⡯⠴⡇⠢⠍⢀⠰⠈⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢀⢦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⡆⣿⣿⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⢱⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣾⢞⣿⣾⡮⠃⠀⠀⠀⠀⠀⠀⠀⡠⠤⣶⣶⣂⣾⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠ ⢿⢿⡿⡉⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠪⠿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⡉⡈⣽⠁⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡀⠉⠻⠿⠿⡿⠿⠻⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⠀⠀⣹⡄⠀⠀⠀⠈⠀⠀⠉⠝⠙⠻⢷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀ ⠀⡀⡀⠔⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠊⢷⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠋⠀⠀ ⡀⠀⠼⣗⠒⠀⠀⠀⠀⠀⠘⠀⠀⢣⠈⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠯⡻⣿⣿⣿⡿⠿⠿⠏⠉⠙⠲⣆⡀⠀ ⠀⠀⠀⠹⠙⠒⠤⠀⠀⠀⠀⠠⠴⢶⣵⡄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠍⢁⣀⠀⠀⠀⠀⠀⠀⠘⢷⠀ ⠀⠀⠂⠀⠄⠀⠀⠀⠐⠂⡆⠀⠀⣈⣿⣿⣾⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⡇⢀⡴⢿⣛⢿⡿⣟⣿⣷⠔⠀⢤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠝⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢌⣼⢿⣷⣷⣿⢿⠋⠉⠀⠀⠈⣿⣿⠷⠂⠀⠀⠀⠀⣀⣴⡿⣿⣻⣷⣏⠉⡏⠉⠁⠀⠀⠀⠀⣽⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡞⣰⣿⡲⡟⢁⡽⠀⠀⠈⢲⣶⣯⣁⠀⠀⣼⣴⣶⣯⢯⠾⠹⢋⣈⣁⡀⠄⠃⠀⠀⠀⠀⢀⣴⡿⡩⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠇⢺⣳⣿⠀⢚⢏⠀⠤⣄⣘⡿⠋⠉⠁⠀⣘⣿⡿⡿⣿⣿⢿⣿⡿⠶⠦⣄⠀⠀⠀⠀⢠⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⠏⠀⠀⠁⣟⣿⠀⡸⠈⠀⠈⣿⣿⠷⠆⠀⠀⣰⠋⢽⣾⡐⢵⣹⣷⠦⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠀⣯⠇⠜⠀⠀⠀⠀⠉⠀⠀⢀⣔⠟⠋⢠⢿⢛⣿⡿⣿⠹⡆⠀⠀⠀⠀⢀⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣴⣿⣧⣺⡿⠀⡿⠐⠁⠀⠀⠀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢶⣯⡾⢋⠖⠋⢀⡴⠁⠀⠀⢀⡴⠚⡡⠱⢦⡄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠞⠀⠀⠀⠀⠀⠁⠀⠀⣰⡵⠋⠀⠀⠈⠀⠀⠈⠑⠡⣶⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢠⠂⠀⠀⠀⢀⠀⠑⠀⠀⠀⠑⠫⣢⠀⠀ ⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠐⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣃⠠⠐⠉⠀⠀⠀⠀⠀⠀⠁⠈⠂⠀⠀⠈⠢⡀⠀⠀ ⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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