Shrugging Emojis & Text

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