⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡯⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠗⠲⠤⣄⡀⠀⢀⣿⠃⠀⢻⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣷⣼⢃⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠠⠈⢳⡄⣼⡿⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠃⠀⠙⣆⣀⡀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡹⣾⠇⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣩⡾⠋⠀⣀⠴⠊⠁⠀⠉⣿⠋⠂⠄⠤⠀⠀⠸⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠧⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡾⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡄⠀⠀⢠⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⣸⣧⣾⠁⠀⠀⠀⠀⠀⠀⣾⡿⢻⣿⣄⣧⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⣿⢷⣶⢶⣤⠿⢷⡷⢾⣟⡿⢻⠷⢶⡶⣶⣶⡶⠾⣿⡷⣿⡇⣤⣾⣶⡶⣟⣷⢶⢦⡀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠿⣼⡿⣿⠿⡿⠿⢦⡼⣷⡿⢯⣷⠟⠶⠿⠿⠿⠿⢷⡿⢿⣿⠍⣇⠻⠿⠿⠭⠿⡿⠿⠿⠿⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⣧⠞⠑⠒⠒⠛⠛⠋⠁⠀⠀⠀⠉⠛⠙⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⡀⣀⣠⣤⣤⠶⠶⠒⠒⠛⠛⠻⠷⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢖⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⣁⠀⠉⠛⣷⣦⣶⠾⠋⠉⠡⠤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣶⠶⠶⠚⠉⠀⠀⣽⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⡿⠟⠛⠷⢶⣤⣄⣀⣀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠘⢷⣄⠀⣠⣶⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⢤⣤⣶⣶⣶⠿⠋⠁⠀⠁⠛⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⠻⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠛⠻⣿⣿⣿⡿⣿⣿⣿⣇⠈⠉⠛⠋⣁⣀⠈⠻⢿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⢠⠈⠙⢿⠇⡏⠘⣇⠙⠲⢶⣶⣿⣛⣛⣧⠄⠀⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣰⡟⠻⠃⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠐⣶⠚⠋⠉⣳⣦⣬⣴⣇⡀⠉⠳⢦⣴⠟⠛⠉⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⣡⣼⣾⡄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣆⣈⡛⠩⠉⠁⣨⡿⠟⢁⣀⠀⢠⠞⢿⣷⣶⡾⠛⢺⢤⢀⢀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣾⠏⠀⠐⠋⠉⠂⠀⠀⠈⠻⡿⠁⠀⠀⠘⠛⠹⢼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣤⣽⣿⣿⠟⢀⠄⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣠⣴⣿⠇⣼⣿⡿⢋⣴⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣩⣸⣿⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣄⠹⣷⡀⠀⠀⠀⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⢁⣾⣿⣿⣷⡿⢁⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣿⣿⣿⡋⠀⠀⢠⣿⠛⣿⡿⠻⣿⣿⣿⣷⠹⣷⠀⠀⢀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣫⣴⣿⠏⢀⣴⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⢂⠀⠀⢿⣿⡟⢳⣶⣿⣿⢻⣿⠀⢹⡶⣠⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠃⠀⢰⣿⣿⣿⣿⣿⡟⢁⣴⣿⠏⢀⣼⡆⠀⠀⠹⠇⠁⠻⠙⠟⠇⣿⣿⣿⢠⣄⠈⢿⣿⡄⣿⣿⣿⢸⠇⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣿⠟⠁⣠⣿⡿⠃⠀⢀⣠⣤⣤⣤⣄⣀⠀⢻⣿⣿⣿⣿⣦⣈⠛⢃⣿⡿⠿⠂⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⡟⢁⣠⣾⣿⠟⠁⠀⣰⡿⠛⣿⣿⣿⣿⣿⣯⡬⠛⠿⠿⠿⠿⠿⠿⠿⠛⠷⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⢸⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠖⠂⠀⠼⠋⢀⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⢸⣿⣿⣿⠟⠀⣰⡞⢠⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣋⣠⣤⡄⠈⠰⢻⡿⣿⢿⣿⠿⣻⡿⢛⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢸⣿⣿⡟⢀⣾⣿⣱⣿⡞⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠇⠀⡀⠀⠀⠁⠚⠁⠘⠋⢠⡾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀ ⠼⣻⣿⢡⣿⣿⣿⣿⣿⣷⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣀⡿⠀⣠⠄⠀⠀⠀⠀⠀⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠣ ⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⡄⣿⣿⣿⡇⢠⣿⡀⣾⢣⣾⣰⣆⢿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠃⠀ ⠀⠺⠟⠋⣿⠟⠛⣽⣿⣿⣿⣿⣿⣿⢿⡿⠋⠘⣿⣿⣿⣿⣿⣇⣾⣿⣷⣿⣿⣿⣷⣄⢿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠉⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠟⠛⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠹⢿⣿⡝⠿⣇⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⣿⣿⠿⣿⣿⡿⢻⣿⣿⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠘⠋⠀⠈⢿⠇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⠖⠒⠒⠦⢤⣀⡤⠤⠤⠖⠒⠒⠲⠤⠤⣄⣀⡤⠖⠒⢢⡀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠲⣄⠀⣧⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢔⠀⢙⡟⢡⢄⡀⠀⠈⠳⣼⠀⠀ ⠀⣠⠻⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠓⠒⠒⠋⠙⠒⠚⠳⢤⡀⠀⠘⣆⠀ ⢠⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠸⡄ ⡞⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣧ ⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸ ⡇⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠾⠏⠉⠱⠀⣀⢀⢀⠐⠾⠉⠩⢆⢿⠀⢸ ⢧⠀⠀⠀⠀⢷⠀⠀⠣⣀⡠⠃⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠢⢸⠀⣸ ⠈⢦⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢠⠏ ⠀⠀⢓⢤⣀⠀⠀⠙⠲⠤⣄⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠶⠚⣁⠴⠋⠀ ⠀⢠⠋⣇⠈⣩⠖⠒⠶⠤⠤⠤⠤⠤⠿⠦⠤⠤⠴⠖⠒⢿⠉⠁⠀⠀⠀ ⠀⠸⡇⢸⣰⠟⠠⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⢳⣠⠃⠀⠀⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠴⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⣀⡀⣠⠔⠒⠲⢤⡀⠀ ⢀⠖⠉⠉⠑⣄⠴⠚⠉⠀⠀⠀⠀⡠⠊⠒⠠⡤⠉⣓⣦⣀⠀⠀⠹⡄ ⠏⠀⠀⠀⠀⢹⡀⠀⠀⠀⣀⠔⠈⠢⠀⠀⢀⢁⣀⣀⣀⣈⣳⣀⣴⣷ ⠀⠀⠀⠀⠀⠀⣇⣠⣔⣬⣤⣶⠒⠒⢃⠀⠈⡅⠈⣿⣿⣧⣀⣻⠿⡿ ⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣿⣷⣶⡏⠀⠀⠘⢄⠈⢻⣿⣿⣿⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⢄⠀⠙⠿⠿⠿⡻⠁⠀⢂⣀⠔⠉⠀⠀⠠⠍⠺⡁ ⡄⠀⠀⠀⠀⠀⡧⠄⠁⠒⠠⠐⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⠀⢡ ⢣⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢣⠀⠀⠀⠀⠀⠁⠀⡜ ⠈⣆⠀⠀⠀⠀⡇⠈⠙⠒⣲⣤⢤⠤⢤⠤⠖⠒⠓⠤⡀⣀⠀⡤⠊⠀ ⠀⠸⡄⠀⠀⠀⡇⠀⠀⣸⠁⢀⡛⠂⠈⢏⢳⠀⠀⠀⡇⠀⠀⡇⠀⠀ ⠀⠀⢁⠀⠀⢸⠀⠀⠀⡇⠀⢢⠃⠸⣉⠇⣹⠀⠀⠀⢃⠀⠀⡇⠀⠀ ⡀⢀⡜⠀⢠⠇⠀⠀⠀⡇⠀⢺⠄⠀⠀⡞⡇⠀⠀⠀⠸⡀⠀⣇⠀⠀ ⠛⠂⠤⠐⠁⠀⠀⠀⠀⡇⠀⠈⡆⠀⢀⠇⡇⠀⠀⠀⠀⠙⠦⠈⠱⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢱⠀⠆⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⣀⡤⢀⡠⠔⠂⠉⠉⠁⠒⢡⡄⠘⠄⠀ ⠰⡁⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀ ⠀⠑⠰⠀⠀⠀⠠⡄⠠⠖⣴⠖⠀⢠⡀⠀ ⠀⠀⣀⠀⠉⠟⠃⢀⠳⠃⠰⠄⠀⠀⡟⠀ ⠀⠀⢯⡀⠀⠠⠒⡅⠂⡔⠀⠀⣀⡦⠄⡄ ⠀⠀⠀⠀⠂⢀⣐⠂⠀⠒⠈⠇⣉⠀⠉⠀ ⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢈⠁⠀⠀⠀ ⠀⠀⠀⠚⠂⠀⡇⠀⠀⠀⠀⠀⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠁⠀⢠⣤⠠⠤⡀⢢⠀⠀ ⠀⠀⠀⠀⠀⡘⢀⠃⠀⠀⠀⠀⠑⠤⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⣃⡔⠁⡇⠀⣀⣀⣀⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠱⡀ ⠀⠀⠀⠀⠀⢸⠏⠁⡠⠛⠙⢦⠀⠀⠈⠉⠙⢤⡀⠀⠀⠀⠀⢰⠁⠀⣠⡇ ⠀⠀⠀⠀⠀⢸⢀⠎⣰⡞⢢⢸⣠⣤⣄⡀⠀⡠⠛⢦⠀⠀⢀⡆⠀⠀⠛⡇ ⠀⠀⠀⠀⠀⢸⣿⠀⢿⣿⡿⣻⣿⣿⣿⣿⢎⣴⠒⡌⡆⣠⣿⠀⠀⠀⢰⠇ ⠀⢀⠔⢉⠉⠑⣟⢷⡀⢠⠠⣬⢿⣿⡟⠋⢾⣿⣿⢃⣗⣹⢻⣀⢠⢄⠟⠀ ⠀⣧⡶⠤⠤⡀⢸⠦⡻⡻⢇⠙⡿⠶⢏⣙⠦⡬⠋⠀⠈⠉⢸⣿⣿⣡⠄⠀ ⢠⣿⠯⠁⢺⠿⠯⠔⠋⢪⠙⠛⠶⠶⢳⣾⠟⠀⠀⠀⠀⢰⠬⣿⣏⠀⠀⠀ ⠀⡟⠀⡰⢏⣀⣀⣀⣴⠃⠀⠀⠀⠀⡏⠀⢀⡠⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠧⠔⠁⠀⠉⠉⢁⡏⠀⠀⠀⠀⠀⣇⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠷⢧⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠞⠳⢄⠀⠀⠀⠀⣠⣋⣀⢨⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⡹⡃⠒⠉⠉⠀⠘⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠐⠠⢀⣀⠤⠐⠂⠀⠒⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡠⠤⠤⠤⣀⠀⢣⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠉⠚⢆⠀⠀⠀⠀⠀⠐⠒⠠⢀⠀⠀ ⠀⠀⠀⣀⢴⠁⠀⠀⠀⠀⢀⡠⣂⠭⠓⠒⠒⠒⠠⠵⣤⠲⠬⠉⠛⠋⠉⠼⢷⡄ ⠀⠀⡜⠁⠈⠀⠀⠀⢰⣚⣒⣈⣀⠠⢤⡴⣶⣤⡈⠉⢱⠄⠒⢀⣽⣿⣿⣍⠉⠻ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠨⡑⠤⣀⣾⣿⣿⣽⠿⠤⡢⠤⠀⣸⡿⠿⠶⠿⣦⠎ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⢒⡲⠎⠉⠀⣀⠀⠀⠀⢀⡠⠔⠁⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠉⠋⠉⠀⠑⢄⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⡰⠉⣀⣀⣉⠉⠐⠒⠂⠤⠤⠄⠀⠀⢀⣀⠠⠤⠐⠊⡽⠀ ⢃⠀⠀⠀⠀⠀⠀⡄⠣⠤⠤⠤⠄⣈⣉⠁⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⡪⠀⠀ ⢈⣦⣀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⢒⡲⠒⠈⠀⠀⠀ ⠀⠊⠑⠫⢕⡒⠠⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠀⠀⠠⠤⠤⠤⠐⠒⠉⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⠖⠁⠀⠀⠀⠀⠈⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠗⠒⠠⠤⠐⠀⠉⠐⡨⠄⠠⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠊⢀⠀⠰⠘⡜⠑⡲⠊⠀⠀⠀⠀⠈⠒⠠⡘⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠂⠠⠃⠀⢸⠊⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡞⠄⠀⠀⠀⠀ ⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠸⣀⠀⠀⣀⠈⠁⢀⣀⠀⠀⠀⠠⠃⠘⡄⠀⠀⠀ ⠀⠀⢀⠇⠀⠸⡀⠠⠀⠀⠀⠈⢆⠀⢩⠁⠀⠀⡄⠀⠠⠞⠁⠀⠀⠇⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⢣⠀⠆⠀⠀⠀⠀⠑⢶⣀⠠⢀⢰⡐⠁⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠱⣰⠀⠀⠀⠀⠀⠀⠳⢥⠦⠊⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⠀⢰⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀⠐⠊⠰⠀⠀⠀⠀⠀⠀⠈⢇⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⢀⠜⡄⠀⠀⠀⠀⠀⢘⠀⠀⠁⠣⡀⢀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⡠⠊⠀⢣⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⢈⠞⠀⠀⠀⠀⡸⠀ ⠀⡇⠀⠀⠀⢀⡔⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢂⠀⠆⢰⣧⠀⠀⠀⢀⠔⠁⠀ ⢸⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢂⢰⠀⠀⠑⠑⠒⠊⠁⠀⠀⠀ ⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠓⠀⠀⠤⠤⠼⠾⠀⠀⠀⠀⡤⠠⢤⣶⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠀⠀⠀⠀⠀⢀⡠⠔⣪⠽⠛⠒⢄⠀ ⠉⠻⢍⠉⠑⠒⠒⠤⢄⣒⠒⠢⢤⣝⣷⣄⠀⢀⡴⢋⠔⠋⠀⠀⠀⠀⠈⢇ ⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀⠭⠶⠄⠈⠛⠛⣳⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢙⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣀⡰⠃⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⣯⣀⠀⠀⠀⠀⢀⡤⠒⠉⠙⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⣠⠋⠀ ⠀⠀⠀⠀⢹⡉⠂⢠⡆⠀⢀⣤⣖⠀⠀⠀⠀⠀⢀⠘⢤⣀⣀⡤⠊⠁⠀⠀ ⣀⣀⣀⣠⡼⠯⣱⣾⣿⣶⡁⢈⡝⠀⣀⣀⣀⠠⠤⡽⠭⠍⠐⠃⠀⠀⠀⠀ ⠇⠤⠤⠿⣿⣿⡛⡟⡟⠁⢾⠛⢻⢟⠒⡲⠖⠒⢶⡁⠠⠤⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⢀⡝⠋⠛⡟⢿⣿⠮⠶⣴⡿⠟⠳⠶⠭⢑⡛⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⣰⡧⠊⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⢺⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢛⠚⠋⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢰⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢤⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢰⠁⠀⢸⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠦⠮⠀⠀⡜⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢆⠀⠱⡄⠀⠀⠀⠀⢀⠼⣴⢀⠀⡄⡀⢺⠀⠀⠀ ⠀⠀⠀⢀⠨⠦⠀⠈⠦⠄⠧⡀⠀⠀⠀⢸⠐⠉⠋⠁⠉⠊⢀⠇⠀⠀ ⢀⡠⡜⠁⠀⠀⠀⠀⡤⢄⠠⠜⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⠸⡀⠁⠀⢠⣀⠀⠠⢅⡉⠉⠈⣼⡀⠀⢘⡄⡄⢠⠀⣄⡄⠀⠘⠙⡄ ⠀⠈⠉⠒⠒⠚⠒⠒⠒⠓⠒⠚⠊⠀⠀⠈⠒⠓⠚⠒⠙⠒⠒⠒⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠠⠄⠠⠀⠀⠀⠄⠦⠀⠠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀ ⢀⡤⠔⠦⣄⠤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠓⠿⣿⡎⡆⠀⠀⠀⠀ ⡎⣼⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⠀ ⠙⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠃⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣀⣀⡀⠀⣾⣿⠴⠀⠀⠀⠀⠁ ⢧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠀⠀⠀⠀⢀⣬⡢⢀⣀⠀⠀ ⠘⣆⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠟⡷⠉⣦⠏⠀⠀ ⠀⠈⠲⣄⡀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⢀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡨⠟⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠁⠘⠦⣀⣠⠞⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⡄⠀⢀⡆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⣱⡄⡄⠇⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠉⢳⣿⣟⣟⠉⠘⠁⠀⠀⠞⠋⠑⡄⠀⠀ ⠀⠀⠀⢀⣴⣶⣷⣶⣶⣦⣵⣤⣄⡀⠀⠑⠂⠋⣠⣄⡀ ⠀⠀⢠⣾⣿⣿⢯⣷⣷⣮⣿⣿⣿⣿⡄⠀⠀⠀⠙⠋⠀ ⠀⢀⣿⣿⣿⣿⣞⡯⠯⣏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⢥⣄⡀⠀⢀⣀⡛⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠚⠉⢣⠚⠁⠀⠈⠚⢁⣀⠀⠑⡤⠇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠊⠀⠄⡇⠀⣰⣯⣷⡄⣼⣿⣷⡄⠸⣄⠢⠀⠈⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠰⡟⢇⠀⢻⣿⣿⠇⠿⣿⡿⠁⢠⠋⡆⠁⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠀⢸⡈⠒⢤⠤⢒⡺⠿⣒⠤⢴⢃⡾⠀⢠⠖⠁⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⣄⠀⢾⠘⡄⠀⠈⠻⣶⣾⠋⠀⠀⡸⢠⢇⡇⠀⢠⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⡷⣌⠒⠤⢀⠤⠥⠤⢴⡪⠔⢇⠈⠁⢠⠃⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠉⠑⠦⢄⡀⠴⠋⠀⣠⣎⣀⠔⠁⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢊⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢌⠢⡀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡎⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠘⡦⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⡄⠀⠀⠀⢀⡬⣦⠘⡃⠀⠀⠀⠀⠀⠰⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⢱⢀⠀⠀⠀⣯⠙⠈⣇⠀⠀⠀⠀⢀⠇⡘⠀⠀⡇⠀⠀⠀⠀ ⠀⢀⠤⠒⠉⡠⢦⠊⠈⠀⠀⠀⢸⠄⠤⡞⠀⠀⠀⠀⣞⠀⠀⠀⠀⠧⢀⡀⠀⠀ ⡼⠋⠁⠀⠀⠀⡃⠆⠀⠠⠀⠀⢸⠀⢠⡁⢀⠀⠀⠠⡈⢇⠀⠀⠀⠉⠑⠪⡑⠄ ⠳⣀⠀⣀⡤⠖⠓⠦⠤⠴⠤⠤⠊⠀⠈⠣⣄⣇⣀⣠⡯⠞⠢⣄⡀⠀⠀⢀⣱⠜ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣄⣀⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣸⣄⡀⠠⠤⠤⠄⠀⠀⠠⢤⣤⣀⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⣭⠭⠭⠤⠤⠤⠤⣍⣉⠳⣄⣀⠤⠴⢒⣊⣉⡭⢭⣍⣁⣒⣒⡿⣦⡀⠀ ⠀⠀⠀⠀⢀⡴⠚⢹⠁⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⣩⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣻⠖⠚⠉⠉⠀⠀⢀⣀⣀⣀⣀⣈⣉⣻⣿⣀ ⠀⠀⠀⢠⠏⠀⠀⣾⠀⠀⠀⠀⠀⠀⣶⡛⠓⠒⠉⠀⠀⣀⣀⡤⠴⣶⣶⣿⣯⣍⡉⠀⠀⠈⢳⠴⠒⠒⠉⠉⣽⡿⢿⣿⣿⣦⡀⠈⠉⢻ ⠀⠀⢰⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣯⡉⠉⠁⠀⢠⣾⣿⣴⣿⠟⢿⣿⣆⠀⢠⠇⠀⠀⠀⠀⢸⣿⣿⣿⣟⢻⣿⣷⠀⢀⡼ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣈⠓⠦⢄⣸⣿⣿⣿⣿⣷⠾⠿⠟⠒⣩⠗⠒⠒⠤⠤⠿⠿⠷⠿⠿⠛⠛⠛⣿⠟⠁ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⣴⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠲⢤⣀⣀⣀⣀⣀⠤⢴⡊⠁⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠛⠒⠒⠦⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣻⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠐⠶⠶⠶⠶⠦⢤⣄⣀⣀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⣰⠟⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠘⠦⠤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠉⠉⠙⠛⠒⠒⠲⠶⠶⠶⠤⠤⠤⠴⠶⠶⠒⠒⠒⠛⢻⡄⠀⠀⠀ ⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠼⠋⠀⠀⠀⠀ ⢠⣼⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠠⠈⠛⠶⣭⡙⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣈⡉⠙⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣶⠾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠋⠁⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠴⠶⠶⠖⠒⠒⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣛⣋⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠋⠉⠉⠉⠉⠙⠛⠒⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠛⠷⣄⡀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢿⡀⠀ ⠀⠀⠀⠀⠀⣠⣿⣷⣦⣤⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠈⠙⣦⡀⠀⠙⠓⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢿⠀⠀⠀⠀⢿⠀ ⣀⣀⣀⣰⣟⠻⠿⠿⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⡇⠀⠀⠀⢸⡆ ⢿⡍⠉⠉⠙⢶⣤⣤⣀⣀⣤⣤⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⢉⣿⣿⣿⣶⣤⠀⠀⢈⡇⠀⠀⠘⡇⠀⠀⠀⠸⡇ ⠀⠻⣦⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠸⡿⠛⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⣿⣿⣿⡿⠙⢷⡀⣸⠇⠀⠀⣠⣇⣀⣀⡀⠀⡇ ⠀⠀⠈⠻⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⠃⢸⡟⠉⢻⡿⠿⣦⡀⠀⠀⠀⠻⢦⣄⣀⣉⠁⣀⣀⣼⣿⡟⠀⠀⢸⠋⠉⠉⠉⠉⣿⡇ ⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣤⣼⡀⢀⣾⣀⣠⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢠⡿⠀⠀⠀⣿⠀⠀⠀⢀⡼⢻⡇ ⠀⠀⠀⠀⠘⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠐⣿⣤⡤⠶⠋⠁⣼⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⢶⡟⠀⠀⠀⠀⢠⡟⠙⣷⡀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⣦⣄⡀⠀⠀⠉⠙⠛⢲⣶⣶⠦⠤⠴⠶⣶⠶⠛⠛⠋⠉⡿⠀⢠⡟⠀⠀⠀⠀⣠⠟⠀⠀⠘⣷⡀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⣼⠁⠈⠛⣷⣄⡀⠀⠀⣼⠁⠹⣧⠀⢀⡾⠋⠀⠀⠀⠀⠀⣷⠀⠻⣦⣄⣀⣠⡾⠋⠀⠀⠀⠀⠘⠷⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⢻⣴⠇⢀⣿⠈⠙⠓⠚⣿⠀⠀⢹⣶⣿⠿⠛⠛⣷⠀⠀⠀⠘⢷⣦⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣿⠀⠀⢸⡟⠁⠀⠀⢀⣿⠗⠲⠶⣤⣄⣸⡇⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⠶⠟⠻⢶⣤⣀⣀⣴⡏⠀⠀⢸⡆⠀⠀⠀⣼⠃⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠻⠶⠶⠿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣄⣀⣀⣤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀ ⠀⠀⡇⣿⠟⢁⣴⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⢄⠀⠀ ⠀⠀⢃⢻⣶⣿⣿⡟⠉⠁⠀⣀⣀⡀⠀⢀⡤⠤⢷⡀ ⠀⠀⢸⢸⣿⣿⣿⡇⠐⠊⠉⠉⠉⠉⠀⡌⠀⠀⠀⣧ ⠀⠀⢸⠸⣿⣿⣿⣷⢀⣀⣀⣀⣀⡤⠀⡇⠤⠔⠚⢹ ⠀⠀⠀⡆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠏⠀⢀⠇ ⠀⠀⠀⡇⣿⣿⣿⣿⡆⠀⢯⣒⣒⣲⡶⠊⠀⢀⡞⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⡇⠀⠀⠙⠭⠒⠓⠂⣠⠎⠀⠀ ⠀⠀⢠⠃⣿⣿⣿⣿⣿⠀⠀⢐⠒⠠⠤⠞⠁⠀⠀⠀ ⠀⢀⡞⢠⣿⡏⠉⢻⡿⢍⢩⢟⣦⣀⡀⠀⠀⠀⠀⠀ ⢠⠎⣰⣿⣿⡇⠀⠈⠷⡀⠼⠿⠘⢦⣱⠀⠀⠀⠀⠀ ⡎⢰⣿⣿⣿⣧⠀⢠⠽⠕⠀⠒⠒⠊⠙⢢⠀⠀⠀⠀ ⠳⡘⢿⣿⣿⣿⠀⠸⡄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠈⠑⡝⣿⣿⠐⠒⣿⣆⠀⠀⠀⠀⠹⣳⠀⠀⠀⠀ ⠀⠀⢀⢇⡿⠿⠀⠀⡿⠿⣧⠀⠀⠀⠀⢹⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠙⠳⡄⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡿⠃⠀⠈⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠤⢤⡿⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠛⠙⠳⢾⡁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠳⡄⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⣾⡤⢀⠀⢠⣤⡀⠀⠉⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢹⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠯⠉⠱⠟⠶⠌⠹⠭⠇⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠖⠒⠛⠓⠀⠀⠈⠉⠉⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣄⡼⣆⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀ ⣰⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⣰⠆⢀⡼⢦⠀⢀⡘⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀ ⢻⡄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢸⡆⢠⡄⠀⣤⠀⢠⠀⣠⡄⠀⠀⠀⠃⠘⡇ ⠀⠙⠒⠲⣄⣀⣀⣀⣹⣄⣀⣀⣀⣀⣹⣀⣀⣠⣴⣋⡼⠁⠀⠀⠀⢸⣅⣸⣇⣀⣿⣀⣸⢾⣍⣀⣀⣠⣄⣠⠾⠃ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠀⠀⠐⠒⠂⠐⠒⠂⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⡴⠃⠈⠀⠀⠀⠤⢀⠀⠀⠀⢸⠦⢄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡠⠊⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠁⠢⡉⠢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⡠⠄⠒⠒⠒⠒⠀⠈⠘⡀⠀⠀⠀ ⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡤⠂⠁⠀⠀⠀⠔⢒⣀⡀⠐⠂⠈⢄⠀⠀ ⠀⠀⠀⠀⠀⠉⡛⠿⣿⣿⡇⠀⢠⠊⠣⣀⠔⠓⡀⠀⠀⣼⢶⣶⣦⠖⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⢸⠙⡄⠀⠙⣧⣀⠈⠒⠀⠑⢤⢶⣿⡦⡀⠀⠉⠉⠁⠀⠀⠀⡗⠀ ⠀⠀⠀⠀⠀⢘⠀⣇⠀⠀⣘⣹⣿⣿⠉⢂⠀⠏⠉⠉⡇⢀⡀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⢰⠞⠀⠋⠛⢿⣿⣿⣿⡏⠀⠀⠃⠐⡀⠀⠈⣈⡠⠔⡟⠀⠀⡘⠀⠀ ⡀⣠⣄⣰⡟⡆⡇⠀⠀⠳⣿⣿⣿⠃⠀⠀⡆⠀⠈⠢⢄⡉⠒⠚⠁⢀⠜⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠙⢉⠀⠐⠒⠂⠀⠀⠂⢄⠀⠁⢒⡖⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠐⠂⢄⡀⠤⢆⠀⠀⠀⠀⠔⡠⠐⠒⠈⠁⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠣⠀⠀⠸⠀⠀⠀⠐⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡐⡄⠀⠀⠡⠀⠀⠀⠑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠗⢄⡀⠀⢀⠀⠀⠀⠀⠀

⠁⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣻⣿⣿⣯⠉⠁⠀⠀⠀⠈⠈⠉⠉⠁⠁⠀⠈⠈⠈⠀⠁⠁⠁⠀⠈⠈⠈⠀⠀⠁⠁⠁⠈ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⣙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠋⠀⠀⠀⠈⠑⠃⠙⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠘⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⣁⣀⣀⣀⣂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⡿⠛⠛⠉⠉⠉⠉⠉⠉⠛⠲⢶⣄⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠋⠉⠠⠤⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢹⣧⡀⠀⠀⠀⠈⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠘⠛⠛⢶⣤⠀⠀⠀⠀⠠⡾⡛⠋⠉⠁⠀⠈⢯⢳⣆⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⡀⢀⣈⣳⣄⠀⣀⠀⠀⠀⢀⣴⣶⣴⣦⣤⣤⣤⣤⡇⢻⡆⠂⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣿⡿⣿⣿⣿⣿⣿⠀⠀⢀⣿⢹⡿⣿⣿⣽⣿⣿⠟⠁⠀⢻⡄⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⣿⣠⡿⣿⣷⣨⣿⣧⡀⠀⢻⣏⢡⣿⣿⣿⣷⣯⠀⠀⠀⠘⣿⠀⠀⠃⣦⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣏⠙⠻⠿⢿⣏⣾⠿⠿⣦⠀⠻⠷⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠉⡏⠀⠀⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⠀⣿⠀⣀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠻⣦⣀⡶⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⣿⠀⠈⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣮⢷⡀⠀⠀⢀⣼⠿⠤⢤⣀⣀⠀⠀⠀⠀⠀⠸⠁⢀⣾⠟⠀⠀⠀⠸⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣧⡑⠀⠀⠘⠛⠛⠋⠉⠙⠛⠁⠀⠀⠀⠀⠀⣠⡟⡵⠚⠀⠀⠀⠓⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣧⣄⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠈⠁⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⢠⠀⣶⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢷⣦⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⣴⡿⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⢋⣿⣿⣿⢿⣦⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢠⡿⣷⢀⣄⡠⠝⠲⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⠋⣴⣿⣿⣿⢃⣿⣧⢀⡆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⢀⣼⣷⣿⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⣰⣿⡧⢠⡿⠉⣿⣿⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⣶⣿⣿⣿⢢⣾⣄⠀⠀⠀⠠⢈⡷⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⠛⠁⢰⣿⣿⣷⣾⣿⡿⣟⠀⠀⢀⣤⣾⡿⠋⠁⠀⠀⣠⣾⣿⣿⣿⣿⠾⠀⠻⣷⣀⣀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠉⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣉⡁⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⢻⡾⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠿⢊⣻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣷⣄⣸⣷⣾⣿⡿⠋⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⡟⠛⠛⠿⠟⠻⣧⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠤⠤⠤⠶⠛⠋⠀⠀⠀⠀⢀⣴⡏⠂⠀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠚⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠒⠈⠁⠀⠀⢀⡀⠈⠉⠐⠂⢄⠀⠀⠀ ⠀⠀⡠⠊⠀⢀⣀⠀⠀⠀⠀⠀⢄⣀⡈⠁⡆⠀⡘⠀⠀⠀ ⠀⡐⣠⠔⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⢳⡤⠇⠀⠀⠀ ⣸⠜⠁⠀⠀⠀⠀⢀⣴⣿⢿⣿⣷⣦⣀⠀⢸⠇⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠉⠻⢿⣷⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⣀⡀⢹⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⠁⢀⣤⢤⣀⡞⢹⣧⢀⣿⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣇⠈⢻⣦⣽⢈⡺⠏⢼⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⠍⡉⢚⣉⡤⢰⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣏⠉⠹⠖⠊⣿⣿⣇⣸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⣼⠟⠀⠀⢀⣿⣿⣿⣽⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆⡤⣼⣿⣿⣇⠙⡇⢠⣦⡰⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠯⣿⣷⣾⣿⣿⣿⣷⣿⣤⣼⣾⠼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠴⠤⠤⠤⠴⠤⠤⠄⠀⠆⠶⠶⠖⠶⠒⠶⠀⠀

⢸⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⣧⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⣸⠛⢿⣿⣿⠿⣿⡇⠀⠀⢻⣿⣁⡀⠀⠀⠀⠀⠻⢤⣄⣀⠙⠲⣤⠀⠀⠀⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢻⠀⠀⠙⢿⣿⣿⡇⠀⠀⠘⡆⠈⠙⠒⠒⠒⠒⠦⣄⡀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⠿⢧⣀⡀⠀⠋⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠻⣿⡇⠀⠀⠀⢷⢠⠔⢲⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠾⣟⠻⠶⠀⠀⠀⠀⠀⠀⠸⠿⣶⡦⠀⠀⠈⠙⠲⠇⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠹⡇⠀⠀⠀⢸⠁⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⣤⣀⡀⠀⠀⠀⢠⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠺⢿⣦⡀⣀⣴⡳⣄⣀⣀⣾⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣙⡒⠦⠬⣽⣶⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠈⠹⣅⣿⣹⠏⠉⠉⠉⢩⣷⡒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⣀⡀⠀⠀⢀⣠ ⠙⢲⣤⣀⡀⢸⠃⠀⢠⡖⠛⠒⠚⠻⢤⡀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢉⡹⠗⠊⠉⠀ ⠒⠉⠉⠉⠉⢹⡀⣤⣾⠀⠀⠀⠀⠀⠀⠉⠳⣿⠛⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⠟⠋⠀⠀⠀⠀⢀ ⠠⠤⣤⣤⣤⡴⣟⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣳⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⢄⣀⣀⣀⡀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣠⣾ ⠀⢀⡿⠋⠁⠀⢘⣆⠀⠨⠷⣄⡀⠀⠀⠀⠀⠀⠀⢳⡛⠟⠙⠦⠤⠴⠒⣻⣯⠋⢀⣀⣰⣾⡇⠀⠀⢠⡽⡿⠻⢤⣀⢀⣀⣠⠴⠟⠛⠉ ⠰⠿⢤⣤⠒⠚⠉⠈⠓⢤⣀⠀⠉⠓⠲⠤⡤⡤⠶⠚⠁⢠⣶⣦⠀⠀⣠⠟⠛⠉⠉⠉⠁⠈⠉⠉⠛⠒⠿⣄⡀⠀⣬⣭⠀⢹⡀⠀⠀⠀ ⠀⠀⠸⣿⣀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠑⠒⠷⠷⣠⣤⠤⠤⣍⠁⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠘⠛⣡⠤⠖⠓⠶⠶⣛ ⠀⢀⡤⠿⠯⠛⢢⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠈⠳⣄⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⣰⣇⣀⡀⠀⠀⠀⠀ ⠀⣾⠷⠤⠀⠤⠾⡄⠀⠀⠈⠑⠲⠤⠤⠤⠤⠐⠒⠉⠁⠀⠀⠀⠈⠻⢏⡀⠉⠓⠶⠤⢤⡤⠤⠤⠖⠋⠁⠀⣠⠞⠁⠀⠙⢯⣉⣳⠖⠢ ⠀⠙⣦⠄⢀⠠⠴⡇⠀⠀⠀⢀⡀⠠⢤⣤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣸⣿⣇⣀⣀⡠⣤⠖⠋⠙⣗⣦⣄⡀⠀⠈⠻⣄⠀ ⠀⠀⠧⣄⣀⣠⠴⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⠋⣹⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠘⣿⣿⡏⢳⡦⢄⣘⣦ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠉⠒⠃⠰⣁⡀⠀⢨⠓⢄⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⢘⡷⢄⡀⢹⠏⣰⠟⠁⠀⠀⠉ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⢤⡀⠀⠈⠙⠃⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⣸⠀⠀⣠⡟⠁⣠⣭⠉⣼⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠸⣄⣀⠴⠃⠀⣰⠏⣀⠴⢿⡏⢰⠇⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠣⡀⠈⠉⠓⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠊⠁⠀⠀⢹⠋⠀⠘⣇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⢀⣤⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣄⣀⠀⢀⣠⣴⠶⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣿⣿⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢋⣩⣤⣬⡙⢷⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⣽⠆⠀⠀⠀⠀⠀⠀ ⣾⠁⣿⣿⣿⣿⣿⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣆⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀ ⠀⢹⡷⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⢀⠎⠀⠀⠀⠀⠀⠀⠂ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⠀⠀⢠⣀⣤⣠⡄⠀⠀⠸⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠸⡧⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⢿⣌⠑⠒⣶⠂⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢻⣿⡆⠙⣷⣴⠏⠀⠀⠀ ⠀⠀⠻⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡏⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠶⣤⣀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠟⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣨⡽⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠒⠦⣤⡀ ⠀⠀⠀⠀⠀⣠⣤⣼⣿⡆⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣠⡇ ⠀⠀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⢠⣿⡈⡠⠀⣳⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣠⣅⠀⠿⡟⠡⣴⣶⣂⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⣩⣿⠿⣷⣦⣀⡈⢭⣉⠈⠿⣈⡁⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢶⠒⠲⠤⢤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢷⣦⣆⣘⣋⠂⠀⠀⢀⣠⣾⣿⠏⠀⠀⠀ ⣴⣾⣆⠀⠀⠀⢸⡄⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢸⡟⠷⠦⢿⣿⡟⠛⠁⠀⠀⠀⠀ ⢿⡈⣟⡀⢀⣀⠬⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣶⡀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠘⠳⢌⣷⠋⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢨⡿⠃⠀⠹⢿⡀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠛⣿⠉⠁⠀⠀⠀⣀⣽⣦⡄⠀⠀ ⠀⣰⠇⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠻⠟⠾⠆⠘⠛⠉⠀⠀⠀⢸⣏⣀⣈⢦⢸⣯⢀⣴⠏⠀⠀ ⢺⣅⣀⣠⣟⠋⠙⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠙⠷⠬⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠒⠚⠋⠓⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣤⣄⠶⠬⢦⣠⠄⠀⠀⠀ ⠀⠀⠀⠀⠸⡷⠂⠀⠈⠀⠘⣿⠀⠀⠀ ⠀⠀⡠⢄⠜⣖⣇⣀⣶⡆⢀⡐⡀⠀⠀ ⠀⠈⡄⢡⣧⣌⠻⠃⠹⡝⠁⠀⢸⠀⠀ ⠀⡠⠂⠘⠈⢸⢰⡦⢀⠃⠀⣦⣚⣄⠀ ⢘⠀⠀⠀⣼⣿⠓⠦⠳⠇⠀⠀⠀⠈⡄ ⠘⠤⠤⠾⠳⣡⣴⣦⣠⣼⣦⣀⣀⡰⠃ ⠀⠀⠀⠁⠁⢿⣿⢯⣻⣿⣿⠈⡀⢡⠀ ⠀⠀⠀⠁⡄⠈⣳⠊⠙⣆⠀⠀⠇⠸⠀ ⠀⠀⠀⠡⡘⢄⡀⠀⠀⢀⡠⠊⢠⠃⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠙⠛⠻⠿⣷⣤⣄⣀⣀⣤⣤⣴⠶⠾⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢶⣦⣤⣄⣀⠀⣠⣴⡾⠟⠛⠉⠁⠙⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣧⣄⡀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣄⡀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⣠⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢴⠦⢠⡄⠘⠿⣿⡿⠟⣤⢀⡀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⡀⠙⠁⣤⠈⠁⢀⣼⣿⣇⠀⢸⡬⢁⣾⠆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠉⠙⠿⣶⣤⣤⣴⣶⠿⠛⠈⠻⠷⢶⡶⠿⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀ ⠀⠀⠀⣼⣟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠻⣧⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢿⣆⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢸⣿⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⣿⡆ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡧⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠈⣻⠇⠰⣿⡀⠀⠀⢹⡇ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⢙⠛⠓⠒⠒⠒⠛⠉⠀⠀⢶⣖⣢⣦⣤⣶⠆⠀⠈⠛⠛⠒⠒⠒⠚⠉⣠⠄⢿⡇⠀⠀⢸⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡁⠀⢸⣿⠀⠀⢸⡇ ⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣸⡏⠀⠀⣿⡇ ⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢠⣿⠃ ⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢀⣾⠏⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⢀⣠⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠟⠋⠁⠀⣀⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⢷⣄⠉⠛⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠈⣿⡀⠀⠀⠀⢨⣿⡿⠻⠿⠿⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠿⣶⣤⣤⣤⣤⣴⡶⠶⠿⠿⠿⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⢹⣇⠀⠀⣴⣿⡏⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠸⣿⡀⣴⣿⣟⠁⠀⣶⡆⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠻⣿⡟⢈⠄⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⣰⡿⠀⠀⠀⠀⠀⣹⣿⡄⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⡀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⡶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢤⣤⣤⣤⣤⠤⠤⠤⣀⣀⠀⠀⡠⣿⠕⡝⠁⠀⠀⠀⣀⡤⢤⡶⠖⡻⠟⠋⠁ ⠀⠀⠈⠑⠢⡀⠈⠉⠒⠤⣀⣭⣿⣿⠉⠉⣷⣷⣶⡯⡉⡠⠚⠁⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡀⠣⢄⡰⢣⠿⣫⡥⠀⠀⢀⣈⠻⡆⠘⡄⢠⠁⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣩⡦⠤⠃⠤⣎⣀⣱⡀⢀⣎⣀⣱⣈⡠⠭⠵⣮⣀⣀⠠⠤⠀⠀ ⠀⠀⠀⠀⢈⠝⠓⢤⡄⣀⡀⠈⠙⣍⣇⣀⡏⡩⢊⡡⢤⣒⡪⢭⣽⣦⡄⠂⠀⠀ ⠀⠀⠀⠀⡿⡶⡝⡰⠛⡶⠾⢉⡶⡾⠓⡟⠙⢟⠃⠩⠤⠲⠉⠱⢰⠱⢷⠀⠀⠀ ⠀⠀⠀⠀⠑⠓⢺⡳⠤⠼⣒⠀⠀⡇⢀⣃⠀⢇⠂⠤⢤⠔⠒⢺⠚⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⠀⢀⠏⢳⢢⠺⡌⣀⣰⠃⢣⢦⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⠀⠈⠀⠀⢹⠒⢹⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠈⢻⢦⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠒⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⡇⠀⠀⢀⠤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠄⠚⠂⠤⠤⠤⠤⠤⠒⠡⠐⠈⠀⠄⠀⠄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣣⠞⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⡿⠟⠒⠂ ⠀⠉⠙⠻⢿⣟⠛⠛⠿⠯⢭⣍⣉⠉⠙⠛⠒⠦⢤⣀⡀⣠⣿⣽⣟⣁⣼⣁⣀⠀⠀⠀⣀⣀⣤⠶⠞⠛⣩⡽⠟⠉⢁⡴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠓⠦⣄⡀⣠⣾⣿⣿⣿⣏⠁⠀⢹⣿⣿⣿⣿⣿⣯⣀⠀⢀⡴⠛⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢲⡀⠀⠀⠀⢈⡿⣫⣿⣿⠿⠛⠁⠀⠀⠀⠉⠛⠿⣿⣯⡁⠙⣶⠏⠀⠀⡖⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⠲⠤⣴⠋⢰⡿⢋⣥⢶⡖⠀⠀⠀⠀⢠⣤⣄⠈⠻⣧⠀⠈⣧⠀⣰⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣀⣠⡏⠀⠉⢠⠟⠁⠀⢳⠀⠀⠀⠀⡾⠁⠈⠳⡄⠙⠀⠀⢸⣛⣡⣴⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠟⠃⠀⠀⠀⠀⠙⠛⢶⣶⣶⣾⣷⠀⠀⢼⣷⣶⡶⠖⣿⠶⠚⠛⠉⠉⢉⣹⡿⣿⡖⠒⠊⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠲⢦⣄⣀⡀⠀⠀⠀⠀⠙⢧⡀⣿⢀⣀⣸⡇⠀⣠⠞⠁⣀⣤⠴⠚⣋⣩⣥⣤⣤⡿⢷⡤⠶⠒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣶⡶⠊⣹⣯⣉⣛⠒⠶⠤⣄⣀⣻⢿⣯⣽⡿⢿⣾⣵⣾⡯⠿⠒⠛⢉⣩⠴⠲⡟⠻⡛⣿⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⢻⠏⢸⠀⡼⠁⠀⣹⠛⠿⠭⠽⠷⠿⡿⠀⠉⡏⠀⠀⠹⡯⠤⠤⠤⠒⠛⠉⠿⢄⠀⢸⠀⡇⢸⠻⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⠸⣤⣬⣷⣧⣀⣀⣉⣧⠤⠄⠀⠀⢸⡁⠀⠀⢧⠀⠀⢸⠁⠠⣀⣀⢀⣀⣀⡤⠤⣶⣿⣤⠧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡄⠈⠁⠀⢹⣠⣄⠀⠀⠀⢧⠀⢖⠚⠒⠀⣏⡴⡄⠀⠀⠀⡟⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢸⠇⠸⣾⠛⣶⠾⣦⣀⣉⣀⣠⡟⠀⢹⡶⣦⣼⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⠀⠀⠿⠀⠛⠀⠹⣮⣉⡭⢿⡇⠀⠘⠃⢿⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣸⠃⠀⠀⠀⠀⠘⣷⣄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠇⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠹⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠠⠤⠤⠤⠤⢤⠤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠀⠀⢀⡠⠖⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠈⠉⠓⠒⠒⠒⠒⠒⠒⠚⠋⢉⠄⠒⠁⠀⣀⠀⡄⠂⠀⠁⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⠀⠨⠿⠧⠀⠐⢧⠄⠠⣄⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡎⡢⢄⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠄⠀⣀⡀⠀⠸⠩⣍⠉⠒⠈⠉⠈⠁⠋⢪⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢠⠊⠁⠀⠀⠑⣄⢱⠚⠀⠀⠀⠇⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡎⢀⣦⣀⣤⠧⡜⠐⠲⢶⡞⠉⡁⠁⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⣇⡉⠪⠟⠋⠁⠀⢇⠀⠑⣝⣠⠏⠁⠀⠀⠀⡰⡇⠀⠘⣤⡽⣢⠀⠀ ⠀⠰⠈⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⣀⡠⣊⠜⡀⠀⠀⠛⠓⠃⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠛⠉⠉⠉⠐⠊⠁⠀⠅⠀⠀⠀⠀⢸⣿⡇ ⠀⢰⠀⠀⠀⣠⣀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⡀⠀⠎⠀⠘⠑⢠⢰⠀⠀⠀⠠⢃⣀⣠⡴⠊⢰⠀⣠⣤⣄⠀⠀⠀⠀ ⠰⡄⢁⡎⠀⠀⠀⠣⠼⠀⠃⠀⠀⠎⠉⠁⠀⢱⠀⢠⠀⠹⠿⠟⠀⠀⠀⠀ ⠀⠈⠈⠁⠘⠒⠒⠚⠀⠀⠸⡀⠈⡄⢠⠤⠤⠀⠑⠗⠃⠒⠒⠛⠛⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡰⠡⢀⣟⡧⠿⠓⠛⠛⠥⢖⣤⣩⢳⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢔⠡⡤⠄⠀⠀⠀⠀⠀⠀⠀⡠⡀⠈⠻⣿⠀⠘⠄⠀⠀⠀⠀ ⠀⠀⠀⠘⢡⡊⢀⠐⣿⣛⣢⣀⠠⢰⠩⠒⢙⣦⣆⢡⢣⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⡘⠀⢰⣹⠇⠀⡎⠀⢠⢡⣿⡿⢸⢸⠀⠀⢡⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⠇⠀⠘⡟⠀⠐⡄⠀⠸⡘⡿⢀⢸⡎⠀⠀⠘⡀⠀⠀ ⠀⠀⠠⠦⡎⢰⢃⠎⢁⠩⢈⠃⠀⠈⠒⣒⣊⠀⠈⢛⠟⣵⠀⠀⠈⢢⠀ ⠀⠀⠀⠠⢁⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠀⡀⢒⠆⡹⠀⠀⠀⠀⠆ ⠀⢀⣴⣥⣾⡛⠫⡑⠤⢀⡀⠀⠀⠀⠀⢀⡠⠔⠉⠒⠈⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⠋⢙⣻⡆⠈⡆⢀⠔⣟⣫⠝⡹⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢆⠹⣧⣦⣬⣿⢃⠔⠉⣭⣿⠊⡆⡐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠪⢵⣾⣓⡨⠒⠈⠏⠗⠠⠳⡝⢔⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢡⠀⡌⡆⠀⠘⣀⣎⡔⠑⠂⡜⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠂⢠⠋⠕⣲⣆⡤⢀⣀⡀⠈⠀⡐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠉⠉⠉⠉⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⣀⡤⠞⠋⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⢼⡵⠛⠉⠓⠒⠦⣤⣀⣴⠚⠉⠁⠀⠀⠀⠀⠈⠁⢠⡤⠴⠒⠢⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢠⠀⣿⢀⣤⣀⠀⠀⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⢰⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⡏⠀⢻⡈⣦⠈⠛⠶⢶⡶⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⠦⣀⠀⠈⠣⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡴⠀⠀⠀⡞⠀⠀⠀⢣⠈⠃⢀⣠⠞⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣄⠀⠀⣯⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣸⠁⠀⠀⢸⠃⠀⠀⠀⠈⣇⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣧⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢸⠁⢀⡾⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠐⠿⡿⠇⠀⠀⠀⠀⢛⡛⠋⠀⠀⠀⠀⠀⣼⣢⠎⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠹⣄⢀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡟⠀⠀⣀⣀⡀⢀⠀⣹⠃⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣞⠋⡅⠀⠈⡟⠀⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣛⣛⣿⣣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠛⠋⠁⠀⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠊⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠘⢷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⢧⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡿⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣼⠁⠀⢀⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠈⢻⡽⠳⣦⡀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠉⠛⠉⠛⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣷⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣶⡾⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡤⡄⢀⡀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠨⣿⡻⠇⠋⠗⣻⣟⣧⠇⠸⠠⣜⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⣋⣁⣀⠀⠀⠙⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠉⠻⣿⣷⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣍⠉⠉⢟⣧⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀ ⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣕⣢⣼⣿⠃⠀⠈⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡏⠀⠀⠀⠀⣬⡽⠿⢿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠘⢿⡖⠤⣈⡙⢿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⡇⠀⠀⠸⡄⠀⠀⠀⠈⠙⠒⢾⡿⠷⢄⡙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢰⠦⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⢸⡓⠢⢬⣉⠒⠃⠀⠈⠀⠀⠀⠀⠐⠤⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡀⠀⠀⠀⡸⠁⠀⠀⠉⢲⠢⢴⣿⣷⡦⣄⣉⠁⠒⠦⠤⠄⣀⣀⣤⣴⠶⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢄⠀⠀⢳⠀⠀⠀⠀⠀⡷⠀⠀⠉⠓⠲⠬⢭⣍⣓⣒⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⡀⢸⡇⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⣀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠑⠦⠄⠀⣜⡁⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠛⠋⠁⠀⠈⠙⠳⢤⣰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠉⠛⣦⠀⠀⠀⠀⣸⠀⢰⠏⢰⠞⠉⠙⢷⡼⠟⠲⣌⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⢀⣤⠴⠶⢤⣴⡏⠀⠀⠀⠀⠀⠈⣷⠖⠚⠛⠛⠀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⢠⡟⠁⠀⠀⠀⠘⢃⣀⣀⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢿⠀⠘⣧⡀⠀⠀⠀⠀⣴⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣷⢼⡁⠀⠀⠀⠀⢰⠟⠁⠀⠙⢧⠀⠛⠳⣆⠀⠀⠀⠀⠘⢷⡀⠈⠛⢦⣄⣴⠟⠁⣠⡿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⢧⡀⠀⡀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠲⣤⣤⣀⣤⡴⠞⠋⠘⠊⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⠏⣿⠃⠀⠘⢦⣀⣀⡤⠏⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⢰⡇⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣧⠀⠀⠀ ⠀⠀⠀⢠⡟⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⣼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⢤⣄⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣇⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠈⢻⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⣸⡇ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠙⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⡇⢰⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠻⠻⠃⠀⢿⢸⠃ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⣴⡿⠟⠛⠛⢻⠇⠀⠀⠀⠀⠀⠀⢰⣶⡶⠀⠀⠉⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀ ⠀⢈⣻⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀ ⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣹⡷⢦⣄⣀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠉⠙⠛⠶⠦⠭⠷⠦⠤⠤⠤⠤⠴⠶⣴⣦⣄⣀⣤⠴⠶⠟⠛⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠙⠓⠦⣤⣤⣀⣀⣀⣤⠤⠴⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣐⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⡈⢑⠨⠓⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠌⢄⡬⠂⣉⢾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⢶⣏⣈⣤⠿⠝⠚⣁⣌⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⠖⣸⠏⠄⠀⢰⣺⣿⡍⠉⢻⡿⢦⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⢸⣿⠉⠀⠀⡾⠟⠉⢳⣸⣉⣠⣜⣰⣼⡿⣦⠀⠀⠀ ⠀⠀⠀⡜⣲⢛⣾⠠⡂⢐⠣⣀⣀⣼⠻⠖⠲⠿⡿⠛⢁⣿⠀⠀⠀ ⠀⠀⢰⠇⡀⠈⠘⡆⠀⠄⠀⠰⢢⠀⢀⣀⣀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⡼⠁⡇⠀⠀⠹⡅⠀⠀⠀⢠⢖⣭⣷⣾⣷⡄⢠⠏⠀⠀⠀⠀ ⠀⢠⡇⠀⠁⠈⠀⠀⠘⢧⡀⡀⠽⠥⠚⠁⠄⢀⣠⠿⡄⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠌⠑⠺⠾⠖⠶⣿⠍⠀⠀⢿⡄⠀⠀⠀ ⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠌⢿⡀⠀⠀ ⢰⢆⣟⠔⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠀⠀⠂⠀⠁⠰⠀⠸⣷⡀⠀ ⢸⢏⡇⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢧⠀ ⣸⡀⡇⠀⠀⠈⠀⠀⡇⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢿⣥⠀⠀⠉⣿⣿⣿⡀⠀⠀⠸⣇⣀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠉⠀⠀⠈⠿⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠡⡌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⠒⠒⠒⠢⠤⠴⠒⠒⠊⠉⠛⠀⠿⠢⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠴⠊⠉⢀⣀⠠⠤⢄⣀⠀⠀⢳⠉⠻⢲⠆⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⣠⠞⠁⠀⠀⠀⠀⠈⠷⣄⠀⢳⡴⠓⠂⠉⠂⠀⠐⣏⠀⠈⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢀⠎⠀⠀⠀⠀⠀⠈⣻⠆⢈⡇⠀⠀⠐⠁⢀⡀⣠⣤⠦⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⢠⡏⠀⢀⣴⣄⡀⠠⣤⣿⣄⣼⠀⠉⠉⠿⢿⡿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠃⣄⠸⢿⣿⣿⠟⠋⠀⠀⡇⠀⠀⠲⣤⢾⡟⠒⣶⠴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⡋⠉⢳⡀⠀⠀⠀⠀ ⠀⠀⣹⢄⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⢄⣀⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⠀⠀⠀⢸⡗⣿⡟⣉⣷⠀⠀⠀ ⠀⣼⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢁⡽⢩⠀⠀⠀⠘⠿⢿⣦⡿⠁⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠦⣄⣀⣀⣀⣀⣀⡤⠴⢛⢱⡶⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠒⠯⠭⠥⠤⠤⠤⠖⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉ ⠀⡇⠀⠀⠀⠀⠀⢳⣤⣀⠀⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⢀⡴⠁⠀⠘⡗⢄⡀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⣤⠞⠀⢠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⡼⠀⡄⠀⠀⡞⠀⠀⠀⠀⡇⠀⠈⡷⠺⡇⠀⠀⠀⠀⠀⡞⣡⣤⣤⠴⡾⣿⠁⠀⠀⡞⠀⢠⣾⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣄⣀⣧⠀⢹⡀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠹⡄⠀⠀⡇⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠙⢆⣘⣾⡦⠀⣀⢀⡀⠀⠀⡈⠉⠁⠀⠀⣇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠷⡀⢠⣙⣦⠀⠀⠀⢹⣧⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠃⠀⠀⠀⠀⢹⡈⠀⠀⢳⡀⢠⣤⣤⣤⡤⠄⠀⠈⠻⣟⠉⡀⠛⠉⠈⠛⠛⠉⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠿⠿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠖⠛⠉⠉⠙⠳⣴⣿⣳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⣶⠛⠁⠀⠀⠈⠉⠀⠈⠳⣽⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⣁⣤⡀⠀⠀⣠⣀⡀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⣠⠖⠒⠦⡞⠀⢿⣾⣧⠤⣼⣷⣿⠀⢀⣀⣀⠳⡄⠀⠀⠀ ⠀⠀⢻⠀⡏⢳⢹⡄⣘⠸⣿⡿⠀⢹⣩⠟⠁⠀⠸⡄⢿⡄⠀⠀ ⠀⠀⠈⡆⢱⣸⠟⣿⢻⠆⠀⠀⠠⠀⡟⠀⠀⠀⢸⠀⡿⠁⠀⠀ ⢀⡤⠞⠃⠀⠀⠀⢹⠘⡇⢿⣿⠄⢠⡇⠀⠀⠀⣾⣼⣙⣦⡀⠀ ⡏⠀⠀⠀⠀⠀⢀⣾⣶⣿⡶⣤⣖⣷⣷⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⡇⠀⠀⠀⠀⢀⣼⠿⡿⠃⠀⠈⠁⠈⠙⣆⠀⠀⠀⠀⠀⠀⢸⡇ ⠻⠤⠄⠠⠴⣿⢋⡞⢀⣴⣾⣷⡄⣠⣤⣾⣦⣄⡀⠀⠀⣠⠟⠁ ⠀⠀⠀⠀⢠⠃⡸⠀⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⠏⡏⠉⢳⡀⠀ ⠀⠀⠀⠀⣸⠀⡇⠀⢻⣿⡟⠛⣦⡼⠿⠿⡿⠛⠀⢸⡀⠈⡇⠀ ⠀⠀⠀⠀⢻⠀⢇⠀⠈⠻⣷⠞⠁⠹⣦⠀⠀⠀⠀⢰⠁⠀⡇⠀ ⠀⠀⠀⠀⠘⡄⠘⣆⠀⠘⠋⠀⠀⠀⠘⠇⠀⠀⣠⠏⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠹⣄⣈⡢⣄⡀⠀⠀⠀⠀⣀⡤⢞⡁⢀⣰⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⢀⣠⣴⣶⡖⠲⡂⠀⠀⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡼⠙⢿⣿⠃⠀⠈⡀⠀⢸⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠘⡄⠀⡀⢀⣿⣦⣤⣾⡇⠀⣸⡞⠉⠉⠳⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⢣⠀⠻⣿⠋⡇⢸⠟⠁⠐⢇⠀⠀⠐⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠚⠚⠢⡄⢮⣘⣠⠧⠄⠂⠀⠘⡄⠀⠀⠀⠸⡀⠀⠀⠀ ⠐⠒⠒⠺⣀⠀⠀⢀⡸⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠓⠒⠒⠂ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⠤⠤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣴⠶⠚⠛⠶⢦⣄⠀⠀⠀⠀ ⠀⠀⣀⣤⠶⠶⠶⣦⡀⠀⠀⣀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⢠⠤⣀⡀⠈⠉⠙⠛⠾⣯⣀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⢀⡼⠋⠀⠀⠀⠀⠈⢿⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠉⠉⢒⠆⠤⠤⢈⣙⣷⣦⡀⠀⠀⠀⠈⢿⡄⠀ ⡾⠁⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠙⢆⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣼⣧⡀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠈⢣⠀⠀⠀⠠⣧⠴⠒⣶⣶⣶⣶⡶⠒⠺⢿⣴⣿⡾⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣠⣴⣖⣭⣤⣴⣶⣶⠂⠀⠀⠺⡇⠀⠀⠀⢣⠀⠀⢸⣿⣿⣿⣿⣄⠀⠈⣿⠿⠖⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⣿⣿⣿⣿⣿⣿⣦⣀⢀⣰⡏⠀⠀⠀⠈⢆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠣⣀⠀⣈⣿⡿⢿⣿⣿⣿⡇⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠲⡀⠀⡄⢀⠜⠋⠁⠀⠀⠀⠀⠈⠙⢦⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⢄⡀⠀⠀⠉⠉⠉⢉⡥⠋⠀⠀⠀⠀⢱⣴⡿⠁⠀⠀⠀⠀⠀⠀⢠⠉⡆⠀⠙⡄⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣄⣀⣉⣑⣒⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⢹⠀ ⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠛⠳⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠷⢄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡞⠛⠿⣍⡿⠉⠉⢹⣯⣅⡀⠀⠀⠀⠀⠈⣿⠒⠒⠒⠊⢹⡏⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡏⠀⠀⡀⢸⠙⠂⠤⠼⢷⡈⣷⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠁⠀⢀⡇⡞⠀⢠⡤⣤⢤⠳⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⠀⠀⠈⢧⣤⠟⢀⣼⠇⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠠⣿⠀⠀⠀⠀⠀⣰⠟⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⣦⣠⠤⠞⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡋⠑⠒⠒⠒⣿⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⣧⡀⠀⡀⠀ ⠙⠓⠲⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣇⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣩⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡀⠀⠀⠘⢧⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣧⠀⠛⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠀⣸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣠⠞⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢶⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣴⠋⠁⠸⣿⠀⢀⣀⣀⣀⣀⣀⣀⣸⣦⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢧⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⠙⠀⠀⣠⡿⠛⠻⣅⠀⠀⠀⠀⠘⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⠞⠁⢀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠞⣏⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣰⠇⢀⣾⡏⠉⣇⠀⡧⣀⣶⣤⣀⡀⠀⠀⠀⣠⠴⠛⢿⣆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⠛⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⡇⠀⣿⣿⣷⣶⡟⢸⣿⣿⣿⣿⣿⣿⣦⡀⡼⠃⣀⣀⠀⠻⡄⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣇⠀⠻⣿⣿⣿⠇⣽⣿⣿⣿⣿⣿⣿⣿⡿⢠⣾⡏⠉⢳⠀⡇⠀⣰⣿⣿⠄⠀⠀⠀⠀⠈⡟⠇ ⠀⠀⠀⣤⡴⠛⠛⠛⠲⣤⣿⢾⣦⣀⣀⣀⣀⣀⣈⣹⣿⣿⣿⣿⣿⠟⢡⣿⣿⣿⣾⡿⠀⣧⠞⢩⣿⢧⠀⠀⠀⣄⢀⣾⠅⠀ ⠀⢠⡞⠃⠀⠒⠄⠀⠀⠈⣿⡀⢳⣴⣤⣼⣄⠉⣽⣏⣩⡟⠻⣯⣄⢰⡀⠛⢿⣿⣿⡧⠴⠿⢦⣼⠅⢼⣧⣤⣴⢋⡞⠁⠀⠀ ⠀⢺⣶⣽⠶⠶⢶⣄⠀⠀⠹⡷⣄⠙⢏⣳⠿⡍⠉⢻⣿⡿⢾⢯⠈⢙⡿⣤⣀⡴⠁⠀⠀⠀⠁⠀⠀⢿⣾⣿⣷⣋⣰⠄⠀⠀ ⠀⣼⣿⡿⣶⠄⢀⣠⣷⣶⡼⠃⢀⣷⢄⣑⠤⣽⡶⣌⣠⣀⣀⣬⣛⣻⣧⣼⠟⠀⠀⠀⠀⠀⠀⣀⠀⠾⢿⡯⣿⠛⠋⠀⠀⠀ ⢰⣿⣿⠓⠒⠀⠈⣼⠿⠛⠛⠲⠋⠀⢀⢹⡷⠈⠉⠙⠛⠟⠋⠠⣽⣵⠿⠋⠀⠀⠀⠀⠀⠀⠀⣹⡟⢹⣬⣿⣤⡀⠀⠀⠀⠀ ⠀⢹⠧⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣠⣼⡏⠀⡀⠀⠀⠀⠀⠁⣹⠋⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠛⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀ ⠀⢸⠀⠀⢀⠎⠙⠷⣴⣤⣤⣴⠿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⣦⡴⠋⠀⠀⠀⠀⠉⠉⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠻⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠘⠿⣽⠈⠸⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⡀⠀⠀⣥⣿⡞⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠓⢦⣤⣤⣤⣤⣴⠿⠛⠋⠙⢿⡀⢿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⠀⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣧⣄⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡿⠛⠛⠛⠻⠶⢦⣤⣀⠀⣀⣠⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣄⣀⠀⢀⣤⡶⠞⠛⠛⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣄⡀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠻⣶⣄⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⣤⠀⡀⠸⣿⣿⠟⡀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣇⠉⠁⠄⠁⣀⣾⣧⡀⠾⢉⣶⠂⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀ ⠀⠀⠀⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠙⠛⠲⠒⠛⠋⠁⠈⠛⠛⠛⠙⠻⣦⣄⠀⠀⠀⠀⠹⣧⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠹⣇⠀ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⢻⡆ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠸⣷ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠤⠤⢤⡀⢸⡇⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⠿⠧⠤⠤⠜⠃⠀⣤⡄⣀⣀⣤⠀⠙⠿⠧⠤⠤⠾⢃⡘⣷⠀⠀⢸ ⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠰⣄⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⣎⠀⣿⠀⠀⣸ ⠈⢿⡀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⣿ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣰⡏ ⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠃⢀⣼⠏⠀ ⠀⠀⠀⠀⣈⡻⢶⣄⣀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠋⠉⣀⣤⡶⠛⠁⠀⠀ ⠀⠀⠀⣸⠋⢿⡄⠈⠙⠛⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣤⣀⣀⣀⣀⣀⣤⣤⣤⡶⢶⡟⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠸⣇⠀⢀⣾⡟⠁⠀⠀⠀⠈⠉⠉⡉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⢿⣠⡿⠟⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⢈⡿⠁⠂⠀⠸⣷⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣦⣼⡇⠀⠀⠀⠀⠙⠷⣦⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢛⣩⡽⠿⠛⠛⠷⣄⠀⠀ ⠀⡷⢶⣶⡶⠶⠤⠤⢤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣤⠾⠋⠁⠀⠀⠀⠀⠀⠘⣷⠀ ⠀⠃⠀⠈⠻⢦⣄⠀⠀⠀⠀⠉⠉⠛⠲⠦⣤⣀⠀⠉⠙⠻⢶⣦⣍⣻⣿⣦⡀⠀⢀⣴⠏⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣤⣀⣀⣈⣻⣿⣿⠎⠻⣤⠟⠁⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣠⡴⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⢀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠻⠂⠀⠀⠀⠀⠀⠈⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣶⡄⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠑⠀⢰⡄⣶⠀⠀⠀⢀⣤⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⢿⣤⣀⣀⣀⣀⣤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢦⣄⡈⣷⣿⡀⣠⠶⠋⠻⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⠤⠽⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⣤⣄⣀⣀⣴⣟⠛⠻⢦⣹⢿⣿⣿⣿⣿⣄⠀⢀⣰⠇⠀⣀⣀⣀⣤⣤⠤⠴⠶⠶⢶⠟⠒⠒⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⡿⢿⡿⠛⢀⣬⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣴⣤⣴⣏⣀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠉⠉⠉⠉⠉⠙⢿⣿⣿⣷⣬⣷⡈⣧⣄⣀⠹⣧⠀⠀⡟⢹⣦⣄⣴⡟⠁⢀⣀⣀⠙⢦⡀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠉⠉⠛⣿⠿⣯⣿⣿⣗⣨⣷⣶⣟⣿⡿⠿⠾⠿⠿⠭⣍⣉⡙⠛⠻⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢠⡏⢀⡴⠋⠁⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣸⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣠⣾⣷⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡧⠤⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠒⠒⠒⠒⠒⠒⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡏⢸⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠈⣿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⣿⣷⣴⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣷⡀⠀⠀ ⠀⠀⠀⠀⢸⡆⢹⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⡤⠶⠶⠶⢶⣶⣤⠀⠀⠾⠛⠉⠀⠀⠈⣿⡀⠀ ⠀⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⣷⠘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡇⢀⣀⣀⣠⣴⠟⣿⠁ ⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⠀⠤⠶⠦⠤⠤⠤⠴⠾⠋⠀⠀⡇⠉⡉⠉⠀⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⢸⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠇⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⣶⠤⣀⣀⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢦⣀⣈⣉⣉⣿⡿⠏⠁⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⣍⣛⣶⣤⣷⣤⠄⠀⢀⡶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡛⠒⠒⠶⠤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⣼⣿⣿⠟⠿⢿⣿⣿⣿⠓⠲⡶⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⣸⣿⣿⣿⠀⠀⠈⢯⣯⠙⢷⡄⣓⣻⡼⣷⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠏⢀⣼⣿⣿⣿⣿⠀⠀⠀⠘⣏⣆⠀⢧⣿⣿⡇⠘⢷⣄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⡼⡜⡆⠀⠉⠉⠀⠀⢀⣹⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⠗⠛⠛⠒⠒⠋⠉⠉⠉⠀⠀⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⣄⡙⢿⣿⣿⣿⣿⡇⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢶⡉⢿⣿⣿⡟⠑⠒⠺⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⣧⠿⠿⠿⠷⠀⠀⠠⡿⠿⠿⠿⡿⠦⠤⠄⠀⠀⠀⠀⣘⡧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠭⠨⢕⠓⢃⠀⢀⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⡐⠣⠈⡢⢼⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⠆⢄⡔⠊⠙⡦⢦⠵⠒⠊⠉⠉⠉⠑⠢⢄⣁⠐⠤⡀⠀⠀⢃ ⠀⠀⠀⠀⣄⡞⠀⠀⡸⠎⠂⠀⠀⢸⠀⠀⢀⡀⠀⢤⣤⣀⠰⡀⠉⠢⣼⠀⠀⠀ ⠀⠀⠀⠀⡜⠈⠉⠁⢀⠕⠀⢠⡄⡎⠀⠀⢈⡁⡴⣽⡄⢸⡿⡄⠀⠀⢹⣄⣀⢤ ⠀⠀⠀⢸⡇⠀⠀⢠⠞⠢⣒⡩⠊⠀⠀⠀⠀⠈⢳⠉⢐⡺⠻⡁⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠐⠱⡤⠤⠊⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⣙⡦⠤⠗⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠠⠀⠒⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣀⢴⠁⠀⠀⠀⠐⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⣻⡟⠛ ⠀⠀⠀⡎⡹⠙⠘⢸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠀⢠⢱⠀⠀⣗⡩⠻⠭⣘ ⢀⡠⢼⡭⠄⢔⡄⢆⢣⡀⠀⠀⠀⠀⠠⣎⠀⠀⠘⡀⠀⣨⣼⣄⣠⢟⣂⡤⠤⠀ ⣎⠀⠀⠈⢱⢀⠵⠥⠭⠽⠦⢯⣀⡀⢀⡶⢽⣦⡶⣿⣫⡷⠿⠧⡾⠄⠀⠈⠉⠁ ⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀

⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠴⠾⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢔⡭⠋⠉⠣⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢼⠗⢁⣤⡶⢆⠀⡆⠀⡨⠭⠭⢶⡀⠀⡱⣄⢠⡀⢀⠀ ⠀⠀⠀⠀⠀⢎⠃⢠⣿⣿⣧⣼⠀⢇⡴⢺⣿⣿⣶⣝⢀⠃⠘⢄⠈⠀⠀ ⠀⠀⠀⠀⡞⠸⠀⠘⣿⣿⣿⡿⢁⢻⣦⡈⠛⠻⠿⠟⡾⠐⢺⡌⡐⠀⠀ ⠀⠀⠀⡜⢠⠀⠱⢄⡈⠉⣉⡴⠃⠀⠙⢷⡀⠀⣠⡶⢧⣿⣿⡧⡇⠀⠀ ⠀⠀⡜⠀⢸⣤⡖⠈⠉⠉⠉⠉⠉⢉⠉⠐⠚⠭⢀⠀⡄⠿⠿⢃⠁⠀⠀ ⠀⢸⠀⢠⠇⠘⢟⢦⣄⠀⠀⠀⠀⠀⠉⠁⠐⠂⠀⠉⠻⢆⠄⡎⠀⠀⠀ ⠀⡌⢀⠎⠀⠀⠀⢱⡏⢙⡀⠀⢀⠀⠀⠀⠀⣀⣀⡀⠠⡴⠒⢃⠀⠀⠀ ⠀⡇⡞⠀⠀⠀⣠⠞⠀⣶⠃⢰⡇⠀⠀⠀⢠⠟⠁⠀⠀⢡⠀⠈⡄⠀⠀ ⠀⢰⡇⠀⢀⠎⠀⠀⠴⢿⠀⠘⠇⠀⠀⠀⡎⠀⠀⠀⠀⠈⠢⡀⠸⡄⠀ ⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⢉⢦⢀⠀⠀⣀⠇⠀⠀⠀⠀⠎⠀⠈⢢⡇⠀ ⠀⠀⠈⢄⠻⡄⠀⠀⠀⠐⢢⣸⢾⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠂⠵⢤⡀⡀⢐⡾⡳⠜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⠿⠷⠶⠶⠶⢦⣤⣤⣤⣀⣀⡀⣴⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠉⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣤⡀⠀⠀⢀⣤⣤⣤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡋⠀⠀⠀⠀⠀⠀⠐⢶⣤⣀⣀⡀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣶⣾⣿⣟⣉⣤⣤⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠟⠛⠉⣡⣾⣿⣿⣿⣆⠀⠀ ⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⣻⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣄⠀ ⠀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠿⣿⣿⣿⣷⣄⠀⠀⠀⣄⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡀ ⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠛⣻⣿⣿⣿⣿⣿⡟⠁⢻⡿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣦⣈⠛⢿⣿⣿⣷⣦⣀⠉⠻⣦⣄⠀⠀⠀⣿⣿⣿⣿⡇ ⢠⣿⣿⡇⣀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣷⣦⣀⠙⢿⣶⣶⣬⣿⣿⣿⡇ ⣸⣿⣿⣿⡟⠀⢾⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠃⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠟⢛⣿⣿⣿⣿⡟⠻⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣎⢻⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⣿⣿⣿⣿⠀⢆⠀⢿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣿⣧⠹⣿⣿⣧⡀⢻⣿⣿⣿⣿⠟⠀⠀ ⢿⣿⣿⣿⠀⠸⣷⡜⣿⣿⣿⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣷⡘⣿⣿⣧⡘⣿⣿⣇⢨⣿⣿⡿⠋⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⢹⣿⣿⣿⡹⣿⣧⡀⠀⠻⡏⢻⣿⣿⠛⣿⣿⣿⣿⣿⠃⠀⠀⣀⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣷⢹⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣎⠛⠿⡆⠀⠁⠀⢿⡇⠀⢹⣿⢿⣿⣿⡀⣾⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⣷⣄⣀⠀⠀⠀⠈⠗⠀⠘⠏⠈⢿⣿⣷⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣷⠀⠀⡀⠀⠈⣛⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣇⠀⠹⣦⡀⠘⣦⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣆⠀⢻⣷⣄⠈⠻⣷⣤⣀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣦⡀⠛⢿⣷⣄⠈⠻⢿⣿⣷⣶⣽⣿⣿⣿⣿⡟⠸⣿⠙⣿⣿⣿⣿⠏⠻⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠙⢿⣷⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠋⠀⠈⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣾⣿⣿⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠛⠿⣿⣦⡀⠀⣀⣀⣀⠀⠀⣠⣶⣿⠿⠿⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⠿⠿⠿⠿⠿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠈⠛⠛⣃⣤⡴⠶⢦⣤⣘⠛⠛⠁⠀⠀⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⡾⠋⠀⣴⣶⣦⠈⠙⢷⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⣿⠀⠀⠀⠿⠿⠟⠀⠀⠈⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠘⣿⠀⣤⡀⢀⣶⡀⠀⣠⠀⣿⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠻⣦⡈⠙⠋⠀⠙⠛⢁⣼⠏⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣨⣿⡿⣦⣀⠉⠻⢶⣤⣤⣤⠶⠛⠁⣠⣴⢿⣿⣅⣤⣶⣾⠿⠿⣷⣶⣤⡀⠀⠀ ⠀⣰⣿⠟⠋⠁⠀⠀⠉⠻⣿⡉⠀⠀⠉⠛⠷⠶⠦⠤⠴⠶⠾⠛⠉⠀⠀⠉⣿⠟⠁⠀⠀⠀⠀⠉⠻⣿⣆⠀ ⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄ ⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀ ⠀⠘⢿⣷⣦⣄⣀⣀⣤⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣴⣾⡿⠋⠀⠀ ⠀⠀⠀⠈⠙⢻⣿⣉⣡⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⣿⡟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠁⠉⠙⢻⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣀⣠⣴⣾⡿⠉⠀⠀⠈⠻⣿⣦⣄⣀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⢊⣀⡀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣀⠤⠚⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⡟⠉⠀⠉⠙⠒⠲⠁⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡜⠀⡇⢏⠓⠦⠤⡴⠃⠀⠀⠀⡆⠀⠀⠀⠙⠲⠤⣀⠀⠘⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⠀⠀⡸⠁⠀⠸⡌⠁⣠⠞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠁⠀⠠⠇⠀⠀⠀⣧⠈⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠘⠀⡜⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠙⠛⠁⠀⠀⠀⢩⠁⠀⠀⠀⢠⣮⠎⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⠀⠀⠀⠀⠘⡄⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⡞⠀⣀⣄⣀⡀⢹⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣠⣤⣤⢃⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠟⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡎⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠈⠳⣄⡰⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⡆⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢰⠃⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⢻⡿⣦⡀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠁⠀⠀⠀⠉⠉⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠠⠼⠥⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿⠿⠸⠿⣿⣿⠇⠀⢀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣹⣿⣶⣤⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⣾⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀ ⠀⣨⣿⣿⣿⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢟⣛⣿⣿⣿⣿⣿⣟⣶⡦ ⠴⠿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⢹⠛⣿⣾⡿⣿⠃ ⠀⠀⠘⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠋⠤⠀⢸⠂⠚⡀⠅⠀⠀⠇⠀ ⠀⠀⠀⢻⣿⣿⣿⣄⠉⢿⣿⣿⣿⣿⣿⣿⡼⣿⡣⠀⠀⣟⠠⣄⠐⠀⠀⠐⠀⠀ ⠀⠀⠀⠸⠻⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣙⡿⠈⣔⣄⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠛⠻⠿⠿⢻⠿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⣯⠽⣥⣦⠶⠉⡘⠃⠙⡈⣭⣍⡙⠿⢛⣛⠓⠒⠶⢤⣀⠀⠀⠀ ⠀⠀⠀⣠⣿⣻⠼⣿⡿⣼⠃⠠⠀⠃⠀⠀⠀⠀⠛⠻⠜⠻⢄⠀⠀⠀⠻⣄⠀⠀ ⠀⠀⣰⣟⢧⢯⣛⣧⢿⣥⣣⣤⣤⣤⣜⠀⠀⠀⢰⡃⢀⣄⣄⣀⡀⠀⠀⢹⡄⠀ ⠀⣼⣟⡞⣯⣞⡽⢮⠿⠿⣿⣽⣿⣿⣿⣿⡶⠘⢿⣿⣯⣿⣿⠿⠟⠀⠀⠀⢻⡄ ⢹⣟⣾⣹⢳⣮⢽⣫⢟⣳⣶⣦⠀⣴⡿⣞⣳⠀⠘⣿⣦⡀⠀⠀⠀⠀⠢⣀⠀⣷ ⠃⣿⡶⣯⣟⢮⡗⣯⣾⣿⡻⣼⣟⢯⣿⣿⣿⣀⠀⢹⣿⣷⠀⠀⢰⣤⣤⣹⢄⡷ ⠀⠹⣷⣻⡽⣮⣷⣿⢿⣫⠷⣿⡝⡾⣿⢿⣿⣻⣶⣾⠟⠉⠲⡀⠘⢿⣭⢻⣼⠃ ⠀⠀⠘⣷⣻⣿⣿⡿⣿⠿⣿⠿⣿⢿⣟⡛⠿⠷⢶⣶⣦⣤⣤⣤⣤⣬⣿⣦⠏⠀ ⠀⠀⠀⠹⣷⣻⣧⢟⡮⣟⢾⣹⢎⡷⣎⡗⠀⣤⢀⡀⠀⠈⠁⠉⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠈⠻⣽⣞⡵⣻⢮⡝⣯⢾⣹⡛⠒⠠⠄⠠⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣯⣾⣭⡏⡟⣿⡄⠒⢰⠀⢠⢰⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠿⡵⣿⣶⣦⣀⡀⠀⠀⣀⣀⡴⠋⠀⠀⠀ ⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣼⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠛⢻⠉⡉⠍⠁⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⢀⡼⡄⠃⠤⠀⠀⠀⠀⠀⡐⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣸⡎⣀⣷⣤⣶⣶⣶⣦⡀⠀⠈⠓⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣤⣯⣿⣿⣿⣿⣿⣿⣿⣭⣯⡆⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⣿⣼⠀⢹⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢘⣿⠙⠡⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣯⠏⠀⢀⣿⣿⣿⣯⣠⡀⠀⠀⠀⢀⣾⡏⠒⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢘⣏⣺⣤⣬⣭⣼⣿⣿⣯⡉⢻⣦⣌⣦⣾⣿⣿⡚⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⡟⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣧⡞⣻⣩⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣬⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡟⠻⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠓⠲⠤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢯⡁⠀⠀⠀⠉⠹⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀⠹⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠀⢸⡄⢹⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⡄⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡀⣀⣰⣿⠀⠄⠹⣾⣿⣿⡿⣿⠀⢠⣤⣀⣴⣤⣤⡴⠶⠶⠿⠿⠛⠛⠋⠉⠉⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡱⠏⠉⡟⠃⠀⠀⠀⢸⣿⣿⠇⣿⡴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢋⣡⣶⣿⣂⡼⠁⠉⠙⠋⠙⠿⠟⣢⣄⢿⡟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀ ⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⣸⡿⠟⠀⠀⠀⠀⠀⠀⠲⣾⡛⣿⣬⡄⠀⠀⠁⠠⣤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡟⣿⡟⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠆⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⢀⣼⡟⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀ ⠀⣼⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀ ⠀⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡇⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣷⠀ ⢸⣿⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⣿⣶⠀⠀⠀⠀⠴⣿⣭⣭⣿⣯⣴⡯⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀ ⠸⣿⠀⠀⠀⠀⠘⠛⢫⣿⡟⠉⠙⠷⣤⠀⠀⠀⠀⢀⣴⡶⡟⣉⣍⣹⣷⣟⢹⣿⠖⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠀⣿⡄⠀⠀⠀⠀⠛⠛⢻⡿⠯⢿⢒⣿⡏⠀⠀⠁⣿⡿⠞⢻⣿⢼⣯⣽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀ ⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⣿⣷⣶⣶⣶⠾⣿⠟⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠂⠀⣶⣿⣯⣏⣿⣧⠽⣿⣿⣯⣿⣿⣿⣶⣶⣿⡟⣿⣿⣷⣦⣠⠀⠀⠀⠀⡄⠀⠀⣾⡇⠀⠀⠀ ⠀⠀⠀⢀⣧⠀⢣⢸⣿⣿⣿⣿⣿⠿⠿⣮⣿⣧⣿⠿⠤⠿⠷⢿⣿⣿⣿⣿⣿⡀⢰⠀⣀⠀⠃⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⣻⣆⠈⡏⠿⠛⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⠟⠋⠹⠇⣼⢰⡟⠀⠀⠀⣼⣿⣻⡀⠀⠀ ⠀⠀⠀⠀⣏⣿⣇⠀⠀⠀⠐⣆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣴⡟⠀⠀⠀⢠⡏⣼⡇⠀⠀⣸⣿⣿⢫⢧⠀⠀ ⠀⠀⠀⠀⣿⣸⣿⡆⠀⠀⠀⣈⢷⣦⣀⣀⣀⣠⣤⣤⣤⣶⣿⠋⠉⠀⠀⠀⢰⢟⣼⠏⠀⠀⢀⣿⣿⣿⠂⣿⠀⠀ ⠀⠀⠀⠀⠇⠀⢹⣧⠀⠀⠀⢿⠀⠈⠙⠛⠛⠛⠿⠟⠋⠉⠛⢷⡄⠀⠀⠀⠈⠛⠉⠀⠀⠀⣸⣿⣿⣿⣼⢿⠀⠀ ⠀⠀⠀⠰⡄⠀⠀⢻⣦⣀⠀⠘⣧⠀⠀⢹⡄⠀⠀⣠⣦⡀⠀⠘⣷⠀⠀⢠⣤⣴⣤⣀⣀⣶⣿⣿⠿⠋⢁⣼⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠻⣿⣧⣀⣿⡄⠀⢸⣿⠀⠀⢹⣿⡇⠀⠀⣿⣇⣠⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⢠⡜⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⡀⢀⠴⠁⢈⢿⣿⠇⠀⠈⣿⡆⠀⠈⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠋⠀⣠⣮⠞⠛⠓⠒⠶⣼⣷⣤⣤⣬⣿⣤⣤⣴⡟⠛⢻⡟⠛⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⣠⣯⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⠿⢿⡇⠀⠈⢧⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⢀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⢷⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⡀⣀⣀⣀⣠⣴⡿⠀⠀⠀⠀⠀⠀⢀⣷⣀⣠⡈⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢭⣷⡶⠟⠋⠉⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⣀⣀⣤⡶⣀⠁⣠⣾⢟⣫⠟⢹⣿⢸⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⠶⠶⠶⠾⠟⠛⠋⣴⣿⣧⣾⣿⣾⡏⠀⢸⣿⣾⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣆⡀⠀⢀⣠⣾⣿⣿⣍⣹⣿⣿⣴⡇⠀⠈⣿⣿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠿⠟⣩⡿⢿⣯⣿⠉⠉⠀⠀⠰⣿⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡙⠻⠶⠟⢻⡇⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣛⠶⣄⣩⣷⣶⣴⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⣿⣶⣮⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠟⠓⣊⣿⠿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢹⡿⠮⠀⢾⡛⣛⣛⢻⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠒⠛⠛⠒⠶⣦⣴⡉⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣷⠀⠲⢾⣭⣭⣿⡭⣿⣿⡄⠀⠀⠀ ⠀⠀⣴⡿⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⡀⠀⢀⣤⣤⣤⣬⣿⣿⣿⡆⠀⠀ ⠀⣼⣟⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡀⠀ ⠀⢿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀ ⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⡻⠿⠿⠿⠿⠿⠿⠟⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠔⣯⠤⠚⠛⠟⠀⠀⠀⠀⠀⠾⠿⠿⠿⢶⣄⠈⠣⡀⠀⠀ ⠀⢀⡠⠖⠉⢀⡠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⡀⠀ ⣠⠋⠀⠀⠀⣠⠖⣡⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠢⢄⡀⠀⠀⢷⠀ ⡇⠀⠀⣜⡵⢡⠞⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⡄⠀⢘⡄ ⠛⠒⢺⡉⠀⣾⠀⠀⠀⠀⢀⣀⡀⢹⠀⠀⠀⡏⠀⠀⠀⠀⣀⣀⠀⢻⠀⢸⡇ ⠀⠀⠸⡇⠀⠙⣆⠀⠀⠀⣿⣿⣿⡞⠀⠀⠀⠹⡄⠀⠀⢸⣿⣿⡷⡟⠀⢘⠟ ⠀⠀⠀⢧⠀⠀⠈⢷⣤⣤⠬⠿⠁⠀⠀⠀⠀⠀⠘⣶⣤⡤⡭⠟⠁⠀⠀⡾⠀ ⠀⠀⠀⠈⢦⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⠃⠀ ⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⠘⠘⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀⠀⢐⣽⡀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠙⠏⠓⡂⠙⡄⠀⢘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡦⠋⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡄⠀⢀⠄⠀⠀⠀⠀⠀⣀⡔⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⢤⡤⠟⠒⠓⢒⠥⠄⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⡪⠔⠊⠁⠀⠀⠀⢀⡇⠀⠀⠀⢀⡠⢛⠦⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⡰⡕⠉⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⢠⠎⣀⠎⠀⠀⠀⠈⠉⠉⠁⠈⠈ ⢰⠁⠀⠀⠀⠀⣀⠔⠙⢄⠘⠢⠤⠔⠚⠓⠉⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀ ⠐⠤⠄⠀⠤⠊⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⡀⢿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⣼⣮⣻⣿⣮⣿⡿⠛⠋⠉⢉⣽⢻⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠙⠂ ⠀⠀⢻⣿⣿⠏⠁⠀⠀⠀⠀⠀⢀⠏⠈⢷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣅⣀⠔⠂⣻⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⡀⢨⣟⣿⠀⠀⠀⡀⠀⠀⠀⠥⠬⠤⠤⠜⠀⠮⠥⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⢻⡆⠉⢉⣨⢦⡀⠀⠀⣎⢤⣶⠟⠾⢦⡄⠀⠀⣼⣿⣿⡿⣿⣿⣿⠙⠛ ⠀⠀⠀⢀⣷⡰⢋⣭⣝⠵⠀⠀⠈⠈⢱⣿⢿⡆⠙⡆⢠⣿⣿⣿⠇⠈⣻⣿⡆⠀ ⠀⠀⠀⣼⡾⢷⠈⢿⣿⠇⠀⢴⣤⣀⠪⠻⠛⠡⠐⣥⡿⠟⡿⢃⠴⡪⢣⠈⠁⠀ ⠀⠀⠀⠀⠠⠋⣃⠉⠈⠅⠀⠄⠫⡛⠁⠒⢄⠀⢸⠃⠀⠈⣠⣼⣴⣧⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡆⠈⠁⠘⠀⠒⠐⠵⣄⢀⠵⡌⠀⢀⢾⣯⡿⣯⣩⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⢂⢀⠀⠒⠒⡢⠤⠔⠒⠊⠀⠘⠄⢁⡼⣿⡀⣿⣿⣿⣦⣤⣄ ⠀⠀⠀⠀⢠⠇⢨⡈⣄⢌⠐⠀⢜⠀⠀⠀⠀⠀⠀⢘⣿⣯⡎⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⣆⠣⠀⢰⣌⠐⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⡄⠀⣠⡤⡲⢟⠢⣀⡄⡇⠈⣾⣷⣤⣤⣶⣾⣿⡿⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣶⣿⣿⠿⢛⠭⡫⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡤⠴⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⢀⣼⡏⠁⠐⠀⣄⠙⢶⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡿⠃⠀⠀⠈⣶⣼⣿⣟⣻⣿⣿⣿⣁⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⣀⣤⣤⣤⠀⢸⣿⣇⢸⢿⣿⡿⣿⣿⣦⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⠉⣠⣾⣿⣇⠈⠉⢻⣷⣿⣿⡏⠁⠢⢄⡀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢶⡀⠀⣉⣿⣿⣻⣤⡄⠀⠙⠦⣀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣯⣇⣸⣿⣿⣿⣿⣿⡁⠀⠒⣦⠈⢻ ⠀⠀⠀⠀⣿⣿⡿⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢋⣀⣼ ⠀⣴⡷⠟⠛⣩⣶⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⢁⡄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠻⠿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡉⠉⠳⣄⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣿⣿⣿⡄⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣦⣹⡅⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠻⠿⣿⣿⣿⣿⢿⣿⣿⣷⠀⢠ ⠀⠀⠀⠀⠀⢠⡴⢚⣽⣿⣿⣿⣧⠀⠀⢸⣿⣿⣋⣘⠻⣿⣿⠀⠀ ⠀⠀⠀⢀⡴⢛⣾⣿⣿⣿⣿⠋⠛⠓⠿⠟⢻⣿⣿⣿⣧⣼⣯⣄⢸ ⠀⠀⢠⠟⢰⡟⠉⠟⠉⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⡿⢻⣿⣿⣼⣿ ⠀⢠⠏⠀⣿⡇⣿⡇⣤⡿⣿⠀⢀⡤⠀⢸⢛⣟⣫⠾⣿⠟⢻⣿⣿ ⠀⠁⠀⠀⣾⣿⢸⠁⠙⠛⣿⣤⡿⢧⡀⣿⣦⣠⠀⠤⢻⣶⣿⠛⢿ ⢠⣰⣶⣿⣿⡇⠾⠀⠀⣼⣿⣇⠀⠀⠉⣿⣼⣿⣇⣤⣿⣿⠻⣶⣾ ⠰⢿⣿⣿⣿⠃⠤⠄⠀⣿⣿⡜⠆⠀⠀⣿⣿⣿⣿⣿⣿⣟⠀⣿⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠋⠀⠀⣀⣀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠀⣼⠿⠧⢍⡉⠁⠀⠊⠄⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⡀⠀ ⠀⣸⡟⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠔⠀⠀⠀⠀⠀⢳⠀ ⢠⣏⡵⠀⠀⠀⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⡀⠀⠀⠀⠀⠀⠈⡆ ⢘⡿⢷⣤⠤⡤⣀⢀⠀⣀⣀⣀⣠⣤⣤⣤⡶⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⣷ ⢸⣧⡬⣿⣬⣿⣾⣫⠍⢸⣿⣿⡟⢫⣠⠘⠃⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡟ ⠸⣽⢧⡈⠛⠿⣿⡈⠐⢻⣉⣻⢖⣤⡭⢼⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃ ⠀⢻⣼⣿⣆⣼⠻⡇⢀⣖⣼⡛⣓⢤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠈⢻⣟⣿⡟⡉⢧⣜⠁⠐⠄⠈⢃⢱⠀⡤⠖⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠻⣿⣷⠱⡀⠹⡀⠀⠹⡀⠘⡄⠙⡏⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣷⡈⠀⡇⠀⠀⠱⣤⣡⠈⠂⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠤⣀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀

⣿⢎⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢠⠀⠀⠀⠁⠀ ⡿⠁⣾⢧⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣙⣆⣀⣀⣸⢧⠲⡀⠀⢆ ⠇⡀⠁⢸⠇⣯⡛⢳⡾⣼⣶⣦⠀⡾⡄⠀⠀⡄⠀⢹⣛⣩⠹⡄⢰⣈⣆⣡⠀⢸ ⠀⠇⢰⣈⠀⣛⣆⣸⡁⢄⡰⡠⡀⠐⣱⠂⠀⡇⠀⢸⢄⣠⣴⣿⡟⠙⢿⣿⠒⡎ ⢰⠀⢸⢤⣵⡿⠋⣿⣿⣿⣮⣝⣧⡀⢱⡁⢀⢿⢀⣼⣿⠿⡟⣻⡇⠀⣿⢿⠀⣆ ⣸⢀⢼⠀⢻⢧⢠⢹⣿⡙⢋⣿⣿⠛⢪⣳⡸⠈⡠⠃⣿⣦⣴⡿⡏⠘⢉⢸⠀⡿ ⣷⡟⢸⢀⠎⡎⢻⡌⢿⣿⣾⣿⠟⠀⣸⣽⣷⣾⡱⢁⢻⠿⢿⣋⡠⠔⠛⢸⠀⢹ ⣿⠃⣯⣾⡄⢸⠀⠶⢄⣉⣛⣁⢖⣿⢫⣿⡟⡑⡰⡑⢝⣭⡯⡫⣳⣠⠾⡄⠀⢸ ⠇⢘⣏⣿⣧⠀⣿⡞⣵⡛⡵⠣⣗⢟⠋⠁⠁⠀⠌⢈⣸⡘⢱⢽⢓⣢⢮⡇⠀⠈ ⣪⣿⣣⢻⣿⢀⣟⢬⢎⡼⠁⠉⢤⣤⣠⡐⣒⡀⠉⠀⡞⠀⠀⣀⣶⣿⣾⠀⣼⠀ ⡏⠈⣿⡶⢺⡜⠈⠛⠮⣥⣪⠁⠀⢩⠈⠁⠀⠀⠉⠡⣇⣤⣾⡟⠁⢻⣿⢰⠋⣱ ⠙⣆⠸⣟⣜⠁⠀⠀⠀⢸⠙⢿⣷⣶⡗⣄⣀⣆⣠⣾⣼⣿⡋⠀⢀⣿⢇⢿⢠⢻ ⠀⠈⡆⠘⣿⣆⠀⠀⠀⢸⠆⠸⡿⡟⣯⣿⣿⣽⣿⣿⣿⠏⠈⢦⡚⢸⣸⢈⢣⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠈⠉⠉⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⢙⣦⡈⣷⡄⠀⠀⠀ ⠀⣀⠶⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠿⢿⡟⣌⢿⠀⠀⠀ ⣠⡿⠀⢠⣜⠉⠀⠀⠙⢷⢄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⡆⢧⡀⠀ ⣯⠃⠀⢾⣿⠗⠀⠀⠀⠀⡽⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⡰⠃⠘⣵⡄ ⡏⠀⠀⠘⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢱⡇ ⡅⠀⠀⠀⠙⠒⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡗ ⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣇ ⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⣸ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇ ⠀⠀⢇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡤⢰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡼⠋⠀⠀⠻⠿⠿⠿⠛⢉⣩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠈⠙⠻⢿⣿⡿⠋⠰⠿⠇⠀⠀⢀⣄⠀⠀⣀⠴⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡠⠔⠒⣊⣉⣉⣉⣉⡒⠒⠒⠠⠤⠤⠤⠄⠀⡀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⣀⡤⢚⡥⣐⡺⠭⠍⠁⠠⣤⠄⠉⠉⠁⠀⢀⣀⣀⣉⣉⡉⠓⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣁⡔⡱⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢩⠆⠀⠀⠀⠈⢣⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠛⠛⢛⣛⡛⡿⠋⢁⡈⣠⡴⣾⣿⣿⡟⠓⠶⣤⡁⠀⠀⠀⠀⠼⣀⣤⣤⠤⣤⡈⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⢶⠞⢙⣛⣛⣧⣈⠋⠀⠛⠒⠛⢛⣿⠛⠶⢤⣨⠟⠀⠀⠰⠶⣾⠿⠛⠓⠒⠚⠋⠈⠙⠋⢑⡮⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠁⠇⣰⠟⠁⠀⡆⠉⠛⠷⠤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣄⣠⡶⠾⠲⢶⢹⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⡀⣿⢀⣠⣴⠛⠶⢤⣄⡀⠀⠀⡠⠤⠤⠴⣴⠖⠂⠀⠀⠀⠀⠉⠻⣦⡄⠀⠉⠉⠁⣷⡀⠀⡸⢠⣱⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣄⢇⠸⡆⠀⠘⣧⣀⠀⠉⣿⠳⠶⣤⣀⡀⠈⢧⡼⠟⠛⠓⢀⡀⢀⣼⠟⠋⠓⠢⢀⣠⡿⣧⠨⠔⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣍⠃⠀⠀⠘⣿⡻⢶⣾⣦⡀⠀⠀⠉⡿⠲⠶⠦⣤⣄⣀⣉⣉⣁⣀⣀⣠⠶⠛⡇⢷⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⢷⡄⣸⠙⠻⠿⣶⣦⣧⣀⣀⠀⠀⢸⠀⠀⢹⡏⠉⣀⣸⣇⣀⣷⣾⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠹⢯⣀⠀⠀⠀⣹⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠙⠳⣦⣠⠏⠀⠀⠀⠀⣿⠀⠈⠉⣹⠿⢄⣴⠟⠿⡇⡼⣹⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡉⠒⠭⣓⠦⣀⡉⠙⠲⠶⠦⢤⣿⣤⣤⣠⣏⣀⣴⣯⡶⢄⡈⢙⣧⣀⠀⠸⡇⠀⢀⣤⣶⣶⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠉⠓⢤⣀⠉⠲⢭⣒⡦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠿⢤⣈⣳⣄⡇⢀⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⠀⢀⠈⠙⠲⣦⣀⠈⠉⠉⠒⠲⠿⠯⣍⣉⣉⣁⡉⠉⠉⣀⣀⠴⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡄⠘⣦⠓⢤⡀⠀⠉⠛⠶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠉⠛⠿⣿⣿⡿⠟⠀⠀ ⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣷⣤⡙⢦⡀⠀⠀⠀⠉⠉⠉⠙⠛⠶⠦⠤⣤⣀⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣈⠻⣝⢦⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠳⣌⡳⣌⠲⣬⡓⠦⡄⠀⠀⣀⡤⠄⢠⣄⢠⣟⡄⢸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡈⠳⣌⠳⢌⡙⠢⡀⢀⣼⡋⠀⠀⠀⢹⠀⠟⣡⢸⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠳⢄⠈⠳⣄⠙⠆⣰⡟⠈⢷⡄⠀⠀⢸⡇⠀⢃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡙⠢⡈⠓⠂⣿⡇⠀⠈⢿⣦⣄⠸⣝⢦⠈⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠙⠛⠿⠂ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠂⠀⣀⢀⣿⠇⠀⠀⣸⠛⣿⠀⠹⣷⡑⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⢁⡾⠋⠀⠀⠀⣿⠀⠘⠇⠀⠈⢿⣆⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⢆⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣶⣤⠀⠀⠀⠈⠙⠻⢦⣴⠶⠟⠋⠁⠀⠀⠀⣠⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⡶⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⣷⣄⠀⠀⠀⠀ ⠠⣿⣥⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣦⡀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⠀⣾⣏⣀⣀⣀⣀⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀ ⠀⠉⠉⠉⣩⡿⠋⠁⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠲⠿⣯⣄⡀⠀⠀ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣷⢾⡇⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⠀⢀⡿⠁⠀⣀⣀⣴⠄⠀⢸⡧⠖⠒⠛⠂⠀⣠⠀⠀⠀⠀⠀⠉⠉⠙⠢⡀⠈⠁⢸⣧⣀⣀⠀⠀⢀⣤⡶⠟⠉⠀ ⠀⢸⠷⠞⢛⣿⠟⠁⠀⠀⢸⡇⠀⣶⡦⠀⠀⡏⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠘⢿⠋⢻⣇⠀⠈⠻⣦⡀⠀⠀ ⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢙⣾⡿⢀⡀⠀⠈⢷⣄⠀ ⠀⠀⠀⣸⡇⠀⢀⣠⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣸⡇⠀⢿⣶⣤⣀⢿⡆ ⠀⠀⠀⣿⣤⡶⢿⡏⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢻⣏⠙⠻⠗ ⠀⠀⠀⠙⠉⠀⢸⡇⠀⢀⣸⡇⠀⠀⣠⠞⠉⠓⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠾⠛⠉⣷⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣸⡿⠁⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⢻⣤⡀⢀⡀⠀⢀⡀⠀⣀⡇⠀⠀⠀⢠⣿⠁⠀⠘⢿⣿⠶⢦⣤⣀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠙⠉⠙⠶⠋⠉⠛⠁⠀⠀⠀⠀⣿⣿⣷⣶⣤⣄⣿⡀⠀⠀⠉⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣏⠛⠷⠶⠶⠟⢛⡿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣦⣴⣶⣤⣴⠋⠀⢠⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⠟⠲⠎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠀⠀⠻⠿⣿⣧⠀⠀⠾⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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WHY IS THERE BEEF ON THIS WEBSITE?????

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⡏⠀⠀⣀⠀⢀⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⠖⢉⣾⢛⢍⣴⣾⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢫⠖⠉⠻⣧⠀⠀⠀⠀⠀ ⠀⠀⠛⣦⣾⡿⠛⢿⡄⠉⠀⠉⠛⠛⠛⠛⠻⣗⣶⡀⠀⠀⠀⢸⣿⣿⠋⠀⢀⣀⡀⣀⢻⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⡿⠲⠤⣸⡇⠀⡄⠠⣶⠿⠷⠖⣾⠿⠿⠁⠀⠀⠀⠈⠛⠃⠀⠀⣞⠀⠁⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⣠⡶⠖⠺⣿⠀⠁⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡤⠔⠋⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⠶⠒⡻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⢀⠎⣰⠁⠀⠀⠀⠋⢻⡍⠑⠦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢲⠂⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢸⡰⢿⡤⠀⠞⠉⠉⠉⠀⠀⠀⠙⣤⡄⠘⡀⠀⠀⠀⠀⠀⠀⢸⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⡄⢸⠁⠀⣀⠤⢤⣲⣶⣿⢿⠿⢶⣦⣸⣷⠀⡇⠀⠀⠀⠀⠀⠀⢸⣼⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡌⠣⡸⣿⣿⣟⣫⣩⣷⣾⣾⣿⣿⠛⢹⢰⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡈⢿⣟⠿⠿⠿⠯⠟⢚⡡⠋⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢮⣯⠙⠒⠒⠊⠉⠁⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢈⠁⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠤⣤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⢇⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀

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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⣴⣶⣶⠿⠟⠛⠻⠷⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠰⠆⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣇⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢾⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣦⡀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣦⠙⠻⠟⠛⠀⠀⠀⠀⠀⠀⣶⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣶⣤⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡍⠛⠻⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠻⠛⣿⡿⠁⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣦⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣶⣶⡶⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⠇⠀⣠⣴⣾⠟⠛⠉⠉⠉⠉⠛⠻⣶⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⠃⠀⠀⠐⠿⠿⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⡇⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⣿⡿⠿⠟⠛⠛⠀⠀⣀⣀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢣⣾⣿⣥⣾⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣀⣤⣶⠿⠛⠛⠛⠻⣿⣧⠀⠀⠀⠀⠀⣠⣶⣿⣶⣤⣾⡟⠁⠈⢱⣿⠁⠈⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⣠⣿⡟⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⠿⠿⠛⢋⡉⠁⠀⠀⣠⣾⡿⠋⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣦⣤⣶⣿⣛⣋⣠⣴⡾⠟⠋⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣤⣶⣶⣄⢀⣴⡿⠋⠀⠀⣸⡟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⣿⣿⣿⣿⠿⠋⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠛⠛⢛⡉⠁⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⣿⣧⣤⣤⣤⣶⡾⠟⠉⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⢩⡥⠄⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⢻⣿⣾⣷⣤⣴⣶⣾⣿⣿⣿⣿⣟⣟⣻⣿⣿⠿⠛⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠁⠀⠰⣿⡟⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣀⣀⣀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⣸⣿⣧⣶⣶⠿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⣤⣶⣶⡿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡘⣿⡆⠀ ⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⢻⣧⡀⣠⣿⠉⠙⠛⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢺⣯⡀⣠⣿⠉⠙⠛⢻⣿⡄ ⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⣿⣧ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿ ⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏ ⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠛⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⢁⣤⠴⠷⠶⠼⢿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⡆⠈⠍⢰⣾⣯⣅⠀⠙⠻⣿⣿⣿⡇⣏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠰⠋⣽⣿⣍⠁⠀⠀⠈⠛⠛⠀⡿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣋⠀⠐⠻⠿⠁⠐⠀⠀⠀⡀⠀⢰⣀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡏⠀⠒⣲⠤⡀⠀⠀⠀⠀⣸⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢶⢙⣉⣀⠴⠲⡄⠀⢠⠃⠀⠀⢀⡏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡛⠛⠒⠃⠀⢀⡔⠁⠀⢀⡴⠋⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⡳⢤⣀⣠⠔⠋⠀⢀⡴⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠤⠒⢩⠏⠀⠀⡇⠀⠸⣍⢉⣷⠺⢥⠀⠀⠀⠀⣰⣿⡿⠛⠛⠻⣿⠉⠁⠀⠀⠈⢑⠒⣤⣄⣀⠀⠀⠀ ⠀⢠⣤⠖⠊⠁⠀⠀⢀⠏⠀⠀⠀⣇⠀⢀⡸⠃⢸⢤⠟⢣⡉⠀⡰⢹⣿⠁⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠈⠉⣿⣿⣧⡀⠀ ⢠⢻⡇⠀⠀⠀⠀⠀⠺⢄⣀⠀⠀⠸⢴⡏⠀⢀⡏⠀⡇⠀⠙⠖⠁⣼⡇⠀⠀⠀⣠⣴⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀ ⡜⢸⡇⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠸⠇⢠⢾⡇⠀⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇ ⠀⠀⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡇⢸⢱⠀⣇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⣿⣶⡶⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠇⢸⠘⡄⢹⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⢸⣿⡿⠋⠉⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢹⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⡀⠀ ⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀ ⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⡞⠁⠀⠀⣀⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇ ⠀⠀⠀⠙⣳⣤⢤⣤⠤⠶⠋⠁⠀⠀⠀⢸⠗⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠉⠉⠉⠉⠁⠻⣄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⠶⠂⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⢻⡛⠛⠋⠉⠉⠉⠉⢉⠀⠀⠈⢻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⠀⠀⠀⠄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣴⣯⢀⣶⠀⠀⠙⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣄⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠳⣶⣤⣼⠀⠈⡆⠀⠀⠀⠀⠀⠀⢀⣿⡿ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣨⠁⡉⠉⠙⠛⠿⣿⣷⣄⠈⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠘⣿⣷⡾⠀⣿⠀⠀⠀⠀⠀⠀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⡇⡰⠋⢀⡔⠁⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠿⠛⠁⡸⠙⡆⠀⠀⠀⠀⣰⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⡴⠀⠀⡰⠁⠀⠁⠀⠀⠀⣰⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠿⠁⠀⠀⢀⡠⠞⠀⠀⢸⠁⠀⠀⠀⠀⣰⣴⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠇⢠⠀⠀⢰⡏⠙⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⢷⣄⡀⠀⠣⡈⠒⠒⠊⠁⠀⠀⠀⠀⡏⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⢸⠀⠀⣿⠛⢦⣀⠀⠀⠈⠉⠒⠤⠄⣀⠀⠈⠷⣌⣉⡩⠟⠀⠀⠀⣀⠀⠀⠀⡼⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡏⠙⢦⡘⠄⠀⢻⡤⠌⠈⠓⢦⣄⣀⡀⠀⠀⠀⠉⠒⣦⣄⠀⠀⠀⠀⠀⠁⠀⡄⠀⡰⠁⣀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⠀⠀⠙⢄⡀⠈⢷⡄⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡴⠗⠊⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠿⠛⠛⠛⠲⠤⣄⡀⠙⢦⡈⠻⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⠞⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠙⠢⣀⠙⠳⢦⣅⣼⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠑⠤⡀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⣄⠀⠈⠑⠦⣀⡀⠀⢀⣠⡤⠒⠉⠀⠉⠻⣿⣷⣄⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⣉⣍⠉⠉⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⡏⠉⢩⣿⣿⠏⠉⠉⠉⠉⠉⢩⣼⠟⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢙⣿⣿⠉⠉⣽⣿⣿⣿⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⢹ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⢠⡿⠁⠀⡴⠞⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣿⣿⠀⢠⣿⡧⣿⣿⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠘ ⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⣿⣿⣅⣀⣠⣤⣤⣤⣾⣧⣤⣼⣧⣤⣤⣤⣬⣿⡶⠾⠿⠿⠿⠛⠛⠋⢩⣿⢹⣿⡇⠀⣾⡿⠀⣻⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⡤⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⡁⢠⣿⣿⠉⠉⡉⠉⠁⣿⣿⢿⣄⠀⠛⠷⠛⠋⣠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⣿⣇⣼⣿⠃⠀⢻⣿⡆⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠍⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢀⢸⣿⡇⠀⠀⠓⠀⠀⣿⣿⣀⣙⣷⣤⣤⣴⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣸⣿⣿⣿⠇⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⢰⢸⣿⡇⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⣿⣿⡟⣀⣤⣤⣾⣿⣧⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠘⠁⠀⠀⢸⣿⡟⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢘⠀⠀⠀⣿⣿⣿⣶⣶⣶⣿⣿⣷⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⢛⣩⣿⠟⣿⣿⣡⡴⠾⠿⠛⠛⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿ ⠀⠀⢰⣶⠈⠀⣾⣿⡇⠀⠀⠀⠈⠉⣿⡏⠙⢿⣯⣍⣉⠉⠉⠉⠁⠀⢹⠉⠀⠀⢸⡀⠀⠀⢀⣠⣴⠿⠛⢁⣴⣿⣻⣥⣤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿ ⠀⠀⣾⣿⠀⠀⣿⣿⡇⠀⣤⣤⣤⣤⣼⣷⠶⠦⢬⣭⡛⠿⣶⣤⣤⣄⣸⠇⠀⠀⠀⠻⢤⡒⠛⠋⢀⣶⣶⠟⢹⣿⣿⣿⣾⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿ ⠀⢰⣿⣿⠀⢸⣿⣿⣿⠀⠘⣿⡏⠁⠀⢳⣠⣶⣶⣶⣍⠳⣆⣭⠭⠀⠁⠀⠀⠀⠀⠀⠀⢹⠏⢀⣼⣿⠋⠀⠃⠻⣿⣿⣿⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣿⣿⣿ ⠀⢸⣿⣿⡄⣾⣿⣿⣿⡆⠀⠸⣷⠀⠀⠸⣿⣿⣿⣿⣿⠀⠘⢿⡇⠀⠠⠦⠴⠶⠶⠶⢖⡿⣤⠚⠁⠇⢀⠀⠀⠀⠈⠉⠉⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿ ⠀⣾⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⠙⣧⡀⠀⠹⠿⣿⡿⠟⠀⠀⠈⠃⠠⡀⠻⠦⠀⠒⠀⠾⣸⣁⡀⠀⠒⠿⠶⠶⣶⣶⣶⣚⡛⠛⠛⢸⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣿⡿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⣿⠶⠤⠤⣤⣤⣤⣶⠶⢒⡶⢾⡟⠂⠀⠀⠀⠀⠀⠋⠉⠛⢓⠲⠤⢤⣄⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡴⠋⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⠴⠚⠁⢸⡏⠙⢶⡀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⣦⣀⠀⠀⠀⠠⠔⠉⠘⠧⣀⣀⣠⣿⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⢸⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⢿⣻⡶⢤⣀⡀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠠⠤⠤⠝⣦⡀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣶⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⠀⣭⡉⠉⠀⠀⠀⠀⠙⣿⡆⠀⢠⡄⠀⠀⠀⠙⠲⢤⣀⢀⣤⡤⠞⢻⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢿⡆⠘⣷⣄⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣠⡔⠀⣾⠏⠀⠀⠀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢧⠀⠙⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⠁⣰⡇⠀⠀⠀⣠⠈⠀⢸⡿⢿⣿⡛⠉⠁⠀⢀⡖⠈⠀⠬⣠ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠁⠀⠈⢳⡌⢿⣆⣀⣂⡀⠀⠀⠐⠀⣠⣤⣶⠟⢋⣀⢰⠃⢀⡟⢀⡀⠀⣠⣿⠀⠀⢸⣿⠀⢹⣿⡄⠀⠀⠘⣿⡿⠃⠟⠛ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣧⠀⠘⣆⠀⠀⠀⠀⠀⢳⡈⢻⣯⣍⣉⠉⠉⠙⣋⣩⡟⠁⣴⠋⠀⠀⠀⠀⠀⡼⠀⣰⣯⠟⠀⠀⣿⣿⡄⠀⣿⣧⣤⡄⠀⠘⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣷⠀⠸⡄⠀⠀⠀⠀⠀⢷⡈⢧⣌⠉⠉⠉⠉⣩⠟⢀⡼⠁⠀⠀⠀⠀⠀⣴⡇⣰⠗⠋⠀⠀⠀⣿⣿⡇⠀⢹⣿⢿⣂⠀⠀⠀⠀⠀⠀ ⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠙⣧⡀⢳⡀⠀⠀⠀⠀⠀⢻⣄⠈⠉⠉⠉⠉⠀⣠⡿⠁⠀⠀⠀⠀⠀⣸⣿⠓⠃⠀⠀⠀⢠⢰⣿⣿⣿⠀⠈⣿⣿⡿⣀⠀⠀⠀⠀⠀ ⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⡇⢿⣿⠀⠀⠀⢀⡞⢷⠈⣇⠀⠀⠀⠀⠀⠈⠻⣶⣶⣶⣶⣶⣾⠟⠀⠀⠀⠀⠀⠀⢠⣧⡿⠀⠀⠀⠀⣴⠋⣼⣿⣿⣿⡇⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⢸⠃⠘⣧⢸⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠁⠀⠀⢀⡼⣣⠞⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⣧⣤⣄⠀⠀ ⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⡇⠸⣿⠀⠀⠀⣾⠀⠀⢻⣧⣷⠀⠀⠀⠀⠀⢰⠤⠤⠀⠀⠀⠀⢲⠂⠀⠀⠀⠀⣸⢣⡏⠀⠀⣰⣿⡶⠋⢰⣿⣿⣿⣿⢿⡆⠀⣿⣿⣿⣿⣿⣿⠉⠈ ⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⣿⡆⠀⠀⡿⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⡾⠀⠠⣮⡿⠋⠀⠀⣸⣿⣿⣿⠇⠘⣧⣰⣿⣿⣿⣿⣿⣏⣄⣴ ⣿⢿⡄⠀⠀⠀⠸⣿⣿⣿⡇⢀⣹⡇⠀⠀⣇⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢹⣇⣴⠟⠉⠀⠀⠀⢠⣿⣿⣿⠏⠀⠈⣟⣻⣿⣿⣻⣿⢿⢓⣿⢾ ⡏⠸⣷⠀⠀⠀⠀⠹⣿⣿⡇⠀⠙⢗⠀⠀⢻⡀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⡿⠹⣿⣷⠿⣿⡿⢜⢹⠟ ⠀⠀⠹⣷⡀⠀⠀⠀⢻⣿⡇⠀⠀⠘⠀⠀⣾⡿⣦⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⣿⡀⣿⣿⣄⠀⠀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠶⠖⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣤⣴⣾⣿⣿⣿⡏⠉⠻⢇⠀⠀⠀⠀⢰⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡟⠹⣿⣿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠈⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⢠⡄⠀⠘⠁⠀⠈⠛⢿⡋⠀⠀⠀⠀⣼⡀⠀⠀⠀⣿⢀⣤⣄⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠈⣷⠀⠀⠀⠀⠀⢠⣿⣿⣶⣤⣴⣾⣿⡇⠀⠀⢀⣿⡟⠀⠌⠀⠐⢻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄⠀⠸⣶⣶⣿⣿⢿⡟⠉⣽⣿⡿⠃⠀⢠⣿⠉⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣇⠀⠀⠙⠿⣿⠃⢸⠃⢀⡿⠋⠁⠀⠀⠘⢻⡀⠀⠠⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⡷⠾⠷⠿⣤⣀⠀⢠⡏⢠⠟⢀⡼⠁⣀⣠⠴⠂⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢷⡈⠛⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠚⠓⠒⠒⠒⢿⡀⠀⠀⠀⠀⠀⠀⣸⠟⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠚⠻ ⠀⠀⠀⠀⠀⠈⠙⠛⠦⠴⠦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⡻⠋⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⡿⠦⣤⣤⡈⠳⡙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠛⢹⣅⣠⠤⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⡇⠀⠀⠙⠉⠛⠛⠀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣻⡟⠁⢰⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⣀⡾⢽⠗⢲⠏⠘⠋⠉⢛⠉⠉⠉⠉⠑⠲⣄⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⣼⠤⠖⡻⠃⠀⢸⠀⡜⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡄⠈⢳⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠁ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡤⠒⢩⠇⠀⡴⠁⠤⢀⣘⣸⡀⠀⢀⣧⢀⣿⣸⡀⠀⠀⢀⡇⠀⢀⠙⣆⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀ ⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢡⠀⢠⠋⣀⠞⠀⠀⠀⠀⢸⡏⠀⠀⠀⢇⢸⠙⣿⠀⠀⠀⡸⡇⠀⣾⠀⠈⢷⡀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠿⡇⠀⠀⡇⠀⡏⢠⣏⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢠⠃⡇⣰⠀⡇⠀⢸⢳⡈⣧⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⡇⠀⢸⣇⡸⠀⠈⠛⢿⣶⣤⣄⣐⠠⠤⡀⠀⠀⠘⠁⠀⠏⠀⢀⠎⠀⣿⠷⣄⣣⠀⡎⠀⠹⣼⡄⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⢠⠞⠀⠀⠀⠸⡄⢸⢻⡇⠀⠀⠀⢸⣇⠈⠉⠛⣿⡿⠇⠀⠀⠀⠀⠀⡇⣠⠋⠀⠘⠁⠀⠀⠙⢲⠇⠀⠀⢹⣧⠀⠀⠀⢠⠁ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⡼⢼⠇⠀⠀⠀⠘⠿⣶⣴⡾⠋⠀⠀⠀⠀⠀⠀⢸⠟⠁⣷⣦⣤⠀⠀⠀⢰⢻⠀⠀⣰⠀⣿⠀⠀⢀⡞⠀ ⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⢸⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠷⣶⣦⣤⣼⡀⠀⡇⠀⣿⡀⠀⣼⠁⠀ ⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⢀⣼⡿⠙⠀⣸⠃⢸⣿⠀⣼⠇⠀⠀ ⠀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⡇⡰⠟⢀⡟⣿⣠⠏⠀⠀⠀ ⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⢦⡁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⢁⣧⠞⢀⣿⡏⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⠀⣷⡄⠀⠀⠀⠀⢸⠛⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢄⡾⢃⡴⣼⢻⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⡄⢿⠙⣦⡀⠀⠀⠈⠦⣀⡀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⠏⢀⡞⣽⠃⣾⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣷⣿⢠⠇⠙⢦⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⡄⠏⣠⣿⠞⠁⠀⣿⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡏⣸⠀⠀⠀⠉⠢⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠒⠚⢉⡴⠋⢸⣠⡾⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⡀⠀⢹⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣥⣾⣿⡟⠀⠀⢀⡴⠋⠀⢀⣿⠋⠀⠀⣀⣀⣠⣤⡿⠀⠀⠀⠀⠀ ⠙⢦⣴⠃⠀⠀⠀⠀⠀⢸⠋⠉⠻⣿⡀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⢈⣹⠇⢀⡴⠋⠀⠀⠀⣼⣷⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⣙⠀⠀⠀⠀⠀⠀⣏⣀⣀⡀⠙⠿⣦⣀⣤⢶⠋⠀⠀⣠⠶⠶⠚⠉⣹⣰⠞⠀⠀⠀⠀⢰⠏⠉⠉⠙⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⡄⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡇⠀⣾⣿⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣟⠀⠀⣀⣈⡘⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⢀⠀⢻⣞⡉⠈⠹⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣾⡷⠏⢀⣤⡄⠀⢹⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⢲⡆ ⠸⣧⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠹⠳⡄⠘⠛⠉⢁⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⢠⡏ ⠀⠹⡆⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⣸⠳⠤⠤⠾⠳⣄⣀⣠⠞⣀⡀⠀⠀⢻⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⢀⡟⠁ ⠀⠀⢻⡄⠀⠀⠀⠈⠂⠀⠈⠙⢦⡄⣰⢇⣄⠀⠀⠀⠀⠀⢀⣠⣤⣿⡟⠒⠀⠘⡇⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀ ⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠈⣿⣿⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠠⠄⠀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣼⠋⠀⠳⣾⣿⠟⠉⠀⠋⣁⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⡾⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣧⡀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠈⢳⣿⡶⣤⣀⠘⠻⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⠿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠸⣄⣨⣟⠺⢿⣲⣤⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣺⠯⠟⠋⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡌⠉⣿⠋⠀⠀⠈⢫⡉⠓⠒⣿⠛⠛⠛⠛⠓⠋⠉⠉⠀⠀⠀⢀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡙⠶⣄⣀⣀⣸⠸⢦⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣤⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠉⠙⠒⢶⠤⣤⣄⣀⣰⡆⠀⠀⠀⠀⢠⡖⠒⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠲⠦⠤⢤⣤⠾⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⡆⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠉⢻⡟⠓⠒⠚⠛⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣾⢟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠟⠉⠉⠉⠻⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠏⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣠⣤⠀⢠⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⣣⠶⠚⢀⣀⣀⣀⠀⠀⢄⠈⠂⠻⢿⣿⣿⣧⣴⣿⠻⡏⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢀⡀⠀⢸⣷⣶⠛⠋⠉⢙⣿⣿⣦⣸⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇⡀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠀⣇⠀⣼⣿⣷⣀⡀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠙⠿⢿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡁⠀⠇⢰⣿⣿⣿⣿⣿⠛⠋⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⣀⣸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⡾⢿⣏⠀⠀⠀⠀⠀⠀⢀⣴⠟⠿⠿⢿⣿⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⠃⠀⣹⣧⣄⠀⠀⢀⣤⠾⠉⠀⠀⠀⠀⠈⠻⣄⠀⠀⠹⡦⣄⡀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠛⣿⠃⠀⠀⠉⠻⣿⡿⠿⠿⠛⠉⢸⣿⡇⣦⣴⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠀⠀⠀⣸⠗⠘⠆⠀⠐⣿⡀⠉⠒⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡶⠀⠀⠀⠀⠹⣧⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣧⠀⠀⣠⣴⢿⠀⠀⠀⠀⠀⢻⠙⠲⢤⣀⠀⠉⣳⠤ ⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢁⠃⠈⠀⠀⠀⢀⠀⠀⠀⠀⣸⣶⣾⠿⠃⡋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠙⠋⢉⡄ ⠀⠀⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⠀⠈⠀⠀⠀⠀⣀⣸⣷⣤⣶⣿⣿⠿⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⡠⢃⣤⠏⠀ ⠀⠀⠀⠀⢀⠞⠀⡼⣿⠀⠀⠀⢀⣼⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠎⣠⠟⠁⠀⠀ ⠀⠀⠀⢠⠎⢀⡼⠁⠘⣧⠀⠀⠀⠙⠛⠛⠀⠈⡿⠿⢿⣿⣿⢿⣟⣋⣉⣤⣤⣾⡛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠇⢠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⣿⡒⠻⢄⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⢀⣼⡤⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠦⣀⠑⢦⡀⠈⢳⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠉⠉⠙⢷⣵⡂⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠟⠏⠁⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣹⡿⠿⣷⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣠⣴⣶⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⢩⠇⠀⢠⠏⠈⠉⠙⠛⠿⢷⣶⣶⣶⣾⣿⣿⣿⠿⠟⠋⠁⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⡖⠒⠚⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠑⠒⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⣸⣡⣏⠀⠀⠤⠤⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⢤⣤⠀⠀⠀⠀⠀⢦⡀⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣾⣿⡇⠀⢻⣆⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢹⡇⠀ ⠀⠀⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀ ⠀⣰⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⡃⢰⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣧⠀ ⢠⣿⠉⠙⣿⣿⣿⣿⠿⠿⠿⣿⣷⣮⣽⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠉⣿⡆ ⣸⡇⠀⢼⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇ ⢿⡇⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⢸⣧⠀⠐⠻⠿⣶⣤⣄⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀ ⠈⢿⡄⠀⠀⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠈⢿⣆⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢑⡂⣰⠀⠈⠳⣦⠈⠙⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣿⣟⡀⠄⠛⠉⠀⣠⠔⠚⠛⠮⡉⢫⠉⠐⠪⣇⣠⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⠃⠀⡠⠐⠂⠀⢀⣼⠏⢀⣤⠀⠀⠈⢞⠀⠀⣔⣉⠪⠿⢌⡉⢹⣿⣿ ⣧⣼⣿⣿⢀⡠⠔⢈⣄⢞⣟⣇⡆⠀⠀⠀⠀⠀⢸⠀⣰⡟⠁⠀⢀⡀⠘⣼⣿⣿ ⣿⣿⠏⠹⡅⠀⣴⠞⢅⣮⡁⠛⢿⡢⠄⣰⣠⡵⠃⠀⢏⢇⠀⠀⠈⠁⠀⣟⢿⣿ ⣿⣿⡄⠀⢳⣊⣕⣠⡌⠀⢙⣋⣈⣈⠟⠛⠃⠠⠄⣀⠈⠦⣓⣢⡤⢦⡾⠁⣰⣿ ⣿⣿⣯⣥⣤⠸⡀⡁⠁⠀⠀⠀⠀⣼⣶⣶⣶⣤⣤⣀⣈⣙⠈⢭⣉⣇⣀⣴⣿⣿ ⠋⠉⣿⡋⢁⠠⠐⢌⠢⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣞⠑⠢⣸⠙⡀⣹⣿⣿ ⣧⣤⣾⣄⣁⣠⡴⠀⡽⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣆⣰⣟⡉⣿⣿ ⣿⣿⣿⣿⠛⣿⠁⢤⠇⢡⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣶⣧⢻⣿ ⣿⣟⢙⣿⡄⢘⢧⡾⠀⠀⢳⡗⠉⠀⠀⠀⠉⠻⣿⣿⠁⢀⣼⣿⣿⣿⣿⣇⠀⣿ ⣿⣿⣿⣿⣻⣸⠞⠃⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠙⣏⣴⣿⣿⣿⣿⣿⣿⣿⠄⣿ ⣿⣿⣿⣿⣧⣿⣦⣶⣶⣶⣤⡄⠀⠉⠒⠒⠒⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣶⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠧⠚⠹⡀⣿⣿⣿⣿⣿⣿⣥⣤⣤⣼⣿⣷⣯⠻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠠⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠙⠲⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⠉⠒⠢⢄⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠳⠶⠤⠤⣀⡀⢸⠀⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⢀⠞⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣰⠇⠀⠀⠀⠀ ⠀⢀⠎⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⣴⠿⣿⣷⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠠⣶⣿⡟⠛⢳⡴⢧⡀⣿⣿⡇⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠘⢿⣿⣦⣸⡇⠀⠻⠿⠿⠡⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣄⡈⠻⢿⡿⠃⣸⡿⠆⢀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⠀⣠⣤⣴⣾⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠋⠉⠈⠙⣧⠴⠚⠙⣿⣿⣿⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⣷⣦⡄⠈⠀⠀⠀⢠⣿⣿⣿⣿⣟⠿⡟⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣼⣳⣿⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣻⣿⣇⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⣠⣶⡄⣿⣿⣿⣿⣿⡀⠈⣿⡇⢀⣴⣶⣀⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣶⣿⣮⣱⣿⣿⣿⣿⣿⣿⣦⣿⣇⠘⠁⣹⣇⣽⢛⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠾⠿⠿⠿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣀⡀⢀⠀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠞⠛⠿⠛⠛⠛⠟⠻⠛⠐⠛⠛⠛⠃⠀⠐⠈⠳⠟⠛⠛⠛⠛⠒⠉⠛⠛⠀⠀

⠀⠀⠀⠑⠢⢤⣀⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠛⠳⣦⣤⣶⠾⠛⠛⠛⠛⠳⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠿⣿⣄⣠⠶⢶⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⠾⢿⣶⣤⣶⣄⠈⢻⣧⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣄⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢶⣄⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠻⣧ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⢻⣅⣨⡇⠀⢈⡉⠢⡀⠀⠀⠀⠀⠈⣿⡄⢹ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠖⠂⢢⠀⠘⣿⠀⠀⢹⡆⠀⠉⡹⠁⠀⠈⣿⠓⠁⣴⠶⣦⠀⠀⢹⣇⣼ ⣠⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⠏⠀⠀⢸⠀⠀⣿⠀⠀⣾⠃⠀⢰⠃⠀⠀⣰⠏⠀⢰⢿⣤⣾⠇⠀⢸⡿⠋ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠇⢰⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⡀⠠⠾⣿⠀⢀⡞⠀⠀⠀⠀⠀⢸⡇⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⣰⣇⠀⠸⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠳⣄⣀⣉⡴⠋⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⣧⡀⡄⠀⠀⠀⠀⠀⢀⣤⣶⠶⠦⠀⢠⣤⠿⠁⠸⡆⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀ ⠈⠻⣷⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⢸⣆⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢦⣤⠾⠁⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣀⣀⣀⣀⡤⠖⠃⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠛⠻⠿⣦⣴⣿⠋⠉⠉⠙⠻⣧⣤⣤⣴⣶⡶⠿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠙⢿⣧⣤⣀⣠⣴⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡿⠀⠀⣀⣤⣤⡴⠶⠾⢿⡟⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⣿⡀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢰⣟⠁⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠈⢿⣶⣦⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣄⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⣀⠀⠀⠀⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⢀⠄⠉⣀⡀⢉⠁⣠⣶⣶⣶⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⢁⠔⠀⠀⠪⢂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡇⢀⣴⣿⡿⢀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢉⠡⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠐⠂⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⡿⠛⠐⠂⠤⡐⠄⠀⢠⠀⠀⠊⠶⠛⠛⠛⠊⠥⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡏⠀⣀⣴⠶⠶⢾⠰⠀⠀⠀⠀⠀⠠⠤⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠊⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠣⡞⢟⠁⢀⠠⢘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡹⠂⠀⠀⡐⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠀⠀⡌⠀⡘⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⢰⠀⢈⢃⡀⠀⢠⠐⠀⠀⠀⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⣀⠠⠄⢀⣀⣤⣀⠀⠈⡄⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⠀⡀⠀⢀⠤⠒⣈⣩⡤⢶⠞⠟⢙⠉⡋⣛⣿⡆⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢄⠐⢄⠠⣿⣿⡋⡁⢁⣀⣤⣷⣾⣿⣿⣿⢿⠃⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⡜⢜⠻⣿⣿⡿⢻⣻⠹⠕⠋⢁⠊⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⢄⠢⢀⣉⡁⠁⠀⠤⠐⠊⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⡁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠐⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠰⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢻⣤⠶⠶⠲⢦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⣾⠃⠀⠀⠀⠀⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⢀⣴⠖⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠁⠀⠋⠙⠛⠈⠀⠀⠀⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠉⠻⣥⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠫⣤⣿⡄⣀⠀⠀⢠⣤⣄⠀⠀⠉⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡖⢫⠻⢁⣸⣷⣄⡙⠿⣜⢳⡆⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣦⣄⠀⠀⠀⠸⣧⣤⡤⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠀⠀⠈⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣤⣀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⢀⣴⠞⢛⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡍⠉⠁⣰⣄⡉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀ ⢸⡁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠙⠉⠙⠃⠀⠙⠂⣽⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⣶ ⠘⢿⣄⠀⠀⠀⠀⠀⠀⢶⢦⣄⠀⠀⠀⠐⠶⠶⢤⡄⠀⠀⠀⠀⠀⣠⠿⣤⡀⠀⠀⠀⠀⣸⡧⠀⣾⠀⠀⢸⠀⠀⢸⠀⣠⣿⠆⠀⠀⠀⠀⠁⠄⣹ ⠀⠀⠉⠙⠳⢦⣄⣀⠀⠀⢀⣿⣀⣀⣀⣀⡀⠀⣀⣿⣀⣀⣀⣴⣞⣋⣴⠟⠀⠀⠀⠀⠀⢿⣅⣀⣽⣆⠀⣼⣆⠀⣸⠿⣧⡀⠀⠀⣀⣴⣄⣠⡼⠏ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠁⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⢤⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠚⠒⠘⠃⠀⠐⠐⠛⠚⠃⠀⠊⠛⠀⠀⠀⠐⡒⠐⠂⢂⠀⠈⠑⠃⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣜⣷⣾⣛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠉⠛⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠸⣿⣦⠀⠀⠀⠀⠀⠀⣼⡿⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⢿⣦⡄⠀⢀⣠⣾⠟⠁⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣤⠿⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠠⣄⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢸⣷⡆⠀⢀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣦⣿⣧⠀⣿⣆⠈⢛⡀⠀⠀⢀⣠⣾⠋⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠉⠻⢿⣶⣿⣿⣶⣿⣿⣿⠷⠛⠋⢁⣼⠏⠀⠀⠀⠀⠀⢠⣾⡯⠿⠋⢹⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⡿⣿⣝⣸⣁⣙⣿⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣾⠓⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⣴⣏⣀⣀⣀⣀⣀⣀⠛⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⣀⠀⣶⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⢀⣴⢶⣦⣄ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢟⣭⣭⣭⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣾⣲⠟ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⣰⡟⢻⣿⣿⠟⢷⠼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠿⠿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣧⣾⣷⣬⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀