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