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