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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⠒⠯⣕⢷⡝⢆⠀⠀⠀⠀⠘⠰⠀⢸⣼⠀⣠⣴⣿⣿⣿⣿⣿⣿⣼⣀⠉⠉⢻⡦⠀⠀⠀⠀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠃⢸⣿⠛⢻⠟⠉⣭⣿⣿⡿⠋⠀⢈⡿⠀⣸⣁⣠⣤⡖⠋⠀⣠ ⣦⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⢸⣄⣾⣿⣿⣿⡦⠀⣴⡟⢁⡴⣻⣿⣿⡟⢁⠴⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠄⢠⠀⢰⡄⢀⠀⢈⣿⣟⡽⠋⠀⢀⣾⠋⣰⢫⣾⣿⢿⣿⣿⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡠⠔⠉⢀⢜⣠⡿⠇⣸⣄⣼⣿⣿⠁⠀⢀⡾⢁⡼⠃⠀⠀⣠⣾⡷⣾⣫⣶⠀⠀ ⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣴⠶⢖⣶⠏⢁⠀⠀⢰⡟⣼⣿⣴⣿⣿⣿⣿⣿⠿⣷⣌⠾⠓⠋⢁⣤⠒⠚⠉⡟⣿⣿⢋⣼⠀⣠ ⠂⠀⡀⠄⠀⢀⠠⠀⠀⠀⠀⠤⠒⠉⢀⣀⣬⠴⣖⡏⣀⠔⢩⣯⣏⠑⣿⣿⣿⣿⣿⣿⢏⢻⣧⡀⠀⠀⠨⠿⢗⡀⠀⣿⣷⣷⡾⠡⠞⠁ ⠞⠉⠀⣀⡀⠤⠄⠒⢂⡲⠤⠶⠤⣤⣬⣭⣭⣭⠷⢿⣷⣦⡈⣷⠉⠀⢀⣉⣙⣿⣯⣿⠀⣈⣿⣿⣿⣷⠶⣤⣴⡇⠀⢹⣿⠟⢀⣠⠆⠀ ⡤⠖⠉⣁⡠⢴⡒⠍⠁⢀⣠⣴⠊⣰⡟⠙⢷⣄⡀⠀⠛⢿⣿⣿⣧⣿⣈⣿⣿⣿⣿⡻⣆⠘⢈⡉⣻⢷⣖⣡⣾⠁⢀⣾⣿⣀⡀⠀⢀⣴ ⣤⠖⠉⠁⠈⠁⠀⠠⠞⠩⣾⡟⠛⠋⠀⠀⠈⢻⣿⣿⣰⣶⣯⣝⣻⣿⣿⣿⣿⣿⣿⡶⢻⣟⠻⠶⢖⡶⠋⣩⣵⣶⡿⣿⠏⣿⣥⡾⠯⠓ ⣷⡾⢭⣄⡠⣴⢶⣯⢔⠂⣿⠁⠀⠀⠀⠀⠀⠀⠻⣆⠈⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣦⢻⡇⠈⣉⣴⣾⣿⣿⣭⣿⠏⡤⠾⣛⣛⠿⠭ ⡿⢰⡟⠀⣹⣿⠛⠿⢉⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢿⣿⣟⣀⣹⣿⣧⢽⣿⣿⣿⡇⡇⣸⣿⣿⣿⣿⠏⣰⢣⡾⠛⠛⠋⠓⠂⠀ ⣿⡄⢇⢸⢃⠟⠁⠰⢇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠿⠦⣑⣮⢻⣀⣞⡉⠿⣿⡿⠟⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣎⢘⠘⠄⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠳⡞⣿⣿⡿⠉⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣌⠓⠒⠚⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡟⢇⠀⠀⠀⠀⠀⡆⢹⠇⠀⠀⠐⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⣸⣿⠓⣦⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣷⠛⡆⣀⡤⠄⢠⡇⠈⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⡏⠹⠀⠇⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣵⣶⣤⣀⣷⣄⡁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⡆⠀⢰⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣌⣩⡿⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⡇⠀⢸⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣈⡽⠭⣍⣉⣁⣤⣤⠤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⠀⡇⠀⠈⡆⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣏⠙⠃⠀⠀⣶⡶⢿⣿⡝⠉⣼⣠⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀ ⣾⣿⠀⡇⠀⠀⢳⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠗⠶⠬⠿⠥⠒⠒⢿⠀⣸⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⣿⡇⠀⡇⠀⠀⠸⡇⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠔⠉⠸⠿⡇⠨⣶⣤⣤⣤⣤⣤⡊⢠⣿⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⢸⠀⠀⠀⡇⠀⠀⢘⣿⣿⣿⣿⣷⣦⣄⡀⠈⠀⠀⠀⣼⡇⠀⠈⣿⣿⠁⠀⠉⠀⣼⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣶⣿⢿ ⡿⣿⣦⣸⣧⡀⠀⢻⠀⠀⣼⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢹⠁⠀⠀⠻⢿⣄⠀⠀⣴⠿⣫⣴⣿⣿⣿⣿⣿⣷⣾⣿⡟⢋⣿⣿⣿⣿ ⡿⠿⣿⣛⣿⣿⣶⣾⣤⠀⠈⡆⠈⠿⣿⣿⣿⣿⣿⣭⣶⣿⣿⣦⣷⣄⣀⣀⣀⣈⣠⣾⣿⣿⣿⣿⣿⣿⣮⣴⣾⡿⠟⣛⣃⣾⣛⣿⣷⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠖⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⢀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⣠⠖⠁⠀⣀⣤⠆ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠇⠀⢀⣠⣴⣿⣿⢋⣠⠴⣞⣡⣴⣶⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡜⡎⣴⣿⣿⣿⣿⣭⣿⢾⣿⣛⠉⢁⠞⠁⠀⠀⠀ ⠒⠶⣶⣶⣶⣤⣴⡷⠀⢸⣸⢸⡿⠋⣿⣿⣿⡋⠀⠾⣿⢿⡶⠟⠇⠀⠀⠀⠀ ⠀⡢⠬⢻⣿⣿⣿⣿⣆⠀⠹⣿⡴⠖⢁⡼⠿⢿⡿⠛⠛⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣽⣿⠟⣻⣿⡻⣿⡆⠀⠉⡼⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢻⣦⣿⣿⠿⢻⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠁⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢗⠚⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠴⠖⢫⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢸⠃⠈⢉⣀⣠⣤⣤⣶⣶⣶⣶⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡥⠿⢿⠿⠟⠋⣁⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠊⠁⠀⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠴⠞⠃⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣈⣷⣦⣀⠀⠀⠙⣿⣷⠈⢿⣿⡄⢸⡇⠀⠙⣦⠀⠈⢳⣆⠀⠈⠛⢦⣙⣷⠈⠳⣄⠀⠀⢀⡾⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⡶⠞⠛⠛⠻⣷⣤⣤⣈⠙⢻⣿⡳⣄⠀⢹⣿⣧⣀⢻⡇⠈⣇⠀⠀⠹⡄⠀⠀⢹⣷⣄⠀⠀⠙⠿⢧⠀⠘⢧⡀⣼⠀⢹⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣦⡤⠴⠚⠋⠻⣿⣷⣭⡛⠛⠷⠤⢽⣾⣿⣿⣿⣿⣿⡄⣿⠀⠀⠀⣷⠀⠀⠀⢹⣿⣇⠀⠀⠘⣦⠁⠀⠀⢻⣟⠀⢸⣿⠹⡄⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣶⠤⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣆⢰⡀⣿⠀⠀⠀⠘⣿⣿⠀⠀⢠⣿⠀⡸⡀⢸⣿⠀⢸⣿⠀⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣮⡕⣿⠀⠀⠀⠀⣿⣿⠀⢀⣾⡿⣰⢷⡇⣸⠃⠀⣾⣿⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⣄⡀⢈⣿⡿⠿⠷⠤⣄⡈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣎⢧⡀⠀⠀⢺⠇⢠⣿⣿⣿⠏⠾⣋⠁⢀⣼⣿⠃⠀⠀⢸⡇⠀⠀⢀⣤⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣨⣿⣿⣟⡛⠲⢤⡀⠀⠀⠙⣿⣿⣿⡹⣿⡀⠀⠀⠀⠀⠀⠈⢿⣟⡻⢿⣿⣷⡝⢦⡀⠸⢀⣿⣿⠟⢁⣴⡟⠁⣠⣿⣿⠃⠀⠀⢠⡟⠀⠀⢠⠞⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⡛⠛⠉⠉⠁⠀⠈⠉⠻⣾⣿⣷⣄⠀⣿⣿⣿⡇⠈⠳⠄⠀⠀⠀⠀⠀⠈⢿⣿⣦⡉⢿⣿⡆⠙⢧⢸⣿⢃⣶⣿⣏⣤⣾⣿⠟⠁⠀⠀⣠⠟⠀⠀⠀⡼⠀⢸⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣄⡀⠙⣿⣿⣿⣷⣿⣿⣿⡹⡄⠀⠀⠀⠀⠀⠒⠦⣄⡀⠻⢿⣿⠀⢹⣷⢀⠸⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀⣴⣾⣿⣶⣶⣶⡾⠃⠀⠘⡇⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⡟⠛⠉⠉⠉⠙⠳⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠈⣷⠤⢿⣌⢳⣼⣿⣿⢛⣟⢿⡀⠀⠀⠀⣿⣿⣿⣿⡿⠟⢁⡀⠀⠀⣰⢃⣤⡎⠀⠀ ⠀⢀⡈⠿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⢄⣀⣀⡴⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣮⡛⠲⢤⣿⣿⢋⣥⣶⡿⠋⢀⣤⠾⠛⠉⣼⠀⠀⠀ ⠀⠈⢳⣤⡉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣉⢻⣿⣯⡙⠿⣿⣿⣿⣿⣷⣦⣤⡞⠋⣿⠆⠀⢠⡆⢠⣄⠀⠹⣿⣽⣿⢷⡄⢹⡇⠀⢸⢿⣧⣿⡿⠋⢀⠔⠋⠀⠀⢀⣠⠃⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣋⡉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣦⠀⠙⣮⠉⠉⣹⡿⠁⢀⡏⠀⠀⣿⢁⣾⣿⣧⠀⢻⣿⠏⠀⢧⢸⡇⢠⣼⠘⣦⠹⣴⠏⠁⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⠟⠛⠛⠓⠒⠶⣿⡻⢿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⣼⠀⠀⢀⣿⣸⣿⣿⣿⣇⣈⣿⣴⣤⣼⡀⣿⡄⣿⡄⣿⣸⠓⠦⣄⣠⡿⠋⠀⣀⣤⠄⠀⠀⠀ ⣿⣿⣿⣶⣾⠉⠀⠀⣀⣀⣠⣤⣀⣀⡙⠦⣄⠹⣿⣶⣿⠿⣿⣿⢋⣾⠋⣼⡇⠀⣿⠀⠀⣿⣿⣿⢏⡝⠁⠀⠈⠁⠀⠀⠘⣧⡙⢿⣿⡀⡈⣿⣀⡀⢸⣛⢉⣉⣩⠟⠁⠀⠀⠀⠀ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢀⣸⣷⣿⣿⠏⣴⣿⠁⣾⡇⡸⢻⡇⠀⢻⠀⢸⠿⢿⡏⣸⡅⠀⠀⠀⠀⠀⠀⢠⠿⠻⣦⣹⡇⢹⠈⣿⣿⠊⢿⡿⣟⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠇⣼⣿⡟⠀⣿⣠⣧⢸⣿⡄⠈⣧⠸⡋⠉⠛⢻⣟⢦⣄⠀⠀⠀⣴⣯⠤⠔⠚⣻⢀⣿⠀⣿⢸⡆⠈⠻⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠋⢠⡟⣿⣿⣿⣧⡴⣻⣿⢻⣸⠿⣿⣙⣧⢻⣿⣤⣀⠛⢿⠯⣤⣴⠾⠿⠿⣽⣦⡿⠓⠚⠛⠋⣿⣿⣻⠇⣼⣿⣎⡻⠄⢀⣌⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⡿⢁⣤⣼⣿⢭⣿⠟⣹⣏⣿⣿⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣳⡄⠀⠀⠀⠈⠁⠀⠀⠀⢀⡏⣠⡿⣿⣿⣿⠿⢿⣦⡀⢹⠷⣽⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣉⣙⣿⣿⣿⣿⣟⣉⣭⣴⣿⣡⣴⣿⣿⣿⠿⢺⣿⣿⣿⣿⡟⠛⠫⣟⢿⡛⠛⠛⠻⢷⣱⡀⡆⠀⠀⠀⢠⡀⢀⣾⣿⡿⣿⢹⡟⠙⣷⡄⠏⠹⢾⡇⠈⠻⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡟⠿⣿⣿⣿⠳⣶⣿⣿⣿⣿⣿⣷⡒⠒⠛⣳⣮⡓⠦⣄⡀⢹⡅⠙⣦⠀⡀⠘⢃⡾⣻⠏⢰⡏⢸⡆⠀⢻⡇⡇⠀⠘⠃⠀⠀⠀⣀⣀⡀ ⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡟⢸⣿⣿⣿⣿⣿⣿⣯⡿⣄⠁⠘⠧⢯⠟⠲⢬⣭⣽⣿⣟⣾⣥⣼⣏⣠⣴⠚⠋⠀⣼⠙⠀⢸⣿⠃⠀⢀⣴⠞⠛⠉⠁⠀⠀ ⠀⣀⣠⣶⢾⡿⣫⢟⡥⠞⣻⢿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠐⠛⠛⠒⠊⠁⠲⠶⠿⣿⡟⠛⠉⣿⠉⠉⣿⠟⠁⠀⠀⠀⣿⣀⣀⣘⣁⡤⠶⠿⢿⣿⣿⣿⣿⣿⣶ ⢞⣹⢿⣽⣿⣿⣿⣏⣠⣾⢣⣾⠟⣿⣿⡄⢿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⢹⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣶⣦⣄⡀⠈⠉⠙⠻⣷ ⣿⣣⣾⢟⣛⣩⣥⠞⢩⡇⣼⠏⢠⣿⣿⣿⣿⣿⣷⣄⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢰⣿⡆⠙⠮⣙⠛⠉⠉⠉⠛⠆⠀⠀⠀⠀ ⣿⣿⣿⢟⣼⡿⠁⣠⡟⢠⡏⠀⣿⠇⣿⣿⡿⣧⣉⡉⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡀⠀⢀⣿⣿⣿⣤⠘⠪⡓⢤⡀⠀⠀⠀⠲⣄⠀⠀ ⣿⣿⢣⣾⣿⣷⡿⠋⣀⡞⠀⣸⣿⠀⣿⣿⠃⢿⢻⣽⡶⣾⢻⣿⣿⣿⣿⣷⠀⠀⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠊⢉⣸⠇⠀⢸⣿⣿⣿⣿⣧⠀⠈⠺⣝⢦⣀⠀⠀⠈⠙⠦ ⣿⣿⣿⣿⣿⣯⣴⣾⣟⣡⣶⣿⣿⠀⣿⣿⠀⢸⡌⣿⣶⣿⣾⣿⣿⣿⣿⣿⡄⠀⠘⢾⢿⣗⠒⠒⠒⠶⠶⠶⣶⣶⣶⡾⠟⠃⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠑⣝⢦⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⢀⣾⣿⡿⢿⣿⣿⡛⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⠳⠖⠒⠚⠛⠋⠉⠁⠀⢀⡤⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⢷⡙⣦⠀⠀ ⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠋⠀⠘⣿⣿⣿⣮⡛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠰⣄⠀⢀⣤⣤⣤⣤⣾⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⡈⢇⠀ ⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣶⣍⡻⢿⣷⡀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠛⠛⠁⠀⢀⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣧⠸⡆ ⣿⣷⣄⠻⣿⣿⣿⠿⠟⠛⠛⠛⠉⠉⠉⠉⢿⣿⣄⠀⠀⠈⣿⣿⠀⢿⣿⣿⣿⣶⣝⡻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⠀⡇ ⣿⣿⠙⢦⡙⣯⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⣿⣿⣿⣷⣄⠀⣿⣿⣆⠈⢿⢿⣿⣿⣿⣿⣷⣽⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣜⢿⣿⣧⠙⢻⣿⣿⣿⠀⠀⠀⢸⠀⡇ ⣿⣿⣇⠀⠹⣌⠳⣄⠀⠀⠀⠀⣾⠇⠀⠘⣹⣿⣿⣿⣿⡟⣿⣿⣿⣄⢘⣧⠈⠻⢿⣿⣿⣿⣿⣿⣿⡶⠶⠶⢤⣴⣾⣿⡿⠋⠀⠀⠀⠈⢻⣧⢻⣟⠊⢸⣿⣿⡆⠀⠀⠀⡞⠀⣧ ⣿⣿⣿⡀⠀⠈⠳⣌⠳⣄⡀⢀⡷⣊⣴⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠉⠙⢧⡀⠀⠛⠛⠛⠉⠉⠀⠀⠀⢀⡾⣿⣿⠋⠀⠀⠀⠀⠀⢀⣾⣿⣷⢻⣶⣾⣿⣿⣧⠀⠀⢀⠃⠸⠣ ⣿⣿⣿⣿⡀⠀⠀⠈⠳⢬⡓⢾⣱⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⡇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢻⣿⠀⠀⠀⠀⠀⣠⠟⠉⠙⢿⣷⣻⣿⣿⣿⣿⡀⠀⡼⢀⠆⣾ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣧⠀⠀⠈⠳⡄⠀⠀⣿⣶⣶⣿⡏⢸⠀⠀⢿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡇⢀⠇⡎⢸⣿ ⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠙⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣄⠀⢿⣿⣿⣿⣇⠈⡀⢀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⣸⣿⣷⢹⣿⣿⣿⡇⣸⣰⠀⠀⢿ ⣿⣿⣿⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⢷⡈⠻⣿⣿⣿⣤⠶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣾⣿⣿⣿⠁⡏⡿⠀⠀⠈ ⣿⣿⣿⣿⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢳⡀⢻⣿⣿⣿⣿⣿⣯⡀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠛⢦⡀⠀⣿⡏⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⢰⢻⡇⠀⠀⠀ ⣿⣿⣿⣿⣷⡀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⢧⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣄⠀⠙⢿⣇⢠⣀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠲⠄⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⡄⠀⠀⠀ ⣿⣿⣿⡻⠿⣿⣿⣷⣄⠀⠙⠂⣿⣶⡀⠀⠀⢣⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠰⣄⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢿⣧⠀⠀⠀ ⣧⠈⠻⢿⡀⠀⠉⠙⠛⠓⠂⠀⠻⣿⣿⣄⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠳⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠸⣿⣦⡀⠀ ⣿⣧⠱⣤⡀⠀⠀⣿⣶⣦⣄⠀⠀⠙⣿⣿⡆⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢻⣿⣷⡄ ⣿⣿⣷⡙⣿⣦⡀⢹⣿⣿⣿⣷⣄⠀⠘⣿⣿⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠻⣿⣿
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