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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡆⠀⣀⡤⠄⠒⠀⠒⠒⠂⠐⠒⠲⠤⣤⣀⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠋⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣷⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⣇⠀⠐⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠞⢻⠀⠀⢹⡄⠀⠈⣯⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠤⠤⠒⠚⢋⣴⠇⠀⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣷⣾⡄⠀⠀⢳⡀⡀⢸⣇⣠⠴⠾⠯⠬⠭⢽⣦⡴⠋⣁⣀⣀⣀⣤⡼⢁⣀⡔⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡿⢿⣿⣆⠄⠀⣿⠝⠛⠉⠀⣀⣀⣀⡀⣀⠀⢸⠷⣍⠉⠉⠛⠻⢿⣇⠀⠙⠁⠒⣼⣤⡝⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣆⠈⠴⣿⣿⠿⠿⠋⠁⣠⠴⠊⠉⠁⢀⡴⠋⠁⠀⡿⠀⠀⠉⠲⣄⠀⠀⠈⠙⠳⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⡿⣿⣿⠋⣧⣀⢀⠀⠀⠀⢐⠋⠀⠀⠀⠀⡴⢋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠙⢿⣿⡿⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⣿⠻⣿⣿⣿⠟⠁⠀⢀⡴⠃⠀⠀⠀⢀⡜⠀⡸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⠀⠀⠀⠻⣧⠤⠼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⢹⣿⣿⡟⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⡜⠀⢰⠇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢣⠀⠈⢣⡀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢃⠀⠀⣿⡟⠀⠀⢠⣶⠃⠀⠀⠀⠀⠀⣼⠁⠀⡏⠀⢸⠃⠀⠀⠀⠋⠂⠀⠀⠀⠀⠀⠈⣧⠀⠀⢣⡀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⡀⡴⡿⠤⠀⣠⢷⠃⠀⠀⠀⠀⠀⠼⠁⠀⡸⠁⣠⣿⡇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣎⠁⢰⠇⠀⢠⡏⠃⠀⠀⠀⠀⢀⠀⠀⢀⡼⠵⠚⢡⣿⠹⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣧⠏⠀⠀⡞⠀⠀⠀⠀⠀⣰⠋⣴⠃⠛⠀⠀⠀⡼⠘⡄⠳⡄⠀⠀⠘⣆⠀⠀⠀⡀⣸⠀⣿⡄⠀⠀⢤⠀⠀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⣠⡼⠃⠀⠀⣼⠁⠀⠀⠀⣠⡞⠁⡴⠃⠀⡀⠀⢀⡞⠁⣀⣱⡀⠙⣆⠀⠀⠸⣆⠀⢰⢣⣿⢠⠋⢧⠀⠀⠸⡆⠀⠀⠀⣆⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⠁⠀⠀⣤⠞⠋⢠⠞⠁⠀⠀⣇⡴⠛⠋⠉⠉⠉⠹⣄⠈⢢⡀⠀⢹⡒⢋⡿⣿⠞⠢⢼⡆⠀⠀⠘⡄⠀⠀⠸⡆⠈⠓⠀ ⠀⠀⠀⠀⣰⠋⠁⡴⠁⠠⠴⠋⠁⢀⡴⠋⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠱⣄⠀⢷⠋⠀⠃⠀⠀⠀⢻⡄⠀⠀⠹⡄⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⡼⠃⣀⣘⡀⠀⠤⠄⢺⡟⠋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠠⠤⢄⡀⠀⠀⠙⢦⡈⢳⣬⢧⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡿⢆⡀⢸⠀⠀⠀ ⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡴⣿⠁⠀⠀⠀⠀⠀⢠⠇⣠⡤⠶⠟⠛⠻⠿⢦⡀⠀⢠⡄⠙⢮⣧⣈⣻⡶⠶⣤⣄⠀⣾⡀⠀⠀⡿⠀⠙⢮⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⡄⠀⠀⠀⠀⠀⣾⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠞⠛⣿⡏⠀⠀⠀⠀⠈⢱⣿⣷⠀⠀⣧⠀⠀⠀⣹⡄⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡾⠀⠀⠀⣧⠀⠀⠀⠀⢠⠿⡀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠘⣷⡀⠀⠀⠀⢀⣼⣿⣿⡆⠀⢹⣄⠈⠁⠙⣿⠀ ⠀⠀⠀⠀⠀⠠⢗⠟⠀⠀⢠⡾⢹⣷⣰⡄⠀⢸⣄⣈⣲⠼⠿⣶⣤⣀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠘⢿⣦⣄⣀⣠⣾⡿⣾⠃⢀⠈⡏⢷⣄⠀⠀⠁ ⠀⠀⠀⠀⢀⡴⠋⠀⣀⡴⠋⠀⠀⢳⡹⡇⠀⢸⢿⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢩⠟⢀⡟⠀⣼⢀⣿⣀⣉⡛⠂⠀ ⠀⠀⠀⠀⠋⠀⠀⠚⠁⠀⠀⠀⠀⠀⠳⡽⡀⠘⣧⢿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⠞⠀⡰⢋⠜⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣏⠀⠈⢯⣧⣈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⡴⢋⣤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣄⠀⠙⢿⣷⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠱⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠳⣿⢶⣝⣷⣄⠀⠀⠀⠈⠉⣹⣶⣶⣿⣷⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠠⢼⣿⣄⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠛⢻⡆⠀⠀⠙⣿⡿⣷⡀⣼⣿⣿⠿⠻⣿⣟⣫⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠖⢶⣿⣿⣿⣿⣿⡿⠆⠀⠀⢰⡿⠲⣶⡾⠟⢻⡎⠋⣹⣽⣧⡀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠒⣶⣶⣻⣿⣿⠀⢸⠀⠹⣿⣿⣿⣿⣿⡿⠷⠟⠀⠀⢀⣀⢀⣰⡿⠀⠈⠉⠙⠻⡿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠸⣿⣿⠟⠛⠈⢸⠀⠀⠀⠫⠙⠻⣿⣷⣂⣄⣀⡀⢙⣿⣿⣿⣇⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⠟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣿⣿⠛⠙⠦⢀⠀⠀⢀⠝⣛⢿⡷⠿⠏⠀⠀⢹⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣄⠀⠋⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⣨⡿ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠈⠑ ⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⢣⠀⢣⠀⠀⢠⢀⢾⠈⠢⡠⡀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠊⣦⠀⠡⡠⠈⡀⡄⠀⠀⠈⠛⢦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢄⠈⠳⡂⠠⠤ ⠀⠀⡟⢷⣄⠘⠢⡟⠀⠀⠉⣉⣁⣀⠈⠁⠂⠤⣀⡀⠀⠀⠀⠀⠘⡑⢀⠈⠂⠀ ⠀⢀⣗⣼⡟⢿⣦⣌⢒⢄⠈⠐⠛⣿⠿⣿⢉⠋⠀⢀⠏⢲⢤⡀⠀⢇⠀⠀⣿⣷ ⠠⣼⣏⣿⣷⣶⠉⢿⣿⣾⡇⠀⠀⠈⠉⠉⡇⠀⡠⣊⠔⢁⡎⢹⡌⢸⠳⡄⠸⣿ ⠀⠀⠹⣄⠀⠀⣆⡼⠀⠀⠻⣄⠀⠀⠀⢠⡏⠉⠉⢀⠔⣿⡴⢿⢇⡎⠢⣈⠄⠀ ⠀⠀⠀⠈⠙⠒⠛⢅⠀⠀⠀⠈⠛⠒⠖⠋⠀⢀⠔⠁⢠⣿⣷⡞⢿⣧⣠⣼⣿⣾ ⠀⠀⠀⠀⠀⠐⠂⠤⠵⢠⡀⠀⠀⠀⢀⠄⠊⠀⣠⣾⣿⣿⣿⣿⣷⠙⣿⡿⠿⠿ ⠀⠀⠀⠀⠀⠄⠂⢰⢞⣉⠝⣦⢔⣚⣟⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣇⠀⠛ ⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠜⠁⠁⠀⠈⠱⠉⣿⣿⣿⣿⠿⠟⠛⢛⠶⣤⣼⡀⠀

⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡆⠀⠀⠉⠺⣟⢦⣀⣼⣾⣧ ⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣽⣷⣄⠀⠀⠀⠀⠐⣾⣿⣿⣿ ⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣅⠀⠀⠀⠁⠈⢯⣿⣿ ⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⣼⣿⡿ ⢠⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠿⣿⣁ ⠈⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠑⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀ ⣇⠈⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢷⡀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠀⠀ ⢹⠀⢹⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣆⠀⠀⢠⣿⡇⠀⠻⣄⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⣧⠀⢷⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⠀⢠⡟⢹⠇⠀⠀⠘⢦⡈⢷⡀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠸⣆⠘⣧⠀⠀⠀⠹⣦⠀⠀⠀⠀⢹⡆⠋⠀⣾⠀⠀⠀⠀⠀⠙⠷⣝⣦⡀⠀⠀⠀⠈⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢾⣷⡄⠀⠀⠘⢦⡀⣆⠀⠀⣇⠀⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠹⣯⠉⠓⠒⠲⠤⠤ ⠀⠀⠀⠀⣼⡿⡿⣄⠀⠀⠈⠳⣼⡆⠀⢿⢀⡏⠀⠀⠀⣠⡤⠤⣐⣶⠶⠒⠒⠚⠙⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠈⠳⣄⠀⠀⠁⠂ ⠀⠀⠀⠀⢸⣷⠹⣎⠳⣄⡀⠀⠻⡝⢦⣼⡿⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠙⣢⠀⠀⠀⠈⠃⢀⣀⠀ ⠀⠀⠀⠀⢸⡗⠀⠾⣿⣾⣿⣦⣄⡀⠀⠝⢧⡀⠀⠀⠀⠀⢀⡤⠖⠛⢛⣉⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⠽⠟⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠲⠤⠄⣀⣀⣀⡠ ⠀⠀⠀⠀⣼⣟⢗⣐⣻⣿⠿⣿⢿⣷⣤⡀⠉⠙⠲⣄⠀⠀⠀⠀⠘⡽⠟⠻⣯⣿⣿⣿⣿⣿⣏⠉⢙⡟⠁⠀⠀⠀⠀⣿⠈⠽⠳⢦⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢤⣾⣿⣷⣿ ⠀⠀⠀⢠⣿⣿⣾⣿⣿⡇⠀⠘⢎⢿⣿⣿⣶⣤⣄⣏⣳⣤⡀⠀⠀⠀⠀⡀⢻⣿⣏⣋⡉⢿⣿⣠⠞⠀⠀⠀⠀⠀⢰⠏⠀⠀⣴⡟⢈⣿⣄⠀⠀⡆⠀⣷⣄⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⢀⣤⢸⣿⡛⠛⣿⣉⣭⣴⣦⣦⠈⠛⢻⣿⢻⣿⣦⣌⣿⡏⠀⠀⠀⠀⠈⠀⠉⠛⠚⠛⠉⣿⣇⠀⠀⠀⠀⠀⣰⠏⠀⣠⡾⠋⢀⣾⠋⠙⣷⡀⠹⠀⣯⠹⣦⡀⠀⠀⠙⣿⣿⣿ ⠀⠘⠿⠿⣿⣿⡾⠿⠿⠾⠿⠿⢿⡀⠀⠈⣿⣿⠿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⡴⠞⣁⡤⠞⠁⠀⢠⣾⡿⠀⢀⣿⣧⠀⠀⣿⡇⠈⠻⣦⡀⠀⢹⢿⣿ ⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠰⡇⠀⠀⣿⡇⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠖⠿⠿⠚⠛⠁⠀⠀⢀⣴⣿⣏⣀⣠⣾⣿⣿⡀⢀⡟⢧⡄⠀⠈⢓⠠⠄⠂⠀ ⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⢹⠀⣼⡿⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⡰⠋⢸⣿⢛⡛⣻⠛⡟⢻⡇⣸⠇⠈⠻⢶⣤⡀⠣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢸⣿⣾⣯⡀⣀⣿⣾⣧⣿⠀⠀⠀⠀⠉⠟⣳⣶⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠋⠁⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣃⣲⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠦⠤⠤⠤⠬⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣦⡀⠀⠀⠀⠀⠀⢀⣤⣾⡁⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⡏⠋⠉⣉⣉⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠒⠒⣶⡟⠉⠉⢉⣡⡽⣶⣤⣤⣴⠾⠿⠻⡇⢿⡀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣷⠀⠀⢹⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⣠⣴⠶⠛⠁⣴⡿⠏⢀⡴⠶⠶⠶⣷⣞⣿⢟⣱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⢠⠿⠁⡰⠃⠀⠀⠀⠀⠀⠉⣰⠿⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣳⣦⣄⡀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣾⣿⡿⠜⠀⠀⠀⣰⠏⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠀⣴⠞⠛⠛⣻⣿⣓⣿⡄⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠠⡺⠑⢂⡠⠜⡫⢥⠠⠤⠤⢤⡚⢦⡊⠀⣀⠄⠋⠈⠛⣄⠀ ⠀⠀⠀⠰⢬⡴⠀⢔⠕⢡⠊⠰⠀⠈⡏⢩⠁⠂⠙⢄⢈⣻⣿⣿⣿⣿⣿⣷⣅ ⠀⠀⠀⣰⡵⢄⢦⠇⠀⡆⠀⠃⠀⠀⠃⠀⠇⠀⠀⠈⡄⠉⢻⣿⡻⡲⣿⣿⣯ ⠀⠀⢀⡿⡰⣣⢞⠀⠀⠁⢀⠀⠀⠀⡎⢸⢸⠀⠀⠀⢱⠀⠀⢻⣿⣿⣿⡿⡿ ⠀⠐⢹⠟⡾⠒⣿⡤⡀⠀⡸⠀⢀⣼⠙⠈⠈⣆⠀⠀⠘⣇⠀⠀⢿⡿⠋⠀⠀ ⢠⡔⠁⡜⠀⣜⣨⣧⠀⡷⢁⡴⡻⠺⡦⡇⠀⢹⢆⠀⠀⡟⢆⡀⠈⠹⠄⠀⠀ ⠀⠉⢻⢡⣾⢻⢫⣯⠷⡸⡕⠈⣀⣄⣙⢼⠀⠈⣎⠢⡀⠘⡄⠈⠱⣖⡚⠤⠒ ⠀⣠⠷⢻⡿⢸⠈⣶⣷⣭⠓⠊⢩⣼⣿⣿⡧⠄⢻⢞⡜⣖⡸⠦⡀⠻⡄⠀⠀ ⠀⠀⠀⠆⡹⣧⠼⠃⠀⢿⠀⠀⠈⠳⢶⠟⣹⠀⢸⢸⡺⣇⠙⢶⡉⠀⠱⡀⠀ ⠀⠀⠀⠘⣇⠈⡦⡀⠄⠈⠳⠤⠤⠴⠋⠊⢺⢠⣿⡞⣚⠓⡖⠓⢟⠛⠯⠷⠀ ⠀⠀⠀⠀⠈⠰⢓⣽⢄⡀⠀⣀⣀⢤⠔⠈⣼⠎⣿⡑⠿⠺⡉⢒⠬⠦⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣽⣏⢠⣿⣿⣿⣷⢊⣀⢈⣤⣾⡿⣷⣜⡆⠱⣄⠑⢄⡀⠀⠀ ⠀⠀⠀⠀⢠⣾⣟⡇⢸⣿⣽⣯⣿⣵⢶⣿⣿⣥⣾⣿⣿⣿⡀⠱⡑⢄⠈⠀⠀ ⠀⠀⠀⢀⢞⠽⠸⣅⢟⣹⣯⣠⣿⣷⣿⣿⢟⡿⠿⠏⠉⠹⡻⣄⠘⢄⡑⢄⠀ ⠀⠀⠀⡚⡋⣀⣼⡷⣿⣿⢟⣿⣼⠙⣿⠛⠁⠀⠀⣘⣼⣷⣵⡈⢦⠀⠃⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠉⠻⣿⠃⠀⠀⠀⠀⢄⠀⠀⠰⠞⠉⠙⠳⣾⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⡇⠀⠄⢿⡄⢀⣀⡠⠤⢄⠀⠀⢀⣀⡀⠤⣤⣿⣇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⠃⣸⣄⣤⣺⣿⣥⣴⣤⣄⡀⠙⡞⠁⠀⢀⣠⠿⢠⠃⢒⠷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣿⣿⣟⣾⠿⠛⠉⠁⢀⣉⣹⣟⣳⣧⣴⢊⣉⣉⠉⠛⠶⣿⣤⣯⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠤⠊⠁⠀⣠⡴⠋⢩⠋⠉⠷⣤⡉⠑⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣍⣁⠀⠀⠀⢀⠄⠀⠀⠀⡔⣱⠁⠀⢸⠀⠀⠀⠈⢳⠀⢀⠀⠈⢣⡹⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⢀⡴⠋⠀⠀⠀⡜⠀⡏⠀⠀⠘⠀⠀⠀⠀⠀⢣⠈⢃⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠂⠀⢠⡿⠁⠀⠀⠀⠜⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⡆⠈⠆⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣄⣿⠿⠟⠡⠃⠀⣠⡏⠀⠀⢀⡤⠀⠀⡠⠃⣠⠇⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⠤⠴⡟⠀⠀⢐⡿⢁⠶⠚⠑⢸⢿⡄⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⠋⠀⢀⡼⠀⣠⠴⠋⡰⠃⠀⠀⣰⣃⠼⣷⠂⠀⠸⡀⠀⠀⢠⡤⣼⡆⠀⢸⠀⠀⠈⣿⢦⣤⠤⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠇⠠⠴⠯⠤⠬⢥⣴⠞⠁⠀⢰⠞⠁⠀⣀⣹⣷⡀⠀⢧⠀⢠⣾⣷⠃⠹⡀⢸⠀⢠⡀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠾⠃⣀⠄⠀⢀⡴⠁⢸⠁⠀⠀⠀⣯⣴⣾⣿⣿⣯⡹⡟⢄⠘⣷⣾⢻⣿⣶⣦⣷⡈⣆⠀⢹⠒⢾⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠊⠁⠀⠀⠀⢀⣠⡼⠁⢀⣿⡄⠀⠀⢀⣿⣻⣿⠿⣿⠏⠁⠘⣦⡳⣼⣽⣿⣿⡿⢙⣿⣧⠈⢢⣼⡳⡄⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠒⠒⠒⠲⠿⣭⠝⢁⣴⠋⠘⣷⡀⠀⠸⣧⣿⠋⠀⠉⠀⠀⠀⣿⡿⢿⡏⠉⠘⠑⢺⣿⣿⣆⠀⠱⡿⡜⣦⣬⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⢉⡏⠀⠀⣹⣷⠀⢰⡟⠛⢯⣀⠀⠀⣠⡾⠋⠀⠀⠻⣄⡀⢀⣿⣿⡟⠘⣆⠀⣷⠘⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⣶⣿⣿⣿⠀⢸⣷⣄⠀⠉⠉⠉⠁⠀⢀⣀⠀⠀⠀⢉⣽⣿⡄⢡⣀⣿⡄⢻⠄⠨⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡆⢾⠘⣿⣗⠦⣄⡀⠀⠀⠉⠁⠀⣀⣴⣯⣰⠋⢱⠀⠙⠛⠀⡼⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣸⣦⡙⣿⣷⣤⣭⣵⣦⣤⣴⣿⣿⣏⡀⠙⠂⠀⢣⣀⠀⠀⡇⠀⠀⡇⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⢻⡽⠿⢶⡄⠙⠿⣷⣷⣤⣀⡇⠻⣧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣾⠀⢀⡈⠉⠻⣿⣿⣯⣽⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠿⡆⠁⠉⣙⣶⣿⡀⠀⢸⣿⣿⣿⣷⣄⡈⠙⢦⡀⠀ ⠀⠀⠀⠀⢸⣅⡸⢿⡟⠋⢸⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⡿⣧⣀⠀⢀⣼⣿⣿⣿⠀⠀⠀⡨⣏⠿⣧⣀⢸⣿⣼⡇⠹⣿⣿⣶⢤⣱⡄ ⠀⠀⢀⣤⣎⣼⣧⣸⣧⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡇⠉⠳⣼⠿⢿⡇⣇⣷⠀⠙⣎⢻⣄⠙⢿ ⠠⠐⠛⠁⣧⡟⠉⢻⣿⣾⠀⠈⠁⠒⠒⠂⢀⠜⠁⠀⣿⣿⣿⢿⣿⠀⣽⡍⠛⡛⠛⡟⠙⢆⢣⠀⠀⠀⠙⢿⣟⣻⣹⡄⠂⣸⣟⠿⣧⡀ ⠀⠀⠀⢰⣃⡠⠴⣾⣿⢟⡧⠀⠀⠀⣠⡶⠃⠀⣀⠀⠈⣧⡀⠀⠀⢠⠁⢿⣦⡠⣴⠧⠄⢈⣿⠉⠐⠀⠀⢻⣿⣿⡟⠿⠿⠷⠋⠀⢹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡾⢋⣡⠴⠒⢒⠀⠀⣙⣭⠿⠸⠟⡀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⣿⡀⣠⡶⠋⠁⠀⠀⠀⠀⢀⣴⠟⠉⠉⢲⣝⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣩⠗⠉⠉⢀⠐⢈⣴⠖⠋⠉⢉⡟⠓⠾⣍⠉⠛⠓⠶⠶⠶⠶⣾⣯⡉⠙⠻⣧⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠈⠉⡳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⢉⣠⠞⠁⠀⣠⠞⣡⠞⠉⡰⠋⠀⢰⠏⠀⠀⠀⢿⠜⠟⣿⠛⠶⣄⡀⠈⠛⢷⡄⠀⠈⠻⢶⣴⣾⣭⣴⣶⣶⣶⣶⣿⣿⣿⣿⣶⣍⡘⢦⠀ ⠀⠀⠀⠀⠀⠀⠪⢥⣤⣶⣺⡿⠁⠀⢠⠞⣡⠞⠁⠀⣴⠃⠀⢠⡟⠀⠀⠀⠀⠘⡆⠀⠘⣧⠀⠀⠙⠀⠀⠈⠻⡄⠀⢀⣀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠏⠀⠀⣀⡥⡾⠃⠀⠀⢰⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢻⡆⠀⠙⢿⣿⣾⣽⣿⣯⣝⠿⠿⠛⣛⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⣰⣏⡴⣧⣔⠒⢊⣥⣾⠁⠀⠀⠀⡾⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⠂⠀⢧⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⣿⣿⣿⡟⣳⡖⢿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⡟⣽⡗⠀⢈⡽⠉⣹⠃⠀⠀⠀⢠⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢻⣿⣿⣿⣭⣽⣦⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢀⣿⡛⢀⣴⠟⢀⣰⣿⠀⠀⠀⠀⢸⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⢀⠀⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡗ ⠀⠀⠀⠀⢀⣼⢟⣴⠟⣁⣴⠟⠉⣷⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣼⡟⡌⠀⢧⠀⢾⡀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢳⡽⣿⣿⣿⣿⣷⡷⠶⠈⠻⠃ ⠀⠀⠠⠞⢫⢶⣫⡵⣞⣯⣴⠶⢺⣿⡀⠀⠀⠀⢸⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⡿⠁⡇⠀⢸⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⢷⣿⣿⣿⠿⣿⠻⡄⠀⡀⠀ ⠀⠀⠀⠀⣰⡿⠋⣸⡟⠉⠀⢀⣿⢿⣟⠛⠦⡄⢸⠀⠀⣸⠃⠀⠀⠀⢠⣾⡟⣇⠀⢿⠀⠘⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠈⢿⣻⡟⠀⠁⠀⠀⠂⠀⠀ ⠀⠀⣠⠾⠋⠴⢠⡟⠀⠀⢀⣾⠏⠘⣾⣆⠀⠀⠘⡇⣰⠏⠀⠀⢀⣶⣿⣁⣀⣿⠀⠘⡆⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢸⡏⢿⡀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀ ⣴⣿⣇⠀⠀⢀⡾⠀⠀⢀⣾⣇⣰⣤⣿⣽⡄⠀⠀⢧⠏⠀⣠⡴⠟⣉⡿⠋⠉⢿⡟⠶⣷⠀⠀⠀⠀⢿⡛⣇⠀⠀⠀⠀⠀⣧⠈⠻⣦⡀⠀⠀⠀⠀⠘⠷⠄⠠⠄⠈⠀⠀ ⠀⠘⠻⢿⡓⢻⠇⢀⣄⣼⣿⣿⣿⠟⢿⡟⣿⣆⠀⢸⣦⠞⢋⣤⠞⠉⠀⠀⠀⠈⢿⡀⠸⡇⠀⠀⠀⢸⣧⢹⣷⡀⠀⠀⠀⠻⣆⠀⠀⠙⠳⠦⣤⣀⣠⣤⣴⣂⠤⠀⠀⣀ ⠀⠀⠀⠀⢉⡟⠀⣾⣟⣿⠎⣿⡛⣶⣾⣿⣸⡏⢷⡈⢷⡐⠋⠀⠀⠈⣉⣭⣶⣂⡈⢻⣄⣿⠀⠀⠀⠀⣿⣠⠈⠻⣦⡀⠀⠀⢹⣦⠀⠀⠀⠀⠚⢿⣩⠉⣉⣤⡤⠖⠋⠁ ⠀⠀⠀⢀⣼⢁⣾⣿⣿⣿⡇⣿⡇⢿⡉⣛⢻⣄⠀⣿⣌⣳⡀⠀⠰⣻⣯⠝⠻⣿⣿⣷⣿⢿⡆⠀⠀⠀⢹⣿⣇⢳⡈⠳⣦⡀⠀⠻⣧⡀⠀⠀⠘⣿⣿⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⢠⣞⡵⢾⠏⡿⡏⢿⠀⣿⠱⣄⢿⣿⣽⣏⠳⣼⣄⠙⢟⠳⠶⠁⢀⣶⣾⣿⣿⣿⣿⣿⡷⠤⣼⠀⠈⣿⣿⡌⢷⡈⢷⣍⠓⠶⠽⣷⣠⡀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠁⠀⢸⠀⢻⣷⣸⣷⡟⠀⢀⣾⡟⠛⠛⢿⣿⣿⠀⠀⠀⠀⠀⠸⣿⠙⠿⠟⢿⣿⣿⣿⣦⠈⡀⠀⣿⡇⢻⣆⢳⡄⡟⢿⣦⣄⠀⠈⢿⣦⡄⠈⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠙⣿⣿⣧⣤⣾⠟⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠻⢦⣤⣴⣾⣟⠋⠁⣿⠀⠇⠀⣿⠀⢿⣿⢷⡽⣿⠀⠛⢿⣟⡦⠌⠇⠀⠀⠈⠻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣳⡀⢰⣧⠟⢿⠉⠁⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⣴⣿⠀⠀⢀⣿⠀⣸⡿⠆⠙⠺⣧⣀⠀⠙⢻⣶⣄⡀⣀⡀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣿⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⠀⠀⠀⣠⣾⡟⠳⣾⣍⣰⣿⠄⡀⣾⣷⣴⡟⣿⠚⢿⡿⢦⣤⠶⠿⢦⣬⣝⣿⣮⣽⡙⠛⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⣿⡟⢦⡀⠈⠙⠒⠂⠀⠀⠉⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⢀⣸⣿⠀⣻⣿⣿⣿⡇⢹⡀⡾⠀⠀⣿⡄⠀⠀⠘⣦⡀⠀⠉⠉⠙⠳⠿⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⣟⡵⠏⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⢠⡿⣴⠟⢸⣿⡟⢷⣜⣿⣇⣤⡾⠋⠹⣦⣄⡀⠈⢳⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⣠⣾⡿⣿⠷⣄⡀⠀⠀⠀⣀⣀⣠⣤⣴⢞⣿⠏⠀⠀⢀⣼⡷⠋⠀⢸⣿⣷⠀⠈⣿⠋⠈⢳⡀⠀⠘⢯⠙⠓⠒⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⣟⣼⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⠀⣼⠃⠀⠀⠀⠛⠋⠀⢀⣴⣾⣿⣿⣦⡀⠸⣦⠀⠈⢷⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⡏⢻⣿⣿⡷⠁⠀⢀⣀⣀⣠⣤⣞⣿⣿⣿⣿⣿⣿⣿⣦⣹⣷⠀⠀⢿⡴⡀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⡏⠀⠀⣿⣿⡿⣿⣿⣇⠸⣿⣹⣧⠞⠋⣉⣠⣴⣿⣿⣿⡿⠋⡁⣰⣿⣿⠿⣿⣿⣿⣆⠀⠈⢷⡙⢦⡀⠀⠀⠙⠳⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡏⣿⠀⠀⢰⣿⣿⣣⣸⣿⣿⣠⣿⣿⢯⣴⣾⣿⡿⣿⣿⣿⣿⣶⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢷⡄⠻⣦⡀⠀⠀⠀⠉⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⡇⣧⣿⠀⠀⣼⣿⣿⣿⣿⣿⢿⡟⢿⢿⣿⠋⣡⢙⣯⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠻⣄⠈⠻⢦⡀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣹⣿⠁⢹⣯⠀⣸⡿⠁⢸⣿⣿⡃⠀⢰⣿⣾⣿⣶⣬⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠍⠀⠈⠉⠹⣿⠿⣿⣆⠀⠀⠙⢧⡀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⣡⣾⠏⡟⠀⠀⡟⣰⠟⢁⣴⣾⣫⣼⣷⣴⣾⢿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣴⠿⠓⠋⠉⠀⠀⢢⣄⣀⠀⠹⣆⠈⢿⣳⡀⠀⠈⠻⣔⠄⣀⠙⠦⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣿⠟⠁⢰⡇⠀⣼⣿⣧⣶⣿⣿⣿⣿⣏⣿⣿⣷⠈⣿⠛⠻⣿⣯⣵⡿⠟⠋⠀⠀⠀⠀⠀⠀⣰⢃⣼⣿⣷⣄⠹⣆⠀⠻⣿⡄⠀⠀⠹⣆⠀⠙⠲⢬⡀ ⠀⠀⠀⠀⠀⢀⣞⣁⡔⠀⢸⣦⣼⡿⣾⢛⡻⣿⣿⣿⡿⠇⣼⣿⣿⣿⣿⣧⠀⠙⡿⡄⠀⠀⠀⠀⢠⠀⠀⠀⢠⣟⣾⣿⣿⣿⣿⣷⣿⣦⠀⠘⣟⢆⠀⠀⠈⠀⠀⠀⠀⠀

⠃⢨⡿⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣸⠁ ⠘⡾⠁⠀⡀⠀⠂⢴⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀ ⠰⢁⠂⢀⠁⠀⢠⣿⠀⠀⢠⠀⠀⠀⠀⠀⡆⠀⢡⠀⠀⠀⣄⠀⠄⢣⠀ ⠀⠊⠀⡘⠀⡠⠻⠂⣆⠀⠀⢆⠀⠀⢀⢰⠑⡀⡀⠣⡀⠀⠸⡄⠈⠀⠁ ⠀⠀⡴⢁⣴⡗⠁⠠⠛⣦⠀⠈⢇⠀⠼⠂⠀⠐⢔⡀⠙⢆⠄⢫⠀⠀⠀ ⠀⢸⢗⡩⠊⢀⠔⠁⠀⡑⣕⢄⠈⢒⠁⢐⡊⣁⠀⡙⢄⠀⠑⢤⠁⠀⠀ ⠠⡎⡆⠀⣰⢭⡖⣟⣿⣿⠂⠑⢕⠢⡢⡠⣞⣿⣿⡗⣮⣦⠀⠀⡘⠢⠀ ⠀⡠⡇⢰⣸⠀⠡⠫⠀⠝⠀⣸⠴⠿⣿⠄⠩⠀⠘⠑⠁⣹⣧⠀⡇⠁⠀ ⠀⢀⢇⢿⠙⢷⡄⠀⠀⢀⣠⠏⠀⠀⠘⢧⡀⠀⠀⢀⣼⠏⣸⢰⠏⠀⠀ ⠀⠈⠜⡜⢇⠀⢫⡙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⡹⠁⢠⠊⡶⣌⠀⠀ ⠀⠀⠀⠰⡀⢣⢰⠚⢦⣄⡀⠀⠀⠀⠀⠀⣀⣴⠞⢃⢠⠁⡘⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠞⢁⣼⣿⣿⡄⠑⠀⠀⠂⠁⣿⣿⣷⣄⠛⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⡢⣄⢀⡴⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⠼⢿⣿⣿⣿⣿⣧⠼⠻⢼⣿⣿⣿⣿⣿⠿⢤⠄⡀⠀⠀⠀ ⡖⠚⣉⠴⠁⠑⢤⢙⠿⣿⠿⡇⠀⠀⠀⡿⢿⠿⣏⢥⠔⠁⠳⣍⠙⠲⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠿⠓⠦⢄⡀⠀⠀⠀⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠀⠀⢀⣤⠀⠀⠁⠀⣀⠀⠈⠳⢌⠛⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠁⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣭⣿⠿⠟⠛⠁⠀⡴⣢⢪⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⣳⣦⠀⠀⡴⣾⠟⠁⠀⠀⢠⠃⠀⢸⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⡀⣄⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢠⠊⣸⠃⠀⠀⠀⠀⡟⠀⠀⡇⡾⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⢳⡈⢧⡀⠈⢻⡷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢰⠃⣰⠃⠀⠀⠸⢠⣾⠁⠀⢠⢿⣣⠀⠀⠀⢸⢸⡇⠀⠀⠀⡆⠀⢧⠈⣿⡄⠀⢿⡻⢷⣦⢤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢏⡞⠀⡟⢰⠃⠀⠀⠀⡆⣘⡏⠀⠀⣼⣯⢻⡀⠀⠀⠀⣾⢇⠀⡄⠀⢸⠀⠈⣇⢸⡄⠀⠲⣤⠤⠼⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⢛⡵⠿⠁⠀⣷⣏⠀⠀⠀⠀⡇⣿⠃⠀⠀⢰⡏⢾⣇⠀⡆⠀⠹⣼⠀⢷⠀⣸⡄⠘⡇⢧⠇⠀⠀⠙⣗⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⠴⢶⡿⠛⠀⠀⢀⣠⠇⡟⠀⠀⡀⣾⣇⣴⢿⣗⠓⡄⠀⣟⣶⡇⠀⣿⡗⢶⢇⣸⡆⣆⡀⠀⠈⠳⣕⣄⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣰⡶⠞⠋⠀⠀⣀⣴⣿⡇⠀⡇⠀⡇⣷⣿⡏⢁⣀⣛⣶⣌⡦⢸⣿⣄⡼⢉⣰⣿⣾⣿⠟⣿⡷⣤⡤⠤⠶⠚⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⠟⠛⠒⠒⠚⠫⠿⣿⠏⢇⠀⡇⢸⣿⢹⣿⣿⠛⣋⣻⡛⠻⣟⡏⠙⣿⣟⣿⠋⣽⢸⣿⡇⢹⣷⠈⠙⠲⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠋⠉⠁⠀⠀⠀⠀⠀⢀⣼⡟⢀⣼⣧⡇⡎⢿⣄⣿⣿⣾⣿⣿⠃⠀⠙⣿⣠⣼⣿⣿⣾⡇⢸⣿⣷⡀⠻⣷⡢⠤⣤⣭⣷⠆ ⠀⠀⠀⠀⠀⠀⠀⠙⠧⠤⣤⣴⣦⣤⣤⣶⣤⣴⣾⣿⠟⣠⣿⠛⢿⡇⡇⠀⢻⣮⢯⠉⠛⠛⠀⢀⣴⠋⠉⠀⠈⢿⣍⣂⣼⣿⠛⠳⣦⣤⣝⣯⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢠⡿⠉⣉⠁⢷⠀⠘⣧⡇⠀⠸⡿⠿⣷⣶⠶⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⠀⠈⠻⡇⠉⠛⠷⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣋⡤⡾⠁⣠⡼⣿⣤⣿⣇⠀⡀⠹⣶⠴⠚⠉⠀⠀⠀⠀⣀⠤⠀⠀⢀⣴⠏⡼⠻⣄⣀⠀⣷⡆⠀⠀⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣿⣿⣿⣿⣿⡀⢸⣦⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⡏⠀⠀⠀⠀⣼⣿⣠⠎⠆⣸⠇ ⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣮⢿⣦⡙⢢⣤⣄⣀⣀⣠⣾⠙⠁⠘⠳⠦⠀⠀⠰⠛⠉⠀⢠⡾⠋⠀ ⠀⠀⠀⠈⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡑⢫⡻⠦⣽⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⡶⠏⠙⢒⣶⣶⣶⣶⡶⢶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠟⢁⣠⣴⠚⣋⣥⣤⣥⣖⣯⣾⣿⣿⣦⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣏⣠⣄⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⣁⣴⡿⠛⠛⠋⢁⡼⣿⣿⣹⣽⣼⠀⢹⡿⠀⠀⠀⠈⢿⣿⣻⣿⣿⣿⣿⣿⣿⡤⠀⠚⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣯⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣧⠟⡏⠀⠀⠀⠀⢺⡅⢹⣿⣿⣿⣿⠀⢸⠇⠀⠀⠀⠀⣸⢿⣿⣿⠉⣹⣿⣏⡹⣷⣦⣼⣿⣿⣿⣿⣯⡀⠀⠙⢿⣿⡝⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⠀⠀⠀⠀⠀⠀⣼⠛⣷⣿⣿⡏⠀⢀⡿⠀⠀⠀⠀⣴⣿⠋⠛⠁⢰⣿⣿⣿⣿⣿⠺⣽⣿⢿⡿⢿⣿⡝⣦⡀⠈⢻⣧⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀ ⠈⠸⣿⠀⠀⠀⠀⠀⠀⣿⡶⠋⠙⢿⡃⢀⣼⠃⠀⠸⡀⣼⡿⠁⠀⠀⠀⠛⠋⣿⣏⣁⠄⢀⡟⠛⣮⣷⡀⡽⠁⠘⣿⣶⣄⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠃⠀⠀⠀⠀⠀⠻⣇⠀⣄⠈⠻⣦⡘⢦⣀⠀⣿⡟⠁⢀⣀⣀⠀⠀⠀⠀⡛⣧⣀⣸⣧⡀⠈⣿⣿⣃⠤⢴⠞⡿⣿⣿⣧⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠼⣯⣭⡞⠛⢀⣼⠻⣭⣳⣶⡟⠋⠙⣷⣄⠀⠻⣭⣭⣍⡻⣦⣹⡿⣷⣯⣤⠶⢯⣴⣧⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠺⢧⣄⣠⣏⣿⠹⣦⠘⢮⣿⣶⣦⣴⠻⣬⣉⠛⠛⠳⡾⠛⠚⠀⢀⣿⡟⣱⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠾⠧⠄⠉⠻⢿⣿⡒⠀⠀⠀⢸⠀⠙⡄⠀⣰⡿⣻⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢷⣶⡦⣾⢤⣤⣶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠂⠈⡾⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣰⣿⡵⠀⠀⠀⢹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⢾⣿⣯⡁⠀⠀⢀⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⢠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣉⣻⣿⠀⣠⣨⣿⣿⠀⠀⠀ ⠀⠀⠀⢀⡀⢀⣀⣰⣦⣙⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⣿⣿⣾⣿⠟⢩⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⡿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⡿⣿⠁⢀⡿⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⢋⣠⢶⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠹⣻⣶⡟⠁⠀⠀⠀⠀ ⠿⠿⣦⣤⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢸⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢯⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢀⢼⡞⣆⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡰⠃⡴⠋⠀⢠⣿⣿⡇⠘⣆⠀⠀⠀⠰⠹⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣾⣟⣸⡀⠀⠹⣦⠀⠀⠀⠀⢻⡄⠀⠀⠀⡼⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⠀⠈⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢘⡿⠋⠉⢹⡏⠉⠋⠙⢷⡀⠀⠀⠀⠹⣄⢀⣴⣃⣻⣧⡀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⣤⡾⠋⠀⠀⠀⠈⢻⡀⠀⠀⠀⠙⢦⣄⡀⠀⠘⢿⡉⠉⠛⠻⣿⠶⢤⡀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠉⠲⢦⡀⠀⠀⠀⠀⣰⣶⣶⡾⢿⡟⠀⠀⠀⠀⠀⠀⠈⣧⡀⢀⠀⠀⠀⠹⣿⠲⣦⣬⣷⣤⡀⠀⠙⣇⠀⢷⣄⡴⠋⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠠⡀⠀⠀⠀⠀⠀⢰⡀⠀⠙⢦⡀⠀⠀⣽⣿⠋⢠⡿⠁⠀⣠⡤⠤⠤⢤⣄⡘⢷⣈⣷⣄⠀⠀⠙⢷⣇⠀⠀⢀⠀⠀⠀⠘⣧⠘⣯⠀⠀⠈⣿⣶⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠻⣆⢤⣾⣟⣦⣠⡿⠋⣠⣿⢧⣴⣶⠿⠿⠿⠿⢶⣤⡈⠀⢙⣷⡙⠷⣤⣀⣘⣟⢻⣿⣯⣽⣯⣽⣶⡈⢷⣜⡆⢃⠀⠘⣿⠈⢻⠛⠿⠈⠒⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠳⣄⣿⡯⠯⠾⣆⢹⣿⡄⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⣸⣿⣭⣷⣼⣿⡿⣌⠻⢿⣿⣿⡿⣿⠻⣿⣏⣻⣧⣸⠀⠀⡿⣧⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⢦⣄⢙⣾⣿⡿⢦⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⣿⡇⡝⠀⠀⠀⠉⠛⠛⠚⠁⢀⡿⣿⣿⠀⠀⣿⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⡎⢹⣿⣧⡉⠁⠀⠀⠀⠀⣠⣴⠿⠁⠀⠀⠀⠀⢸⣷⠁⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣿⣿⠀⠀⣿⣿⣦⡈⠻⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠈⢷⢷⠈⠹⣯⠙⠛⠶⠶⠿⠟⠋⠁⣤⡄⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠙⠋⢱⣶⣾⣿⣿⠀⣰⠿⣿⠻⣿⣷⡏⠙⠒⠦⠀⠀⠀⠀ ⠀⠀⠀⠉⠖⠒⠒⠒⠚⠳⠦⣄⡀⠀⠀⠀⠘⣾⣇⠀⢘⣧⡀⠀⠀⠀⠀⠀⠀⣧⠙⠓⠶⠶⣾⡿⠁⠈⠻⢶⣤⣤⣀⣤⣶⣿⣟⣩⣿⣿⣴⡟⠀⢹⣦⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⠀⠀⠀⠀⢀⡤⠖⠂⠀⠙⠗⢦⡀⢠⠟⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⠳⢄⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⣠⣾⠛⠉⠙⣿⣻⠟⠈⠻⠦⢬⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠟⢁⠀⠸⡛⣿⢻⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⡀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣖⠒⠉⢩⣙⠿⠿⢽⣿⣷⣯⣀⠙⢿⣿⣧⠙⠓⢦⣀⠀⠀⠀⠀⣀⣤⡴⣶⣿⣿⣿⣿⡛⢻⣿⣦⡺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣾⡯⣿⠟⣾⣿⣶⣶⣯⡳⠀⢻⣿⣷⣤⣀⡈⠉⠓⠊⠉⠉⢀⣴⣿⡛⠿⣿⣿⣿⣿⣿⣿⠙⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣴⡋⢰⠃⠛⣿⠷⠿⠻⣍⢻⣿⣿⣿⠈⠛⣦⣴⡆⣠⡶⠋⣿⣿⠇⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣿⣧⡟⠀⣰⠇⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⣸⣷⣿⡃⣠⣾⣿⣥⡄⠀⣴⣿⡖⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠑⠀⣠⣿⣿⠇⣼⣇⠀⠆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠟⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡏⠑⠲⢴⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠞⠉⠉⣿⣾⣽⣿⣿⠀⣠⠋⣿⣿⣿⣿⣿⡿⠃⠀⠐⠤⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⣧⠀⢻⡗⠦⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⣀⡴⠾⠋⠁⠀⠀⠀⠈⠉⠀⣫⣿⣿⣿⣶⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣮⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠘⢧⡀⠙⠓⠲⣄⡈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠟⠉⢸⣿⣿⣿⣿⣿⠿⣾⠀⠀⠀⠀⠀⠀⠀⣸⣷⠿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢸⡇⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠛⢛⣿⣿⣇⣲⠟⠳⠄⠀⠀⠀⠀⣘⡟⢛⣆⣠⣼⡻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠘⠁⠀⠏⡄⠀⠀⠀⠀

⣏⣽⣿⣿⡦⠊⡵⠉⡐⠁⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣏⡁⢀⠊⠀⢠⠁⡀⠀⠓⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠋⠀⠀⠀⢀⡢⠊⢨⢂⠀⢠⠀⠀⠀⠀⢘⣎⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠈⠀⠀⠄⠷⡕⠀⡑⠄⠀⠀⠈⠈⢣⠀⠀⠀⡀⠔⠁⠁⡀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⢘⠀⣀⣬⡦⣄⠀⠀⢠⣾⣾⣾⡂⢄⢟⠆⠀⢀⡄⠰⠀⠀ ⠁⠀⠀⢤⢶⠀⠀⠀⠀⣾⣿⣿⣿⠚⠢⣐⢞⢸⣿⣿⠃⠀⠎⠀⣴⠥⢀⡇⠀⠀ ⠀⠀⡠⠺⠀⢇⠀⠀⠀⠻⣄⠻⠻⠃⠀⠋⠖⠺⠍⠃⠘⠇⣤⡐⠑⢀⠁⠺⠀⠀ ⠀⠀⣠⠕⡙⡀⢢⡀⠀⠀⣜⢍⠁⠀⠀⠀⠀⠀⠑⣰⢄⢠⣇⢿⣭⡺⠂⠉⠐⠁ ⠀⠀⠁⠹⢄⠐⢊⣿⡄⠀⡐⡈⠀⠀⠀⠀⠀⠁⣰⢡⠹⠂⡿⢠⣾⣀⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣦⣌⡂⠠⠤⢀⣠⣼⣿⣎⠀⣸⠁⡜⠻⣿⢯⣘⠆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⢉⠁⠂⡀⠀⠃⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢶⣶⠚⢁⡤⠞⡁⢀⠀⠀⠀⠂⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠄⠍⢀⢠⠁⣤⠀⠀⡄⠀⠈⠔⡄⢳⣄⡀⠀ ⠀⠀⠀⠀⠀⣀⣠⠫⢁⡌⠀⢠⡇⠀⡟⡄⡀⢯⢀⢰⠘⠄⠀⢖⡋⠀ ⠀⠀⠀⠀⠀⢀⢉⣤⠜⢁⣠⡎⢃⣼⡗⣹⣕⣼⣇⢞⣽⡶⣦⣀⠸⠖ ⠀⠀⠀⢀⡠⠔⠊⠉⠉⣩⢏⣧⠘⣼⣯⣾⠊⢳⡹⣿⡆⣿⡘⢤⡕⠦ ⠀⠀⠀⠀⠈⠉⠛⠉⡹⡛⢩⡘⡆⠸⡳⣤⠖⠁⠀⠈⢈⢧⠈⢃⠓⢤ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⣿⣿⣷⢰⣵⡀⣀⠀⠁⡴⢿⡁⠉⠾⠐⡼ ⠀⠀⠳⣦⠄⣀⣀⣀⣤⣾⣿⣿⣿⣿⣯⣩⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⣐⣡⠶⠝⢶⣾⡟⢻⠋⠛⣿⣿⣿⣿⡅⢹⣿⣿⣶⣶⣦⡄⠀⠀⠀ ⢰⡏⠁⠀⢨⢺⣿⠋⡜⠀⢠⡞⠋⣾⣷⠿⣿⡿⢿⢄⠙⣿⡇⠀⠀⠀ ⠀⠙⠀⠀⠘⢅⣌⣮⠢⡰⣏⡠⣄⠀⡱⢥⡇⣹⠮⡬⣻⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠚⠤⠿⣲⡚⢶⣜⠫⢛⠻⠋⣸⣯⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠖⠚⠋⠁⠀⠀⠀⠀⠀

⢀⠊⠀⢀⡇⣸⠃⠀⡦⡈⠀⢀⡆⢠⣿⣿⣿⡄⠀⣿⢿⡉⠻⣷⢡⠀⠀⠁⠀⠀ ⠀⠄⠀⣼⠀⠏⠀⢰⠳⠁⠀⡼⠃⣺⣿⡟⠛⣧⠀⡏⠣⡑⡀⠡⣯⠱⡶⡄⢀⡀ ⠌⠀⣨⠞⠎⠀⠠⣣⡁⠀⡐⡼⢰⠇⣼⠁⣶⠙⢠⠀⠀⣸⢴⠠⡇⢱⣿⠃⠸⡉ ⠀⠈⠀⡀⠌⠃⣰⡟⡠⠊⠔⢸⣴⣸⠇⢠⣿⠇⣆⡤⠊⢠⣼⡄⠳⡀⢿⡄⠀⠡ ⣀⣈⣁⢠⣤⢞⢏⠔⠁⠈⣠⢾⣟⡜⢀⡞⡜⡘⢁⣦⣶⠛⣟⣧⣤⢕⢌⢛⠶⠖ ⡉⠓⠐⠚⠒⠋⠀⠀⡠⢞⣗⣽⡱⢁⠞⠰⡑⠹⠛⣾⡿⠄⠁⣿⡏⡄⣷⣄⡈⠐ ⠘⠓⡶⡒⣒⣶⣱⡜⢾⣿⣇⡩⢻⡊⣰⠏⠀⠀⠀⠀⠀⠀⠔⢹⠃⡡⣿⠯⠍⠀ ⡆⠰⠀⡙⣼⢊⠀⣁⢠⠀⣔⠕⢁⠜⠁⠀⠀⠀⠀⠀⠀⠢⠶⢵⣶⠛⣯⠙⢧⣊ ⣠⡇⠀⣟⣹⠁⢀⠤⠼⠚⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣎⢂⠘⣫⠲⠌ ⡸⡇⠀⠑⢽⠀⠈⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣄⠑⠁⢈⢷⡀ ⣴⡻⣦⡀⠀⠄⠀⠈⠐⠀⠠⢀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠈⢾⡷⡙⢧⠪⢢⡁⢪ ⢳⡇⣿⣿⢂⠈⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢀⡴⡇⠀⠸⠟⢖⡌⢷⣵⡙⡆ ⢸⡇⢿⡇⢂⠹⣦⣄⡀⠀⠀⠀⠀⠈⣷⣶⣤⡴⠟⢁⠇⠀⢸⠀⠀⢻⢸⠟⠳⡈ ⢸⠇⠈⣷⠀⠗⡾⠻⠉⠂⠀⠀⠀⠀⢄⠈⠁⠀⠀⠌⠀⠀⢸⠀⠀⣸⡌⠀⠀⠱ ⡆⣟⡀⢻⣻⠀⠈⢢⡁⠠⠀⠀⠀⡬⣀⠁⢒⣤⣸⣤⡀⠀⢸⠀⠈⢩⡗⠁⠂⠀

⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⠀⠀⠘⠻⠢⣤⣿⣧ ⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀⠀⠀⠈⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⣿⣿ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣇ ⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠘⡄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⡄⢱⡀⠀⠘⣆⠀⠀⠀⠀⡇⢀⠞⡹⠀⠀⠙⢄⡳⣄⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢄⣷⡀⠀⠈⢦⠀⠀⠀⢻⠀⢀⡇⠀⠀⠀⠀⠙⢮⣷⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠤⣀⣀⠀⠀ ⠀⠀⠀⣽⣿⣄⠀⠈⠳⣴⡀⢸⡆⡟⠀⠀⢀⣀⢀⣤⡤⠬⠿⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠈⠣⡀⠀⠉⠉ ⠀⠀⠀⢹⡏⢿⡳⣄⠀⠸⠷⢤⡿⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣂⠀⠀⠈⠂⠀⠀ ⠀⠀⠀⣸⣇⡘⣿⣿⣷⣶⡄⠈⠱⢤⡀⠀⠀⠀⠊⣩⣭⣽⣿⣶⣶⣶⡶⠶⣶⡶⠛⠉⠓⣶⢤⣄⡀⠀⠀⠀⠀⠸⡆⠀⠉⠒⠀⣤⣤⣄ ⠀⠀⠀⣿⣇⣶⣿⡏⠙⣿⣿⣷⣤⣀⣙⣦⣀⠀⠀⠉⠀⠹⣿⡿⠟⢿⣷⢠⠏⠀⠀⠀⢀⡿⠀⢉⡿⢳⣄⠀⢠⠀⣿⡀⠀⠀⠰⣿⣿⣿ ⠀⣀⣰⣿⡛⢻⣿⣷⣦⣤⠙⠛⣿⣿⣿⣍⣿⡇⠀⠀⠀⠁⠙⠛⠛⠚⢻⡇⠀⠀⠀⣠⠞⢀⡠⠟⢠⡾⠋⣷⡀⠃⢹⠻⣦⡀⠀⢹⣿⣿ ⠀⠙⠛⢿⣷⠛⠛⠛⠛⢛⡄⠀⢹⡿⠛⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⣞⡡⠔⠋⠀⣠⡿⠇⢀⣿⣇⠀⣸⡇⠈⠳⡄⠀⠛⠻ ⠀⠀⠀⠈⢻⣦⠀⠀⠀⠈⢃⢀⣿⠃⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠉⠀⠀⠀⢠⠞⣿⡷⠶⡾⣿⣿⠀⡟⠙⢦⣀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣼⣿⠋⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⣀⣠⣾⠟⠀⠀⠀⠀⣠⠔⠁⠀⣿⣿⣇⢁⣽⣾⣽⡃⠀⠀⠉⣛⣶⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢦⡀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⢀⡤⠚⠁⠀⢀⣴⣿⣿⣿⣿⡍⠹⢿⣿⣧⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣉⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣄⠀⠀⠀⠀⢀⣠⣖⠉⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣟⠉⠉⣉⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢐⣾⠋⠈⣡⠴⢻⣦⠴⠞⠛⢻⣟⡧⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⠀⠀⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⡞⠋⠁⢀⡿⢁⠔⠋⠉⠉⠻⠞⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠀⠀⢠⠏⠀⠂⠀⠀⠀⠀⠀⢸⠃⠀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢀⡴⠿⢿⣶⣶⣿⡀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⢲⠋⠁⠀⠘⡷⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡴⠒⠢⡄⠀⠀ ⠀⠀⠀⠀⣠⠋⠁⠀⠙⢾⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠱⡜⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠈⢣⠀⢀⠖⠉⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣄⠀⠀⠀⠀⠈⠳⢄⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⡀⣀⡔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠖⠒⢼⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡼⠀⠀⠀⠀⡾⠋⠉⠛⠳⣄⣴⠃⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢾⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠳⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣲⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣯⡿⣽⡷⣿⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣽⣷⡟⣯⣿⣽⣯⣿⣽⠂⠀⢠⣶⣿⡟⣦⠀⣶⣶⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⣻⠏⠀⠈⣿⣞⠟⢀⣴⣿⣻⢾⣽⣟⡿⣯⢿⣽⢯⣷⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⢀⠻⣾⡽⣷⠀⠀⠸⣻⠀⣸⣟⠾⣽⣯⠷⣻⣽⣟⡿⣾⣻⢧⠀⠀ ⠀⠀⠀⢠⣾⣇⣀⢧⣨⣇⣏⡙⠯⣧⡄⠀⣟⠀⡿⠀⠀⠈⠀⠀⢀⣿⢾⣻⡷⣟⣿⠃⠀ ⠀⠀⠀⠘⢷⡏⠐⠊⠰⠃⠈⠛⢷⡷⣄⡀⠀⠀⡅⠀⢀⣠⣶⡿⠻⠏⢛⡓⠛⠋⠁⠀⠀ ⠀⠀⢀⣤⣦⣴⡶⣶⢶⣴⣤⣀⠀⠙⢟⡿⣦⠀⠀⠀⠛⣉⣴⡴⣞⡿⣟⣿⣻⣗⣦⠀⠀ ⠀⢀⣾⡿⣽⣯⢷⠛⠈⠉⠛⠛⠂⠀⠘⢷⣻⠀⠀⠀⠒⠛⠉⠁⢻⡷⣟⣯⡿⣽⢿⡄⠀ ⣠⣿⢯⣟⣷⣻⢿⣤⣤⡤⠤⠶⣶⠆⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠙⢻⣽⣻⢯⣟⡿⡄ ⠙⠋⢿⣻⣞⣯⣿⣽⠚⢁⣤⡾⠁⠀⠀⠀⣾⠀⣿⣇⠀⠀⢰⣦⣀⣠⣼⢯⣟⡿⣽⣻⢿ ⠀⠀⠀⢿⣽⠳⠏⣠⡾⣟⣷⢿⣦⣤⠀⠀⢸⡄⢸⣯⢿⣶⣻⢾⣟⡿⣞⣿⣽⣻⢯⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣯⡷⣟⣧⣤⣿⣻⡀⠹⣟⣾⡽⣿⣞⡿⣯⠃⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠻⢿⣧⣟⡿⣿⣻⢧⣟⣧⡇⠀⠘⠟⣿⣧⢿⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣿⣳⣿⣻⣽⢯⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣽⡾⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣴⣶⣤⠤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠁⠉⠙⠙⠛⠽⠖⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⠀⢀⣐⣦⠀⠀ ⠀⠀⠀⠀⠀⢰⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣫⡫⠦⣏⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⢸⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⢠⣶⣊⣉⣳⣀⣈⠷⣇⠀⠀ ⠀⠀⠀⠀⠀⢸⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡇⣊⠪⠎⠷⠦ ⠀⠀⠀⠀⣔⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡋⠀⠀⠀⠀ ⠀⠀⠀⣸⡕⣯⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⣎⢭⢷⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡇⢻⡃⡇⠀⠀⠀⠀⠀⠀⠀⢸⢙⡟⡏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣯⡣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠞⠿⠝⠓⠋⠛⠙⠉⠉⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⡦⣀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠋⡦⡖⠉⢵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀ ⠀⢀⡠⡢⢛⠉⠈⠃⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠚⠯⠥⠤⠼⣂⡀⡬⠂⢓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⣀⡀⠀⠀⠀⠀⠀⠀⣇⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣉⣊⠏⠑⠒⠚⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣟⣝⢗⠀⠀⠀⠀⠀⢰⣗⣩⣭⡆⠀⠀ ⠀⠀⠀⠀⠀⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢗⢡⣿⠀⠀⠀⠀⠀⠈⡕⢯⣟⡟⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣙⣿⠀⠀⠀⠀⠀⠀⠙⠮⠾⠧⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⡞⠉⠉⢳⣤⠤⣤⠀⠀⠀ ⠀⠀⢰⡏⠈⠹⣷⡄⠀⡞⠁⠀⠘⡇⠀⠀ ⠀⠀⣘⣧⠀⠀⠘⢷⡀⠀⢀⣠⡾⢥⣄⠀ ⠀⢸⡏⠁⠀⠀⠀⣸⣿⡞⠋⠀⠁⠀⣬⠃ ⠀⠘⢿⣤⣶⡶⠛⠉⠘⣷⡀⠐⠁⣾⡅⠀ ⠀⠀⠀⢰⣿⠀⠀⣹⡄⣺⣿⣷⡔⣼⡇⠀ ⠀⢀⣠⡾⠛⠶⠾⠻⣿⣻⣿⠊⠉⠁⠀⠀ ⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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💚👓👂🧪

😳🧪🍃👓

🎋🍬🍰

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🦋🌀🍃

🍃💨

🕊️🍃🦋

क्यूब🫖

🍭🍬

🪑क्यूब

🍬🍭🍯

🍠🪣

🧂✨😋

🍃🌪️+🔥/💧/⚡️/❄️➡️✨📉

⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⣶⢻⣗⣻⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣦⡟⣷⢯⡷⠻⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢬⣿⣳⣿⠝⠉⠀⣠⣄⣤⣶⣤⣠⣄⡀⠀⠀⠀⠀ ⠀⢼⣿⣳⡯⠀⢀⣰⣿⣻⣽⣻⣞⣷⣻⡾⣽⢶⡄⠀⠀ ⢰⣿⣟⣿⠁⢀⣾⣿⣷⠟⠉⣠⣀⣀⠀⠙⢿⣟⣿⣖⠀ ⢸⣿⣿⡅⠀⣿⣿⣿⡖⣠⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⡇ ⢸⣿⣿⡧⠀⣿⣿⣿⢃⠉⠿⠿⠛⣿⣿⣿⡆⢘⣿⣿⣟ ⠘⣿⣿⣿⠄⠈⢿⣿⣿⣶⣤⣠⣴⣾⣿⡿⠃⢼⣿⣿⡏ ⠀⠨⣿⣿⣯⣂⠘⠻⢿⢿⣿⣿⣿⣟⠟⢃⣰⣿⣿⡿⠁ ⠀⠀⠈⢿⣿⣿⣾⣄⣠⢀⣀⣀⡀⣠⣴⣿⣿⡿⡟⠁⠀ ⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀ ⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀ ⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘ ⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣽⣾⡶⠤⢕⡄⠀⠀⠀ ⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⣄⣸⡦⠤⣿⣀⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⣿⠀⠀⣹⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠋⣸⠏⠉⣯⠈⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣯⠶⠶⣬⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢈⡃⢾⠀⠈⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡼⠁⠀⠀⠀⢸⢈⡁⢺⠀⠀⠀⠈⢳⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠖⠚⣉⡥⠶⠛⢻⡗⢦⣄⣀⠀⢸⣀⣅⣻⠀⣀⣀⣤⠾⡗⠒⠶⢬⣍⠑⠲⠦⣄⠀⠀ ⣾⠉⠀⠀⡞⠁⠀⠀⠀⢸⣧⡛⠀⣷⠉⣟⠁⠀⢹⠋⢽⠁⢛⣦⡇⠀⠀⠀⠀⢹⠀⠀⠀⢱⡄ ⠙⢦⣀⠀⠈⠲⠤⣄⣀⡀⢣⠈⠉⠒⠒⠾⠶⠶⠿⠒⠚⠋⠉⡸⢁⣀⣠⡤⠖⠋⠀⢀⡤⠞⠀ ⠀⠀⠈⠉⠑⠒⠴⠤⣬⣍⣉⣉⣓⣒⠒⠒⠒⠒⠒⠒⢒⣊⣉⣉⣉⣭⡤⠤⠖⠒⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠫⠯⢭⡭⠭⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤⠀ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⡼⢁⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⣴⠥⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢍⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⢂⣽⣿⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟ ⠀⠀⠀⠀⣀⣤⡶⢿⣋⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⢀⣠⣾⠿⠋⠀ ⠀⢀⣴⣿⠟⠉⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⡿⠛⠋⠉⣀⣤⠶⠟⠋⠁⠀⠀⠀ ⢰⣿⡟⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⣿⣿⣟⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣧⣀⡠⠤⢾⣿⣷⠤⠄⠀⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁ ⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀ ⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣰⡿⠛⠛⠿⢶⣦⣀⠀⢀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠹⣷⣄⣤⣶⡶⠿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⢹⡟⠁⠀⠀⣀⣀⠘⣿⠉⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⡋⣽⠿⠛⠿⢶⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢈⣻⡏⠀⠀⠀⠀⣿⣀⠀⠈⠙⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⢷⣄⣀⣀⣼⣏⣿⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡉⠉⠁⢀⣠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠾⠟⠋⢹⣷⠀⠀⠀⠀ ⢀⣤⣤⣤⣿⣤⣄⠀⠀⠀⠴⠚⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣈⣿⣀⣀⡀⠀ ⠀⠀⠀⠈⣿⣠⣾⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡤⠶⢦⡀⠀⠀⠀⠀⠹⠯⠃⠀⠀⠀⠈⠉⢩⡿⠉⠉⠉⠁ ⠀⠀⣤⡶⠿⣿⣇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣯⣀⣀⠀⠀ ⠀⢰⣯⠀⠀⠈⠻⠀⠀⠀⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠉⠉⠁⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠈⠙⣷⠀⠀⠀⣴⠟⠉⠉⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⠟⠉⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⠀⠀⠀⠙⢧⣤⡶⠟⢀⣿⠛⢟⡟⡯⠽⢶⡶⠾⢿⣻⣏⣹⡏⣁⡿⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⡌⠀⡂⠹⣷⣄⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠙⠛⠛⠋⠀⠀⢀⣽⠟⠛⠖⠛⠀⠀⡅⠀⠀⡌⡂⠀⠀⠀ ⠀⠀⡂⠀⠃⠀⠀⠙⠻⠷⠶⠿⠟⠋⠹⣷⣤⣀⡀⠄⣡⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⠆⠉⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣉⣻⣏⣉⣡⠞⠁⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠃⠀⢀⠒⠀ ⠀⠈⠂⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⣀⡠⠋⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡆⡸⠁⡠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⢧⣯⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⡨⣧⠀⠈⠉⠙⠃⠀⠀⠀⠀⡄⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠁⠀⠙⡆⠀⠀⠀⠀⠀⢦⠀⡇⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣉⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡟⡕⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⡠⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠊⠸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⡼⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠉⠉⠙⢤⠀⢀⠴⠒⠒⠒⠒⣄⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢳⡏⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠁⠀⠀⠀⡏⠉⠉⠉⠙⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⣉⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⣀⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢲⠀⣀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⢴⡟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⠎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠓⠦⢇⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⢀⣠⠞⠋⠉⠛⠻⠿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠙⢿⣦⣤⣤⣤⣴⡿⠋⠁⠀⠀⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⢩⠁⠀⠀⠀⠀⠀⠀⠻⠧⠀⣀⣀⣀ ⠀⠀⠀⠿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠛ ⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠛ ⠀⣀⣀⡉⠙⠃⠀⣤⣦⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⢰⣦⠀⠀⠀⡀⠀⠀⠀ ⣼⠟⠛⢿⣇⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢰⣿⠀⠀ ⣿⠀⠀⠘⠛⠛⠛⢷⣦⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠦⠤⠄⣿⡄⠀⠀⠀⢰⣿⠃⠻⠿⠻⢿⣧⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢀⣀⣸⣿⠀⠀⠀⠸⣿⣄⠀⢠⣾⠏⠀⠀⣤⣤⡾⠟⠀⠀⠀⠀⠀ ⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠿⣶⣾⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣿⣶⣶⣶⡿⠿⠛⣿⠀⠀⣤⣤⣤⣤⣶⣶⣾⠿⣷⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⠋⠁⠀⠀⠀⠀⠀⠻⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠟⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣷⣠⣿⣤⣤⣦⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣷⣄⠀⠀⠀ ⠀⢸⠟⢁⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡈⠙⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀ ⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢣ ⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿ ⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏ ⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃ ⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀ ⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⠀⣀⣴⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⠆⠠⣿⡿⣿⣿⣿⢿⣿⣦⣴⣿⡿⠿⢿⣿⣷⣄⠀⢾⣿⣿⣿⣿⡿⣿⠆⢸⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣠⣿⡿⠁⠀⣰⣿⡿⠁⠀⠀⠀⠈⠻⣿⣧⡀⠀⠘⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣧⡀⠀⢰⣿⡿⠁⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣷⣴⣿⡟⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⣧⠀⠀⠀⠂⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣿⣿⣇⣀⡀⠀⠀⠀⠘⢿⣿⣦⣀⠀⢀⣠⣾⣿⠏⠀⠀⠀⢿⣿⣦⡀⠀⠀⣀⣼⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀

⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣙⣏⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⡏⠉⠹⣿⣿⣿⣿ ⣿⣿⣿⠿⠿⢋⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠉⢛⢻ ⣿⣿⣇⢇⠐⢀⣠⣶⣶⣿⣿⠿⠿⠿⠷⠶⠶⠶⢦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣦⡤⠴⠶⠶⠶⠾⠿⠿⠿⣿⣿⣷⣶⣄⡀⢠⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠚⠛⠓⠛⠛⠚⠳⠷⡏⠙⣿⣿⣿⣿⣿⣿⣿⠋⣹⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣮⣼ ⢿⣿⣿⣿⣿⣿⣿⠋⠠⣞⣽⠀⠀⠀⠀⠀⣧⡀⠻⣿⢀⣿⣿⣿⣿⣿⣿⣿⡀⣿⠟⢁⣼⡄⠀⠀⠀⠀⠩⠳⠆⠙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⡥⣤⣠⣤⣤⣤⣤⣤⠤⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⢀⣠⣤⣤⣤⣤⣄⣤⣤⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿ ⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿ ⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣰⣿⣿⠏⢰⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⣁⣴⣾⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣁⣈⣁⣉⣈⣁⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢿⣿⣿⣿⣿⣿⣿ ⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

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⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣿⣿⡿⢋⠏⣿⡿⢻⣿⣿⣿⣷⡘⡅⠂⠄⡀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠳⡀⢸⣿⠋⢀⣬⢾⡿⠷⠄⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⡟⢰⠉⠓⠸⠁⡰⠛⠁⠘⢹⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⣀⣠⣤⣽⢿⣿⣿⢼⠀⠰⠀⠀⠶⠀⣀⡒⢼⠀⠘⣹⣿⢏⠅⢫⠙⠀⠀⠀ ⠀⠈⠉⠛⣿⠛⠈⠻⣿⢈⣦⠴⡀⠀⢒⣋⡝⢄⢄⠫⡲⠁⠀⣎⡀⢸⡀⠀⠀⠀ ⠀⠀⠀⢀⢹⠀⠀⠀⡿⡆⠀⠁⡅⢢⣥⣶⡌⢄⠠⡑⢌⢧⣠⠖⣡⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡄⣇⣠⠓⡀⠀⠑⣾⡟⠁⠀⠈⠄⠈⣄⢀⢱⠚⠛⠉⡇⠀⠀⠀ ⠀⠀⠀⢸⠠⠔⡩⠀⢸⠄⡄⠢⡀⠈⠤⠶⠃⠀⢸⠀⠉⠀⠀⢃⠰⡈⠁⠀⠀⠀ ⠀⠀⠀⠈⡀⠈⠐⠂⡹⠄⡿⡆⠇⠑⡦⠤⢤⠐⠚⠇⠀⠀⠀⠈⢤⣥⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠉⠒⠈⠀⣠⠃⠹⢰⠀⢱⠀⠤⠕⣄⠘⡄⠀⠀⠀⣼⣿⡇⠀⠀⠀ ⠀⠀⣰⣿⣿⣤⣠⣤⣾⢇⠀⠀⠀⢆⠀⠣⡀⠀⠀⠉⠉⠒⣤⣾⣿⣿⠇⠀⠀⠀ ⢀⠔⢻⣿⣿⣿⣿⣿⠏⢂⢆⠀⠀⠀⠑⢄⡈⠂⢄⠀⡄⠀⢀⠟⠿⣷⣆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠔⠒⢺⠻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⢀⣴⢳⣖⢁⡴⠂⢹⣉⣳⡀ ⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣁⣈⣯⣛⡦⡤⠠⠔⠋⣠⠊⡸⠋⡠⢾⣹⡀⠀⢵ ⠀⠀⠀⢸⡟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡴⠋⣀⣠⡷⠬⣉⡗⠒⢲⣾⣿⠔⢁⠜⢁⠜⠁⠀⠀⠀ ⠀⠀⠀⢸⠁⢀⣾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⢁⠎⡠⠊⢙⠿⠓⠒⠢⡯⣁⠒⠋⢁⡤⠋⡠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣦⣾⠏⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡎⡸⢰⢁⠔⢁⡤⠒⠉⠉⡗⠢⢍⣉⣁⡠⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠟⠒⠉⣉⣀⣈⣉⣹⣑⡗⠢⢤⣆⣀⠀⠀⠀⢸⡼⣹⠃⡇⡎⡠⠃⠀⠀⢾⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⠟⢹⡐⠊⢉⣀⠠⠤⠾⠿⠀⣉⣉⢺⠻⢷⢍⣹⣾⢟⡠⠊⣸⢰⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡿⠁⣠⣾⣿⣿⣧⡄⠤⠐⠒⠒⠒⠤⣤⣨⣍⣛⠒⠤⠄⢀⠠⠔⢹⣯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠰⡟⠉⢳⠊⢹⣷⠔⠒⠀⠉⠁⠐⠛⠛⠦⠬⣉⡑⠒⠠⠤⠔⢻⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡀⠳⢄⢸⡎⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢒⣶⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⠤⠴⣗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⡻⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⢀⡠⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣯⠄⠀⠈⠉⠉⠙⢖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⣀⠀ ⠘⣧⣄⠀⡀⠀⠀⠀⠀⠉⠪⠢⡀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⣟⢋⠀⠀⠀⠀⠀⠀⠠⠀⢄⡘⣴⠶⣶⣶⣶⡋⡁⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇ ⠀⣟⠂⠀⠀⠀⠀⠐⠓⠊⢁⢈⣹⡟⣺⣸⣷⠿⠖⠂⠀⠀⠁⠀⠀⠀⠀⢄⣾⠀ ⠀⡟⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡶⣶⣶⣄⡀⠀⠀⠀⠹⡏⠀ ⠀⣿⡂⢀⣴⣿⠟⠙⠉⢙⣿⣿⢫⠋⠀⠘⡿⡌⠻⢟⠙⠛⠿⢿⣿⣄⠀⢀⠇⠀ ⠀⠘⢵⣾⣛⣁⡴⠔⠚⣡⣿⡿⠏⠀⠀⠀⢰⡿⡄⠀⠈⠒⢤⣈⡽⢿⣷⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⢻⡽⠀⠀⠀⠀⢸⡞⠛⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠉⠜⢡⠁⠀⠀⠀⠀⠀⣇⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⡈⠄⡼⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⢀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢛⡿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⣼⡀⣴⢢⡖⠒⣦⢠⡶⠒⣦⠒⢲⡶⣴⠖⠲⣄⢰⠞⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⢿⠃⠸⣍⣉⡭⠸⣍⣉⣽⣴⣋⣠⢿⣍⣩⠍⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣄⡀⣀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⢷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⢉⣯⣍⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⠰⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⣼⢿⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠯⠭⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣛⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠺⠷⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣓⡧⢨⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠚⣹⣥⣴⣇⠉⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⣳⡄⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣏⠙⠊⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠚⢹⡀⠀⠀⠀⠀⠀ ⠀⠰⣫⠀⠇⢼⡆⡜⢀⣼⡷⣿⣟⡏⢳⠀⠀⠀⠀⠀⠀⣀⣼⠳⠥⠚⣇⠀⠀⠀⠀⠀⠀⡤⣾⣿⣿⣿⣿⡍⢩⣿⣿⣝⣶⣄⠀⠀⠀⠀⣀⠴⢺⡿⣦⠀⣠⣿⣶⠤⣀⠀⠀ ⢠⣧⡈⠐⠂⠀⠁⠃⠸⡟⠷⣼⢸⢇⠀⠇⠀⢀⣴⣾⣿⣿⣿⣷⣶⡶⠋⢹⣒⣤⡀⠀⢰⣽⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⢣⠀⠀⣞⡄⠀⠀⠀⠈⣷⡏⠀⠀⠀⠈⡇⠀ ⢸⣿⠅⡇⡄⠀⠀⠀⠈⠇⠀⠀⢐⠧⡠⢰⠀⣼⣿⣿⣿⣿⣿⣿⣯⣁⣏⣼⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢻⡇⠀⠀⠀⠀⣿⠁⢶⣤⣤⡐⣻⡀ ⠀⢏⠁⡁⠀⠀⠀⠀⠀⠐⠀⣠⡌⢓⠣⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣨⣿⣿⣿⠀⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⣼⢻⡇⠀⠀⠀⠀⡿⠃⢠⠀⠈⢸⣽⣧ ⡄⠿⢠⢇⠀⠀⠀⠀⠀⢰⠀⣿⣿⡞⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣽⣿⣿⠻⣽⢻⣿⣿⣿⣿⡇⠛⣬⡇⠀⠀⠀⠀⣿⠆⠈⠁⠀⢸⡟⠉ ⠁⠀⠸⣼⠀⡆⠀⠀⠀⠠⢰⡹⣸⠀⠀⢸⠀⢸⠉⣿⣿⣿⣿⡁⠾⢿⣿⣿⡟⢻⠋⠀⠹⣿⣿⣿⣿⣿⣟⣿⢔⣿⢸⣿⣿⣿⣿⡇⠀⡇⣇⠀⠀⠀⠀⢻⣄⠀⠀⢀⡠⠀⠀ ⠀⠀⣼⣼⠀⡄⠀⠀⠘⡶⠻⡿⣿⠀⠀⢸⠀⠘⡆⣿⣿⣿⣿⣿⣄⣸⣿⣿⣷⠋⠀⠀⠀⠻⣿⣿⣗⣿⣿⣿⣼⣿⣾⣿⣿⣿⡟⠀⠀⡇⢹⠀⠀⠀⢀⣾⠁⠀⠀⢨⡇⠸⠀ ⡀⠀⣷⢻⣼⡁⠹⠘⢠⢷⣣⢳⣿⠃⢀⡜⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣇⣾⠃⠀⢠⠏⢸⠀⠀⠀⠀⡇⡇⠀ ⡅⠀⣃⠘⠛⠃⢸⠀⠀⠀⣇⣿⣟⣀⢠⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣧⣿⣿⣿⣤⣽⢿⣟⣠⣾⣿⡏⠀⠀⠀⢹⣷⣤⣤⣥⣴⣼⣤⣶⣤⣀⣼⠁⠀ ⢸⣧⣿⣷⣦⣄⢸⠀⠀⢐⣹⣾⡧⣜⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠈⠻⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⡏⠉⠉⠉⡉⣿⠩⠍⠉⠉⡇⠀⠀⠀⠀⣿⣿⡯⢼⣿⣿⣿⣿⣧⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⠆⡀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠠⢞⣿⣡⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⡏⠘⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⡧⠀⠀⣼⢻⢸⠂⠀⠀⣿⠀⠀⠀⠀⠀⠈⡇⢀⣿⣿⠇⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢾⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⠃⠀⢠⠇⡈⢸⠣⠀⢄⡇⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠀⣽⣿⣏⢻⡄⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⡀⣤⠏⠀⡇⡌⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢿⣷⠀⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣼⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠞⠁⠐⢸⠁⡷⠿⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⣿⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠇⠀⠀⠀⢠⠷⠅⢀⣠⡎⢰⣷⣤⣷⢿⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠀⢹⡿⢸⢹⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⣿⣿⣿⡏⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡄⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⢀⣷⡀⠀⠀⠴⣶⣿⣶⠦ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⢻⠀⠀ ⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⡀⠀⠀⠀⢀⣤⣄⣀⣀⣀⠀⠀⠀ ⠀⢰⠋⠉⠓⠚⠛⣾⣿⣿⣯⣀⣼⡆⠀⠀ ⠀⢸⠆⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⡗⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢋⣧⣀⡀ ⠉⣯⡁⠀⠿⠀⢀⣀⠀⠀⠿⠀⠠⡾⠄⠀ ⠈⡨⠷⣆⡀⠀⠈⠉⠀⠀⠀⣀⡽⠳⠄⠀ ⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⡀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣯⣿⠿⠀⠀⠀⠀⠀⣾⢛⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⠇⠀⠀⠀⢀⣴⡶⠟⠛⠉⠉⠉⠉⠉⠉⠛⠳⠶⣦⣄⡀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣴⣿⡟⠉⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡀⢿⡇⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣦⣴⣿⡏⠀⠀⢀⣠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⢿⡿⠁⠀⣠⣿⠋⠁⠉⣹⣿⡆⠀⢀⣠⣤⣴⣶⣦⣽⣿⡃⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⡟⠘⠿⠿⠛⠁⠀⢀⣿⣿⣷⣿⣿⣿⣿⢧⣾⣿⡿⠛⠛⠉⠻⣿⣿⣷⡄⠀⣤⣾⣿⠀ ⠀⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⢏⣿⣿⠋⣼⣿⣿⣿⣦⡹⣿⣿⣿⠀⢹⣷⣿⡆ ⠀⠀⠀⠻⣷⡀⠙⠷⣤⡀⠀⠀⠙⠿⠿⠟⠁⢸⣿⡿⣌⢿⣿⣿⣿⣿⠇⣿⣿⡏⠀⠸⠟⠀⠀ ⠀⠀⠀⠀⠈⠻⣶⣄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣬⣭⣍⣥⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠟⠛⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⠋⠀⠀⠀⠀⠀⠀⠰⠶⠛⠋⠁⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣏⣀⣤⡿⠋⠙⠛⠛⢻⡇⠀⠀⠀⣴⣿⣏⠉⣉⣿⣧⡀⠀⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠘⣷⣤⣴⡾⠋⠈⠻⠿⠟⠁⠙⠻⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠑⢆⡀⠠⠌⠈⠁⠈⠈⠐⠀⠺⠄⣀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⣀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⡸⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠄⠀⠀⠀⠀⣀⡞⠁⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢀⠋⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠛⠉⠉⠈⢂⠀⠀⠀⠛⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⡎⠉⣀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠶⠶⠶⠶⠶⠶⢤⣀⠱⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠺⢦⣄⡠⠀⠉⠁⠀⠀⠸⠐⠋⠁⠀⢀⣀⣤⣽⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀⠀⠀⠁⠀⠱⡀⠀⠀⠐⠓⠚⠛⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠀⠀⠀⢀⠇⣠⠴⠶⠛⠉⣡⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠷⢦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⠤⠤⠼⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠶⠶⠿⢿⣷⠀⡐⠁⠀⠀⠀⠀⠀⠈⠒⠤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣴⠿⠩⠤⠄⣀⠀⠀⠀⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡸⠁⠀⠀⠀⠀⠀⠙⢄⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠢⠄⣀⠀⠀⠀⠀⠀⢀⡠⠜⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠆⠀⠀⠀⢀⠠⠄⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢇⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡠⠐⠁⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⠓⠂⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠊⠀⠀⠀⢀⠄⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⡠⠂⠁⠀⠀⠀ ⠴⠒⠒⠂⠤⠀⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠙⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡠⠔⠋⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠐⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠒⠂⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠢⠤⠤⠤⢄⣀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠓⠒⠤⣰⠋⠹⡄⠀⣠⠞⣿⠀⠀ ⠀⠀⠀⢀⠄⠂⠙⢦⡀⠐⠨⣆⠁⣷⣮⠖⠋⠉⠁⠀ ⠀⠀⡰⠁⠀⠮⠇⠀⣩⠶⠒⠾⣿⡯⡋⠩⡓⢦⣀⡀ ⠀⡰⢰⡹⠀⠀⠲⣾⣁⣀⣤⠞⢧⡈⢊⢲⠶⠶⠛⠁ ⢀⠃⠀⠀⠀⣌⡅⠀⢀⡀⠀⠀⣈⠻⠦⣤⣿⡀⠀⠀ ⠸⣎⠇⠀⠀⡠⡄⠀⠷⠎⠀⠐⡶⠁⠀⠀⣟⡇⠀⠀ ⡇⠀⡠⣄⠀⠷⠃⠀⠀⡤⠄⠀⠀⣔⡰⠀⢩⠇⠀⠀ ⡇⠀⠻⠋⠀⢀⠤⠀⠈⠛⠁⠀⢀⠉⠁⣠⠏⠀⠀⠀ ⣷⢰⢢⠀⠀⠘⠚⠀⢰⣂⠆⠰⢥⡡⠞⠁⠀⠀⠀⠀ ⠸⣎⠋⢠⢢⠀⢠⢀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⣬⣅⣀⣬⡷⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡇⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣭⣤⣦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣭⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⠿⠿⠻⠿⠿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢿⠿⢿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⢒⣰⣦⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣾⣿⣿⣿⣿⣷⣌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣦⡠⡀ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⣮⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣴⣾⣿⣿⣿⣿⣿⣷⡇ ⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠈⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣢⣤⡤⣤⣤⢤⡤⣤⣤⢤⣤⢤⡤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠚⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⢠⣤⣶⣾⣧⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠴⠶⠤⢤⡀⣧⣀⣀⠀ ⠻⠶⣾⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢹⣿⣭⣽⠇ ⠀⠀⠙⠤⠴⢤⡤⠤⠤⠋⠉⠉⠉⠉⠉⠉⠉⠳⠖⠦⠤⠶⠦⠞⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣘⣩⣅⣤⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⣻⣿⣿⢷⣾⣭⣯⣯⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠻⠿⡻⢿⠿⡾⣽⣿⣳⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡶⢈⠐⡀⠀⠀⠁⠀⠀⠀⠈⢿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢅⢠⣥⣐⡀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠡⠱⠒⠖⣙⠂⠈⠵⣖⡂⠄⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠰⡈⢆⣑⠂⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠱⡈⢆⠙⠉⠃⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡡⢘⠩⠯⠒⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢔⡢⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠸⡁⠋⠃⠁⠀⢀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡰⠌⣒⠡⠄⠀⢀⠔⠁⣸⣿⣷⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣐⣤⡄⠀⠀⠘⢚⣒⢂⠇⣜⠒⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣔⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢀⢠⣤⣶⣿⣿⣿⡆⠀⠀⠐⡂⠌⠐⠝⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⢐⡑⣊⠀⡴⢤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠷⡈⠀⠶⢶⣰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠑⠚⣙⡒⠒⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠀⠀⠤⣬⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⠀⢠⠲⠖⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣰⢘⣙⣛⣲⣿⣿⣿⣿⡿⡻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢾⡠⢤⣭⣽⣿⣿⣿⣿⡟⣱⠦⠄⠤⠐⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡕⠶⠶⣿⣿⣿⣿⣿⣿⣗⣎⠒⣀⠃⡐⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⣏⣛⣛⣿⣿⣿⣿⣿⣿⣿⣞⣍⣉⢉⠰⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢼⡧⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣣⣡⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅ ⡿⣷⣽⡿⠛⠋⠉⣉⡐⠶⣾⣾⣟⣻⡕⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗ ⢸⣿⣟⣥⡶⢘⡻⢶⡹⣛⣼⣿⣯⣽⢯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀ ⠘⢟⣾⣿⣿⣚⠷⣳⢳⣫⣽⣿⣛⣾⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢋⣿⣿⣯⣙⣯⣵⣿⣿⣯⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⡗⣮⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢤⣀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠉⠛⠲⢦⣤⣤⣤⠤⢴⡞⠁⠀⠀⠙⣿⠋⠁⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢺⢉⡷⠛⠳⢦⡤⠴⢼⡄⠀⠀⠀ ⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣈⣽⡀⠀⠀⣸⢧⡀⠀⢹⠀⠀⠀ ⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⠶⣶⠛⠚⠀⣠⡟⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠉⢻⡀⠀⠀ ⠀⠀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡷⠦⠤ ⠈⠉⠈⣿⠈⠀⠀⢀⡏⣭⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣼⣇⡀⠀ ⠀⠀⠐⠚⣿⠁⠀⠈⡇⠀⠀⠀⠀⠀⣯⣉⡷⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀ ⠀⠀⠀⣀⠼⠿⣏⣀⡇⠀⠀⠀⠀⠀⡇⠀⢀⣀⡀⠀⡀⠀⠀⢀⣼⠟⠙⠲⠄⠀ ⠀⠀⠈⠁⠀⠀⢨⠟⠉⢳⡄⠀⠀⠀⣇⣀⣼⠀⠹⠋⣹⡶⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠹⡆⠀⠀⣏⣸⡃⠈⡲⠀⢹⠉⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠾⠧⠤⠴⠃⠀⠓⢦⣤⣴⣋⣠⣞⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⡿⠋⣉⣩⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡳⠊⠁⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠉⠁⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣿⣄⡀⠀⠀⠀⠀⠀⣀⠀⣀⣈⣑⠒⠒⠒⠒⠢⢄⡀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀ ⣿⣿⣿⣱⢹⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢦⡄⠀⠀⢧⠀ ⠹⣿⣿⣿⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⢸⠀ ⠀⢹⡻⣿⣿⡻⣝⡞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀ ⠀⠈⠳⡘⢿⣿⣿⠇⡗⠢⢤⡀⠀⢀⠔⠒⠒⠒⠒⠒⠒⠒⠒⠉⠀⠀⠀ ⠀⠀⠀⠉⠓⠮⠭⠼⠁⠀⠀⢱⣀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠉⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡀⠀⠑⡄⠀⠀⢹⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠱⡄⠀⠈⠢⣄⣀⣃⣀⠑⠢⡤⠤⠤⢄⡀

⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⡿⠋⠉⠁⢠⣿⠏⢁⣿⣿⣿⠏⠉⢸⣿⡏⠉⢻⣿⣿⡇⠈⠙⢿⣿⣿⣿⣷⡆⠀⠀⢇⠢⣈⡒⡤ ⣿⣿⣿⣿⣿⣏⣴⡇⠀⠀⠀⢠⡿⠋⠀⠀⠀⣰⣿⠋⠀⣼⣿⣿⠏⠀⠀⡾⣿⠁⠀⠀⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣄⢀⣿⣷⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣿⠇⠀⢰⣿⣿⡷⠀⣀⣜⣁⣻⣀⣀⣀⣸⢻⣿⡇⠀⠀⠀⠘⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⣿⡿⠛⣩⣿⠿⠛⢻⡏⠉⠉⢹⠉⢿⣿⡀⠀⠀⠀⠹⣿⣿⡆⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⡟⠀⠀⠀⢀⣾⣿⠀⠀⣸⣿⡿⢥⣶⠝⠁⠀⠀⠀⡇⠀⠀⡜⠰⡀⢻⡇⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣿⡿ ⣿⣿⢿⣿⣿⡃⠀⣼⣿⣿⡇⣀⣀⣤⣾⣿⡇⠀⠰⣼⡟⣠⠎⠁⠀⢀⣠⠔⠁⢹⣀⣠⣧⣶⣦⣤⣷⣤⣤⣠⣤⠼⣿⣿⡆⠀⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣏⣁⣼⣿⣿⣿⠀⢠⣾⣟⡔⠁⠀⠀⠀⢸⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣇⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣟⣹⣿⣿⣿⡿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣾⢟⣻⡿⠛⢻⢋⣻⣏⣱⠞⠙⣄⡀⠀⣿⡽⣿⢀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡅⠚⠋⠉⠁⠀⠀⠀⠀⣔⣾⢏⢦⢄⣿⣧⣿⡦⠀⠈⣿⣿ ⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⢻⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⢂⢻⣿⣿⣿⡇⠢⠀⢽⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⣠⣾⣟⡖⢻⣿⣿⠃⠀⠀⣿⣿ ⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⠟⣻⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⠛⠉⠁⢰⢸⣿⡿⠈⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠰⢟⣿⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢂⢠⡇⣿ ⣿⣿⣿⣿⣿⣿⣏⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢾⣿⡟⠀⠀⠀⣼⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⠏⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣡⣴⣾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⠏⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠤⠚⠚⠉⠉⠉⠙⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⢽⣿⠿⠋⠉⠁⠀⢠⡆⢰⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⢠⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠇⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠈⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡗⠤⣀⠀⠀⠀⠀⠀⠑⢄⣀⡞⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠹⢇⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⣷⣦⣤⣀⡀⠀⠉⠀⠀⠀⣀⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠈⠳⣄⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠉⠐⢄⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠚⠉⠉⠛⠁⠀⠀⠐⠬⠀⠀⠀⢀⠁⠐⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢄⠬⣐⠠⡀⠀⠀ ⠀⣠⡞⠫⠀⠀⠀⠀⠀⠀⠀⠠⣈⠀⢈⠣⠀⠀⠁⠰⡈⠀⠈⢱⠀⠀ ⠀⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣷⣷⣾⣈⡐⠀⠀⠘⠀⠀⠀⢸⠀⠀ ⠀⣾⠀⠀⠀⠀⠠⢠⣶⣿⢿⠙⠋⡉⠹⠻⣿⣶⡈⠃⠀⠀⠀⠁⠑⡀ ⣰⠏⠀⠀⠀⠀⢰⣸⣿⠃⠩⣈⣬⣦⣔⠄⣐⣿⣷⠀⠄⠀⠡⠀⠀⡇ ⢿⡤⠀⠀⠀⠀⠀⣿⣗⠘⠀⠛⠋⡘⣿⣧⠀⣿⣿⠜⠀⠀⠀⡐⡞⠀ ⠀⢳⣖⠀⠀⠀⠀⠸⡿⣷⣄⣤⣠⣾⠏⠙⣾⣿⡋⠀⠀⠀⣀⠀⠃⠀ ⠀⠀⣿⡀⡀⠠⠀⠀⠀⢀⠋⠉⠃⠁⠪⢴⠿⠋⠄⠀⠀⠀⠉⣨⠃⠀ ⠀⠀⠹⢦⣢⣀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠋⠁⠀⠀ ⠀⠀⠀⠀⠁⠙⣬⡠⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠾⠷⠖⢶⣄⣀⣀⡰⠞⠃⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠉⠉⠓⠲⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣶⣤⣀⡀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠈⢹⣿⣿⣿⣿⠄⠀⢠⡿⠀⠀⠈⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣧⡀⣀⣴⣾⡿⢿⣿⣿⡇⠀⣸⣷⣦⣤⣾⡿⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣯⠀⣠⣿⣿⠓⠀⠹⢿⣿⣿⣿⣧⣤⣤⣿⣿⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠟⠈⠩⡭⠭⠍⠉⠉⠃⠁⠀⠀⠀⠀⠁⠘⠐⠑⣥⠈⠐⣠⢶⡭⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢷⡋⠭⠰⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⣿⠈⠉⠈⢩⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⢸⡈⢩⠙⠓⠒⢺⠒⠒⠒⣚⠋⢀⣴⢾⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣸⡿⢾⠷⠷⠶⣿⠶⠶⠶⣿⠾⠏⠁⡿⢀⣰⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⠙⠾⠦⣄⣀⣼⠀⠀⠀⡟⠀⣀⡾⠗⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠋⠀⠀⣀⣤⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀ ⣤⣸⡾⠞⠁⢀⡤⠖⠒⠉⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣤⡈⠻⣄⣠⡴⢒⣲⡀ ⣹⣇⡤⡄⢾⠉⠀⠀⠀⠀⠀⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠛⡆⠈⠉⠘⢻⠀⠀ ⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠀⠘⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠛⠋⢷⡏⠙⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⢀⣾⠋⠘⠳⣤⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣁⣠⠞⠁⠀⠀⠀⠈⢷⣄⡀⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠤⠤⠠⠤⠤⠠⠤⠤⢀⡀⠤⣀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⢋⢰⠀⢀⠀⠂⡄⢠⡀⡤⠀⢠⠀⡄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢀⠜⠀⡃⠇⠃⠀⠅⢠⠊⠁⠀⠁⢤⠊⠁⠈⠙⠄⠀⢨⠀⠀⠀⠀⠀⣠⡄ ⠈⢆⠀⠉⠀⢠⠀⠀⢇⠀⠀⢿⣿⢸⢸⣿⡇⠀⡸⠀⠸⠀⠀⠀⣀⡌⡌⠁ ⠀⠘⡄⢸⡅⠀⠀⠀⠪⢄⢁⠤⠔⠉⠦⠄⠐⢈⡩⠀⢠⠀⠀⠸⠰⠏⡼⠀ ⠀⠀⠘⠀⢸⢹⢂⠀⠀⢸⠒⠤⡤⢠⣤⠭⡟⠀⠀⠀⡇⠀⠀⢀⠳⠉⠀⠀ ⠀⠀⠀⢱⡀⢉⢐⠀⠀⢸⣤⣤⣓⣚⣿⠀⠁⠀⠤⠃⡇⢄⢀⢢⠃⠀⠀⠀ ⠀⠀⠀⢠⠉⡄⠀⡆⠀⠀⠑⠠⠥⠽⠃⠀⠀⠀⠗⢸⣀⡿⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠠⡤⡔⠒⠂⠁⠢⠄⡒⡢⣤⠤⣀⠤⠐⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡟⢻⡇⠲⠾⠟⠿⠿⣋⡿⠿⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⢹⢲⡷⠤⠤⡆⠀⠐⢾⣒⣒⡶⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠇⠁⢸⢙⠉⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢼⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣾⣤⣄⠀⠀⢸⣿⣷⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠛⠛⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠳⠝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡹⢳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠃⠀⠀⠀⠈⠙⠛⠓⠒⢦⡄⠀⠀⠀⠀⠀⢻⡜⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⡄⡀⠀⠀⠀⠀⢁⣠⣀⣦⠀⠀⠘⢧⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀ ⠀⠈⠻⠿⠷⠀⠀⠀⠀⠾⠿⠿⠛⠁⠀⠀⠀⠈⢧⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀ ⠀⢰⣆⠀⢠⡄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⢧⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠘⣿⡄⠈⢳⣟⣋⠀⠀⠀⠀⢰⡉⠉⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣷⣾⣿⣿⣤⣤⣐⣤⣾⡷⠖⠶⠂⠀⢀⡾⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⡟⠛⠂⣉⠙⠉⢙⣧⡤⠀⠀⠀⠐⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡛⠶⠤⢬⣤⣲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡄⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢿⡅⠀⠀⠰⠧⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢯⣉⣽⣷⣤⣀⠀⠀ ⠀⢀⣴⢻⣿⣿⡇⠰⣇⡀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢠⣾⠻⣯⢤⡈⠻⣷⡄ ⣀⣾⣿⣼⠋⣾⣧⢀⣿⣿⠀⠀⠀⢀⣴⠟⠋⠀⢀⣴⡿⣻⣾⠻⣦⣥⣾⣿⡇ ⠙⠏⠋⠀⠰⢿⣿⣿⣿⣿⣦⣤⡞⠋⠁⠀⢀⣴⢿⣿⣿⠟⠉⠀⠙⢿⡿⠿⠁ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠛⠉⠉⠉⣹⡿⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠻⣿⣿⡻⣿⣦⣀⣼⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡷⢀⡀⣿⣟⠛⠿⠿⢻⣇⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣏⢘⣛⣿⣿⠀⠀⠀⠀⣿⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠐⠛⠷⠤⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠐⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠦⠔⠢⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠰⠉⠷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠸⠈⠀⠀⠀⠀⠀⠀⡀⢹⡆⠀⠀ ⠀⠀⠀⠀⢀⣼⡷⣤⡠⠈⠀⠀⠀⠀⠄⣘⢳⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⢀⣦⣶⣮⣧⠀⠀ ⠀⠀⢀⡴⠊⠀⠁⠃⠙⠣⠄⠠⠀⠀⠠⠀⠈⠀⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠁⠀⠀⠀⠀⠀⡀⠀⠈⠋⠈⠙⣸⠫⣆⠀ ⠀⢰⣫⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢌⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⠤⠀⠀⠀⠀⠀⠀⠁⢈⠀⠀⠀⠐⠂⣉⣤⣹⠆ ⠀⣿⣿⣿⣶⣄⡀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⢀⣓⡙⢦⡀⠀⠀⠀⠀⢀⣜⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢠⣴⣿⢿⡿⣿⣿ ⠈⣿⣿⠩⣛⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠱⢾⣦⣳⡤⠐⠒⠀⢾⣟⣣⣬⢮⠤⣀⠀⠀⠀⡀⠀⢄⣰⣾⡿⢏⡜⣣⠟⣿⡟ ⠀⠹⣿⣄⠩⡛⠼⣹⢻⡿⣶⣤⣀⡀⠐⠂⠈⠁⠀⠒⠐⢤⣈⣽⡄⢐⡀⠀⣄⡿⠋⢃⢁⠒⣄⣀⣅⣦⣶⣿⣿⠿⣙⠞⡤⠝⢋⡼⡯⠁ ⠀⠀⠘⠫⣦⢁⠑⠀⠎⠘⡱⢎⠿⡹⣟⡿⣻⢶⡾⣻⢟⣿⣿⣿⡷⠈⠀⢾⣿⣿⣿⣿⡿⣿⢿⣻⢟⣻⠛⠗⠉⠃⠙⣁⡠⢴⠚⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠚⠰⠆⠀⠀⠈⠀⠑⠬⢖⣩⣾⣾⣿⡿⢟⣿⢿⠇⠀⠀⠈⢿⡝⢻⡿⣿⣛⠿⢿⣿⣶⢯⣷⣭⣷⡋⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢤⢒⠞⠉⣙⠜⠃⠁⢤⠿⡉⡎⠀⠀⠀⠀⠀⠹⣦⡈⠓⢯⡚⠄⠨⠈⠛⠮⡓⠧⣍⡓⠤⡀⠀⠀⠀⠀ ⠀⠀⠀⣀⡄⡴⠲⠊⠉⠁⡀⠠⠀⠀⠀⠀⠀⠀⠀⡼⣉⠞⡜⠀⠀⠀⠀⠀⠀⠀⠈⠚⡆⡀⠁⠈⠀⠀⠀⠀⠡⠂⠀⠘⠢⠑⡄⠀⠀⠀ ⢴⡿⡙⠃⠉⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣄⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠘⢆⠀⠀ ⠀⠁⢣⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢓⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀ ⠀⠀⠀⠐⠭⡠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀ ⠀⠀⠀⠀⠈⢅⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠈⢣⡈⠄⠁⠀⡀⠄⣀⢰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣂⠁⠀⢀⠴⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀ ⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀ ⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀ ⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉ ⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⡀ ⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀ ⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⠀ ⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢠⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠀⠀ ⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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