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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠂⣉⠭⡻⠙⢋⡩⠥⠒⠢⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠋⠀⢀⣔⠕⠁⢀⠐⠁⠀⠀⠀⠀⠘⠍⢢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⡐⠀⠀⠀⣾⠂⠀⡔⠁⠀⠀⡈⠀⠀⠀⠀⠸⡌⠿⡄⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠰⠀⠀⠀⠸⠇⢀⠌⠀⢀⠎⠀⠁⠀⠀⠀⠀⠀⠘⡘⡘⡆⠀ ⡆⠀⠀⠀⢠⠏⠀⠆⠀⠀⡀⠏⣴⠋⢀⣀⠎⠀⢰⠀⠀⠀⠀⠀⠀⡀⠁⠁⢹⠀ ⠁⠀⠀⢀⡎⠄⢠⠀⠀⠀⢁⡼⠁⡀⡠⢊⠁⢢⡆⡀⡀⠀⠀⠀⢠⠇⢰⡄⠸⠀ ⠀⠀⠀⡺⢰⠀⡜⠀⠀⢰⢸⣷⣾⣥⣤⣎⡠⠂⣄⢁⠃⠀⢀⣇⡈⠸⢸⡄⠀⠀ ⠀⠀⣠⠃⡆⢀⡇⠀⠀⠈⢸⡀⢰⢳⡻⡟⡎⠰⠃⡞⣀⣴⠏⡧⠉⠐⣿⠀⠀⠀ ⡾⣤⠃⡸⠁⢸⠀⠀⠀⡄⢸⠐⠸⠌⡹⠃⠀⠀⠈⠉⢈⣱⣾⣁⠄⠀⣻⠀⠀⡀ ⣠⠧⢡⢣⠀⡀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣙⡎⢻⣶⡇⠀⢠⡇ ⠟⡱⡟⡈⠀⡇⢇⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⢤⡾⢳⡇⠀⣾⡇ ⢔⢱⢣⠃⠸⢑⢘⠀⠀⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣧⡈⢡⠀⣿⡇ ⣠⠏⡈⢀⢃⢸⢨⡸⠀⣇⢰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⢸⢀⡜⢸⡿⠂ ⡟⠀⠇⣘⠎⡄⢸⣇⡀⢿⢜⡀⠑⢄⠀⠀⢀⡀⠄⢲⢸⠀⡜⡚⡄⣸⠃⡾⠁⠀ ⠁⢰⣰⠋⠰⡇⣿⠿⢇⠸⣶⣷⣤⡀⠁⢸⠁⠇⠀⠸⣈⡜⡄⣇⡗⣟⠜⡇⢇⣀ ⠀⠘⠁⡠⣱⢿⠁⠛⠂⠤⣄⣈⠙⠻⡇⠘⠀⣼⠀⢀⢿⠀⡇⢻⠗⠹⠀⣿⣾⣿

⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢻⣿⡿⣿⠏⢻⣻⡿⢉⣭⢯⠉⢻⣿⢸⡇⢹⡇⠈⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⢹⡟⠀⠸⣿⡧⣿⣿⠀⠙⣸⡗⢸⠃⠀⣿⡀⢻⣿⣿⣿⣷⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡇⢰⣟⡇⣹⠇⠀⢰⣿⢃⣼⣿⡀⠀⣽⣇⣿⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⣾⡇⢸⡿⢀⣿⡄⠀⣼⡿⣼⣿⣿⡄⢸⣿⣿⡿⠒⠛⡏⢻⣿⠙⣿⣿⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣾⣷⣿⣿⣷⣾⣿⣷⡟⣿⣿⣷⣿⣿⣿⠁⠀⣸⣁⣼⣿⣷⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⠇⣀⣴⣿⣿⣿⣯⡿⣿⣿⣿⢿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⡿⠃⢸⣿⣿⣿⡿⡋⠀⠛⠉⠀⠙⠧⣤⣴⣿⣿⣿⣾⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠘⠩⠤⠍⠈⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣄⠀⠛⢯⣉⣩⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⣿⡆⢹⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣌⠑⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣿⣿⡇⠘⣧⢻⠹⣿⣿⣿⣷⣿⡇⠀⢻⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢛⢛⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⡀⠙⣿⣿⡇⠀⢹⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠻⣿⠆⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⡟⠸⣇⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣹⠀⢳⡀⠈⢿⣧⠀⢸⣿⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⢟⣽⣿⣿⣿⣿⣿⣿⠿⠀⢀⣾⠁⢰⣿⣷⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣿⡄⠀⠱⡀⠈⢿⠀⠘⣿⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⣰⣿⠋⣾⣟⣿⡿⣽⢿⣿⣿⠀⠀⣼⠇⢠⣼⢻⣿⣾⣿⣿⡟⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⣻⣿⣷⠀⠀⢣⠀⠘⡆⠀⡿⢷⣿⣿⣿⣿⠋⣿⡄⠀⣀⡤⠖⠋⠁⠀ ⠀⢠⣿⡇⢰⣿⣽⠃⠀⠏⣾⣿⣿⠀⢰⣯⣤⣿⣿⣼⢿⣿⣿⣿⠄⢀⣠⣾⠛⣻⣶⣦⣄⣀⣀⣤⢾⣿⣾⣿⣿⣿⡀⠀⠈⠇⠀⢳⠀⢹⣾⣿⣿⣿⣿⠒⣿⣿⠋⠁⠀⠀⠀⠀⠀ ⢀⡞⢸⠃⣾⣿⠏⠀⡀⣸⣿⣿⢻⣷⣿⣾⣿⢿⣿⣿⣿⣿⣽⡿⢴⣟⣡⣿⣛⣉⡼⠿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢈⡇⢀⣿⣿⣿⣿⣿⢀⡿⢻⠀⠀⠀⠀⠀⠀⠀ ⡼⠀⢸⣰⠏⡏⢀⣾⣯⣿⣿⣇⣬⠿⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⣄⠀⠀⠀⣀⣀⣀⣀⠀⠉⠹⢿⣿⣿⣿⣿⣿⡀⠀⣠⠖⠛⠛⢀⣾⣿⣿⣿⣿⣿⣾⡇⢸⡧⠄⠀⠀⠀⠀⠀ ⠁⠀⢠⣿⣠⡇⣾⢫⣿⢣⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⣀⣀⣀⣀⣴⣿⣿⣿⣿⢿⣿⢹⣿⣧⣨⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠁⢹⣰⢣⡾⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣶⣤⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡟⢸⣿⠙⠿⠿⣿⣿⣿⣿⡿⣿⣿⡿⣸⡇⢸⣿⡋⠈⡇⠀⠀⠀⠀⠀⠀

⢀⠴⠂⠀⠀⠀⠀⢠⣶⣶⣶⡾⢟⣯⣵⣾⣿⣿⡁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⢫⣽⣿⣟⣿⣛⣮⡋⢽⡇⠀⠀⠀⢀⣼⣿⣿⡿⠋ ⠂⠀⠀⡴⠾⠋⠉⠻⣿⣿⣿⣿⣟⡛⡁⡴⡀⠘⢛⣼⠷⣦⣄⢓⢚⢛⣍⡼⠂ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠘⣏⣇⡸⠃⢽⠫⣧⣵⣼⣽⣧⢺⡝⣷⡾⣾⠞⠁⠀ ⠀⣾⢇⡠⡀⡀⠀⠀⣄⢲⠋⡯⠂⡐⠊⣳⢋⣿⠋⡋⣿⡌⣇⠘⣧⣧⡇⠀⠀ ⠀⠺⢧⣦⠀⢉⠶⣭⣿⣾⣼⣧⠰⣷⠬⡏⢸⣾⠀⣷⡟⣿⣿⠄⢹⣿⡇⠢⠀ ⠀⠴⢿⣷⣴⣿⡖⢻⡏⡏⠁⣠⣶⣗⡿⠃⣸⡯⠄⣿⢀⣿⡇⣶⣼⣿⡧⠀⠐ ⠀⠈⣿⢯⣽⡿⣾⢸⡇⣟⢸⣿⣿⣿⣦⡽⣿⣾⡜⠁⠈⠁⠞⡿⣸⡟⠀⠀⠀ ⠀⠀⡟⠛⢻⡷⣧⣸⣟⠿⢣⢍⡿⡏⠉⠀⠻⠗⠀⠀⠀⠀⠀⠈⣇⣇⡎⠀⠀ ⠀⢰⠀⢀⣎⢱⠰⡾⣿⠀⢸⠉⠠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⣧⠀⠀ ⠀⢸⠀⢸⢿⣿⡾⣧⢸⠀⣾⢀⢀⡇⠀⠀⠀⢠⠂⠀⠀⠨⠃⡰⣿⠂⡿⡄⠀ ⡁⢸⠀⢸⠄⣧⡇⠻⢾⠆⣿⣼⣼⡇⠒⢤⣀⠀⠑⠀⠐⢁⠎⢸⣿⡄⢁⣡⠀ ⠑⠜⡀⠘⡐⠚⡇⠀⢸⣷⣿⣿⣿⣧⣀⠈⢉⣉⣿⣶⠆⡅⡂⠘⣿⡗⠁⠀⠀ ⠀⠀⠑⠔⢅⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠻⣫⠕⢻⣤⡆⠀⣠⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣇⡠⢈⢻⣿⣿⣿⡇⢹⣟⢋⠀⠀⢸⣟⢹⡆⢻⣿⡇⠀⠀⠀

⠀⠀⠀⠀⠐⠂⠀⠀⠐⢲⠀⠃⠀⠀⣿⣵⢟⠁⣴⣿⣶⣶⣾⣿⣟⣫⣿⠉⠁⠀⠀⠈⠻⣿⣿⠃⢈⢡⣖⡈⢻⡟⣿⣇⣽⣿⣶⣾⣿⣷⣶⣤⡀⢛⣷⣵⣖⣾⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠛⠛⣶⣶⠦⣍⢻⣦⡘⠻⣿⣿⡿⢿⣮⡿⢿⣿⣿⣿⢞⣿⡟⠛⢿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⣷⣤⡛⠛⠲⠾⠛⢁⣄⠈⢸⣿⣷⡀⠙⠿⣯⣶⣸⣿⠾⢿⣽⣏⣿⡟⣾⣽⡾⣿⠿⣿⣿⣞⢿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⢙⣿⡿⣿⣵⠾⣶⣾⣿⡿⠗⠀⠄⣴⡿⣿⣥⣄⡀⢿⣿⠃⡀⠀⣿⣯⣿⣿⠀⠈⠛⢿⣿⡶⢤⣭⡾⣷⣖⣿⣿⠻⣧⣿⣿⡀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠴⠚⠃⠀⠀⢀⣰⣿⣿⣿⡶⠷⠿⢿⣯⠉⣤⠰⢗⣻⣶⣿⡿⡿⢯⠿⣎⠙⢄⣹⣾⣿⡅⡅⢿⡀⣀⣠⣿⣦⣿⡶⠶⠾⠟⣯⡍⣱⣴⣿⣿⣿⠳⢤⡀⠀ ⠄⠀⠈⠐⢀⣀⠁⠀⢀⠀⠁⠀⣠⣾⣿⣿⣿⡿⣿⢙⡿⠿⡿⠟⠀⡻⣶⣯⡉⣬⣭⠇⣀⡙⣷⣿⣷⢀⣭⣿⡏⠀⠀⢺⣿⣉⣘⡛⠻⠿⢹⡻⠿⠿⢿⣶⣿⣿⣿⣽⣿⣷⠀⠙⢷ ⣿⢀⠀⠠⣶⣿⣿⣿⣿⣥⣤⣶⠿⣿⣿⣿⣿⠀⣇⠈⢹⣶⠃⣀⡀⢿⣹⣿⣣⡾⢛⣀⣶⡟⢋⣽⣿⠟⠁⣿⡇⠀⠀⠀⢻⣏⠉⢹⠄⣾⣈⣿⣦⠀⣀⣽⣿⣿⢿⣿⣿⡿⢷⣄⠸ ⣤⣤⣶⣾⣿⣷⣿⡇⣿⣿⣏⠻⣶⠿⠋⠁⠉⠀⠻⣴⣿⠋⣴⣿⣽⣤⣽⣿⣿⣵⣿⠟⢁⣴⣿⠟⠁⠀⢸⣿⠃⡄⢀⡄⡟⣬⢿⡷⠶⢾⡇⢸⣿⡞⢿⣿⣿⣿⡷⠶⠚⠀⠀⠉⠁ ⣿⣿⣯⣭⣟⣛⣿⣿⣿⣿⣿⣧⡾⠛⠒⠀⠀⠀⠀⠈⠻⣀⣿⣿⣿⣾⣿⣿⣟⡵⣫⣾⣿⠟⠁⠀⠀⢀⣿⡟⢠⢃⡿⣸⢻⣇⢨⡇⠀⣿⡇⠘⣿⠧⠠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠿⢿⡿⣼⣿⣿⣿⣿⣿⣿⠃⢻⣿⣦⣖⣻⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠁⠀⠀⠀⠀⣼⣿⠁⣾⣾⣧⡏⣧⣿⢸⡇⢸⣿⠀⠀⣿⣻⠀⣽⡿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⣻⠸⣿⣿⣿⣿⣿⣿⣄⠈⠳⣽⡙⠿⢡⡶⣷⢀⡼⢿⣿⣿⣿⣿⣿⣿⡿⢯⣥⣄⡀⠀⠀⠀⢰⣿⣟⣾⢻⣿⣿⣼⢹⡟⢸⣵⣾⡟⠀⠀⢿⣿⡄⡏⡇⢻⢿⡄⠀⠀⠀⠀⠀ ⠟⣿⡿⣾⡿⣿⣿⣿⣿⡿⣉⣿⣦⣀⢵⣶⣿⣴⠿⠛⠁⢸⣿⣿⣿⣿⡟⠋⠀⠀⠀⠈⠉⠛⠳⢶⣿⣿⣿⣿⣿⣿⣷⢃⣿⠃⣾⣧⢻⡇⠀⠀⠸⣾⡇⣧⡇⢸⢸⣿⢀⡀⠠⠴⠀ ⢸⣿⣿⢿⣷⣿⣿⣿⣿⡟⠖⠚⠋⢹⣦⢻⣿⣱⡇⠀⠀⣸⢻⣿⣋⡁⠉⠙⠓⠶⢤⣀⠀⠀⢀⣾⡟⣸⣿⣿⣿⣿⠏⣼⡇⢀⣿⣿⣾⠁⠀⠀⠀⣿⣿⡿⣇⢸⣸⣿⡿⠦⠡⢠⣾ ⣿⣿⣿⡶⠂⢀⣿⣿⣿⣷⡄⠀⠀⠈⢻⣷⣬⣩⣽⠿⢿⣿⣿⣷⣶⣾⣭⣭⣆⡤⢄⠈⠙⢢⣾⠏⢠⣿⣿⣿⣿⠋⢰⡿⠀⣸⣿⢁⡟⠛⠲⠤⣀⣿⣿⣿⣌⣿⣿⣿⡶⠒⠔⠷⣴ ⣿⡏⠙⠒⠾⢛⣿⣿⣿⡍⢻⣤⠀⣰⠟⢹⡏⢙⠃⠉⠉⠀⡟⠉⠁⢋⣿⣿⡻⢿⣿⣶⣄⠉⠀⠠⣿⣿⣿⡿⠁⢀⣿⠁⢰⣿⠧⡼⠤⢤⣀⠀⠈⢻⣿⡄⢸⣿⣿⣿⣶⠤⢄⡀⠚ ⣿⠀⠀⠀⠀⣸⣿⣿⡿⠛⠛⠛⠚⠁⠀⢸⡗⠘⠂⠀⠀⢸⡇⠀⠀⠿⠷⢯⣿⡫⠽⠙⠇⠀⠀⠀⠈⠈⠉⠀⠀⠈⣥⣤⣭⣗⣒⣒⣤⣤⣄⣀⡀⢸⣿⠸⠀⣬⢸⣿⣿⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⡀⠀⠀⢸⡃⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠛⣿⣟⣿⣿⣿⣷⣦⣻⣧⡆⠀⢉⠸⣿⣿⠀⢾⡳⠄ ⠇⠀⠀⠀⢀⡇⡝⣿⡤⠀⡇⠀⡇⢀⠀⢸⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⢻⣟⡿⣽⣃⣀⣛⠠⣼⣿⠀⠀⢹⠀ ⠀⠀⠀⠀⢸⠀⠃⣿⣷⠀⡇⢠⠀⢸⠀⠸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⣴⡏⠀⠁⠀⠁⣿⣷⣾⡇⠀ ⠀⠀⠀⠀⢸⠀⠂⣿⣿⢴⡇⢸⠀⢸⠀⠸⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢸⣸⠀⠀⠀⠀⣤⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⠀⠉⡏⣿⣶⡇⣼⠀⢸⡀⠀⠀⢨⠀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⡟⣿⡄⠀⠀⠀⣏⡇⣿⠋⢻⠀ ⠀⠀⠀⠀⡈⠀⠀⡇⣿⣷⠄⣿⢸⢸⡇⠀⠀⢸⠀⣇⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢰⢻⡿⡆⠀⢠⠀⣇⡇⢻⠀⢸⣤ ⠀⠀⠀⠀⡇⠀⠠⡇⣿⣿⢰⣿⣸⢸⡇⠀⠀⢸⠄⣏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣼⣿⡇⡇⠀⣠⢸⣿⡇⢈⠶⠋⠀ ⠀⠀⠀⠀⡇⠀⠈⡇⢺⣿⣼⡇⣿⢸⣇⠀⠐⢾⡇⣿⡠⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢠⡟⣿⣧⠇⠀⣯⢸⣟⡗⠉⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡇⠈⢿⣿⡧⣿⠈⣿⠀⢀⢻⡇⣿⡇⣿⡆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠂⢀⠈⣼⣿⣿⠀⡆⣏⢸⣯⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⣿⣇⣿⡇⣿⠠⣆⣿⣇⣿⣧⣿⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠁⠀⠀⠀⢸⠀⡇⠸⣽⣿⢻⣿⢀⡇⡟⢸⠟⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⣿⡇⣿⡇⢻⣧⣧⣿⣇⣿⣿⣿⡇⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠉⠁⠀⠀⣀⠀⠀⠀⡀⡷⡇⢾⣧⣿⣸⣿⢸⣇⡿⢸⣦⡇⠉⠀⠀⠀ ⠳⡀⠀⠀⡇⠀⠀⡇⠀⠘⣿⡷⣿⣧⢸⢻⣿⡿⣏⣿⣿⢹⣿⡀⠀⠀⠀⠀⠘⠻⣿⣦⣤⣤⠞⢫⣟⣦⠀⠀⠀⣴⠀⣟⠀⠀⠀⡇⣿⡇⣸⣿⡿⣿⡾⢼⣿⣿⣿⣷⠇⠀⠀⠀⠀ ⠀⠹⡆⠀⣧⡀⠀⡇⠀⠀⢻⡇⢿⣿⣼⣾⣿⡏⣿⣿⣿⠈⣿⠙⢦⣀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣼⠟⣿⣁⡄⢰⠇⠀⢿⠀⠀⢰⠇⣿⣣⣿⣿⣧⣿⣷⣾⣯⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠈⠳⣄⣱⠀⠀⠀⣛⣸⣿⣿⢸⣿⣿⣿⣿⣿⣗⣿⡀⠀⠈⠓⢦⣄⡀⠀⣠⡴⠚⠉⠀⣠⣿⣿⢡⡟⠀⢘⣿⣶⣿⣾⠒⠛⠉⣸⣿⣿⣿⣷⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠳⠶⠾⠿⠤⣤⣠⣿⡿⣿⣿⢾⣿⣿⣿⣿⣿⣿⢸⣿⣦⣄⣀⠀⠀⠉⠉⠁⢀⣀⣤⣾⠿⢁⣾⠿⠷⠶⢿⣿⣿⣿⡿⢦⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⣿⢻⣿⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣟⣛⣛⣭⣥⠀⢀⣠⠞⠀⠀⠀⠀⢸⣿⣿⣿⠧⠀⢷⡀⣿⣼⣿⣿⣿⣿⣿⣿⣿⠤⠖⠊⠀⠀⡀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠏⣻⣧⡻⡿⣿⣿⣿⣿⣿⣿⣿⡈⣙⡻⣭⣇⣽⡏⣁⣠⡯⠗⠚⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠈⢳⣫⣿⣿⣿⣿⢿⣿⠿⠁⠀⠀⢀⡠⠄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⡫⣹⠇⣾⣵⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⡀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠘⢷⠿⠋⠡⢚⠉⣠⣻⣟⠻⠿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣸⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⠀⠀⠀⠀⠀⢀⣼⣷⠋⣴⣟⣽⣿⣷⣆⣾⣿⠏⢉⣹⣿⡶⢤⣠⣴⠏⢐⠟⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠄⠀⠀⢸⢀⡩⣾⣻⡶⠛⠉⠀⠀⢨⣧⡀⠸⡇⣨⣶⣛⢿⣧⣀⠉⢀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡔⡜⣁⣀⡀⠛⡩⢤⡞⠉⣠⣼⣿⣦⣄⠀⢀⣴⡟⢻⡷⣶⠟⣿⣴⡖⠊⠙⠛⠛⠚⠢⣄⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣸⠀⠰⢁⣀⣰⣦⠤⣾⣿⣶⣿⣿⠻⣿⣿⣷⣏⣩⣦⣤⣼⣿⣿⣿⡿⢿⣦⡀⠀⠀⠀⢀⣾⣶⣦⣤⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⡔⠃⠔⠀⠾⣿⣿⠇⠀⣿⠿⢿⡟⣿⠀⠙⣿⣻⣿⡟⢿⡿⠻⣇⠙⣯⣢⡀⠈⢷⣄⣀⡴⣿⣿⣿⣿⣍⣙⠛⠛ ⠀⠀⠀⠀⠀⢀⣠⣏⡜⣀⡂⢰⢷⠀⣾⣿⠀⠀⢿⢰⢘⣆⢹⣇⠀⠈⢧⣉⣿⡌⢿⣦⣸⣧⡈⢿⣷⣶⣴⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⣷ ⠀⠀⢄⣀⠀⣽⢿⣰⢋⡭⢠⡾⣾⣤⣹⣇⣀⡤⠾⣿⣼⣿⡘⣿⡄⠒⠒⠿⣿⣿⣌⣿⣿⣿⣿⡌⠻⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⡨⠇ ⠀⠀⠀⣿⡾⠛⢹⠷⠋⣰⡿⢥⢛⣽⣿⡇⠀⠀⠀⢿⣿⣿⣧⠘⣷⡄⠀⠀⠈⠛⢿⣄⡙⢿⣿⣿⣄⠀⠈⢿⣿⡻⢿⣿⣿⣷⣆⡴⠃⠀ ⠀⠀⠀⠀⠀⢀⣮⣴⠚⠃⠘⢷⣾⣿⣿⣧⣤⣀⡀⠈⢿⡿⣿⣦⡈⠻⣦⣂⡼⢿⣿⣿⣿⡦⠝⢿⣿⢦⣤⣄⠙⣷⣄⠉⢻⡿⣿⣿⣶⣄ ⠀⠀⠀⠀⣠⣟⡁⠀⢀⣴⣧⠞⠟⣿⣿⣧⣴⣬⣽⡷⠀⠙⠛⠛⠛⠀⠘⢡⣶⣾⣷⣦⠉⠻⠶⣴⣿⣷⡹⣿⣦⠻⣿⣷⣾⠁⠀⠉⠛⠿ ⠀⠀⠀⡜⠛⠻⠯⣿⢾⢯⡾⢀⢸⡏⣿⣿⢻⢿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠹⣭⣹⣷⠞⣀⠜⢀⣿⢻⡈⣷⣌⢻⣷⣿⣿⣿⡓⢤⡀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠉⠛⠛⡷⡏⠉⠘⣿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⣼⠀⠘⣿⣦⡙⢿⡌⢯⠻⢶⣭⣢⣄ ⠀⠀⠀⠀⠀⠀⠠⣀⡠⡀⠃⠇⠀⠀⢸⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⣠⠃⢀⠀⠘⢿⣷⣄⠻⣦⣷⡀⠙⠻⣿ ⠀⠀⠀⢀⣀⢀⡴⠋⣧⠣⣼⢸⠀⠀⠸⣷⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠁⠀⣎⣷⡀⢮⠻⣿⣦⠻⣿⣿⣄⠀⠀ ⣠⠔⠊⠁⡴⠃⠀⠀⡏⡄⠹⣼⣇⠀⠀⢻⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡄⠀⠀⠘⣾⡏⠢⡑⢝⢿⣷⡌⢿⣿⣿⡀ ⠓⠀⢀⣴⠁⠀⠀⡰⠃⢻⢢⠹⣿⣷⣄⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⠀⠀⠱⡀⠀⠀⠘⢿⢦⡈⠢⣄⠙⣿⣧⡹⢿⣷ ⠀⠱⠋⠀⠀⠀⡜⠀⠀⠈⢦⡇⢹⣿⣿⣆⠸⣿⡙⣶⠤⣀⠀⠀⠀⢀⣠⠖⣹⢻⠀⠈⣦⠀⠀⢻⣄⢄⣀⠀⠱⡝⢄⣩⡟⠁⠉⠻⣦⡹ ⢠⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⢿⣟⢿⣄⢻⣷⣹⡆⠈⠙⠒⠞⠋⠀⠀⣿⣌⠢⡕⢜⣷⡶⡈⠋⣙⠹⣷⡄⠘⢦⠞⠀⠀⠀⠀⠘⢿ ⢨⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠘⡆⠈⢿⣿⣿⣦⣿⣿⡝⠢⢄⡀⢀⡠⠔⠋⠀⡉⠳⠿⣦⡍⠛⠿⠦⣈⣿⣿⣍⣱⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⢄⡀⢸⡄⠀⠀⠘⡆⡜⢻⣿⣿⢿⣏⣿⣄⠀⠘⠁⠀⠀⣀⣼⣿⠀⠀⣀⣀⡀⠀⠀⠀⠀⡠⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠔⠛⠉⠀⠀⠀⢠⠻⣅⢸⣿⣿⣯⣻⣦⣿⣿⣿⣿⣿⣿⣿⠿⢧⣀⣾⣿⣿⡿⠀⠀⠀⢐⡁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠎⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⣠⠧⠐⠚⠉⠛⠛⠛⢿⣿⣿⠉⣹⡿⣿⣏⡀⠀⠀⠀⠀⢻⣿⣷⣦⡾⠉⠉⠉⠀⢂⡤⠂⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⣅⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡜⠁⠀⡜⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠈⢳⡀⠀⠰⡘⢷⣤⠴⠶⠟⠛⠛⢻⠃⠀⠄⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡀⠀⡜⠀⠀⣼⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⡄⠀⠀⠱⡀⠀⢣⠘⣷⡤⠤⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡜⠀⡸⠁⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣧⡀⠘⡄⢣⠀⠘⡇⢹⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠃⢀⠇⠀⠀⡼⠀⠀⢠⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⡇⠀⢹⣷⡄⠹⣼⡆⠀⢡⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣼⠀⢸⠀⠀⠀⡇⠀⠀⣼⠀⢀⠀⠀⠀⣸⠀⠀⣴⠃⠀⠀⡇⠀⡇⠈⠻⣦⣈⣳⣀⣸⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⡘⠀⠀⢰⠁⠀⢠⠃⠀⣸⢸⠃⢀⡇⠀⣰⠃⠀⢠⢀⡇⠀⡇⠀⠀⠈⠻⣏⠁⢹⠀⠀⣿⣿⣿⠿⠿⠿⠶⠖⠀⢠⣴⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⠀⠀⣼⠀⣠⠋⠀⣴⣿⡎⠀⡾⠀⡴⡿⠀⢀⡞⢸⣃⣴⠷⠒⠒⠒⠀⢸⠀⢸⠀⠀⣿⣿⣿⣅⠀⠀⠀⠀⠀⢀⣿⣿⣦⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⠇⠀⠀⣿⣻⠁⣠⠞⢉⡟⢉⡼⣲⠞⢀⡇⢀⡞⢠⣾⢉⡟⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢹⡿⣿⣿⠟⠒⠂⠀⠀⠈⠛⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⠀⢸⠁⠀⠀⠀⠰⣟⣥⠞⠃⠀⣼⣵⠿⠋⠁⢀⠞⣠⡟⡴⠋⣿⠏⠀⠀⠀⠀⠀⢀⣸⠀⢸⠀⠀⢸⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡼⣽⠁⠀⢸⠀⠀⡀⠀⢰⠟⠁⠀⣀⣾⡋⠠⠤⢄⣠⡞⣻⠞⠁⢀⡼⠁⠀⣠⣤⣒⣶⣶⣿⣿⡷⢾⠀⠀⢸⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡼⢡⠀⠀⢸⠀⠀⡆⠀⢸⣀⣲⣾⣽⡷⠿⠟⠛⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⢸⠟⢻⠀⡆⢸⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣾⠀⡀⣼⠀⠀⠁⠀⢸⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢀⡇⠘⣦⠀⢻⣷⣶⣶⣶⣶⣤⣤⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣼⡇⢀⡇⣿⣶⠀⢸⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⢸⠀⡟⢦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣾⣿⠀⡸⡾⢸⠸⡀⢸⠀⢀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⢸⢸⡘⡄⣿⡈⢧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠂⠀⢰⡟⢁⣴⠿⠛⡇⣰⢳⠃⡘⠀⡇⠘⡆⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⡴⢾⣋⣉⣉⣡⠤⣾⣿⠇⠀⠀⠀⣼⣿⡀⢸⣸⠀⣷⢸⣿⣜⢧⢻⡅⢀⠈⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⣠⠟⣰⡿⠁⢀⣼⡿⠁⡞⠀⡇⠀⢻⡆⢇⠀⢹⡏⢿⢦⡀⠀⠀⠀⠀⠸⣦⠞⠛⠋⠉⠉⠛⣻⠃⠀⠀⢀⣼⣿⣿⣇⠀⣿⡇⡟⢎⣯⠸⣮⣯⢿⡀⢰⣿⡿⠉⠿⠿⠀ ⠀⠀⠀⣰⠏⣰⣿⣷⣴⣿⠏⠀⣼⠁⣼⠀⠀⠘⣿⣸⡄⢂⣷⠸⡆⠙⣦⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⡴⠋⠀⢀⡤⠞⣿⢹⢹⣿⣧⣻⣧⡃⠘⢿⡄⢸⡻⣏⣧⠀⠀⠀⠀⠀⠀⠀ ⢻⡆⢀⠏⢰⣿⠀⣠⠞⠁⢀⣼⡏⠀⣟⠀⠀⠀⢸⣿⣷⡌⠘⣾⡇⠀⣸⡄⠙⠲⢤⡀⠀⠉⠳⠶⠞⠁⣠⡶⠋⠀⠀⣿⢸⢸⢹⣽⣿⠙⡇⠀⠈⢧⣨⡟⢻⡜⠀⠀⠀⠀⠀⠀⠀ ⣾⢇⡌⠀⣾⣿⡿⠋⢀⣰⡿⣿⠀⢸⣿⠀⢰⠀⠀⢻⣿⣟⢦⣽⣿⠛⣹⡇⠀⠀⠀⠈⠙⠒⠶⠤⠶⣿⣧⡀⠀⠀⠀⡿⢸⢸⡞⣿⣿⢰⠁⠀⠀⠈⢿⠇⠀⡇⢠⠀⠀⠀⠀⠀⠀ ⡏⠀⡇⠀⣿⡿⠀⣠⡾⣃⡵⡟⠀⢸⣿⡀⠀⣇⠀⠀⠻⣿⣄⣿⠋⠉⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⣦⠀⢠⡇⣸⢠⣷⢏⣿⢸⡀⠀⠀⡄⣾⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠇⢸⣇⢀⡟⢀⣴⢏⡾⠋⠀⣧⠀⠸⣿⣷⡀⠸⣦⠀⠀⠙⢯⡀⠀⠀⢻⢿⣿⣷⣶⣤⣤⣄⣀⣠⣤⡷⢰⠀⠘⢷⢿⣠⡇⢸⢯⣿⣿⣏⡇⠀⢠⠇⣸⣇⡴⠃⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⣻⡞⢀⣾⣿⡟⠀⢀⣴⠾⢷⣤⡙⠯⠟⢦⣜⣷⣄⠀⠀⠙⣦⠀⠘⡄⠈⠉⠛⠛⠛⠿⠿⠿⠛⠡⠸⣦⠀⠈⢦⠉⠛⠺⠼⣿⣿⡜⠀⢠⣟⣾⠏⠋⣠⠞⠛⠀⠀⠀⠀⠀⠀ ⣾⣿⡿⢀⣾⣿⡿⠁⣰⠋⠀⠀⠀⣙⡿⢷⣄⣀⣀⡈⠈⢳⡀⠀⠈⠳⣄⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⠀⠀⠈⢧⠀⠀⠀⢸⡟⠁⣠⢞⡽⠃⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⣾⡿⣹⣇⡼⠃⠀⠀⠀⠀⠈⢿⠳⣄⠈⢿⣶⣖⡲⠿⡄⠀⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠈⢣⡀⢀⡞⠀⡰⠟⠋⠀⡰⠃⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⢸⣿⠃⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢧⠈⢇⠀⢿⣿⠛⢧⣹⡀⢹⡇⠀⠈⢻⡒⠤⣄⠀⠀⠀⠀⣠⠞⢻⠃⠀⣀⠀⠀⢹⠏⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⢮⣿⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠸⡆⢘⡏⠀⠐⠙⡇⢸⡇⠐⣄⠀⢳⡀⠈⠳⣖⠒⣻⠁⠀⢸⠀⠸⣿⣿⢲⡏⠀⠀⢀⣤⠞⠁⠀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠘⣿⣿⠃⠀⢠⢴⡆⠀⠀⠀⣶⡄⠀⠸⡄⡇⢼⣥⣄⣀⣰⣷⣼⠃⠀⢹⣧⠀⣧⡀⠀⠈⠉⠉⠀⠀⣸⠀⠀⠀⢉⡾⡀⡆⠀⣾⡏⠀⠀⠀⠀⢠⠀⢠⢹⡄⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⣿⡏⠀⠀⠘⡾⠀⠀⠀⠀⢻⣿⠀⠀⢳⣇⠀⠈⣿⣿⣿⣿⡟⠀⠀⣼⣻⠀⡇⠙⢦⡀⠀⠀⠀⠀⡟⣀⣤⣶⠟⣧⣿⠃⢸⣿⡇⠀⠀⠀⠐⡾⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀ ⠿⢿⣤⣿⠁⠀⢀⢸⠃⠀⠀⠀⠀⢸⢿⠀⠀⠈⢿⠀⠀⢻⣿⣿⠏⠀⠀⢠⣇⣿⣰⣿⠷⣖⠙⢦⡀⠀⣸⠟⣿⣿⠃⠀⣿⣿⡆⢸⡏⢳⡀⠀⠀⢰⠇⢠⠇⠀⢹⠆⠀⠀⠀⠀⠀ ⠀⢀⣿⡏⠀⠀⢨⠇⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠸⡄⠀⠈⣿⠋⠀⠀⠀⣸⣿⠛⠁⠙⠷⣿⣷⣦⣻⣾⣇⣴⣿⠃⠀⠀⠸⣿⣿⣮⠻⣖⣿⠦⠤⠏⠀⡏⠀⠀⠘⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠢⢍⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⠂⡀⠀⠀⠀⠀⠀⠀⡄⠢⠀⡵⡤⠤⠒⠆⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢠⠁⠂⠂⠸⠁⠀⠀⢀⠀⠀⠀⢠⡀⣡⢠⢫⠁⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⠘⠘⠀⠇⠠⢠⡀⡘⢠⠂⠀⢨⠑⢬⠤⠀⣦⣠⣄⡀⢀⡠⠀ ⠀⠀⠀⠀⠀⢀⠃⡄⠀⢀⡤⣡⢾⠥⡡⡃⡘⡤⠖⠀⠀⡄⠀⢻⣷⠄⠀⠸⣷⠀ ⠀⠀⠀⠀⣀⣸⠃⠁⠀⢸⠊⣡⡒⣉⡰⠖⠪⠋⣀⣤⣴⡧⠀⠘⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢳⠀⡄⠀⢸⠚⠋⠉⠉⠃⠀⠀⠀⠁⠀⠀⡏⣠⢠⠰⣤⣤⣤⣄⡀ ⠀⡀⢀⠔⣱⡏⡞⠁⢰⢸⡆⠀⠀⠀⢀⡀⠐⢀⡀⠀⢠⡁⡏⣼⡡⢻⠿⣿⣿⣿ ⠀⢀⢮⣎⣠⢋⢣⠀⢆⡈⡟⠢⡀⠀⢛⠋⠉⡹⠁⣠⣾⣇⣷⠳⡟⣿⡆⠿⠙⠃ ⡃⠈⣯⠜⣡⡞⣨⢀⠘⣷⣙⡧⡇⠑⠠⠈⣒⣥⠊⠀⢿⣿⣏⠇⠱⡏⡏⠀⠀⠀ ⠇⣀⢃⣴⠕⡇⢿⡄⢆⠘⢞⠉⠷⣤⣄⣀⣀⣧⠑⣴⡈⣯⣿⡂⡐⣇⠄⠀⠀⠀ ⣴⢇⣾⢃⠖⠉⢾⠍⣙⠓⡀⠁⢀⠀⠉⠉⠉⠁⡇⠐⡈⠉⠟⣰⠟⢔⠉⠀⠀⠀ ⡟⣾⢹⠃⠀⠀⠈⡕⡜⡗⢻⡘⣄⠲⠠⣀⣀⠔⡇⣀⣈⠎⠈⣡⠊⠀⡆⠀⠀⠀ ⡇⢻⠇⢠⠄⠀⣆⠘⡄⢣⣤⣷⠁⣧⡣⡈⠈⠀⡆⣈⣍⡄⣾⠀⠀⡄⡰⠀⠀⠀ ⠛⡾⠀⠜⠀⠀⢻⠀⢡⠈⡿⠃⢠⡽⠻⣮⣢⣴⣻⠃⢸⣇⢏⣄⡰⠰⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢨⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠐⣦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣀⠀⢀⣀⢀⡞⠁⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢷⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⣼⠁⠀⠈⠁⢸⠀⣰⠃⠀⢀⡄⠀⠀⠀⢀⠀⠀⣇⠀⠀⠀⠘⣦⠀⡀⢻⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣀⣤⡇⠀⠀⠀⠀⡼⣼⠇⠀⠀⡾⠀⠀⠀⠀⢸⡄⠀⠸⡄⠠⡀⠀⠈⢷⡔⡀⠇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⣷⡟⠀⠀⢸⠁⢸⠀⠀⠀⢸⣇⣄⠀⢻⠀⢳⡀⠀⠈⢿⣾⣾⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣟⣿⠀⠀⠀⠀⢰⣿⠁⠀⢀⣏⡟⡞⡇⠀⠀⡟⡿⣽⡄⠈⣇⠀⢳⣄⠀⠈⢾⣷⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⢿⣿⡟⠀⠀⠀⠀⣾⡿⠀⠀⣾⣿⣳⠧⣷⠠⠤⣷⣧⠹⣷⡀⢸⣦⠈⢻⣷⣤⠬⢿⣧⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⢸⣿⡇⠀⠀⠀⠀⢹⡇⠀⣼⡿⠸⠁⠀⣿⠀⢠⣿⡇⠀⣽⣷⠘⠈⠳⣌⣇⠉⠳⣌⢻⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢸⢸⡿⣷⠀⠀⠀⠀⠸⡇⣼⠟⠀⢠⠤⣐⣟⣲⠿⡿⠁⠀⠘⣿⣾⡁⠀⣀⡭⠧⠤⢬⠿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⡆⠀⠀⢸⣾⣧⣿⡀⠀⠀⢠⡄⢿⣿⣾⣿⣿⣿⣿⣿⡻⠿⣦⡄⠀⠀⠈⠏⠓⠀⣩⣶⣿⣿⢿⣾⣇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠈⣿⢏⡻⣧⠀⠀⠸⡏⠻⡛⡋⠁⣼⣿⣿⣤⣿⠀⠈⠁⠀⠀⠀⠀⠀⠘⢻⣿⣧⣿⠀⣉⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣷⠀⠀⠀⡏⣎⣿⡧⠀⠀⠀⢳⠀⢧⠙⠦⠼⠯⠭⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠯⠴⢻⣿⡄⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡄⠀⠀⡇⠈⣿⣾⠀⠀⠀⠘⣇⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⣿⠁⣷⠀⠘⣯⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⣇⠀⠀⢳⣾⡀⠙⣇⠀⠀⢧⠸⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠃⠀⠀⠀⠀⣿⠀⠸⡆⠀⢿⣏⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢸⡿⡄⠀⠘⣷⣍⡉⣻⡀⠀⠘⣇⢻⣧⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢻⡄⠸⣿⠞⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⣾⠇⣷⡀⠀⠸⣿⣿⣿⣇⠀⠀⠸⡄⢻⡝⢾⣷⡀⠀⠀⠀⣀⣤⢤⣔⣒⣒⣶⣦⡄⠀⠀⠀⣸⠋⠀⠀⠀⢻⡀⢹⡀⠈⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⡿⠀⡏⢧⢧⠀⢻⣿⠛⢿⣆⠀⠀⢹⡄⢻⡀⠈⠻⣆⡀⠀⢻⣿⠷⠟⠻⢿⣿⡏⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢳⡌⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⠁⠀⠀⠀⡇⠀⡇⢸⣎⢧⠀⠱⢳⡀⠙⣆⠀⠀⠹⡄⢳⡀⠀⠀⠙⠂⠀⠙⠲⢤⣤⡶⠋⠀⠀⢠⣾⡅⠀⠀⠀⠀⠀⠀⠈⢳⡘⣧⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⢸⠁⠀⡇⢸⡟⢯⢧⠀⠀⠱⣄⠘⣆⠀⠀⠹⡄⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣽⡟⠀⠀⣤⠀⣿⠀⡆⡇⢸⡇⠈⢷⣷⡀⠀⠘⢦⡈⢦⠀⠀⠙⣄⢣⡀⠉⠓⠦⢄⣀⠀⠀⢀⣤⢿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣳⡿⠁⠀⡸⠁⢀⡏⠀⡇⡇⠈⡇⠀⠀⢹⣷⣄⠀⠀⠙⢮⡳⡀⠀⠈⢧⡻⣤⣀⣠⡟⣿⠙⠛⡏⠀⢸⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣱⣿⠃⠀⣰⠃⠀⣸⠇⢸⠇⡇⠀⡇⢠⠄⣼⡿⠛⡷⢄⡀⠀⠙⢿⣦⡀⠀⠹⣯⡉⠛⠲⢽⣄⡀⢹⡀⠘⣇⠸⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣱⣿⡏⠀⢠⠃⠀⢀⣿⠀⢸⠀⡇⠀⣿⣾⢠⡏⠀⢰⠃⠀⠙⠒⢦⣄⡙⠻⣷⣤⡘⢷⣄⠀⠀⠈⢿⡈⣧⠀⢸⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡟⠀⢠⠏⠀⠀⣼⡿⠀⡿⠀⡇⠀⣿⣿⣿⠁⠀⡾⠖⣊⠽⠏⠉⠉⠉⠉⣩⠍⠉⠑⠚⠦⣄⡀⠸⣧⣹⡆⠈⣇⠀⠀⢹⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⢀⡏⠀⠀⢠⣿⡃⠀⡇⠀⡇⠀⢸⣿⠏⠀⠀⡷⠊⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣷⠀⠸⡇⠀⠈⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢠⡾⠀⠀⠀⣾⠋⡀⢀⠇⠀⡇⠀⢸⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢿⣇⠀⢹⡄⠀⢹⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢠⣿⠃⠀⠀⣼⠏⢀⠇⢸⠀⢐⡇⠀⢸⡏⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢿⡄⠀⢻⡄⠀⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⢠⣿⠇⠀⠀⢠⠏⠀⣾⠀⡿⠀⢸⣷⠀⠰⡇⠀⠀⡏⠀⣄⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠸⣧⠀⠀⢧⠀⢸⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢀⠋⣠⣿⡟⠀⠀⢀⡞⠀⢰⡟⢠⠇⠀⢸⣿⡀⠀⠃⠀⠀⡇⠀⢹⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⡇⠀⠘⣆⠈⣿⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣵⠂⣰⣿⡿⠀⠀⠀⡞⠀⢠⣿⠃⢸⠀⠀⢸⣿⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⣿⠀⠀⢹⡀⣿⠛⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⡴⠁⣸⠃⠀⠀⠀⠀⢀⣾⣿⠀⡾⠀⠀⣿⣿⠃⠀⠀⠀⠀⠇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣿⡆⠀⠈⡇⠘⠆⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢠⠏⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢧⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠠⡞⠀⠀⠀⡏⣰⠁⠀⡄⠀⠀⠀⠀⠐⡄⠀⠀⠙⣄⠀⢣⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⣾⠃⠀⠀⢠⣷⠇⠀⡰⢠⡄⠀⠀⡇⠀⢹⠀⢆⠀⠘⣦⣌⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣸⡟⠀⠀⠀⢸⡟⠀⢠⣧⢾⡇⠀⢸⣿⣧⠀⢇⠈⣦⡀⠘⣿⣇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠸⣿⡇⠀⠀⠀⢸⠇⠀⣾⣿⠞⢶⠰⢾⣯⠹⣇⠸⣦⠘⡷⣤⠼⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣧⣿⡇⠀⠀⠀⢸⠀⣼⠃⠃⢀⣸⣠⣾⡇⠀⢿⣄⠆⠑⠳⡀⠑⣮⡆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⢸⣿⣧⠀⠀⢀⠈⣿⣧⣶⣿⣶⣿⣿⣯⡀⠀⠈⠟⠆⠐⣩⣭⣿⣯⣇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⢸⣟⣹⡇⠀⠸⡇⢻⢋⠉⣿⣿⣯⡇⠈⠁⠀⠀⠀⠀⠚⣿⣿⡇⢈⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡆⠀⢸⠻⣿⡇⠀⠀⢱⠈⠎⠑⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⢋⡿⡆⠈⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠘⣇⠀⠸⣤⡋⢷⠀⠀⡄⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⢸⡇⢳⠀⢻⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⡿⡄⠀⢻⣏⡉⡇⠀⠸⡘⣷⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠈⢧⠈⡿⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢸⡇⣷⣀⠈⢿⣿⣿⡀⠀⠱⡘⣏⠻⣦⡀⠀⢠⣶⣶⣶⣿⣿⡖⠀⠀⢠⠏⠀⠀⠈⢧⢹⡀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⢸⠀⠟⢿⣆⠈⢿⡌⠳⡀⠀⢳⡘⡄⠀⠑⠦⠀⠻⣍⣀⣩⠟⠁⠀⣰⠋⠀⠀⠀⠀⠈⢇⢣⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⡎⠀⡆⢸⢿⣦⠀⠘⢄⠱⡄⠀⠱⡘⣦⢄⡀⠀⠀⠀⠈⠁⠀⣠⡞⢹⠁⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠃⠀⡴⢀⠇⠰⠀⢸⠀⠹⣷⡀⠈⠣⡘⣄⠀⠱⣜⣄⠈⠑⢲⣤⣀⣠⠖⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⡏⠀⡸⠁⢸⠀⡇⡄⢸⠀⡀⣸⡷⣤⡀⠈⠻⣦⡀⠈⢻⡷⠶⢏⣷⠀⢳⠀⢹⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡿⠀⡰⠁⢀⡿⠀⡇⡇⢸⣾⢡⠏⢀⡇⠈⠒⠤⣌⣛⢷⣄⡹⣦⠀⠈⠹⡌⣇⠈⡇⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⠃⣰⠁⠀⣸⡇⢸⠁⡇⠸⣿⡿⠀⢸⣓⠍⠛⠉⠈⠁⣩⠉⠉⠉⠓⠠⢄⣷⣼⡄⢱⡀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⢠⠃⠀⢠⡿⠁⢸⠀⡇⠀⣿⠇⠀⡜⠁⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠉⠻⣷⠀⢧⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⣰⡟⠀⠀⡾⠁⠇⡇⠀⡇⠀⣿⠀⠀⡇⠀⠀⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⢇⠀⠹⣇⠈⢧⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⣰⡿⠀⠀⡼⠁⣸⢠⠃⢸⣿⠀⠻⠀⠀⠁⢤⠀⠀⠀⠎⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⡀⠈⡆⠸⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⣼⣿⠁⠀⡰⠁⢠⡏⢸⠀⢸⣿⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢸⣧⠀⠸⡀⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀ ⢃⡜⢹⠃⠀⠀⠀⢠⣿⠇⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣿⡀⠀⡇⠹⠈⠜⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⠡⠔⠒⠈⠈⠑⠂⠈⡁⠢⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠠⠂⡀⠀⠀⠀⠐⠌⠢⡀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡠⢛⠁⢀⠂⡰⠁⢰⠁⠀⣷⡀⠀⢸⡄⠐⠄⠀⠈⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠰⠏⢀⠂⢠⠃⠀⡞⠀⣸⠀⢻⡄⠘⡏⠂⠘⠀⠀⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣌⠂⣜⠀⡞⠀⢼⠇⢰⡟⠀⠀⣷⠀⡇⠘⡄⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡝⣏⡸⠋⢜⠃⢎⡞⢰⣿⠁⠀⠀⠹⠀⡝⡀⢰⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣹⠋⣿⣦⠀⢎⠺⣐⡽⠃⠂⠄⢀⡀⢸⠀⣀⢀⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠰⣻⡿⠇⠁⠬⠚⠱⣶⣶⣶⣆⡏⠘⢷⣬⣦⠁⣧⡔⠀⠀ ⠀⠀⠀⠀⠀⢀⠈⠧⡆⠄⠀⠀⠀⢀⠀⡿⠿⠟⡈⠉⡖⢾⣿⡯⡱⣼⠁⠀⠀ ⠀⠀⠀⠀⢀⠺⠀⡆⠀⠀⠀⠀⠀⠺⣧⣼⠉⠉⠰⢠⠃⣮⣽⣿⡦⠉⣆⠀⠀ ⠀⠀⠀⠀⢧⠇⡇⠱⡀⠀⣦⣄⠀⠀⠀⠀⠀⠀⣤⡇⠔⢉⣿⣿⠁⠁⠘⠀⠀ ⠀⠀⠀⣰⡏⠀⢠⠘⠈⢄⠘⠋⠀⠀⠀⠀⣀⡰⠉⢿⡛⠋⠁⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⡇⢠⠀⠄⢧⠀⠀⠒⠒⢲⢶⠾⠛⠁⣠⠕⠉⠀⢀⠄⠈⠀⡆⠀⠀⠀ ⠀⠀⢸⠀⢼⠀⠀⠸⢀⠀⢠⠀⠈⢦⡴⠶⠊⣁⣀⣀⣂⠁⠀⡀⠊⠀⠀⠀⠀ ⠀⡔⠀⠀⠀⠑⡄⠅⡈⠀⡎⠀⠀⣜⢄⣴⣾⣿⣿⣿⣿⣿⣶⣦⣤⣴⣄⠀⠀ ⠰⠀⠀⠀⠀⠀⠰⡾⢀⡟⠀⢀⠜⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠂⠀⠀⠀⠀⠀⠀⡇⡾⠀⠀⠔⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉ ⡆⠼⠿⠿⠿⠿⠃⡇⡇⠀⡎⡐⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⢀⣷⡅⠀⡜⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⠀⠀⠀⠀⠀⠜⠄⢃⠘⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠑⢀⠀⣀⡎⠄⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠡⡀⠙⠌⠢⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠀⡀⠀⠀⠀⠀⢉⠒⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠀⢀⠎⠄⠀⠀⠀⠀⠀⢂⠱⡘⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠇⠀⢸⡎⢠⢂⠀⢀⠘⡀⠀⢢⣐⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⢀⣼⠀⠀⣺⠀⣶⣚⢀⣿⣇⢡⠱⣄⢻⡄⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⠀⠀⢁⡼⢉⢀⣤⡟⠸⣮⠑⣫⣐⡅⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⢸⢟⡆⠀⡼⠟⢻⣿⡏⠃⠀⠈⠠⣾⡟⣻⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⡇⠰⢹⣇⠀⣡⢋⠉⠉⠁⠀⠀⠀⢀⠉⠁⡝⡆⢿⡄⠀ ⠀⠀⠀⠀⠀⡼⠀⡷⠀⢻⣺⡀⢡⢦⣂⠀⠀⠀⠀⣀⡀⠀⠀⡇⠰⡘⡟⡄ ⠀⠀⠀⠀⣸⠃⠀⠃⢷⡌⢟⠣⠀⢊⢎⠓⠄⠻⣛⣻⠏⢀⡜⠀⠀⠱⣡⠀ ⠀⠀⠀⣰⡟⢀⢸⢀⢸⠻⡄⠡⡱⡀⢊⢒⠤⣀⠀⠀⣠⠋⡇⠀⠀⠀⠙⠇ ⠀⠀⠀⡿⢀⠆⡄⠄⢸⢠⡹⢦⡈⠲⣄⠙⣖⠮⢏⢩⠸⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⢸⢃⠌⢠⡇⠇⠀⣧⠃⣦⠠⠑⠒⡛⠚⠢⢀⣇⡆⠆⠘⣄⠀⠀⠀⠀ ⠀⢀⢆⡌⠀⡞⢡⢀⠀⡟⠀⠁⠀⠀⣐⠀⠀⠀⠀⠈⢻⡘⡄⢻⣆⠀⠀⠀ ⠀⢌⡾⠀⡘⢰⠘⢸⡆⠇⠈⠠⠀⠀⠱⠀⠀⠀⠀⠐⠀⢇⠘⡘⣿⡀⠀⠀ ⢆⢺⠁⠐⢠⡏⡆⢸⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢁⢸⡀⢡⠏⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠄⠀⡴⠊⠀⠀⠀⠀⠀⢀⠀⠘⢄⠀ ⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠎⠀⡘⢁⠄⡰⢀⠃⡆⠀⢸⡀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠇⠀⢀⡟⢀⢰⡠⡢⠚⡠⣎⣦⡰⢠⡀⠹⣰⠀⡇ ⠀⠀⠀⠀⠀⠸⢠⠀⣼⠃⡶⠾⣳⡾⣯⡰⠫⡻⣡⡶⠃⠄⢻⠀⡃ ⠀⠀⠀⠀⢀⡇⡄⢠⢼⠀⠃⠓⠫⠿⠃⠀⠀⠁⠨⣶⣶⣄⠸⠀⡇ ⠀⠀⠀⠀⢸⢣⠀⢸⣻⢠⢘⠀⠀⠀⠀⠀⠠⠀⠘⠿⠃⢽⡇⢸⠀ ⠀⠀⠀⠀⣿⡀⠀⢸⣯⢸⢸⠀⠀⢀⣤⣄⣀⠀⠀⠀⢠⡎⡇⡎⠀ ⠀⠀⠀⠀⣿⠁⢸⠀⣿⢸⣟⢄⠀⠈⠦⡨⠏⠀⠀⢠⣟⠀⠁⡇⠀ ⠀⠀⠀⠀⢻⠀⠈⠀⣿⢸⡋⠆⠑⢀⠀⢀⣀⡤⡞⠁⣿⠀⠀⡇⠀ ⢀⠔⠊⠉⠉⣾⠀⢃⢸⢸⢹⠦⣤⣀⣩⠋⢺⡇⡇⡰⢻⢰⠘⡏⠀ ⠁⠀⠀⠢⠀⠸⡆⠘⠘⢸⠀⡡⡈⠻⠋⡆⠀⠣⣿⠀⢸⢽⢸⡎⠀ ⠀⠀⠀⡆⠡⠀⢳⠀⠃⡸⠙⣷⣧⠄⡠⢰⢀⠌⢹⠀⢸⠚⢇⣧⠀ ⠀⠀⠀⠠⠄⠡⠈⠆⠘⡅⠀⠟⢇⢣⠀⠈⢾⠘⣾⠀⢸⠀⠀⠈⡆ ⠀⠀⠀⠀⢃⠀⢡⠘⡀⡇⠀⠰⠈⢳⣇⣀⡎⠀⠹⠀⠘⠀⠀⠀⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠂⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢒⡏⣋⡟⢉⣹⣯⣛⣗⡒⢲⡦⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠲⣤⢋⣶⣋⡽⠿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠜⠀⠈⠙⡿⠟⠁⠀⠊⣁⠀⣠⣟⣽⣌⡛⢛⠿⠿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣨⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠄⠀⠀⠀⠂⠀⠀⠀⠀⣴⣫⡾⠋⣴⣿⢋⣻⠿⣷⣦⡰⣾⣿⡆⠋⠉⢩⣿⣷⢤⣄⣀⣀⣼⠇⠀⣿⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⣲⡙⠙⣣⡴⠿⣏⣿⡷⠛⠛⠉⠉⢛⡟⠁⠀⣾⣮⠛⢛⣤⢼⣿⣟⠋⠀⠖⠃⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠠⠴⣒⠂⠀⢀⣥⣄⡀⠀⢘⣤⡞⠙⢳⣾⡛⠁⠀⠀⠀⠀⢀⣼⣿⣾⠀⢈⣧⣴⡟⠛⠚⣙⣿⣿⣶⣄⡀⠔⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⣰⢣⠏⣤⣄⣴⡀⠉⣰⠆⣷⠋⠀⢠⣴⣿⣿⣿⣶⣄⠀⢀⣴⣿⡝⢡⡷⠽⡞⠓⣶⣶⣾⣉⠁⠀⠉⠉⠉⠉⠙⠲⢶⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣻⣠⠇⠀⡾⢡⣀⡀⣰⣠⣤⣴⣟⢿⣦⣿⣿⡇⠻⣿⣿⣿⣷⣏⣀⣠⣆⣠⣤⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⣦⣶⣤⣀⣀⡀⠀⠀ ⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⡟⣥⠟⢀⡄⢀⣸⣯⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣷⠀⠹⣿⡽⣿⣿⣿⣿⣿⣿⡿⣿⠛⢿⣟⠳⡀⠀⠙⢷⣄⠀⠀⢀⣰⣟⣿⣿⣿⡻⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⡿⣸⠃⡀⠘⢡⡄⠉⢹⣿⣿⠀⠀⢸⡇⢻⢹⣿⠸⡿⡄⠀⠙⣿⡘⢿⢿⡌⠻⣏⢄⠙⡷⡄⠙⣷⣝⣆⢀⠈⢻⣷⣴⣿⣭⣟⣿⣿⣿⣿⣷⣶⣦⣤⣀ ⠀⠀⠀⠀⠀⠂⢀⣠⢶⡯⣼⣃⣀⣭⠠⡟⣿⠀⣾⣿⡇⠀⠀⠘⣇⣸⢀⡏⡀⣿⣿⠀⠀⠈⠳⣄⢹⣿⡄⢿⣿⣦⡼⣿⣆⠘⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⠟⠉⠙⠻⠿⠟⠿⣿⠿ ⠠⠀⢠⣀⡀⠁⢩⣾⣿⢀⡟⢁⣴⢀⣶⡧⣷⣆⢉⣿⠇⣀⣀⣤⣿⣿⡾⣿⡇⠸⣿⣇⠶⠶⠶⠿⢿⣿⣿⣄⣻⣿⣿⣝⣿⣧⠈⠻⣿⣿⣽⣿⣿⣯⣛⢿⣷⣄⠀⠀⠀⠀⢀⡼⠇ ⠀⠀⠀⠀⣿⣧⡾⠷⢾⣟⡵⠏⢡⣾⡟⣨⠿⣻⣿⣿⠋⠉⠀⠀⠸⣿⣿⡽⣿⡄⠻⣿⡄⠀⠀⠀⠀⠙⢿⣿⣄⠉⠻⣿⡼⣿⢧⡀⠀⠙⠻⣟⣿⡿⣿⣿⣦⣽⣳⣦⠄⢀⡼⠁⠀ ⠀⠀⠀⠀⠛⠋⠀⠀⣼⠋⢁⣴⠛⢋⣥⡋⣰⣿⣿⣿⠀⠀⠀⠀⠀⠹⣯⣿⣿⣷⡀⠙⣿⣆⠀⣀⣠⣤⣤⣽⣿⣷⣄⡈⢻⣞⣮⢳⡄⡀⠀⠙⢯⣷⡈⠛⢿⣿⣿⣯⣗⣯⣅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⠋⠉⠉⠈⠛⣾⣿⣿⣿⣿⣽⣶⣮⣭⣀⠀⠹⣯⢻⣟⣿⣄⠈⠻⣿⣡⡶⠞⢛⣿⢷⣶⣽⣛⠂⠙⢻⣷⡙⣾⣾⣦⠈⣻⣿⣤⡀⠈⣿⠻⢿⣷⣮⣟⠦ ⠀⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⢠⣳⣟⣴⢻⠛⣿⣿⣿⣧⣶⣶⣭⡹⡷⠀⠈⠓⠟⠛⠿⠇⠀⠟⢁⣴⣿⣿⣛⣶⣄⠉⠻⠷⣶⣼⡿⣷⡌⢿⣿⣷⡘⢿⣿⣿⣶⠏⠀⠀⠈⠙⠻⢿ ⠀⠀⠀⠀⣰⠿⠿⣿⣓⢲⣦⣾⣋⣽⠁⠀⢺⡏⢻⣿⡷⠿⣿⠞⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢛⢿⡥⣤⠟⠀⡴⠇⢰⣟⢳⠉⢿⣆⠣⢻⣷⣼⢿⣯⡻⠷⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡀⠀⠈⠉⠹⢥⣏⣽⡟⢠⡦⠾⢣⣼⣸⣧⣞⣩⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠚⢋⠴⠛⠀⢠⣟⡓⢸⠰⠸⣿⣷⡄⢿⣿⣜⠛⣿⢷⣤⡙⠦⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡟⢿⠀⠀⠈⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡏⠃⣼⠀⠀⠙⣿⣿⣆⠈⢿⣦⠙⣦⠙⢻⣷⣮⣷⢦ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣠⣤⠀⢱⠸⡀⠀⠀⢠⣧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠃⡼⠃⢀⡀⠀⠘⢿⣿⣷⡀⠹⣷⡼⣧⡀⠈⠙⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢳⡄⢆⣸⠀⡇⠀⠀⠀⣿⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡠⠞⠁⠀⣆⢷⣄⠰⣌⢻⣿⣿⣄⢺⣿⣾⣷⣄⠀⠀⠈ ⠀⢀⣀⠴⠖⠛⣲⠞⠁⠀⢨⢧⠀⢿⡆⣷⠀⠀⠀⢸⣿⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⡀⠀⠀⠀⠙⡞⣿⢧⡈⢷⡝⢿⣯⣧⡘⢿⣝⡿⣷⣄⠀ ⡴⠊⠁⠀⠀⡼⠁⠀⠀⠀⢸⠸⣄⠘⢷⣿⣧⠀⠀⠀⢻⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⢃⠀⠀⠀⠀⠹⡜⣆⠙⢦⡙⠮⡙⣿⣿⡄⠹⣿⣯⣿⠀ ⠙⠀⠀⢀⣴⠁⠀⠀⠀⣠⠋⠀⣯⠱⡌⢻⣿⣿⡆⡄⠈⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢡⡄⡆⠀⠘⣆⠀⠀⠀⠀⠹⡞⡳⣄⠙⢦⣄⠘⢹⣿⣷⡘⢿⣿⣷ ⠀⢱⡴⠋⠁⠀⠀⠀⡸⠃⠀⠀⠹⣄⢻⠘⣿⣾⡾⣳⡀⢻⣿⡝⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠞⡿⡽⢀⠀⠻⡀⠀⠀⠸⣷⡀⣀⢀⠀⠈⠹⡜⢧⡀⢋⣹⠎⠀⠙⢿⣦⡈⢿ ⠀⡼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⡇⠹⣹⣷⢿⣧⠀⢿⣿⡘⣿⡄⠙⠲⢄⣀⣀⣴⡾⠋⠀⢰⣇⠸⡀⠱⣄⢿⣆⢠⡀⢱⡽⢮⣷⣳⡄⠀⠙⣆⠙⣲⠋⠀⠀⠀⠀⠙⢿⣆ ⢰⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠘⡇⠀⢻⣻⢈⢿⣷⡘⣿⣷⡘⣇⠀⠀⠀⠈⠉⠁⠀⠀⢀⡼⢻⣦⠀⡳⣈⠣⣿⣧⡳⣄⠣⢲⡅⢝⢿⡦⣀⠙⡷⠃⠀⠀⠀⠀⠀⠀⠀⢻ ⢸⡀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⠀⠀⠀⠻⡀⠈⢻⣿⣟⣿⣷⡜⣞⣿⡌⠑⠦⣄⡀⠀⣠⠴⠚⠉⠀⢸⡈⠛⠓⢮⣗⡤⡍⠛⠿⢷⣤⣹⣮⣕⠦⣬⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠀⠐⡀⠠⣄⠀⠀⢸⠀⠀⠀⠀⠹⡄⢠⠿⣿⣾⣞⢿⣿⡌⣿⣆⠀⠀⠙⡏⠁⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠁⠀⣈⣳⠶⠊⠀⠀⠀⠀⢀⣧⡞⠀⢸⢿⣟⣦⢻⣿⡜⣻⣧⣤⣤⣦⣤⣤⣶⣾⣿⣿⡏⠀⢠⣶⣿⣿⣷⡄⠀⠀⠀⠀⣰⠃⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠤⠃⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⡞⠈⠳⢄⣸⣿⢻⣿⣯⣽⣿⣽⣻⣿⣿⡏⣿⣿⣟⠿⠛⠉⠓⠒⠛⢿⣿⣿⡿⠃⠀⢀⣀⣀⣹⣀⡴⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⣀⡸⠀⠀⠀⠀⠀⠀⠀⢀⡾⠒⠒⠛⠁⠀⠛⠫⠙⠛⣿⣷⣿⣇⢀⡼⣻⢻⣟⣧⣀⠀⠀⠀⠀⠀⠀⣻⣿⣻⣿⣶⠯⡆⡀⢀⠀⠀⢸⣦⠞⣁⠀⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠐⣿⣟⣁⣾⣷⣿⣾⣿⣩⣟⣉⣀⡀⠈⢿⣿⠁⣡⣦⣌⣿⣿⣧⣽⣷⣾⣿⣷⣦⣄⣻⣿⣶⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡛⣯⣍⣨⡿⠋⠒⢸⣷⡈⠻⣿⣯⢻⣯⣿⣿⡿⣽⢟⣭⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢺⣿⣿⣿⣥⣥⣿⣿⠆⠀⢠⣶⣞⣀⠘⣿⡷⠀⢈⣿⣿⡇⠀⠻⣿⣯⣬⣿⣽⣧⣿⣿⢿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢖⠃⠀⢀⣠⣾⣿⣿⣿⣿⣿⡏⢥⣐⣾⣿⣿⡿⢻⣿⣏⠣⢸⣾⡷⠅⢻⣀⣤⣿⣾⣿⣻⣿⣻⡏⣷⣾⣿⣿⡳⢤⡀ ⣤⠀⠀⣀⣦⣤⣤⠀⢀⣰⣿⣿⣿⠛⡇⢿⣙⠏⠀⢼⣿⣶⣲⡞⢀⣦⣿⣿⣧⠖⣿⡇⠀⠸⣧⠶⢮⠉⡗⣿⡛⠙⢻⣿⣿⣿⣿⣷⡀⢹ ⣁⣤⣤⣿⣿⣿⣿⣿⠻⣯⡿⠛⠙⠀⢧⣴⡏⣴⣷⣌⣿⣿⣯⣴⠟⣩⣾⠟⠁⢠⣿⠀⠀⣀⣟⣳⣾⣤⣿⢻⣷⠶⣿⣿⣿⠿⠿⠉⠙⠀ ⣿⣿⣽⣿⣿⣿⣿⣿⢿⣞⠓⢂⠀⠀⠀⠙⢆⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⣾⡇⣄⣾⣹⣹⣄⡇⢸⡿⠈⡿⡆⢿⣿⣿⡀⠀⠀⠀⠀ ⠛⢻⣿⣿⣿⣿⣿⣿⠈⣿⣿⣾⡇⣀⡀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣸⣿⣰⣿⣿⣧⣿⢯⡇⣸⡇⠀⣿⡇⢸⡿⣿⡇⠀⠀⠀⠀ ⢶⣾⣿⣿⣿⣿⣿⡿⣲⣮⣙⣤⣼⣯⡷⠋⢸⣿⣿⣿⡿⠋⠉⠉⠓⠲⠤⣴⣿⣿⣿⣿⣿⢏⡿⢸⣿⣿⠀⠀⢹⣷⣸⡇⡿⢷⠀⠀⣀⠀ ⣼⣿⠿⡿⢿⣿⣿⠓⠛⠋⢹⣿⣿⣷⣂⣀⣸⣻⣿⣉⣉⠒⠒⠤⣀⠀⢀⣿⢫⣿⣿⣿⡟⣼⠇⣼⣿⣟⠀⠀⢸⣿⣿⠇⣧⣾⡞⠃⠀⠴ ⣿⡿⣟⣁⣼⣿⣿⢷⡄⠀⢀⣿⣿⣶⠟⠻⠿⣿⠿⠿⣿⣾⣵⣆⡀⠡⠟⢁⣾⣿⣿⠏⣰⡏⢠⣿⣹⠋⠉⠓⠦⣿⡟⢳⣿⣿⣏⠁⠙⣻ ⣿⠀⠀⠉⣼⣿⣿⠧⠿⠦⠊⠀⡷⠰⠀⠀⢰⡇⠀⢼⣿⣿⡿⠿⢿⠀⠀⠈⠛⠛⠁⠀⢛⣀⣻⣭⣍⣀⣀⠀⠀⣿⡇⠈⡛⣿⣿⠉⠀⠀ ⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡇⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠻⣟⣿⣿⣿⣎⣿⣴⠀⡉⢿⣿⠀⣶⠤ ⠁⠀⠀⢰⠁⢻⣗⢰⠀⡂⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠟⠛⣯⠤⠁⠲⣿⣀⣸⠀ ⠀⠀⠀⢸⠀⢸⣯⣸⢀⡇⢀⠀⠇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣿⡇⠀⠀⢀⣿⣿⣷⠀ ⠀⠀⠀⢸⠀⢻⣿⣾⢸⡇⢸⠀⠀⢘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⣿⣧⠀⠀⢸⢿⡿⠹⠀ ⠀⠀⠀⡄⠀⢸⣿⡿⢸⣾⣻⠀⠀⢸⠸⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⣿⡻⠀⠀⣼⡌⢡⣠⠗ ⠀⠀⠀⡀⠀⢻⢹⣿⣿⢻⣿⠀⠀⣼⣼⡆⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣿⣿⡄⠀⡆⣿⣷⠚⠁⠀ ⠀⠀⠀⡇⠀⢸⠈⣿⣿⢼⠙⡇⠀⣻⢹⣇⢿⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠐⠀⡈⣿⣟⡇⣀⣇⣿⡇⠀⠀⠀ ⠀⠀⠀⡇⠀⢸⠀⣿⣿⣿⡇⣇⣶⣿⣿⣿⣿⡇⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠸⢸⠀⣿⣿⣿⣁⣿⣿⡟⡇⠀⠀⠀ ⣄⠀⠀⡇⠀⢸⠀⢹⣿⣿⡇⡿⣿⣿⣿⣿⢻⣇⠀⠀⠀⠙⢷⣤⣀⣀⣠⢴⣟⠁⠀⢀⠀⠀⠀⠀⠞⣿⠈⣿⣿⣿⣠⣿⣿⣿⡇⠀⠀⠀ ⠈⢣⠀⢇⠀⢸⠀⠈⢿⢻⣷⣷⣿⣿⣿⣿⣼⡟⠳⣀⠀⠀⠀⠉⠉⠉⢀⡼⢿⣇⡀⡼⠀⣿⠀⢀⠀⣿⣸⣿⣿⣿⣼⣿⣿⣿⠁⠀⠀⠀ ⠀⠘⣄⣀⠑⢤⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣏⣷⡀⠈⠑⠢⢤⣠⠴⠊⠁⣀⣾⢿⣱⠃⣨⣷⣾⣿⡋⠉⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠙⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣶⣦⣤⣤⣤⣤⣶⠚⠋⣡⠟⠉⠉⢹⣿⣿⣿⠹⡄⢸⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⡞⠸⢻⣿⣿⣿⣿⣿⣿⣿⣧⢙⣻⣿⣹⣿⣋⣹⡿⠖⠊⠁⠀⠀⠀⠀⣿⣿⣿⣄⠘⣾⣿⣿⣿⡿⣿⠟⠁⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠆⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⠃⠀⠀⣼⠟⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⠇⠀⠀⣼⠋⢀⠀⠀⡔⢸⠀⠀⠀⠀⠈⡄⠀⣄⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⡎⠀⠀⣰⠃⢠⠃⢀⡞⢀⡇⢸⠀⠀⠀⡀⢧⡀⠈⡇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠀⡄⢸⠀⠀⢠⠃⡰⠃⣰⡟⢠⠎⢀⡇⡰⢠⠀⢷⡄⠱⣄⢿⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⢰⢡⡇⠀⠀⣾⠞⡡⠊⣉⡹⠛⣲⣾⣠⢃⡎⣸⣸⠀⠀⢹⣺⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠀⣸⣿⠁⠀⢰⣯⣎⣤⡾⢏⡀⣠⠟⣿⣧⣾⢠⣿⡿⠒⠠⠄⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡌⠀⣿⣿⠀⢴⣿⠟⣿⣿⣿⣿⣿⠁⠠⠛⢡⡿⢋⡿⠀⢀⠀⠀⢸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⢠⠟⡿⠀⠀⠳⠄⢿⣟⣷⡿⠈⠀⠀⠀⠁⠀⢸⣶⣶⣾⣿⣧⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠐⠁⢼⠾⡽⠀⡄⢠⠀⠈⠉⠁⠀⠀⠀⠀⢀⡀⠀⠈⣿⣿⣾⠇⠙⢿⣇⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠸⣴⡇⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠈⠙⠓⠂⢉⡟⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⠀⠀⣿⣍⠀⢣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡇⢀⠇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⠀⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⢸⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⠀⠀⢻⣿⡆⢸⣿⣆⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⢀⡼⠁⢰⠃⡎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⣿⠀⠀⠀⣿⡇⠘⣿⠋⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⣸⢰⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⣼⡿⢃⠀⣿⠀⠀⠀⢻⣧⠀⣿⣄⠀⠀⠉⠢⢄⣀⣠⣴⠺⡏⠀⢧⣀⠀⢾⣇⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡇⡼⠀⣿⠀⠀⠀⠸⣿⡀⣟⠻⣿⣶⣤⣤⣀⣠⣾⠉⠻⣷⠀⠸⣿⠀⣾⡿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢱⣧⠀⢻⡄⠀⠀⠀⣿⠁⠏⢢⡀⠈⠙⠛⡟⠛⠷⡀⠀⠈⠑⣄⣿⣧⢿⡁⣻⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣏⣼⡀⢸⡇⠀⠀⠀⢹⣾⣤⠀⠑⣄⠀⠀⠙⠒⠃⠙⣦⠀⠀⠈⢻⣿⠈⡇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠟⠋⠉⠀⡇⠘⣷⠀⠀⠀⢸⡏⣿⠀⢀⣬⢆⠀⠀⠀⠸⡀⠘⡆⠀⢀⠎⣿⡆⠃⢸⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⠀⢄⠀⠀⢰⠀⢿⡆⠀⠀⠘⡿⢻⡴⢿⣿⣆⢻⡓⠢⠤⠤⠊⡇⠀⡞⢆⠀⢳⣄⢸⡆⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⢀⠈⢆⠀⠀⠆⠘⢷⠀⠀⠀⣷⡸⡀⠈⢯⠙⡇⠱⡄⠀⠀⠀⠃⠸⡇⠀⢳⠈⢿⠈⡇⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠈⢆⠀⠘⡄⠈⡆⠀⠀⢛⢠⢧⠀⠈⢷⡓⢤⡘⢆⠀⠀⠀⠀⢈⠆⢸⠁⠘⣿⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠈⠆⠀⠹⡀⢹⡀⠀⠸⠠⡄⢣⠀⠀⠉⠲⣍⣿⣆⢀⣇⣰⠇⠀⢘⠀⠀⢹⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀

⠤⠤⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣴⣖⣶⣾⣿⠛⠛⣯⣤⣵⣶⣯⣽⣻⣯⠖⠂⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣉⣽⣿⣿⣿⣿⣿⣷⣿⣿⣟⣽⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣿⣿⣷⣾⡿⠿⣤⣶⣿⣾⣿⣾⣿⣿⣦⣜⣙⣿⣿⠿⢿⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡿⣿⣿⣿⣿⡗⡶⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠻⣦⣾⡿⢿⣿⣿⢋⣩⣿⣟⡛⠙⣷⣦⡀⠐⢴⣿⡿⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡿⣿⣿⣿⣾⣿⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢾⣿⣷⣫⣿⣿⣿⣿⠿⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠛⠛⠛⢻⣦⣤⡏⠙⢳⣤⣀⠀⠀⠀⠀⠀⣴⠞⢛⡷⠾⣻⣿⡿⠋⠓⢤⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⢀⣴⣿⣿⡛⠣⠀⠀⠀⡉⢻⣿⣿⢯⣴⣿⣿⣿⣿⣭⡿⠿⠿⠉⡅⠁⣤⡶⣤⠀⠀⠈⠉⠉⠻⣄⣴⣿⣿⣿⣶⣤⡀⠀⢻⠛⢉⠿⠿⠋⢩⡀⢠⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠙⠻⠚⣿⣿⣾⣿⣿⠟⢳⣗⣹⡆⠻⣆⣹⢷⣌⣷⠀⣤⡆⠀⢷⣾⣿⣷⠀⠀⢿⡿⣿⣷⣄⠷⠋⢰⠀⢳⡀⢷⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡟⢉⡞⠀⠈⢿⡿⠁⠀⣿⡿⢷⡄⣿⡅⣨⣵⣤⣿⡇⢹⣿⣇⠘⣿⣿⠘⢿⣿⣿⣦⣸⣷⡞⢳⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣇⣾⣿⣶⠦⠘⠇⠀⡀⢿⣏⠀⢙⣿⣿⣿⣛⣿⢿⣿⢹⣿⣿⡆⠸⣿⣇⠘⣿⣿⣿⡉⢿⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣿⡃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡍⢠⠲⣶⠟⠓⢺⣋⣠⠄⠀⢰⣷⠀⢻⣆⣾⠃⢻⡟⢻⣿⠸⣿⠈⣿⢻⣿⠀⢋⣿⠀⠈⣿⣿⡇⢸⣆⢸⠀⠀⠀⠂⠀⠀⠀⠁ ⠀⠈⠿⣿⡿⢿⠦⢌⠢⣄⡂⣤⠀⢀⡀⠀⠀⣾⣵⠆⠐⣏⠀⢠⣿⠛⠁⠀⢀⡀⠟⠀⢀⣽⡟⠀⢸⣇⢾⡏⠀⡇⠀⣿⠈⣿⡇⣸⣿⡆⠀⠘⣿⣷⡜⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⣿⣿⠦⣤⠤⠴⠦⠍⠋⠉⢩⣴⡶⢿⢉⣵⣶⣼⣿⢀⣿⣿⡀⠀⢰⣿⣷⡄⠰⢾⡿⠃⠀⢻⣉⣼⠇⠀⣿⣷⣿⠈⣿⡇⣿⣿⡇⠀⢀⠽⣿⣿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⠿⠶⣾⣿⠃⠀⠀⠀⣴⠟⠓⢳⣾⣿⣿⣿⣿⣶⣿⣿⣻⡇⠀⢸⡟⢹⡿⠳⣾⡇⠀⢠⣿⣿⣿⠀⠀⢹⣸⣿⠀⢿⣷⣿⣿⣧⠔⠃⠀⢿⣿⣿⣿⡇⠀⠉⠳⢄⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⣿⣿⣀⣠⣤⣾⣷⣄⣠⣿⣿⣿⣿⣿⡟⠛⠿⠋⠉⢁⣉⣤⣭⣍⣤⣤⣾⠁⠀⢸⣿⣿⡏⠀⠀⢼⣿⡿⠀⢸⣿⣿⣿⠁⢀⣀⠤⢼⣿⣿⣿⠇⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⢰⡿⠙⣿⣿⣿⣗⣤⣶⣾⣿⣿⠉⠛⣿⣿⣇⣺⣧⢀⠀⢀⣤⣤⣿⣿⣭⡝⣻⡿⠋⠑⠒⣻⣿⡿⠒⠒⠒⣿⣿⠇⠀⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⡵⠀⠀⠀⠀⡁⠀⠀ ⠀⠀⠈⠳⣤⣿⣿⣿⡿⣿⣿⣿⣿⠇⣠⡅⣿⣿⣇⢜⣬⣸⢀⣾⣿⣿⣿⣿⣿⣿⡿⢁⣀⣤⣼⣿⣿⠇⢤⡀⢰⣿⡏⠀⢸⣿⠟⠛⢠⣾⢿⣿⠏⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡿⣤⣉⣿⣿⡿⣾⣻⠆⣿⣿⡇⢘⣛⠉⠈⣹⣿⣾⣹⣿⣿⡿⣋⣩⣶⣶⣿⣿⣿⣶⣶⣆⠋⠉⠀⠀⠀⠀⠀⠀⣿⢻⣸⡿⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⣾⡿⢷⣼⢾⣿⣿⣿⡃⢱⠏⠀⢸⣿⣿⢸⣿⣷⡄⢿⣿⣦⣟⣻⣿⣿⣿⡿⠿⠛⠑⣿⡙⡿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⣡⣼⡿⣿⠀⠀⢠⠤⠀⠀⠊⠀⠀⠀ ⠀⠀⠀⠀⢙⡵⡛⠛⠳⣮⢿⣿⣿⢿⡀⠀⣸⣿⣿⣿⣿⣻⠇⢀⣨⢥⣿⢻⣿⡀⠀⠀⠀⠀⠀⢿⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠘⣮⣧⠈⢳⡟⢾⣿⣿⣷⡈⠉⢁⣴⣯⢁⣤⡿⠉⢿⢪⣆⠀⣀⣀⡀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⢀⡇⠀⠀⠀⢠⣾⢸⡇⢸⠸⣷⣶⣿⣿⣿⡅⠠⠜⠀⣿⠛⠃⠀⢰⣿⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⣾⡏⣿⡇⣸⡇⡇⢨⠙⢿⣿⠀⠀⠀⠀⡿⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⢀⣿⢣⣿⡇⣼⣇⣷⣸⠀⠀⢹⠀⡄⠀⣤⣿⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠄⠐⠂⢹⠇⠀⠀⣰⣟⣿⢸⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢸⡿⢸⣿⣷⣿⣿⢿⡝⣷⠀⢸⡇⠅⠀⣿⣿⠀⡆⠸⢷⣿⠄⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣴⢿⣏⣽⢸⠀⢸⡿⢻⡀⠀⠀⠀⠀⠀ ⠳⡄⠀⣿⠀⠀⠀⢸⡇⠸⢹⣿⠏⡇⠀⢹⡸⡆⢸⡇⡂⢀⣿⣿⠀⡇⠀⣸⣿⡂⢦⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣠⠋⠀⢀⡞⠁⢸⣽⣿⡏⠀⠘⡇⠈⣧⠀⠀⠀⠀⠀ ⣀⡇⠀⢹⠀⠀⠀⠀⡇⡇⠸⣿⡇⢹⠀⠘⡇⡇⣸⣧⣷⢸⣿⣿⡇⡷⣦⢸⣿⡁⠀⠈⡷⣦⣄⡀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⡴⢿⠀⠀⢸⣿⢸⣿⠀⠀⣇⠀⢻⡀⠀⠀⠀⠀ ⡏⠀⠀⢸⡄⠀⠀⠀⣇⢇⠀⢻⣷⢺⠀⠀⡇⠁⢸⣿⢸⣸⣿⣿⣇⡇⢹⢹⣿⡇⠀⠀⠀⠺⢿⣿⣿⣷⡶⢦⣄⣀⣀⣀⣀⣠⠞⠁⡏⠀⠀⢸⣿⢸⣿⢀⣠⠞⠋⠉⠁⠀⠀⠀⠀ ⠀⠓⠦⡀⣇⠀⠀⠀⢻⠈⠙⠛⠻⢸⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⢻⣸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⢼⣿⠋⢀⠆⠀⡃⠀⠀⢸⡟⣸⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⢾⣿⣿⣿⣷⣶⣤⣀⣤⣶⣾⣿⣿⠿⣧⣾⡟⠀⢸⠀⢀⠇⠀⢀⠈⡇⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣦⣤⡞⡁⠀⠀⠀⣸⠀⠀⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡻⢭⡍⣠⡶⠛⣿⣧⡀⡼⡀⢸⠀⠀⢸⡄⣷⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⡇⠀⠀⡇⠀⢻⣿⢿⣿⣿⣿⣿⣿⢹⣿⣿⡻⣿⡛⣿⠛⡟⠉⣉⡼⠟⠁⠀⠀⢻⣿⣷⣷⣧⣸⠀⠀⣿⢳⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡇⠀⠀⣇⠀⢸⠘⣿⣿⣿⣿⣿⣿⣼⡿⣿⡇⠉⢛⣿⡢⢿⡋⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⡏⣆⢘⢺⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡤⢟⠆⢸⠀⠘⣿⢿⣿⣿⡟⣷⣿⣿⡇⠀⡞⣵⣧⣧⠹⡆⠀⠀⠀⠀⠀⣾⣿⣧⡀⠈⣇⡿⠸⠀⢸⣳⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠢⡀⠀⠘⣦⣠⣤⠴⠖⠳⡖⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠀⡸⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠱⡀⠰⠘⣧⠤⠀⠀⢴⠄⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡎⢠⠁⠀⡸⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⣧⡀⢆⢃⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠀⡜⠀⢠⠀⠀⡄⠀⡉⠳⣌⢻⣄⣸⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⡁⠀⢸⠀⢀⠇⢀⡟⡇⢰⠃⢠⠇⠀⡄⡇⠀⠃⠀⠈⠻⡉⢹⠀⢸⣿⣿⠛⠓⠒⠂⠀⣴⣞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡆⠀⠀⠀⢨⣴⠎⣠⠾⡿⢠⣃⡴⢻⠀⡸⢠⡧⡾⠋⠉⠉⠀⡇⢸⠀⠘⣿⣿⣦⣀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡂⠀⡇⠀⠀⠀⡿⣣⠞⠁⣸⣡⠾⠋⢠⢇⣴⡡⢻⡿⠁⠀⠀⠀⠀⡇⢸⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠠⡿⠁⠀⡇⠀⠀⠀⡟⠁⣀⣼⣋⣁⣠⡤⠛⠟⠁⠠⠋⠀⣤⣤⡶⠶⠿⣷⣺⠀⠀⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡶⢳⠀⠀⡆⠀⠆⠀⡧⠽⠿⠟⠛⠉⠙⠻⠂⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⡏⢹⢈⠀⣇⠸⣄⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⢠⡞⢠⣼⣇⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡆⣿⡄⢻⣿⣿⣿⣿⣿⣿⣦⣤ ⠀⠀⠀⠀⠀⡠⠋⣰⣿⠃⣼⠃⡙⡀⠁⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠀⠀⠀⠀⢠⡇⢠⣿⢡⢸⡹⡄⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠁⠀⡞⢡⡾⠋⣹⡼⡻⢰⠀⣧⢸⠀⢻⣿⣄⠀⠀⠀⠀⢰⣚⣯⡤⠤⢶⣾⡟⠀⠀⢠⣿⣇⠸⣯⢸⣼⡿⣜⣾⣇⠀⣸⣿⢿⣿⠇ ⠀⠀⢀⡞⣰⣿⣠⣾⠏⢠⠃⡎⠀⠸⣦⡄⠘⣇⢋⠳⣄⠀⠀⠈⢯⡀⠀⠀⢀⡜⠀⢀⡴⣿⣿⣿⡄⣿⡀⠸⣧⠘⣿⣿⡄⠛⠋⠈⠉⠀ ⢲⠀⠘⢰⣏⢉⠟⠁⣰⡟⢠⡃⠀⠀⢻⣿⣌⠹⣿⣀⣿⠉⠂⠄⣀⠙⠲⠶⠋⣀⠴⠋⠀⣿⣿⣿⣿⡿⢻⠀⠘⣦⡿⢻⠃⠀⠀⠀⠀⠀ ⡾⠰⠀⣿⡿⠋⢠⡾⣻⠃⢸⡇⠠⡄⠈⢿⣏⠳⣿⢯⣼⠀⠀⠀⠀⠉⠑⠒⢻⡷⢄⠀⠀⡏⡏⢋⣿⡧⡄⠀⠀⢘⡇⠸⡀⠄⠀⠀⠀⠀ ⡇⢰⠀⡿⢁⣴⣿⠞⢹⠀⢸⣷⡀⢳⡀⠈⠻⣟⠃⠀⣿⣶⣤⣄⣀⣀⠀⢀⣸⢠⠈⢣⣴⢃⡇⣿⣿⣷⢷⠀⢠⠙⣷⢰⠁⡀⠀⠀⠀⠀ ⠀⢘⡶⢁⣾⡿⠁⣀⡼⢷⣌⡻⠿⠦⣹⣆⠀⠈⢳⡄⠘⠈⠙⠛⠻⠿⠿⠟⠛⠸⡆⠀⢫⠙⠳⠿⣿⣟⠎⢀⣮⡾⢙⣡⠾⠃⠀⠀⠀⠀ ⣿⣿⢁⣿⣿⠃⡼⠁⠀⠀⢽⣟⠦⢤⣤⠀⣱⡄⠀⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢣⡀⠀⣸⠋⢠⡾⠟⢠⠿⡀⠀⠀⠀⠀⠀⠀ ⣿⡇⣾⠏⣿⡞⠀⠀⠀⠀⠀⢫⠑⡄⢻⣿⡮⣝⡄⢹⡄⠙⢦⣄⡀⠀⠀⠀⠀⣠⢾⠀⠀⠀⠱⣤⠃⠀⠉⠀⡴⠁⠀⢡⠀⠀⠀⠀⠀⠀ ⣿⠀⣿⢠⡟⠀⠀⠀⠀⠀⠀⠀⢧⠸⠀⡿⠀⠘⢷⢸⡇⢦⠈⢣⠈⠳⣖⢒⡎⠀⠘⠀⢾⣶⢲⠃⠀⢀⡴⠊⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀ ⣿⠀⢻⣿⠀⢠⣶⠀⠀⠀⣶⡀⠈⣆⡗⠣⣤⣤⣽⣾⠁⠀⣷⢈⣦⡀⠀⠁⠀⠀⡘⠀⠀⣨⣇⡔⢠⣿⠁⠀⠀⠀⡄⠀⢷⠀⠀⠀⠀⠀ ⣿⣆⣸⠇⠀⠀⡏⠀⠀⠀⢹⡇⠀⠸⡇⠀⢿⣿⣿⠃⠀⢰⢿⣸⣧⣉⠢⡀⠀⢠⣧⣶⡟⠉⣿⡇⢸⡿⡄⠀⠀⣸⠀⡌⠸⡄⠀⠀⠀⠀ ⠀⢹⡟⠀⠀⡞⠀⠀⠀⠀⢸⡇⠀⠀⢡⠀⠸⣿⠃⠀⠀⣿⠟⠉⠻⢿⣶⣝⣶⣎⣼⡟⠀⠀⢻⣿⣜⢷⣽⡦⠤⠃⡰⠁⠀⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡟⢹⣻⣏⣹⠿⡙⣿⢸⠅⢧⠈⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢿⠇⣸⡟⢼⠁⠈⣿⠝⣿⠈⠠⡿⣸⠀⢸⣇⣽⣿⣿⣿⡏⢻⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⡇⣼⠀⣿⠃⣟⠀⢸⡏⣾⣿⡂⢸⣿⡯⠤⠾⢻⣿⢻⣿⣿⡇⢸⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣦⣿⣿⢿⣿⣷⣿⣿⠃⠀⣆⣼⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢸⣿⣿⣿⠏⢠⡾⢿⡿⠿⢻⣿⣿⢻⣿⣿⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠀⡾⠛⠿⠿⠀⠉⠀⠠⠽⠶⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⠉⠻⣟⠚⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⢻⡌⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣣⡑⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⣿⡇⠘⣏⡟⢿⣿⣿⣾⡇⠘⣷⡄⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠈⣩⢹⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⢇⠘⢿⣿⠀⣿⡇⠘⣿⣿⣿⣇⠀⠘⠿⠂⠀⠀ ⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⡿⠁⢰⠇⢸⣆⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡇⠈⢆⠈⢿⠀⢹⡇⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠏⣾⣿⣿⣻⣿⣿⠀⢀⡟⢀⡾⣿⣿⣿⡷⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡾⣺⣿⡀⠈⡆⠘⡆⢸⣧⣾⣿⣿⡟⣿⠀⢀⣠⠔⠒⠉ ⠀⡼⡇⢸⣯⡇⠐⢧⣿⣿⠀⡼⣤⣿⣷⣿⣿⣿⡇⢀⣴⡟⣹⣶⣦⣤⣀⢴⣿⣶⣿⣿⡇⠀⠸⠀⢰⠀⣿⣿⣿⣿⡗⣿⡟⠉⠀⠀⠀⠀ ⠰⠃⡇⡟⡟⢀⣄⣾⣷⠻⣿⣽⣿⣻⠿⠿⠿⠚⠓⠿⠾⠏⠁⠚⠛⠿⠿⣾⣿⣿⣿⣿⡇⠀⢀⣀⣤⠃⣼⣿⣿⣿⣇⡇⢣⠀⠀⠀⠀⠀ ⠃⠀⣿⢡⢇⡾⣿⢿⠗⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⣤⣶⣶⣶⣦⣤⣼⣿⣿⢿⣿⣧⠀⠋⠀⣀⣾⣿⣿⣿⡿⣿⡇⢸⠁⠀⠀⠀⠀ ⠀⢀⠋⢻⡘⡸⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣀⠀⠉⠙⣿⣿⣿⣿⡿⢻⡟⠿⢿⣿⣿⣿⣿⣿⡿⣸⠃⣿⡟⢹⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡮⠔⠒⠉⠉⠉⠉⠁⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠑⢤⡀⣀⡠⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢄⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⣦⡇⠀⠀⠀⢠⠁⠀⠀ ⢄⡀⠀⠀⠀⠀⠀⠀⡠⣾⠏⠀⢰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⣣⠀⠀⠀⠣⡀⠀⠀⠀⣰⠇⡄⠀⠀⣿⣇⠀⠀⠀⡎⠀⠀⠀ ⠀⠉⠙⠒⠒⢶⠒⠋⢠⡟⠀⢠⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⡅⠀⠀⠀⠱⠀⠀⠀⣼⡴⠁⣸⠀⣏⠈⡷⣄⣰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣧⠀⠀⠀⠀⣇⠠⠚⠉⠁⣰⠇⠐⡾⠀⣧⠈⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⡞⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⣴⡟⠀⢰⡇⠀⡏⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⡃⠠⠀⢸⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⣤⣟⣀⣀⠀⢻⡀⠀⠀⠈⡆⡦⠊⡹⠀⠰⠋⠀⢰⠁⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⢠⠀⢸⠀⠀⠀⠘⠀⠀⢀⠅⠀⣼⣿⠋⠀⠀⠀⠘⡇⠀⠀⠀⡇⢀⣰⢣⣤⣀⠀⠀⡎⡸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡀⣿⣿⣶⣄⠀⠀⠀⣼⠀⣼⣿⡏⣠⣶⣶⣶⣒⡗⢺⣤⠀⡃⣷⠿⣿⣿⣿⣷⠰⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⣟⣿⢻⣿⣷⣂⢾⣯⠜⢡⠿⣶⣿⣿⣿⣿⣿⣿⠻⢿⢿⡇⠘⢰⣿⢳⣿⢻⡆⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⣦⣻⠿⠁⠀⠀⠀⠁⠀⠀⠻⣿⡛⠿⠟⣋⡆⠀⢸⠁⠀⠮⣼⣿⣴⣿⣴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠒⠋⣟⡅⠀⡸⠀⢤⣈⣵⣿⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⠇⣰⡿⣿⠿⡏⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⡅⢇⠀⠀⢤⣤⠤⠤⠤⠤⠤⣤⠀⠀⢀⣿⣶⣿⠞⢰⡴⠃⢸⢁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠳⡈⠣⡀⠀⠑⣄⠀⠀⢀⡴⠃⠀⠀⢨⣿⣿⠁⢀⠟⠀⢀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢹⣤⢸⡀⠘⢆⡈⠲⣄⠀⠉⠉⠀⠀⢀⣠⠖⠙⣿⣇⣠⡞⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠘⣿⡻⣧⠀⠀⠉⠒⢌⡳⠤⢤⣴⣾⣟⣁⣤⡴⠿⠻⣉⣇⡴⠊⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠈⢿⠿⣧⡀⠀⠀⠀⠙⢦⣀⡏⠉⠉⠉⠀⠀⢀⣠⡼⠃⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠀⣀⣤⡶⡿⠁⠀⠀⠀⣠⡶⣿⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡆⠀⠀⢀⡴⠚⢁⡾⠃⢁⡤⠔⣲⡿⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⠎⠀⣠⠖⠉⠀⠀⣼⠁⠀⢀⣠⠞⠉⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⡦⠒⣡⠔⠋⠀⠀⠀⠀⠀⣿⢀⣴⠟⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀ ⠀⠀⠀⢀⠤⠒⠉⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠃⠀⠀ ⠀⣀⠜⠁⣀⣴⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⡠⣞⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠁⠘⠀⠀⠀

⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⢻⣶⣿⣽⣡⠈⡙⣿⣿⣿⣿⣷⣬⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠈⢸⢀⣿⢹⡏⢨⣿⣿⠟⠋⠀⣿⣿⠋⣰⣿⣿⣏⣿⣿⣠⢓⢻⣿⠉⠻⢻⣿⠻⣿⣿⣧⠉⠛⠻⣿⣿⣿⣧⢿⣿⡻⡿⣿⣇⠀⠀ ⠀⠀⠀⠀⠈⠋⣸⠁⢽⢿⠇⠀⢀⣼⣿⣯⢠⠏⡿⢹⢿⣿⢻⣼⡟⣿⣿⡆⠀⢸⣿⣧⠙⢿⣿⣷⣤⣩⣽⣿⣿⣿⡟⣿⠁⢳⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠂⡜⢠⢆⠟⢡⣿⢣⡏⢠⣷⠘⢸⣹⢸⣿⣇⢹⡹⣿⡀⠈⢻⣿⣆⠈⢿⣇⠈⠻⡙⣿⠁⠇⠇⢸⡄⠘⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡎⡌⢠⣿⠃⡞⠀⢸⣿⠀⠀⡇⢸⡏⣿⡤⣇⢃⢡⠀⠈⣯⣿⡄⠈⢿⡆⠀⢱⡸⡆⢰⠀⠀⡇⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣠⣻⠏⡼⠀⠀⣿⣿⡀⢰⠇⠈⣿⢹⣷⣿⡌⣧⣇⠀⣿⢿⣷⠀⠈⢳⡰⣄⢿⣿⢸⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡆⠀⠀⢸⣿⣿⣷⣿⡾⠁⠀⠀⣿⣿⣧⣼⠆⠀⢿⣿⠀⠻⣿⣼⣿⣦⣿⠀⢻⣧⠀⠀⢻⣿⣾⣿⡎⡆⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⢸⣿⡿⢹⣿⠃⣀⣤⠴⣿⠻⣿⣿⠀⠀⠸⣿⡇⠀⠈⠻⣿⣿⣿⠶⢤⣿⣆⡀⠀⠹⣿⣿⡇⠃⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⡀⣿⠷⢾⠏⠉⠁⠀⠀⢿⠀⢻⣿⡆⠀⠀⡏⢻⡀⠀⠀⠈⠹⣿⣄⠀⠀⠙⢏⠉⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠙⡿⠀⢸⠀⠀⠀⠀⠀⠘⡆⠀⠹⣷⡀⠀⠸⡄⠱⡀⠀⠀⢰⡏⠈⠓⢄⡀⠈⠑⢤⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⢸⡇⠀⠀⢠⡇⠀⠸⠤⠤⠤⠤⠤⠄⣙⣄⠀⠈⢷⡀⠀⠙⣄⠈⠓⠀⣸⣃⣀⣀⣀⡤⠤⠤⠄⠀⠉⣩⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣇⠀⢸⡇⣀⢠⣼⣷⣶⣶⣤⣤⣤⣤⣤⡤⠤⠤⠄⠀⠀⠓⠀⠀⠈⠀⠀⠐⠻⠤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⠤⡤⣤⢤⡄⠀⠀⠀ ⠀⣼⣿⠀⣶⣧⠏⠉⢙⣯⠟⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠟⠯⠻⠉⠁⣿⠇⡇⠀⢸⡄⠀⢀⠀ ⠀⠹⠟⠀⣯⢹⡇⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⢸⠀⢸⣿⠀ ⠀⢠⠀⡄⢸⢸⡇⠀⡘⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⢰⠀⠀⣸⠀⢸⡿⠀ ⠀⢸⠀⡇⢸⢺⡇⠀⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⢸⠀⠀⡿⠀⣿⣿⣧ ⠀⢸⠀⣣⢸⡇⡇⠀⢱⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡏⣸⠀⢰⡗⢰⣿⣿⣿ ⠀⣼⣷⣿⢸⡇⡇⠀⢸⣌⡇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣷⡇⣻⠀⢸⠇⣼⣿⣿⣿ ⠀⣿⣿⢿⡆⣿⣿⠀⡸⡎⣿⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠤⡖⠊⠉⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⣿⡇⣿⢠⢘⢠⣿⣿⠿⡯ ⠀⣟⢹⣼⣿⠙⣿⠀⡇⠀⢩⠀⠀⠀⠈⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠁⠀⠀⢸⡿⡀⣯⢠⣴⣾⣿⣿⠀⣿ ⠁⣿⢸⣿⣿⣧⣿⠀⢧⡀⢸⠀⠀⠀⠀⠀⠘⣿⣷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⣿⠇⢸⠀⠀⠀⢸⣷⣧⣿⢸⣿⣿⣿⡟⠀⣿ ⠀⢿⠀⢿⣿⣿⣿⡄⢸⣿⣸⡄⠇⠀⠀⠀⣴⢿⠹⣧⠈⠳⣦⣀⠀⠀⢀⣠⣴⡿⠋⠀⣸⠃⠀⠸⢦⡆⠀⢸⣸⢁⣿⢸⣿⣿⣷⠃⠀⣿ ⠀⠸⠀⠈⢻⣿⣿⡇⢸⣿⣿⡇⢀⣀⠴⠛⠁⢸⡄⠈⠣⡀⠈⠻⣿⠘⣿⣿⠟⠁⢀⡴⠁⠀⠀⠀⠈⠳⢼⣸⣿⢸⡿⢸⣿⣯⠏⠀⢀⠏ ⠀⠀⠁⠀⠈⢿⣿⣇⠘⣿⣽⡷⠊⠁⠀⠀⠀⠀⠁⠀⠀⠈⠢⣀⢈⠀⠋⠁⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣸⣧⣼⣯⣿⡆⠀⡌⠀ ⠀⠀⠀⢀⣀⣀⣹⣿⠰⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠽⠤⠶⢭⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣱⣿⡇⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⣀⡠⠤⠤⠒⠒⠋⠗⠦⠄⠈⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⣠⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠢⣄⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣰⡿⠊⠀⠀⠀⠀⡰⠂⠀⡄⠀⠀⠀⡀⠀⠀⠘⢆⠈⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡼⠋⠀⠀⡠⠀⠀⡔⠁⠀⢰⠁⠀⠀⣧⢣⢆⠀⠀⢘⡆⠀⠈⢆⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱⡞⡈⡴⠀⠀⡰⠁⠀⣾⠁⠀⠀⡇⠀⠀⢀⡿⡵⡎⡄⠀⠈⣼⣆⠀⠀⢣⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠇⠰⡽⠁⠀⣰⠁⠀⣸⠃⠰⠀⢸⠇⠀⠀⣼⠃⠘⣽⣹⠀⠀⠃⡏⢣⠀⠀⢧⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡳⢡⠀⢠⡇⠀⢐⡟⠀⠆⢦⡿⠀⠀⢸⢻⠀⠀⠈⣿⡄⠀⢸⣿⠀⢧⠀⠀⡎⡀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣤⢁⠇⢠⡿⡄⢀⣾⠃⢰⠘⣼⡇⠀⢰⣯⡇⠀⠀⠀⢸⡇⠀⢸⣿⠀⠈⡆⠀⢸⡇⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⡌⠰⣷⡿⠀⣼⡇⠀⡆⢷⡽⠁⡸⣧⡿⠀⠀⠀⠀⠘⡇⠀⢸⠿⡄⠀⠸⡀⠈⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣧⡧⣠⡙⠀⠜⡹⠀⡼⢀⢮⠁⢰⣷⡷⠃⠀⠀⠀⠀⠀⡇⢀⢸⠀⢣⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⡟⠉⢻⣿⣄⡀⠁⡜⠑⢫⠇⡴⢡⡿⠉⠲⠤⣀⡀⠀⠀⡇⠈⡼⠀⠘⡄⢠⠘⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⡇⡀⣿⣽⣿⣶⠀⠤⠒⣡⠜⣚⠟⢁⣀⣠⢀⣀⡉⠑⢲⠼⡀⣧⢠⠰⣱⡀⢣⠃⢸⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠱⣘⡛⠿⠟⠀⠀⠙⠒⠚⠁⡠⢿⣿⣿⣿⣷⣯⣥⣾⠀⢡⠋⢧⢧⢣⢟⣄⠀⢸⡰⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢪⡀⢦⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠈⡟⠻⢾⣄⢪⣳⣯⢮⠚⢦⠈⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⡌⠘⠅⠘⠁⠀⠀⠀⠀⠀⠀⣤⣤⠰⠭⢝⣛⣉⠠⠔⠃⠀⡞⠀⢳⣕⣽⣍⣓⠄⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⢻⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣭⣬⢒⠀⠀⠀⢸⠀⢤⠇⣰⣩⡥⢶⣶⣾⣧⢸⠙⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢏⡸⢸⠀⠸⡄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⠀⠀⠀⡇⢰⡘⠀⣱⠿⣿⣿⣧⣩⠋⢸⠀⡸⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⣄⠇⠀⡇⠈⡝⣄⠀⠀⣹⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣇⠋⢀⣀⡯⣟⡵⡇⠀⠃⠀⡇⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢃⢿⠀⠀⢷⡀⠡⠈⢦⡀⠐⠿⡛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡾⣯⡭⢭⠟⠊⠉⡐⠀⠀⠀⢸⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢸⡈⢰⠀⠸⢇⠈⢦⡀⠱⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡶⠋⠁⡀⢀⣿⠖⠁⠀⢀⠌⠀⡠⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⢸⡇⡄⠠⠀⠋⢆⡄⠉⠀⠘⢲⠒⠒⢻⠿⣿⣿⠟⠋⠁⠀⢀⣼⠴⠋⠁⡠⠐⠁⡠⡪⠊⠁⠀⣘⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⢡⢸⣧⢀⠀⡴⠀⢺⠘⠤⠀⠀⢸⠀⠀⠈⡆⠈⠀⢀⣀⣤⡴⠛⠁⠀⠀⠈⢁⠴⠪⠈⢁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠷⠾⠾⢿⡈⠀⠁⠀⡇⠀⡄⠀⠁⣸⠀⠀⠀⠸⡿⠿⠿⠛⠋⢀⣠⣴⣶⣶⣶⣤⣀⡀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡔⠁⠀⠀⠀⠀⠑⢄⠀⢸⠁⢰⠁⠀⢰⠇⠀⠀⠀⢀⠓⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣤⣄⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⣧⠊⣄⠇⠀⣄⡟⠀⠀⠀⢀⣾⠞⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠿⢀⣼⡼⠀⠀⠀⣠⠞⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⣦⡿⠁⠀⠀⢸⡁⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⢠⠀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⢸⠀⣿⠁⠀⠀⣠⠋⠸⡔⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤ ⢸⡀⣀⣸⣾⣿⣷⡿⣿⢿⣾⠋⢻⢀⡏⠀⠀⢰⠁⢲⠞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡇⠀⠀⠈⢦⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⣰⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡉⠃⣿⠀⢠⠛⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⡔⠃⡜⢄⠘⣄⠎⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠈⠲⡀⠀⠀⠀⢀⡜⠡⡀⠀⠈⠓⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠱⡖⠊⠉⢣⣆⠘⢄⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠙⠦⠈⠣⠀⠂⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⢄⣤⣤⣄⣄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠙⠾⢊⣛⢩⣿⡛⠿⣿⣶⣄⠀⠀⢨⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠋⡀⠀⠀⠰⢛⣵⣿⠞⠛⢚⣏⠰⢛⣭⢶⣃⠊⠁⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠳⢪⠀⢈⢅⣶⣡⡾⣷⣦⡠⢞⢙⣾⣽⣶⡉⠉⠉⠐⣜⡀⠀⠀ ⠀⠂⠀⠀⢠⡛⠣⡀⢿⡿⠈⡟⠿⢷⠘⢟⢿⡻⡟⢏⢫⣀⠙⢦⣠⣾⣿⣿⣟⣛ ⠀⣀⠀⣶⣳⣲⣢⣿⣸⣇⣀⣷⣼⡸⡆⠬⠶⣷⣻⣾⣷⡹⢿⣿⣿⣿⣍⠉⠉⡋ ⠀⠀⠛⢉⢛⣵⢻⣪⣿⡁⠀⠘⣿⣧⠹⣄⠀⣈⣷⣌⡫⣷⣄⡙⢯⡻⢿⣷⡞⡀ ⠀⠀⣠⣏⡁⣠⡶⢻⣿⣯⣭⡶⠈⠛⠓⠈⢫⣶⠯⡙⡲⣼⢯⢻⣞⣿⣶⠉⠙⠻ ⠀⠀⠁⠈⠘⠿⣧⠚⢼⡧⠕⠃⠀⠀⠀⠀⠈⠚⠋⠂⢰⢇⠊⢷⡜⢿⢳⢮⣢⣀ ⠀⠀⠀⠀⡠⣂⡟⠀⠰⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢓⠌⣠⡈⣻⣮⢳⣧⡈⠛ ⡤⠂⠹⠉⠀⢃⢣⣇⠀⢷⡆⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⠀⠘⣏⠲⡝⢷⣝⢿⡆ ⠀⠔⠃⢀⠊⠘⣡⢻⣷⡌⣿⢤⢀⠀⠀⢀⡤⣾⠁⢆⠈⣆⢀⡈⢓⢌⡢⠛⢮⡻ ⠈⠀⠀⠘⢀⠀⠘⡈⢿⣷⡽⣮⢆⠉⠈⢁⡠⠧⣰⢊⢶⣌⠩⣻⠤⡒⠁⠀⠀⠙ ⠀⠀⠀⠠⢀⡇⠀⠐⡘⢻⣿⣯⢧⣈⣊⣁⣠⣶⠀⣈⣀⠀⠉⠩⠋⡀⠀⠀⠀⠀ ⠄⠀⢀⠊⠀⠀⠀⡌⠵⠸⠿⢾⣿⡛⣿⣿⡋⠉⠈⢻⣯⣠⡄⠃⠪⡠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡤⣄⢀⠈⣹⢥⣤⣦⡀⠀⠀⣖⡳⣶⠶⡄⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠸⠑⠙⠛⠐⠃⠈⠻⡭⡪⡀⠂⣿⠀⣟⢀⣧⡟⣸⠇⣶⠦⡄ ⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣷⠺⠈⠀⠙⠋⠸⠷⠏⢠⠏⠀⠀ ⠀⠀⠀⠀⠀⡶⠀⢹⠀⠀⠀⠀⢀⢴⡄⣾⠇⡇⠀⠀⠀⠀⠀⠀⠀⡉⠠⠀⠀ ⠀⠀⠀⠀⢀⣇⡀⠎⠣⠀⠨⡏⣸⢈⠈⠢⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⢀⠄⠂⡛⢇⠐⢀⠃⠀⠓⠉⠛⠓⠤⢀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⢀⢰⠈⡄⢫⠄⠀⠈⠀⡐⠀⢔⢸⠂⠢⡀⠀⠁⠀⢀⠀⡄⠀⠀⠀ ⠀⠀⡇⠀⠀⠱⡆⣰⡴⠋⠈⠐⠊⠀⠀⠠⠾⡀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀ ⢀⠀⡇⠀⠀⠀⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢈⢢⣿⠃⠀⠀⣴⣸⠀⠀⠀⠀⢠⣴⡶⣶⣶⣤⣤⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⠛⢿⣿⣻⠂⢠⢦⠗⠺⣟⣿⡿⡯⢄⠀⠀⠀⢸⣿⡾⠛⣹⡟⠉⢿⡇⣼⡿⠀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡏⠲⠌⠛⠛⠀⠐⠃⠀⠀⠹⠷⡯⠔⡩⢋⡁⢂⢸⣿⠀⠀⣿⡇⢀⣿⣿⣿⠃⣸⡿⠹⢶⣶⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⢳⣤⡸⡌⠿⠇⠀⢹⣷⣾⠟⣼⡇⢠⣿⠃⢀⣾⠟⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡇⠀⢀⣾⣿⢳⠃⠀⠀⠀⠀⠉⠁⠀⠻⠿⠟⠃⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡀⠀⣾⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⢥⢈⠓⠤⣄⣀⣀⡠⢪⡇⡗⠮⡛⠛⠋⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣧⠘⡄⢠⠘⡌⡆⠀⠀⠰⡇⡇⣸⡁⡇⠀⠘⢦⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣜⣻⡾⡇⠘⡄⢡⠸⡀⠀⠀⣏⢰⢻⠸⠓⠂⠐⠒⠓⢄⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⡠⠊⠁⠀⡌⠉⢻⠀⢡⠘⡄⢡⠀⠀⠈⠉⣚⠋⢹⠉⠉⡖⠢⢄⠱⡄⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣜⡁⣀⠀⠀⢸⡄⠀⢇⠘⢶⣱⠘⠒⠒⠒⠉⠀⠀⡌⠀⢠⣡⠀⢸⢄⡈⢆⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⠀⠀⠈⠢⡀⢷⠀⠸⡀⠀⢋⢓⢤⡀⠀⠀⠀⡰⠁⠀⠀⢹⡆⡸⠀⠈⠑⠧⡀⠀⠀⠀⠀⠙⠢⣤⣀⠸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠙⣼⡇⢀⣧⣢⡾⠃⠀⠈⠁⠒⠊⠀⠀⠀⠀⠤⠷⣧⡀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠈⠙⢿⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⣟⠀⠀⠀⠀⠀⠘⣧⢎⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀ ⢀⡀⢨⣿⠀⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀