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⣿⣿⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣭⢃⡌⠀⠀⠀⠀⠀⠀⢠⣾⡿⡿⠛⡛⠟⠛⠙⠋⠛⠙⠳⠀⠀⠀⠀⠀⠑⣿⣳⣟⣼⣣⣏⡿⣜⣧⣫⢏⡷⣯⣷⢶⣻⣤⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠁⠠⠀⢀⣡⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡾⣿⣿⣿⠂⣰⣿⢆ ⣿⣿⢯⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⢧⠻⠄⠀⠀⠀⢠⢖⠀⠸⢅⠃⠠⠙⡰⠃⠰⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⣸⣟⣞⣧⣻⣼⣹⣝⣮⡭⢯⣙⡷⣋⢿⣯⡳⣿⣿⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡽⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢗⣿⣻⢿⣿⣿⡟⠚ ⣿⣿⢧⣛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣦⠄⠀⠀⠀⣞⣭⠀⠈⠄⡘⠠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣛⡿⣞⢿⣜⣳⣭⣛⣮⣽⡹⣏⣿⣹⣭⡟⣶⣝⣯⢿⣿⣿⣄⡀⠀⠂⠈⠀⠀⠡⠀⠀⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣯⣿⡽⣟⣾⣿⣞⡁ ⣾⣿⣯⣛⡟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⣿⣭⣀⠀⠀⠀⣿⣷⡀⠀⠀⢀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣽⣋⣟⡞⣧⢻⡝⣞⣳⢻⣝⣞⣳⢏⡿⣳⣝⢮⣳⣻⢿⣿⣷⣶⣤⢤⣤⠤⣤⡴⢾⡿⠿⠉⠀⣠⠴⠁⠀⢠⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣽⣟⣯⣿⣿⣤ ⢘⣿⣷⠹⣟⣿⣯⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⡀⣀⢈⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣭⡷⣯⡟⣮⠿⣭⢳⡻⣝⢯⠻⣝⠾⣹⢏⡟⡷⣫⢿⣳⣯⣿⡀⠈⠈⠁⠈⠁⠈⠉⠀⠁⠀⢀⡤⣰⠁⠀⣠⣾⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⢾⣽⣿⣿⣿ ⡿⠿⣯⠿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡷⣏⢷⡟⣞⢯⡻⣞⢧⡝⣺⡼⣻⠽⣟⣳⢯⡞⡿⣩⡟⣜⡷⢯⡿⢿⣯⢿⡽⣖⣤⡖⣧⡴⢯⣛⣼⣣⣟⣿⠿⣿⡵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣻⡿⣷⣿⣿⣿ ⣷⣴⣿⢫⢷⣿⣿⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡈⠙⠧⢿⣿⣿⣿⣶⣦⣤⣤⡶⠴⠿⠟⠃⢁⣻⣽⣻⠾⣝⡻⣮⠷⣯⢟⡼⢡⠘⡔⢯⠽⣻⢷⡻⣝⢷⡻⣽⣛⡶⣹⢏⡾⣏⣻⡽⣳⢾⡳⣯⠟⣿⡛⣷⢻⣿⣛⣯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣟⣿⣿⣿⣿ ⣻⣿⣯⢟⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣄⠀⠀⠀⠉⠙⠛⠛⠉⠈⠁⢀⣠⣤⣶⣿⡽⢾⣭⢻⢧⡟⣮⢟⣯⡛⠖⠠⢡⠘⣀⢾⣛⢯⠿⣝⠾⡽⢶⣯⠿⣽⠾⣽⡞⣷⣻⢳⡯⣟⡷⣻⢧⣟⡷⣻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣷⡿⣾⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢃⠀⠀⠀⠈⠻⣷⣟⣯⣗⣯⣊⣿⣜⣯⣟⣼⣫⣝⣳⣭⣛⣬⡻⣟⣾⢧⣤⣀⡤⣤⢾⡽⢧⣏⣯⢷⣫⣟⣮⢽⣮⣽⢾⣟⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⢀⡀⠙⠻⣾⣷⣻⣝⣎⡷⣛⡾⣽⣹⢯⣳⢿⣹⣳⣭⣻⢞⡵⣯⡞⣽⢫⣟⣧⢿⣭⢿⣹⣞⣎⣿⢾⣽⡿⠋⠀⠀⢀⣠⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠘⢿⣦⣄⡀⠙⠳⢿⣯⣿⢧⣟⣶⡹⣏⣟⢯⣛⣷⢫⣟⡾⣻⣗⣻⡽⣛⡾⣭⢷⣫⢟⣳⡿⣾⢿⠏⠋⠀⢀⣰⡞⠽⣻⣿⠃⠀⠀⠀⠈⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⠛⢿⣦⣄⡀⠉⠚⠿⢯⡷⣿⣳⣎⣯⡽⣾⡹⢾⡽⣳⢯⡳⣏⠿⣹⣫⣷⢿⣻⠯⠟⠋⠀⣀⢤⣞⠣⢃⣤⣶⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢷⣎⡙⢿⣞⡷⣦⣄⡀⠉⠛⠳⠿⣽⣻⢷⡿⣯⣼⢷⣋⣷⣭⣿⣶⣟⡾⠏⠋⢁⣠⡔⣯⡛⠮⣑⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⣤⣄⠀⠀⠀⠀⠉⠻⢶⣭⣙⠳⣮⢽⡳⢦⣄⣀⡀⠈⠉⠙⠛⠙⠯⠿⠽⠛⠚⠉⠀⢀⡠⢶⡹⠒⠙⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⢷⣏⣾⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣭⣏⣳⠮⣳⡝⣯⣓⡖⣦⢤⣀⠀⠀⣠⠤⢖⠯⠻⣍⣂⣤⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⠀⠀⢀⣠⣤⠀⠘⡆⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣄⣈⢈⠁⠁⠈⠁⠲⡈⢞⢈⣠⢇⡰⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠀⠀⠀ ⡀⢀⠀⣄⣲⣭⣵⠖⠋⢁⣴⣾⣿⣿⣿⠂⠈⠉⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⢲⣳⣧⠀⠐⢻⣄⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠐⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠁⢂⠀⠀⠀ ⣾⣿⣿⣿⠟⠋⢀⣤⣾⣿⡿⡭⢆⠸⣯⠀⠰⣦⡀⠀⠄⠈⠻⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣷⠀⢸⡞⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣟⡃⠉⢀⣤⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠂⠐⠀⠀ ⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣻⣗⣯⡿⡷⠀⠐⣿⣳⣄⠀⠁⠛⠸⢧⡟⣶⢤⣄⠀⠀⠀⠀⠈⠳⢖⣦⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⢸⡽⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢮⣷⣻⣶⣾⣿⣿⣆⠀⠰⣧⣌⣀⠀⠄⡀⢀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⢶⡿⠏⢻⡟⣟⣾⠳⠟⠎⠓⠿⡉⠀⢀⢓⡳⢮⠓⠂⠀⠈⠳⠙⡎⠷⢎⠛⠴⠀⠤⡀⠀⠈⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠹⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣞⡷⣿⣿⣿⣿⡚⠆⠀⠘⡝⠋⠛⠳⠂⢍⣚⢦⢁⡀⠀⠀⠀⢀⠀⡀