Studio Ghibli Dot Art

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