Sex Time Wanna F U C K ???? Emojis & Text

Copy & Paste Sex Time Wanna F U C K ???? Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠓⠘⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠓⠘⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠠⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠠⠈⠀⠀⠂⠀⠀⠀⠀⠀⠁⡂ ⠀⠀⠀⠀⠀⠀⠀⢀⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂ ⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠀⠀⡁⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⡰⠈⠀⠀⠀⠀⠂⢀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⡀⡀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⡺⠀⢀⡌⡆⠠⠄⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠐⠈⠀⠁⠁⢱⠀⠑⠠⢀⢄⠀⡀⠁⠸⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀ ⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⣃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀ ⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀ ⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀

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