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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠹⢶⣤⠴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣀⣶⣤⣄⣠⣶⣿⠏⢠⡄⣿⣾⣿⣿⣧⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡶⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⣿⣿⡀⠀⠠⢀⣀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣿⡏⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣹⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠁⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣧⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣿⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣻⣷⠈⢿⡄⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠉⠉⠀⠀⠀⠀⣠⣾⠿⠟⠛⠉⠉⠉⠉⠙⠷⠄⠀⠀⠀⠀⣾⣿⣿⡟⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢀⣿⠁⠙⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣴⡶⠶⣶⣤⣀⠀⣤⠏⠀⢠⣶⠟⢉⣀⣠⡇⠀ ⠀⠸⢿⣿⣿⣿⢏⣰⣶⣤⣙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢁⡠⢴⣿⡿⠿⡼⠋⠀⠀⢸⣣⡴⠛⢹⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⡘⠿⠁⠘⠻⢷⠻⣿⣿⣿⣿⡏⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣉⣴⣾⠟⠀⠀⠀⠀⠀⠳⣤⣑⣙⣿⡇⠀ ⠀⠀⠘⣿⣿⣿⣧⠀⠀⣴⣶⣿⣷⡿⠀⠹⣿⣷⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⢤⣉⣿⣿⡅⠀ ⠀⠀⠀⠈⢿⣿⣿⡄⠀⠘⡿⠋⣿⠀⠀⠀⣿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡈⠉⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠹⡄⠀⠀⣿⣧⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⡇⠀⢾⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣀⣀⣀⣀⡀⣸⠀⢸⡍⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢶⣤⣴⡇⠀⠙⠛⠛⠻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⢿⣿⣿⣛⣯⡍⠁⢀⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⣧⡀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⣀⡴⠂⣀⣠⣶⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡌⠙⢿⣿⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠈⠛⠻⢦⡿⢟⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⣀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡄⠀⣹⡟⢖⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢻⠰⠞⢃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡆⠸⢰⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣜⣛⣛⣣⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢐⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠒⠤⠤⡀⠀⠀⠀⠤⢀⠀⠀⠉⠀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠙⡄⠀⠀⠀⠀⠀⠀⠘⠾⠓⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣶⠾⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠢⠤⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠒⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣴⣿⡷⠶⠿⠿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⣉⠙⣿⣒⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣤⡾⢿⠛⠥⢥⣀⣠⡴⠚⢲⡎⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣿⣿⠛⠛⡿⠿⣶⣵⡢⠀⠀⠀⠀⠀ ⠀⠙⢻⠆⣈⡷⣶⡾⠥⡀⠐⠺⠭⠆⢠⡶⠏⢰⡿⠀⠈⠀⣀⠤⠖⢠⠿⣥⣌⣻⣿⣿⠓⠢⣍⣻⣷⣦⣄⡀⠀ ⠀⣰⣗⠋⣯⡴⠉⢔⠾⠋⠁⣀⠴⠚⠁⠀⠀⢸⡯⠄⠂⠄⠀⠀⢠⣟⡁⠨⠉⠉⠉⠓⢶⡄⠞⠋⢀⣹⣿⠧⠄ ⠘⣻⠟⠻⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠑⠖⢀⠉⠥⠄⠀⠀ ⠈⠁⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⣀⣀⣀⡈⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣿⡁⠀⢿⣿⣿⣿⣿⣿⣷⣦⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠉⠀⠀⠉⢉⢸⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⣠⣤⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠓⠒⢲⡒⢻⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢱⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠤⣀⡰⠭⡉⠉⠐⠂⠄⠂⠉⠀⠉⠁⠂⢄⠀⠀⠀ ⠀⢠⢞⣒⡀⠉⠀⠒⢅⢲⠬⠙⠒⠚⠛⠵⡢⢄⠀⠀⠈⣷⡀⠀ ⢠⠁⣿⣻⣿⠀⠀⠀⡔⣽⠿⣟⣦⠀⠀⠀⠈⠒⢠⠀⠀⢹⣷⠀ ⠀⢑⠌⣉⣁⣀⡠⠔⠳⡘⠷⠿⠋⠀⠀⠀⡠⣊⠁⠀⠀⠘⣿⡆ ⠀⢀⠭⠃⠀⠀⠉⠀⠀⠙⠥⠒⠒⠲⠬⠕⠊⠁⠀⠀⠀⠀⣿⡇ ⠀⢸⡊⠩⠭⢭⣉⣉⣁⡐⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠘⠘⡀⠀⢿⣿⣿⣿⣿⣷⣶⣤⡉⢲⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⡜⠀⠀⠀⠀⢀⣿⣿⠀ ⠀⠀⢀⢸⠀⠀⠀⠘⣿⣿⣿⣿⠟⢡⠊⠀⠀⠀⠀⢀⣼⣿⠃⠀ ⠀⠀⠘⡈⠒⠤⠄⠀⠸⠟⢋⡡⠒⠁⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀ ⠀⠀⠀⠘⠩⢀⣒⠒⠀⠉⠁⠀⠀⣀⣀⠤⠶⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠶⠖⠒⠒⠒⠒⠶⠶⠶⠶⢶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣿⣷⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⣀⣠⣴⣶⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠛⠿⣿⣿⢿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠁⣀⣴⣾⡿⠟⠋⢁⣀⣤⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⠿⣷⣮⣝⠻⠷⠀⠀⠀ ⠀⠀⠀⢠⣾⠏⢀⣴⣾⣿⡿⠋⢀⣴⡾⠟⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢠⣾⣿⣿⠻⣷⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠴⠛⠛⠛⠁⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⣿⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⢤⣶⣿⡇⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠙⣿⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⠐⠚⠋⢉⡟⢿⣦⡙⠛⠋⠁⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⠿⠛⠛⠛⠿⢷⣤⣿⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠛⠿⢶⣶⣦⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁⢀⣀⣀⣀⣀⠀⠉⠻⣧⡀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠶⠾⢿⣿⠋⠀⣴⣿⠋⠉⠉⠛⢷⡄⠀⠘⣿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣰⣿⠃⠀⣼⡿⢿⡿⢳⡶⣦⣼⣿⡀⠀⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢰⣿⣀⣼⣥⣼⣇⣼⣇⣽⡇⠀⣼⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⣿⠁ ⠀⣿⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⡏⠀ ⠀⢸⣧⠀⠸⣆⠀⢸⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡏⢠⣿⠁⠀ ⠀⠀⣿⡆⠀⠹⡄⠘⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⢸⣿⠀⠀ ⠀⠀⠸⣷⡀⠀⠹⡄⠹⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⠀⠀ ⠀⠀⠀⢻⣇⠀⠀⠹⡄⢳⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠎⢍⡲⣄⠀⠀⠀⠀⠀⣼⡏⢀⣿⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⢿⡆⠀ ⠀⠀⠀⠈⢿⡆⠀⠀⢱⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣉⠛⠷⣄⠀⠀⢰⡿⠀⢸⡿⠛⠛⠓⠶⣤⡀⠀⣿⡆⠀⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⢧⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠉⠳⣤⡀⠀⠀⣿⠇⠀⣸⡇⠀⠀⠀⠀⠈⠻⣆⢸⡷⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢧⠘⢆⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠛⠳⢦⣄⡈⠙⠦⢠⣿⠀⠀⣿⡷⠶⣶⠶⣶⢶⡶⠿⣿⡇⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠳⡌⠳⣄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⢸⣿⠀⠀⣿⣧⣠⣿⣄⣿⢈⣧⣠⣿⠁⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠈⠦⣀⠉⠓⢤⣀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠀⠀⠘⣿⣏⠀⠈⠉⠛⣿⣿⠃⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠑⠦⣤⣈⠓⠦⣀⡈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⠛⠿⠶⠶⠾⠟⠁⠀⢠⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠈⠑⠒⠠⢍⣑⡒⠒⠒⠶⠤⠄⠀⠈⣻⣧⣄⡀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠛⠒⠲⠄⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣤⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘ ⠁⣾⠿⣦⠀⢠⡞⢻⣆⠀⢠⡶⠲⠆⠀⣴⠖⠶⠀⢰⠶⠶⠀⣾⠛⣶⣴⠟⠷⢀ ⠀⣿⠀⣿⠁⣿⠀⠀⣿⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⣿⣦⡿⠹⣧⠀⢸ ⠀⣿⡴⠋⠀⣿⠀⠀⣿⠀⣿⠈⠛⣷⢼⡇⠙⢻⡆⢸⣷⠶⠀⣿⠿⣧⠀⠘⣷⢸ ⡇⣿⠁⠀⠀⢻⡄⢀⣿⠀⢻⡄⢠⡏⠸⣧⠀⣼⠃⢸⡇⠀⠀⣿⠀⣿⢀⡀⢹⢿ ⡇⠻⠀⠀⠀⠀⠛⠚⠃⠀⠈⠛⠛⠁⠀⠙⠛⠋⠀⠘⠳⠖⠀⠿⠀⠉⠘⠳⠋⢸ ⣧⣤⣤⣤⢤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣠⣤⡤⠤⢤⣤⠤⣤⣤⣤⣼ ⠀⠀⠀⠀⡼⢰⡞⠁⣈⠤⠭⢭⣉⣉⡡⠖⠚⠛⠓⢦⣘⡒⠒⢦⡉⢦⠀⠀⠀⠁ ⠀⠀⠀⠀⠃⢸⡴⠋⠤⠒⠂⠀⣙⡯⠠⠒⡯⠟⣋⣉⣀⠩⠷⡄⢳⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⣶⠟⣿⣶⣦⠈⢲⠊⢱⣿⣿⣿⣀⣸⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⢅⣈⣿⣿⡿⠗⠛⠒⠒⠛⢉⣩⠿⣷⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢰⡚⠉⣍⣙⣛⡒⣒⣒⣒⣒⣊⣩⡭⠴⣾⣿⠃⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣄⠉⠛⠒⠲⠮⠭⠭⠭⠽⠿⠿⠒⠒⣚⣟⠁⣠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡄⠈⢻⡟⠶⣤⣤⣀⣤⣤⣤⡤⣤⠴⠞⠋⠉⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⢀⣤⠔⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⡛ ⢀⣼⣿⣿⡶⠶⠶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠟⠀⠀⠀⠉⠛⢻⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⢤⡆⠀⠀⠀⠀⠀⠀⠙⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⣤⣴⣶⣾⣯⡷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⢀⣀⣠⣶⣞⣩⣽⣿⡿⠷⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⢰⣾⣀⡀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⢿⠟⠃⠀⠀⢀⣀⣠⣤⣤⣤⣦⣶⣤⡇ ⣠⣶⣿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡶⢴⢊⣿⣷⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠃⢀⣀⣴⣾⡿⠟⠛⠛⠛⢻⣿⣿⣿⡏⠀ ⠙⠿⠃⠀⠀⠀⠀⠛⠛⠛⠻⠾⠂⠀⠈⠻⠿⢿⢿⡟⠛⠿⠛⠃⠈⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣿⢿⢰⣾⣿⠋⣁⠀⠠⠀⠀⣰⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢠⣀⣀⠳⣄⡀⠀⣀⡀⠀⣀⣀⣀⣠⣤⣴⣴⣲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣦⣬⣉⣉⣉⣙⠒⠒⠒⠛⠿⠛⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠿⢿⡿⠿⠿⢿⣿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣏⠉⠙⢻⣿⣿⣷⣶⣦⣤⣤⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠤⠴⠤⠤⠤⠤⠖⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⢰⡎⠁⠉⠉⠟⢻⣿⡿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠐⠿⠶⠶⠶⠚⠊⠇⠓⠎⢻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠁⠐⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⡀⢀⣠⣴⣶⣶⣶⣤⣤⣤⣤⣶⡾⠿⠿⠿⠮⠽⢶⣶⡿⠟⠀⠀⠀⠀⠀⡸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣀⣀⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⡐⣦⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⢀⡀⣡⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠈⠉⠛⠿⠿⣿⣿⣄⠀⠀⠀⢀⣾⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣼⡟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣝⣙⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⠀⠀⠀⠀⣀⣤⡶⠢⠤⠴⠒⠄⠀⠀⠀⣀⣀⣠⣤⣴⣶⣷⣾⣿⣿⣭⣭⣽⣙⣿⠿⠿⣛⣛⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣤⠤⠶⠛⠋⠁⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡟⡛⢩⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣏⢉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⡀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠙⠆⠀⠀⠀⠈⠙⢿⣭⢉⣭⣿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣯⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢰⡄⠠⠀⠀⠀⠀⠀⠹⠛⠛⠉⠉⠀⠀⠀⠈⣿⠿⠿⠟⠛⢛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠁⠈⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⠀⣦⡀⡛⠛⠶⣤⣠⣤⣤⣤⣤⣴⢶⣟⡷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢤⢀⠠⡄⢀⠀⠀⠙⠛⡿⠿⢷⣶⠶⢶⠶⠶⢧⡾⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣶⠒⠒⠶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠶⣄⠀⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠈⢳⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⠒⠶⢤⣀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠈⠳⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢤⣻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣀⣠⣀⣀⠀⠀⠈⠙⠓⠒⠚⠁⣀⣴⣿⣿⣿⣿⡆⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣸⡏⠁⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⣿⠀⠀⣠⣿⣿⣿⡿⠟⠛⠛⠛⠋⠙⠻⢿⣿⠞⠋⠉⠀⠀⠀⠉⠙⠻⣇⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⡇⠀⠀⠀⠀⠈⡏⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡖⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⣻⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠚⠉⠑⣦⣀⠀⠸⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠃⠀⠀⠀⣀⣀⣀⣶⣿⣿⣀⡀⠀⠀⠀⠀⠀ ⢀⡞⣹⡷⠒⢶⠏⠁⠉⠁⠀⠻⣦⠀⠈⠳⣤⣀⣀⣀⣠⣤⣤⡤⠴⠚⠛⢳⢻⣽⣟⠿⠋⠉⠛⠘⠀⠉⠙⠲⣄⡀⠀⠀ ⣸⡇⠋⠀⠀⠈⠦⣤⡀⠀⠀⠀⠈⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠙⢦ ⣿⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⣀⣠⣦⣄⠀⢸ ⢸⣳⠀⠀⠀⢀⣻⣤⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡾ ⠀⠙⢧⡀⠀⠿⢄⡝⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠙⠒⠢⠀⢹⡶⠂⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⠖⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡛⠿⢿⡟⢋⣹⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⣤⣤⣀⣀⣀⠀⢀⣀⣀⣠⡤⢤⣀⣩⠷⠒⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠉⠀⠈⠉⠉⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠒⢦⡀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⣀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠑⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⣹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠑⠒⠤⣀⠀⠀⢀⠴⠋⣀⣀⣀⠈⢿⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⢠⠏⠀⠀⣀⣤⣤⣶⣤⣄⣀⠀⠉⠉⢁⣴⣾⣿⣿⣿⡇⢸⡄⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⢀⡟⠀⢠⣾⣿⣿⡿⠿⠿⠟⠿⣿⣿⡿⠛⠛⠛⠛⠻⢿⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠈⡇⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⣠⣽⡆⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⢀⣸⠦⣀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⢀⣹⡿⠁⠀⠀⠀⠀ ⠀⡔⣯⣤⣤⠞⠓⠀⠸⣆⠀⠳⣄⠀⠀⠀⢀⣀⣀⡤⠾⢤⣤⣤⡶⠖⠿⠹⠙⠲⢄⡀⠀⠀ ⢸⠙⠃⠀⠘⢤⡄⠀⠀⠈⣳⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⡠⠖⠋⠙⢦ ⢻⡆⠀⠀⠀⡎⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣤⣴⣶⣄⣸ ⠈⢷⡀⠀⣞⢻⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟ ⠀⠀⠉⠲⠄⠈⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⠿⡿⢛⣳⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣤⣀⣤⣤⣤⣤⠤⠜⠛⠉⠋⠁⠀⠀

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