⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣟⣻⣿⣿⣿⣿⣭⣭⡩⣿⡿⠟⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡽⣯⠯⡝⠋⠋⠉⢻⠏⠁⠉⠉⣿⠁⠀⠈ ⣿⡟⣉⠭⠔⠒⠒⠠⠭⢼⣛⡿⢿⣿⣿⣿⣿⣿⠇⣾⣿⣿⠿⠟⠉⡿⡿⡯⠛⠁⠀⠀⠀⠈⢻⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⡶⡗⡀⣁⠀⣿⡇⠐⠀⠀⣿⠀⠀⠀ ⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠽⣿⣿⡟⠸⡿⣿⣯⣇⣶⣦⣯⣋⣀⣀⣀⣀⣀⡀⠀⠀⢷⠀⠀⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣟⣓⢴⡇⠀⣽⣗⠀⠀⠀⣿⠀⠀⠀ ⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡽⠿⠒⠛⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠙⠛⠙⠫⠶⠿⢲⣤⡄⣀⣸⣿⣿⣿⣺⣿⣿⣿⣦⣽⢳⠖⠀⢻⣷⠀⠀⠀⣿⠀⠀⠀ ⣿⣷⢇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣯⣻⠈⣺⣿⠀⠀⠀⣿⣀⡤⡴ ⣿⣿⣟⡆⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠽⣯⣟⠿⣿⣿⡠⠘⠀⢀⣠⢶⡫⠗⠉⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢷⣌⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣀⠀⠀⠀⠁⠫⢾⣝⠳⣥⡴⡫⠗⠉⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣤⠞⠉⠉⠻⢦⣀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢶⣤⣄⠀⠀⠙⠻⡣⣋⠒⠶⣀⣀⡤⠚⠉ ⡉⠉⠀⠀⡰⠃⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠉⠓⢦⣄⡈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣶⣦⣬⣻⢿⢦⡄⠀⠈⠻⢷⣦⠞⢁⡴⠊⠀ ⠍⠉⠉⡱⠁⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡶⠬⣝⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣷⣶⣙⣷⣄⠀⠀⠙⢷⣍⠀⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠈⠈⠉⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⢯⣷⣄⢰⣮⣿⢣⡀⠀ ⡀⠀⡎⠀⠀⠀⢸⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⣿⣣⠙⢿⣷⣿⣆ ⠀⠀⠇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡇⠀⠀⠀⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡉⠘⢷⣦⣑⡧ ⠃⠀⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡿⠥⠤⠴⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⢻⠛⠻⣦⣴⠊⠙⢦⣀⢀⡔⠁⢨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡆⠀⢻⣏⠉ ⠀⠀⢱⡀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣀⣀⣤⣤⣦⠶⡶⠶⠶⣶⡾⠛⡻⠛⠒⢺⠒⠒⠘⡿⣷⣄⠀⠹⠫⣂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠺⡄ ⣀⣀⣀⣿⣶⣯⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⣿⣿⣿⡍⠀⠀⠀⠀⠈⠒⠂⠤⠐⠊⠀⠀⢀⣿⡄⠀⠀⢻⠈⢻⠟⠀⠁⠊⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠁ ⣀⣀⣀⣀⣾⡏⠀⠀⠀⠀⠀⠀⢁⣼⠫⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⣹⠀⠀⠀⢸⡴⠁⠀⣴⣍⠢⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡀⠀⠰⡟⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⢀⡿⠃⠀⠹⣯⣉⣻⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣾⡟⣋⠿⠃⠀⠀⠀⢸⠙⠢⢞⣁⠙⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠘⢿⣦⡀⢡⠀⠀⠀⠀ ⠀⠀⠀⢨⣷⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢻⣏⠉⠛⠛⠛⠛⠛⣿⠋⠹⠏⠀⠈⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠉⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡌⢯⣷⣼⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡝⣎⣿⡳⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡟⠀⠀⢀⡀⠀⠀⠀⠀⣴⡏⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⢿⣷⠀⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠂⠀⢀⣼⡟⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⠃⠀⠀⠀ ⠉⠉⢹⣧⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠁⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀ ⣿⣷⣿⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⣿⣿⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡶⣤⣄⣀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀ ⣿⣿⣿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⡏⠙⠛⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢰⣿⡃⠀⠀⠀⠀⠀ ⣿⣿⡿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣾⣿⣇⠀⠀⠀⠀⠀ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⣿⡀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠙⡟⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣷⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢹⠈⠿⣄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀

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