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