Coquette Bow That I Drew Emojis & Text

Copy & Paste Coquette Bow That I Drew Emojis & Symbols ⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠋⠉⠉⠉⠙⢷⣠⣔⡶⣶⣄⠀⠀⢸⡀⠀⠀⢀⣶⡶⣿⣿⠀⠀⠀⠀⢻⣷⠀⠙⠒⠚⠉

⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⠾⠋⠉⠉⠉⠙⢷⣠⣔⡶⣶⣄⠀⠀ ⢸⡀⠀⠀⢀⣶⡶⣿⣿⠀⠀⠀⠀⢻⣷ ⠀⠙⠒⠚⠉⣾⠁⠀⡟⣇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⠓⠷⢶⠤⠋ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢃⠀⠀⠀⠀⡇⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⣿⡀⠸⠁⣇ ⡰⢳⠀⠀⠀⡗⠀⠀⠀⠀⠑⢷⣶⡯⠃ ⣧⡈⠁⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⣤⣿⡟⠿⠻⠿⡿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣻⠿⡿⠿⠛⢟⡻⡗⣴ ⣿⣿⠇⡀⠄⠀⠀⢀⠀⠙⠻⣿⣦⡀⠀⠀⢀⣰⣾⠟⠋⠁⡀⠀⠀⢈⠢⣹⡅⣿ ⣿⣿⢀⠃⠄⠀⠠⠀⠘⡀⢄⠛⣿⣿⢿⣿⣿⣿⠛⡄⠀⠃⠀⠀⠠⠀⠣⢄⣿⣻ ⣿⣗⠊⡔⠀⠀⠠⠁⠂⢀⠺⣮⣜⣯⠙⡉⢻⣦⡷⡖⠠⠁⠈⠀⠀⠄⠑⡌⣶⣻ ⣿⣯⠑⡰⠀⠀⠄⠠⠁⢠⣿⣴⠿⣿⠀⡂⢿⠿⣶⣭⠆⠈⢀⠁⠀⠌⠐⡌⣷⣻ ⣿⣯⢒⠡⠀⠁⢈⠠⠐⢀⠠⣰⣾⣿⣿⣿⣿⣷⣤⢠⠀⠌⢀⠀⠈⢄⢊⡴⣻⢼ ⡿⣿⣏⠦⡁⢌⡀⢆⣱⣮⡿⣏⣷⣿⡏⢻⣯⣗⡻⢯⣿⣸⣄⢊⡜⡰⡌⣾⣥⣿ ⠃⣿⣿⣦⣱⣬⣵⡾⡟⢯⠳⡹⣿⣿⠃⠸⣿⣿⠃⢮⡙⢟⠿⣾⣵⣣⣳⣽⣿⣿ ⡆⠈⢹⣿⣿⡋⠴⠐⠌⠢⠁⣻⣿⡏⠀⠀⢺⣿⡟⠠⠜⡠⣉⠆⣙⣿⣿⣿⣋⢿ ⡇⢠⣿⣿⠇⠐⠠⠐⠠⠀⢁⣾⣿⠃⠀⠀⠸⣟⣯⡀⠐⠀⡀⠄⡀⠺⣿⣿⠀⠈ ⡇⣼⣿⡟⠀⡈⢀⠀⠁⠈⠰⣿⡯⠀⠀⠀⠀⢹⣿⠅⠀⠁⠀⡀⠠⠀⢿⣿⡆⢠ ⡇⣿⣿⠃⠀⠐⢠⠈⠐⢠⠘⣯⡗⠀⠀⠀⠀⢨⣿⡆⠈⠀⠁⠀⠂⠁⢸⣿⣧⢸ ⡁⡿⣿⢀⠣⡐⢄⠂⡄⢠⠐⣯⡇⠀⠀⠀⠀⢘⣿⠆⣀⠡⢌⠰⢌⢢⡁⣿⣿⣼ ⠀⢿⣿⣷⢶⣷⡾⣦⣼⣤⣭⣷⡇⠀⠀⠀⠀⢨⣿⢧⣤⣧⣼⢶⡾⣶⢾⣿⢿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢠⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢀⡀ ⢹⢸⡇⣭⣭⢹⣦⣴⢢⣴⣤⣶⣭⣥⡖⣼⢡⠃ ⢈⡯⣷⢝⡛⠛⣿⣿⣖⣽⣿⡟⠛⢛⣧⢿⢿⠀ ⢸⡾⢧⣤⣄⣾⣿⢿⠋⢹⣿⣯⣥⣤⣤⡾⣽⡆ ⠀⠉⠉⠉⡰⣟⣟⡞⠀⠀⢫⣿⣟⡄⠉⠉⠁⠀ ⠀⠀⠀⣰⡵⣹⣸⠀⠀⠀⠸⡞⣎⢾⡄⠀⠀⠀ ⠀⠀⠀⣮⣵⣏⡎⠀⠀⠀⠀⣗⢿⣎⡇⠀⠀⠀ ⠀⠀⠀⠘⢿⣇⡇⠀⠀⠀⠀⢟⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠾⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡿⠟⠃ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⣰⣿⣿⣾⣿⠿⢾⣷⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀
⊹⠀⠀⠀⠀⠀⢠⢄⡠⡄ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⡆⠀ ⁺ ⠀⡤⠔⠒⠢⢼⡀⢀⡀⢀⡧⠔⠒⠢⢤ ⡂ ⠀⠀⠀⠀⠑⣘⣁⠊⣀⠀⠀⠀⠘⡄ ⠀⠑⠤⣀⣀⡠⠭⡧⡼⠩⠅⣀⣀⠤⠊ ⠀⠀ ⡔⠁⢀⠞⢀⡇⠓⢀⠈⠳⡀ ⁺ ⠀ ⢰⡁⠀⠀ ⡸⢣⠀⠀ ⠀⠀⡇ ⠀⠀⠀⠉⠧⠔⠊⠀⠀⠙⠲⠴⠉⠁ ⊹
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀ ⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀ ⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘ ⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀ ⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀fllw me on pinterest : pinkiace ୨୧
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠀⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠀⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⣴⠖⠒⠲⠶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠒⠒⠶⣤⡀⠀ ⢸⡧⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠈⣿⡆ ⠘⢷⣀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣻⣿⣿⣷⣤⣀⣤⣶⣴⣾⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇ ⠀⠀⠙⠿⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣠⠴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠉⠛⠋⠀⠀⠉⠛⢿⣷⣄⠀⠈⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⢤⠀ ⠀⣏⠀⠀⠀⠈⠳⡄⠀⠀⡰⠚⠁⠀⠀⠀⢘⡄ ⢸⠁⠀⠀⠤⣤⣤⡎⠉⠉⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡄⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡇⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⣇⣀⡤⢌⣙⡲⠀ ⠀⠀⠀⠀⠀⠙⠼⠁⠀⠀⠀⠿⠋⠀⠀very preppy⠀⠀⠀
⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⠟⠁⠀⠙⠛⠛⠿⣿⣿⣷⣦⣔⠀⠀⣰⣶⡀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣷⣶⣦⡄ ⣨⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⡿⣿⣿⣿⣿⣯⣥⣉⡉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣾⡄ ⣿⣿⣿⣿⣧⣀⣠⣤⣶⣾⣿⣿⣿⡿⠛⢋⣽⣿⡿⠁⠙⠛⢹⣿⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠃ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢠⣿⣿⡟⠀⠀⠀⠀⠈⣿⡇⠀⠙⠿⣿⣷⣦⡀⠀⠀⠀⣠⣴⣿⣿⠃⠀ ⠀⠹⠿⢿⡿⠿⠿⠛⠉⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠙⠿⢿⣷⣾⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⢐⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢰⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢰⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣾⠙⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣡⡔⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠞⡩⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⣵⣄⢀⣴⠇⣸⠀⠀⠀ ⠀⠀⢀⣤⣴⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⢋⣴⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠥⠋⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀ ⠀⠀⠀⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⠲⢖⣶⣲⣞⠋⢉⣤⢃⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢖⠝⠁⠀⠈⠀⠒⠀⠀⠿⠁ ⠀⡐⢛⠲⢄⠀⠀⣠⣖⠟⢡⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠧⣀⠭⣾⡗⢒⡯⠶⠄⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠈⡙⢩⢻⠙⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡔⢕⠄⠀⡴⢽⣽⠀⠀⠀ ⠀⠀⢀⠎⢠⠃⢸⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠌⠲⢽⣺⡒⠋⠁⠀⠀⠀ ⠀⠀⡎⠀⡆⠀⠈⡄⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡧⠀⠀⠀⠀⠀ ⠀⢰⡷⡼⠀⠀⠀⢱⡏⠑⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⢀⠇⠈⠑⠢⡀⣠⠊⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⢀⢬⡽⡄⢀⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⢠⡒⠒⠒⣢⣀⢀⡤⠶⣶⣶⣲⠀ ⠀⠑⠒⡨⠁⡜⢰⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡽⠞⠉⠉⠲⡢⡀⠀⠀⠀ ⠀⠀⠰⠁⠰⠁⠀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠕⠀⠀⠀⠀⠀⠈⢌⢂⠀⠀ ⠀⠀⢠⢀⠇⠀⠀⢣⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⢣⢁⠀ ⠀⠀⠈⠟⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁ ⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀ ⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀
⢀⣽⠟⠃⠒⠽⣯⢷⣰⡬⠗⠉⠀⠀⡑⡄⣀⠀⠈⠉⠒⠒⠲⠬⣀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠉⠩⢑⣢⢨⢙⣟⡵⠢⣠⣴⠶⣛⣻⣭⣭⣭⣽⣗⣦⡤⡀⠀⢀⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⢟⡝⡡⠊⠀⢉⣴⢟⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣅⠘⢦⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠒⠤ ⢿⢫⢾⢺⣀⠀⢠⣞⣽⣿⡟⢿⠛⠻⡛⢆⢉⢮⣿⣻⣿⣿⣿⣿⣿⣷⣯⢏⢷⣥⡢⢀⠀⠀⠀⠀⣀⠤⠔⢒⣚⣭⣽⡛⣉⣱⣶⣄⣒⣶ ⣶⠋⠘⢴⢺⢬⣟⣾⣿⡿⡁⠈⡷⣠⣵⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⡜⣆⣿⡿⣷⣷⠶⣾⠻⢛⡩⠝⠹⣾⣯⣶⣿⠿⠛⢋⣥⣿⡷ ⣯⣠⣒⣟⣸⣾⣿⣿⣿⣷⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢻⢿⢪⣿⣿⡍⠐⢠⡆⠠⡀⢄⠑⠛⣛⣛⣲⣦⣴⣿⣛⣡⡴ ⣳⣙⣚⣓⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣇⢿⣿⣿⣿⠦⢑⠄⠈⠐⠀⠴⠧⡀⠈⢿⣯⣟⣛⡉⠉⠛⢦ ⠉⠉⠙⠛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢿⣯⣿⡿⢻⢻⣿⣿⣞⡞⣿⣿⣧⣀⠙⠂⠤⠀⠂⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣦ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡼⢫⠕⢳⠉⡈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣾⣿ ⠀⠀⠀⣸⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠿⣿⣷⢝⠿⣿⠀⢈⠘⡡⠒⡀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⠈⠀⠀⠀⠀⠀⠀⢈⣹⠟ ⠀⠀⢠⠟⢻⣿⣿⣿⣿⣿⣿⣿⡷⠿⣛⠝⡙⢯⠉⡆⠁⡀⢂⠁⠆⡡⠳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣷⠀⠀⠀⢀⡴⠋⣩⣴⣶ ⠁⣲⡿⠴⠉⡿⠋⢻⣿⠛⢻⣿⣿⣖⣉⠒⡌⡐⠠⠉⠄⡐⠠⡈⢐⠀⢇⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⢇⢀⡴⠋⣴⣿⠟⠊⢩ ⣿⠗⠁⠃⡜⡠⠊⡂⠹⣭⣾⣿⣿⣿⡵⢣⠐⡁⠆⣉⠰⠒⡁⡐⠂⢌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⡞⠀⢌⠠ ⠁⠀⠐⢜⠂⠐⠠⠁⢨⣿⣿⣿⣿⣿⣿⣶⣇⣘⠰⡀⢆⠡⡐⢡⢸⣾⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠻⡟⠿⡿⣿⣿⣿⣿⣿⣷⣿⣍⣦⢳ ⠀⠀⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⡛⢻⣯⠗⣉⣴⣾⣶⢭⣅⣒⠓⠛⠻⠿⣿⣿⣿⣿⣿⢾⣹ ⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⢉⣿⣿⠿⠛⣿⣫⣴⣾⢧⠞⣋⠳⠌⢪⠱⢈⠎⠩⢒⢤⣀⠄⠈⠙⢾⣭⣛⠳ ⠀⠀⣼⣿⣿⣿⣿⣿⠿⣛⠽⢚⡽⢳⠶⠶⡞⣯⠿⣿⣠⣶⡿⡾⣿⡿⠻⣋⠟⠁⠂⠀⠀⠀⠈⠀⠀⠂⠀⠁⠀⠂⠉⢧⡈⠄⢠⢷⣩⠷ ⠀⠀⣿⣿⣿⣿⡟⡡⠊⠁⡴⠋⠌⠡⠊⡑⠨⠄⠙⡐⢋⠟⢧⠕⠡⠀⢡⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⡜⡰⡘⣿⣎ ⣄⣸⣿⣿⣿⡿⠋⠀⢌⡞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠊⠄⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠌⢳⡡⢱⡘⣿ ⣄⣹⣿⡿⢯⡇⠀⠌⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢌⠢⢡⢳⣅⡲⢸ ⡿⢛⡽⡝⣿⡇⣉⠂⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠡⡀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣈⠤⣃⢧⣓⠾⣽⣷ ⣰⠻⠐⣹⣽⢁⠦⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠡⡐⢂⠌⡐⠠⠀⡄⠀⠄⡀⢄⡊⢖⡡⣞⡱⢮⣝⣟⡾⣽ ⠅⢃⡐⡿⣼⢌⠲⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠆⡁⠀⢀⠀⠑⠬⣐⡌⠰⡡⡐⡉⠔⡈⢆⡹⣌⡳⣭⢻⣝⣮⢯⣽⡟ ⠈⠤⡐⣿⣽⣈⢃⣞⠰⣀⠂⡄⡀⢀⠀⡀⣀⠢⢁⠂⡔⢈⠔⡁⠆⢠⢑⠢⠌⠀⠄⠀⠈⠉⠓⠷⣽⣬⠱⣎⡴⣣⣝⢮⣗⡯⣞⣧⣿⡿ ⢘⡰⣐⣿⣿⣄⣿⣏⣳⣌⠳⡴⡑⡎⢦⠱⡰⢡⢎⡰⢌⣲⠜⠁⡐⢄⢫⡳⠀⠹⢀⠘⡈⠔⠡⠘⡈⠻⣿⢾⣵⣷⣯⣿⣾⣽⣿⣿⣿⣷ ⣞⡶⣽⣿⣿⣯⢷⣻⠶⣭⣛⡶⣽⣹⢧⡻⣕⣣⢎⣷⡿⢁⡐⠄⣁⠊⠶⣹⠀⠒⠀⢂⠡⢈⢂⠱⢀⠃⣌⠻⣞⣿⣿⣿⣻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡻⣕⢣⠻⡼⣏⡿⣵⣻⣾⢿⡟⡐⢢⠐⡂⠄⡘⠰⣩⢧⢀⢁⠢⠐⣀⠢⠡⢆⠥⣀⠣⣝⢺⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠺⠦⣯⣵⣭⣿⣿⣿⣯⢏⡔⡼⢡⠓⠄⠂⠈⢅⢢⣛⠆⠄⡂⠅⡠⢂⡙⢬⢲⣅⠚⣤⢿⣯⣿⣷⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣽⣿⣿⣿⣞⡶⣎⠵⢣⠍⢂⠁⠈⠄⢲⣌⠳⢈⠄⣃⠰⢠⠘⡤⢻⣜⡳⣞⣯⣿⠇⢻⣿⣿⢸⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⡝⣴⣿⣿⣿⡿⡫⠛⣿⣿⣾⣹⣎⢯⠜⡀⠀⠀⡘⢢⡜⢣⠎⡐⢠⠊⢤⠓⣼⢣⡯⣗⢿⣞⣿⣯⠢⡻⣿⣾⡟⠀ ⣿⣿⣿⡿⢫⣿⡿⣿⣷⣿⣿⣿⡯⠊⠀⠀⢹⣿⣿⣛⠾⣫⠖⡠⠀⠀⣌⢣⡜⣣⠆⠑⢢⡉⢖⡹⣎⢷⡝⣮⢫⣟⣿⢿⣧⢨⣿⣿⣷⡀ ⣿⣿⠟⢁⣿⣿⣧⣿⣿⡿⠛⠁⠀⠩⠉⠉⣹⣿⢧⡋⠴⡙⡎⠔⣀⠣⠔⣣⢚⣵⣎⢇⠦⣙⢢⢓⢮⣛⢾⡱⣓⡞⣿⡄⠹⣿⣿⠛⡝⢿ ⡩⠂⢀⣾⣿⣿⡿⡟⣿⣇⠐⠀⠀⢁⠀⣰⣿⣻⢧⡛⡴⡹⣌⠣⡐⠤⢉⠔⡩⢾⣟⢊⠖⡡⢎⡜⢦⡛⣎⠷⣭⢺⡽⣷⣀⣿⣿⣆⠘⠄ ⣀⣤⣾⡿⣿⠏⠀⠈⠚⢿⣆⠀⢀⢂⣴⣿⡳⡙⢮⡱⣃⠗⡤⠓⡌⡰⢁⠢⠁⠎⡙⠌⢢⠑⡬⣘⠶⣹⣌⠗⣎⠷⣹⢯⣿⡫⠈⢿⣷⣌ ⣭⣿⠟⠁⣿⡄⠀⠀⠀⠀⢻⣦⣠⣟⣟⠦⡑⠌⢢⡑⢣⡚⣜⢣⠜⣄⠃⢆⠩⡐⣌⠢⣡⠚⡴⣡⢟⡶⢭⡞⡩⠢⢅⡻⣝⡷⡄⠈⡌⢿ ⠟⠁⠀⠀⢹⣇⠀⠀⠀⠀⣠⣻⣾⣛⢮⠓⡄⠂⠅⣎⡱⣚⡬⢇⡯⣰⡉⢎⡱⡘⡤⡓⡴⣙⠶⣱⢏⣾⣣⡝⢢⠑⡌⣞⡵⣫⢿⣆⠃⠀ ⠀⠀⠀⠀⠀⢳⠑⠤⠀⡔⣳⣿⢲⡝⢪⠱⣀⠃⡘⢤⠳⣝⣞⢯⡖⣧⣙⢎⠶⣙⠶⣹⠶⣭⡻⣝⡾⣧⢳⡝⢢⠱⡘⢦⡻⢵⣫⢿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣯⡿⣽⡷⣿⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣽⣷⡟⣯⣿⣽⣯⣿⣽⠂⠀⢠⣶⣿⡟⣦⠀⣶⣶⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⣻⠏⠀⠈⣿⣞⠟⢀⣴⣿⣻⢾⣽⣟⡿⣯⢿⣽⢯⣷⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⢀⠻⣾⡽⣷⠀⠀⠸⣻⠀⣸⣟⠾⣽⣯⠷⣻⣽⣟⡿⣾⣻⢧⠀⠀ ⠀⠀⠀⢠⣾⣇⣀⢧⣨⣇⣏⡙⠯⣧⡄⠀⣟⠀⡿⠀⠀⠈⠀⠀⢀⣿⢾⣻⡷⣟⣿⠃⠀ ⠀⠀⠀⠘⢷⡏⠐⠊⠰⠃⠈⠛⢷⡷⣄⡀⠀⠀⡅⠀⢀⣠⣶⡿⠻⠏⢛⡓⠛⠋⠁⠀⠀ ⠀⠀⢀⣤⣦⣴⡶⣶⢶⣴⣤⣀⠀⠙⢟⡿⣦⠀⠀⠀⠛⣉⣴⡴⣞⡿⣟⣿⣻⣗⣦⠀⠀ ⠀⢀⣾⡿⣽⣯⢷⠛⠈⠉⠛⠛⠂⠀⠘⢷⣻⠀⠀⠀⠒⠛⠉⠁⢻⡷⣟⣯⡿⣽⢿⡄⠀ ⣠⣿⢯⣟⣷⣻⢿⣤⣤⡤⠤⠶⣶⠆⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠙⢻⣽⣻⢯⣟⡿⡄ ⠙⠋⢿⣻⣞⣯⣿⣽⠚⢁⣤⡾⠁⠀⠀⠀⣾⠀⣿⣇⠀⠀⢰⣦⣀⣠⣼⢯⣟⡿⣽⣻⢿ ⠀⠀⠀⢿⣽⠳⠏⣠⡾⣟⣷⢿⣦⣤⠀⠀⢸⡄⢸⣯⢿⣶⣻⢾⣟⡿⣞⣿⣽⣻⢯⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣯⡷⣟⣧⣤⣿⣻⡀⠹⣟⣾⡽⣿⣞⡿⣯⠃⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠻⢿⣧⣟⡿⣿⣻⢧⣟⣧⡇⠀⠘⠟⣿⣧⢿⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣿⣳⣿⣻⣽⢯⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣽⡾⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀ .☘︎ ܁˖
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⠴⠚⡙⠙⠲⣤ ⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣿⠃⣰⠟⠉⠙⢦ ⢦⡈⢁⣾ ⡟⠉⠳⣆ ⠸⠀ ⠙⣆⠙⢧⡀⢀⡴⠃ ⠛ ⢧⡀ ⢀⡴⠃ ⣰ ⠈⠓⢦⡈⢡⣰⠞ ⡈⠈⠓⢦⡈⢡⣰⠞⠁ ⠀⣰⠃⣰⡏⠀ ⠙⣆⠙⢧⡀⠀ ⢀⡴⠃ ⣰⠏⠀⠀ ⠈⠳⣄ ⠙⠶⣄ ⠈⠓⠲⠖⠚⠀⠀⠀⠀⠀ ⠈⠓⠲⠶⠚
⠀⢠⣤⣄⠀⢀⣤⣤⠀⠀⠀⣤⣄⠀⠀⢀⣤⡄⠀⠀⣠⣄⡀⠀⣀⣤⡀⠀ ⠀⢸⣿⣿⠛⢿⣿⣿⠀⠀⢐⣻⣿⣷⣶⣿⣿⣓⠀⠈⠉⢛⣿⢻⣟⠉⠁⠀ ⠀⢴⣿⠏⠀⠈⢿⣷⠄⠀⠘⣿⠿⠋⠀⠻⢿⡟⠁⠀⣰⡟⠁⠀⠙⠃⠀⠀ ⠀⠈⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣷⣦⣀⣠⣶⣿⠄⢀⣀⣶⣦⡀⠀⣠⣶⣆⣀⠀⣶⣦⣄⣀⣠⣴⣶⠀ ⠀⢻⣿⡿⠋⠻⣿⣿⠃⢀⣽⣿⣿⡿⠿⣿⣿⣿⣇⠀⢨⣽⡟⠉⢿⣯⡁⠀ ⠐⢿⠋⠀⠀⠀⠈⢻⠗⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠟⠉⠀⠀⠀⠙⢧⠀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠻⠿⣷⣤⣾⣿⠦⠀⠀⣸⣿⣷⣤⣴⣿⣿⡇⠈⠳⢭⣷⣤⡾⠵⠋⠀⠀ ⠀⠀⣼⡟⠀⠻⣷⡄⠀⠀⠙⣿⣿⠉⠹⣿⡿⠃⠀⠀⣴⠋⠀⠙⠳⠦⢤⠄ ⠀⠜⠛⠁⠀⠀⠹⡇⠀⠀⠀⠸⠃⠀⠀⠹⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠐⢀⠢⠐⣀⠂⡐⠠⢀⠄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠉⠁⠈⠓⢾⣷⡿⠿⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⡳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡐⠂⡐⠠⡁⠊⠄⢂⠁⢂⠂⠌⡐⠠⠀⠀⠐⠀⡁⠀⠀⠠⢁⠐⡀⠀⠀⠀⠈⠛⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣾⣵⣿⣾⣿⣿⣿⣿⣿⣽⣧⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⠀⡐⠀⡁⠠⢁⠌⠠⠌⠠⢈⠐⠠⠁⠀⠀⠀⡁⠀⠠⢁⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢌⠡⠀⠀⢐⠀⡁⠂⠌⡐⢈⠐⠠⠈⠄⠂⠀⠀⠀⠀⢂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠻⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡐⠨⠄⠀⠠⢁⠂⡀⠤⠁⢂⠐⡠⠈⠄⡁⠂⠀⠀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⣀⠄⣀⣤⡆⠀⡀⣠⣤⣶⣯⠳⡄⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠢⠁⠀⢠⠃⠄⠰⠀⠆⡅⠠⠊⠔⠉⢀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠟⠋⢁⡴⠂⠀⠐⠀⣴⢫⣶⠃⠀⣸⣿⣿⣿⣜⡳⠄⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠂⠀⠠⡁⠀⢊⠐⡁⠎⠐⠀⠈⡐⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠋⠀⠀⠀⠀⣼⡳⣿⡏⠀⢰⣿⣿⣿⣿⣎⡗⣃⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠄⠀⠀⠐⡀⠀⠠⠐⠀⠐⠀⠀⠀⠐⠀⠠⠀⠀⠌⠀⠀⠀⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡜⣧⠿⢡⡇⠀⣾⣿⣿⣿⣿⡿⣼⡁⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠄⠂⠀⠀⠐⡀⠀⠄⠁⡀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⡴⡹⣼⠁⣿⠇⢠⣿⣿⣿⣿⣿⣿⣱⢂⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⠂⠀⠀⠀⠐⠀⠀⠰⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⡜⡲⠝⠒⢸⡿⠀⡼⣿⣿⣿⣿⣿⡷⡭⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⢠⡏⠀⡁⠀⠐⠈⠀⠀⠀⠡⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠂⣰⣶⣨⠥⠖⠁⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠈⠀⢰⡟⣼⡇⢠⣏⣿⣿⣿⣿⣿⡳⠅⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⢀⣿⠁⢰⠀⠀⢈⠀⠀⠀⠀⠘⠘⠃⠀⠀⠀⠀⠉⢆⡀⠀⠀⠀⠀⢇⡻⣶⣶⢦⠶⣞⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⢡⣿⠃⣾⣾⣿⣿⣿⣿⣷⢋⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⣾⡇⢠⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡁⠔⠃⣨⣿⣦⡠⢄⠀⠈⢽⣿⣿⣯⣿⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⣠⣿⡟⢸⣿⣿⣿⣿⣿⣿⠧⢁⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⢸⡿⠀⣾⣿⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠓⣶⢭⣴⣾⣿⣿⣿⠛⣦⣳⣄⡹⢿⣿⣿⡿⠏⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣿⣿⠇⣾⣿⣿⣿⣿⣿⣯⠃⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⡿⠁⣰⣿⡏⢀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠾⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣛⣥⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣸⣿⣿⡟⣸⣿⣿⣿⣿⣿⡿⠆⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠁⣠⣿⡿⠁⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⠿⠿⣻⣿⣿⠛⠟⠛⢿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣿⣿⡟⣰⣿⣿⣿⣿⣿⣟⠣⢁⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠠⢡⣿⣿⠃⠀⠡⢀⢁⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⡿⢃⡰⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣴⣿⡿⠋⣰⣿⢻⣿⣿⣿⠿⡌⢡⣿⡀⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠋⠠⠈⠸⡿⠃⣰⡇⡁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢍⡛⠻⠿⠟⣩⠰⠎⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⡉⠁⣠⣾⣿⢣⣿⣿⣿⢏⠓⣠⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿ ⣿⡟⠁⢌⣴⡇⡁⢁⢠⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠼⡱⣍⠾⣰⠋⠀⢀⡄⡂⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⠹⣿⣿⣿⠟⣡⣿⣿⡿⢏⠌⣴⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿ ⠏⠄⣡⣿⡿⠃⠀⠀⣿⡏⠠⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠄⠹⣜⣣⢭⡃⢀⠷⣨⠥⠰⣀⠃⠀⢀⠀⠀⠀⡀⠦⡑⢀⣼⣿⣷⣭⣉⣁⣴⣿⣿⡿⡙⢠⣾⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿ ⢨⣾⣿⠟⢁⡼⠂⢁⠘⢁⠂⠐⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠐⠸⣱⢋⡞⡱⣌⢣⡅⠻⡤⠙⡦⢋⡕⣣⠹⠤⠈⠀⠀⠠⡜⣱⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⠐⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿ ⣿⡿⠁⡴⠋⣠⣾⣄⠂⢀⠀⠁⠀⠀⢠⣶⣶⡀⠻⣿⢇⣤⡶⣤⠀⠀⠀⠈⠑⠤⣲⣍⡳⣜⢣⢻⣤⢈⡰⣍⢳⠘⠄⣡⠴⡉⠀⠀⠰⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⠌⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿ ⠋⠀⠊⣠⣾⣿⡿⠃⠀⠀⡈⠀⠀⢠⣿⣿⣿⣿⣦⠰⣿⣾⡝⢿⣇⠀⠀⠀⠀⣀⠀⠈⢁⣉⡉⠳⡬⢏⡵⠪⢁⡤⣛⢦⢫⡅⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⠜⠃⢰⡂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿ ⣠⡰⣿⣿⣿⡿⠁⠀⠠⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣇⢻⣿⣿⣷⣽⠀⠀⠀⠀⠀⠈⠛⢦⠈⠓⢧⣌⣯⡼⣳⢏⡶⣹⢎⡷⠂⠀⢱⡀⢹⣏⠸⣿⢿⡻⣝⠲⠉⠀⠀⢺⡅⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿ ⣿⣿⣶⣭⡿⢁⣤⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⡟⠀⠀⠀⠸⡄⠀⠀⡀⠁⠀⠈⣿⣾⣽⣳⡿⣾⣽⣾⡏⠀⠀⠈⢷⡄⢻⡆⢩⠷⣙⢀⠁⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿ ⢏⡕⢪⢋⣼⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⠃⠀⣠⠆⣸⣿⡀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⣹⠄⠀⠀⠙⠂⠁⠘⠢⠁⠈⡄⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿ ⡞⠜⣡⣿⠏⠀⠀⡴⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢀⣠⣵⣾⣿⠟⠀⠰⠁⠀⠁⢀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣿⣿⣿ ⣥⣾⣿⡿⠀⠈⣰⠃⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠟⠉⡀⢠⣿⣿⡿⣻⡵⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣭⣤⣤⣾⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⠠⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠁⠀⣠⠶⡁⣸⣿⣯⠾⡉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⢹⣷⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⣁⣤⣴⣾⣿⣷⢫⠁⣩⡿⣣⠟⢁⣴⣾⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡻⢿⣄⠀⣦⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢋⠠⢈⠐⠀⡀⠀⠀⢀⠀⠀⠀⢋⣴⣿⣿⣿⣿⣿⣿⣯⠇⢀⣿⣧⢉⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡀⠈⢿⣿⣄⢈⠻⣿⣿⣿⣿⣿⣿ ⢇⣴⣶⣦⡜⠀⠀⠀⠸⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⡏⠾⣿⣿⣿⣻⣿⣿⣿⠿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡄⢢⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣕⠿⡓⢉⠀⠉⠙⠦⠘⢿⣿⣶⡳⣌⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⡁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣧⣤⣶⣿⣿⣿⠿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣳⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠁⠀⠀⠠⠀⠀⠀⠀⠺⡜⣿⣿⣿⣞⢧⡹⣿⣿⣿ ⠙⠿⠿⠛⡁⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⠽⡝⠙⠉⠉⠀⢀⠘⠀⡰⡽⣷⣿⣿⣿⣿⣿⣿⡂⢥⢳⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠆⠀⠀⠀⢽⡧⠀⠀⠀⣇⡇⣿⣿⣿⣿⣯⠳⢹⣿⣿ ⡀⢠⣰⣄⡀⠈⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢆⡂⠀⠀⠀⠀⢀⡀⠀⠈⢘⠐⢿⣾⣿⣿⣿⣿⣿⡅⢢⢫⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠔⡀⢀⠀⠀⠁⠀⠀⠈⣨⠃⢸⣿⣿⣿⣿⡇⢈⣿⣿ ⢰⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⡾⢸⣿⣿⣿⣿⣿⣿⢚⠀⠀⠀⠀⢿⣇⡈⠁⠀⠈⠂⣴⢽⣿⣿⣿⣿⣿⡁⢆⡓⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡷⣧⠀⠈⣀⢈⢤⣸⡰⠁⠀⢸⣿⣿⣿⡿⠁⠀⣿⣿ ⡸⢿⣽⣿⣿⣿⣷⣦⣀⠐⣿⣿⣿⣿⣿⣿⡿⣮⢽⠐⣿⣿⣿⣿⣿⣟⣿⡐⠁⠀⠀⠁⠀⠀⠐⠀⠀⡀⡟⣾⣿⣿⣿⣟⢧⠂⢢⡙⢼⡹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣧⣧⣴⣶⣿⡟⠅⠀⠀⠈⠻⣿⡿⠁⠀⢸⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣿⣿⣿⣟⡼⢪⡅⢻⣿⣿⣿⣿⣿⣮⡷⡦⣤⢀⡄⠁⠁⠈⠀⢖⠆⣶⣿⣽⣿⣟⢮⡃⢠⢃⠖⣀⠙⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠳⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⣿⣿ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢷⡌⢻⣿⡟⣞⡜⣣⠆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣖⡤⢑⣲⣿⣿⣿⣿⣿⣿⡻⣜⠆⡁⢦⣉⢞⡡⢖⡈⠐⢏⣞⡻⣟⠿⣿⢻⡟⡽⢣⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡻⡄⢻⡜⣣⠞⡡⠀⠀⠈⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣧⡛⢈⡰⡘⢦⠜⣪⢕⣣⢞⡡⢆⣀⠑⠊⠙⠆⠓⠈⠁⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡙⢦⡙⢦⡙⠄⡞⠀⠀⠀⠙⠯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠷⠙⡂⡔⣣⢖⡹⢎⡝⣦⣻⣼⣾⣵⣫⡔⣫⡙⣜⠢⡍⠀⣀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠸⡛⣿⣿⣿⣿⣿⣿⣿⡷⣭⢣⡙⠆⠌⠀⠀⠀⠀⠀⢀⡟⠈⣉⡛⠛⠿⠿⠿⠻⠟⠛⠓⣉⡬⡴⣹⡜⣵⣳⣮⢿⣽⣾⣷⣿⣿⣿⣿⣷⣯⠵⣙⢦⡙⠀⠀⠗⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿ ⠀⠀⠀⠀⠀⠉⡻⢿⣿⣿⣿⣿⣟⡖⡣⠜⡈⡼⠀⠀⠀⠀⠀⠸⠀⠀⠘⣿⣿⣷⣶⣶⣷⣾⣿⣿⣯⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡱⠆⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠙⠀⠚⠛⠿⠿⣽⢸⠡⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠗⢀⡄⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⢀⣿⠀⡀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠁⠁⠀⠐⠀⠀⠀⠰⠃⢀⣤⣦⣾⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣎⠀⠀⠀⢀⠰⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⢀⡇⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⢀⣠⣤⡔⢆⣩⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⢀⡄⢸⣶⠆⠀⠀⠀⢠⠀⠀⢀⡿⠃⠞⠀⠀⠀⠀⠀⠀⠐ ⢀⡀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⢛⣭⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⢿⣧⡤⠀⠀⠀⠀⢠⡿⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⡏⠀⠀⠀⠀⠀⣤⡜⣯⡳⠩⣞⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣦⡀⢀⣀⠄⠀⠀⠀⣠⠟⠀⢀⠄⠀⠀⡠⠴⠎⠀⠀⠀⠀⠀⠀ ⠀⡀⡀⠀⠒⢀⣼⣻⣿⢟⣷⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⠆⠁⠀⠀⠀⠀⠁⣀⣴⣿⣆⢇⠰⢶⣶⠀⠀⠀⠀⠀⠀⣴ ⢠⣾⡇⢁⣴⣿⡞⢛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡂⣽⡿⠃⠀⣠⣶⣶⣴⣶⣿⣿⣿⠹⠟⣸⣿⣿⠃⠀⠀⠀⠀⠀⠘⢿ ⠸⣿⣴⣿⣿⣿⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⡄⢸⡇⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣰⣶⣶ ⠀⢿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢮⠸⣧⠀⣷⡹⢿⣿⣿⣿⠿⣿⣿⠿⣛⠵⢂⡠⣀⣤⣶⣾⣯⣟⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠤⠤⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢠⠄⢄⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⣠⠋⠐⠒⢂⠀⠀⠀⠀⠢⠔⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⡠⠽⣆⠀ ⢸⠧⡀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⣙⢆⠀⠀⠀⠀⠀⠀⡠⠊⣀⠤⣰⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠪⢤⡿⡇ ⠈⠳⣈⠳⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⡔⠀⢻⠪⣑⢷⡖⠦⠶⣒⡾⢓⡩⠔⠉⡃⢈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡼⠁ ⠀⠀⠈⠳⢌⡳⢤⡀⠀⢇⢀⠇⠒⠤⣬⡦⠥⠄⠀⢹⡸⠀⣀⢀⡏⠡⣤⡀⠶⠚⠉⠀⠀⠀⢸⠩⢱⡠⢞⡡⠖⠉⠀⠀ ⠀⠀⠀⠀⠀⠉⢑⣻⠷⠲⣤⣤⣄⣀⣀⣠⣬⣭⢽⡻⣆⣀⣇⣠⣛⢦⣤⣤⣄⣀⣀⣀⠤⠤⠔⠿⢿⡊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠾⡍⠀⠀⠀⣀⡠⡔⠒⡄⣠⣖⣵⠿⡲⡿⠀⠀⢿⢦⠑⢵⣄⠉⠛⢳⣦⣖⡀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⣠⣶⠋⠑⠄⠃⠄⠒⠋⠁⠀⠑⢒⣿⣻⡟⣍⠞⢡⠃⠀⠀⠘⡎⠳⡄⠙⢧⣴⠋⢣⠈⠉⠒⠄⠀⡉⢈⠆⠉⠳⣄⠀ ⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠐⢈⣴⣃⡁⡞⠀⠀⠀⠀⢱⠀⠈⢦⡀⠙⢖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠘⢦⣎⠀⡁⠀⠀⠀⢀⠀⡀⠈⠀⢀⡴⠋⠀⠀⢰⠁⠀⠀⠀⠀⠈⣇⠬⢄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡹⠃ ⠀⠀⠻⣍⠀⠀⠀⠀⠣⣈⠞⢀⡴⠋⠀⢀⠀⣀⡏⠀⠀⠀⠀⠀⠀⢸⡤⠜⠀⠀⠙⠦⡀⠀⡔⠐⡄⠀⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⠈⠑⢤⡀⠀⢀⡡⢶⠃⠀⠀⠀⠸⠄⢼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣷⢥⡂⠁⢀⡠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⠇⡄⠢⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠂⠐⡸⡄⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠃⠔⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡕⠟⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠠⣰⢏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡺⡁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣆⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⢇⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠄⣸⠈⢦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡜⠁⠀⠸⡌⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⢡⠇⠀⠀⢫⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠹⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣲⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠐⣦⡙⣿⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠆⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⣿⣄⠀⠙⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⢀⡀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡽⣿⣦⣀⢷⣝⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⣴⣾⢶⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⣙⣿⡿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣍⣻⣿⣇⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣟⣿⣷⣿⣿⣿⣟⠻⠷⣦⣄⠀⠀⠀⠀⠀⣼⣿⣿⡿⡍⠛⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⣄⠀⣠⣿⣟⢁⣤⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⣴⣿⠛⠁⣿⢛⣽⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡀⠀ ⠀⠀⠀⣼⡿⢋⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⠿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⢰⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣣⣾⣿⣽⣿⣷⠿⢿⣟⣿⣿⣽⣿⡿⠀⢸⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣶⣿⣿⠱⣿⣿⢛⣶⣿⣿⣶⣶⣮⣭⣭⣀⡹⠧⠀⣼⣿⣿⣿⣯⣀⢀⣿⡿⢋⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡧ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⢿⡇⣰⣿⠛⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣺⣿⣇ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣿⣿⣿⣾⣿⡿⣿⣿⣼⣷⣿⣧⣶⣿⣿⠁⣀⠀⢿⣿⣿⣿⣿⣿⣿⠀⢸⡿⠛⢿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣇⢠⣾⣿⠉⠉⠉⠻⣿⣿⣿⣦⣌⠙⠛⠛⢿⣿⢀⠋⠀⢸⠃⢉⡀⣿⣿⣿⠿⠿⠿⣛⣥⣾⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢹⣆⠀⣀⣠⣌⣻⠿⡿⠿⢿⣷⣶⣾⣿⣿⡀⠀⠀⢀⣨⣿⣿⣿⣀⣤⣶⣿⣿⣿⣿⡿⠟⠀⠹⢿⣿⠃ ⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⠻⣦⠉⣋⠉⠉⠻⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣦⣤⣾⣿⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠛⠿⠶⠦⠤⠀⣻⣿⣏⣱⡾⢹⣿⣷⣶⣶⣿⣿⡿⢯⡙⠻⢿⣽⡿⠋⠉⠀⠈⢹⣿⣿⣿⡟⠀ ⠈⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⠛⠓⢶⠦⠠⣭⣽⣿⣛⡓⠈⠻⣿⣿⠟⢑⣠⣾⣿⠿⠿⢯⣤⣻⣿⣿⠿⠿⢿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⣠⡴⠒⠛⠁⢀⠀⠠⠄⠈⠁⠀⣹⡃⠀⠈⠉⠛⠟⠻⢉⠀⣙⣟⠷⣯⣽⣿⣿⣿⣿⣧⡀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡌⠀⠀⠀⠀⠀⠐⠛⠛⠛⠓⠀⠀⠀⠀⠀⠛⠛⠻⣤⣸⣶⣿⣿⣿⣿⣿⣿⡀ ⠀⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⡇ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⡀⠀⠀⠀⠈⢳⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⠃⠀ ⠀⠀⠘⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠻⣷⣌⡻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⠟⢻⣿⠟⣡⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣶⣦⣌⣛⠻⠿⢿⣦⣄⣙⡻⠿⣟⡻⣾⡿⣿⣋⣉⢀⣸⣿⣁⣾⣿⣧⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣶⣶⣿⡛⠿⢿⣿⣭⣛⡿⠿⣶⣶⣮⣉⡹⢿⣧⡉⢿⡶⠀⢉⣩⣥⣾⣿⣛⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣝⣃⠀⠉⠛⢿⣿⣷⣸⣷⡍⢿⣧⠈⠉⠷⡘⢷⣰⡿⠉⠿⠏⠉⠉⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡄⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⢿⣿⢿⣿⣿⣿⣄⡀⠀⠀⠈⢿⡍⣻⣿⣮⣿⣤⡀⢸⣿⣾⣏⠀⠀⠀⠀⢠⣴⣿⡟⢛⣹⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣤⣬⣍⡀⠙⢿⣿⣿⣿⣿⣦⡂⠀⠁⠉⠉⢻⣿⡏⠻⣦⣿⡟⠉⠀⠀⣆⣴⣿⣿⣏⣠⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠈⡛⢻⣿⣿⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢙⡑⠒⠛⠛⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⣾⣄⣴⣾⠃⣈⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣻⣋⡻⠿⣷⣴⠛⠘⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠙⠋⠀⠀⠀⠀⣀⣼⣟⣾⣧⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠧⠴⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣁⣿⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⡿⠻⠘⠟⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣛⣋⠙⢛⠛⢻⣿⡿⢿⣿⢿⣿⣿⣠⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⢻⣿⣿⣏⠉⠀⣭⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣶⡤⠴⠒⠀⢀⣼⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡈⠿⣶⣭⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⡄⠈⠀⠂⢂⣴⠟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠾⣶⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣶⡾⠟⣡⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠃⢀⠺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⠛⠿⠿⣛⣛⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠼⠿⢿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣿⣋⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠛⠏⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⣀⡀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠛⠋⠀⠀⠛⠹⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⣔⣦⣀⢠⠄⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡶⠒⠶⢦⣄⠀⠀⠀⠀⣾⠓⢆⠀⠀⡀⠀⣠⡞⠹⡆⠀⠀⢀⣤⠶⠛⠙⢶⣤ ⠹⢆⠀⠀⠀⠉⠳⠦⠀⣼⠇⠀⠊⠙⠉⠋⠙⠉⠠⠀⢷⠀⠴⠋⠀⠀⠀⢀⡼⠋ ⠀⠀⢳⡄⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠴⡏⠁⠀ ⠀⠀⣟⡁⠀⠀⠀⢸⠇⠀⠀⣈⠉⠃⠀⠀⢐⠋⠁⠅⠀⠈⡧⠀⠀⠀⣈⣿⠀⠀ ⠀⠀⣸⠟⠀⠀⠀⠈⠳⣠⣀⠀⠁⠀⠀⠀⠀⠈⠀⣀⣴⠞⠁⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠉⠶⠖⠆⠀⠀⢰⠞⠉⠠⠛⠓⢤⠀⣰⠞⠂⠘⢦⡀⠀⠀⠘⠛⠛⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣤⣤⣴⠛⠀⣿⣀⣤⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⢶⣄⠀⠀⠀ ⠀⢠⣾⣿⡟⠁⠀⠀⠙⣷⡄⠀ ⠀⠻⡿⠛⢿⣦⣀⠀⠀⢹⣷⠀ ⠀⠀⠁⠀⠈⠛⢿⣦⣀⣾⡿⠀ ⠀⢠⣴⢷⣤⣀⣠⣽⣿⣿⣃⠀ ⣴⡟⠉⠀⠉⠛⠛⠛⠉⠈⠻⡷
⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⢤⠀ ⠀⣏⠀⠀⠀⠈⠳⡄⠀⠀⡰⠚⠁⠀⠀⠀⢘⡄ ⢸⠁⠀⠀⠤⣤⣤⡎⠉⠉⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡄⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡇⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⣇⣀⡤⢌⣙⡲⠀ ⠀⠀⠀⠀⠀⠙⠼⠁⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀
⡐⢛⠲⢄⠀⠀⣠⣖⠟⢡⠀ ⠧⣀⠭⣾⡗⢒⡯⠶⠄⣸⠂ ⠀⠀⠈⡙⢩⢻⠙⡈⠁⠀⠀ ⠀⢀⠎⢠⠃⢸⠀⠱⠀⠀⠀ ⠀⡎⠀⡆⠀⠈⡄⠀⠡⠀⠀ ⢰⡷⡼⠀⠀⠀⢱⡏⠑⢧⠀ ⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⢠⡾⠛⠳⠶⣤⣀⣠⣤⣤⣴⡟⠁⠀⠙⣷⠟⠋⠉⠉⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠉⠀⠀⠀⡿⠀⢠⣟⣿⠿⠳⢦⣤⡴⣼⣇⠀⠀⠀⠀ ⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣽⣏⠀⠀⢸⣷⡄⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⢾⡟⠛⢁⣼⣟⠀⠀⠀⠀ ⠀⢀⣼⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣥⣽⢤⠀⠀⠀ ⣀⣈⣷⣏⣁⠀⠀⢀⠀⠉⠙⠻⣶⣾⣳⣶⠟⠉⠁⢀⠀⠀⠀⠶⢻⡟⠒⠒⠀ ⠀⠀⠸⣇⣀⠀⠀⠛⠉⠂⠀⢀⡿⣉⣉⢿⡄⠀⠒⠉⠋⠀⠀⠠⣼⠧⢤⠀⠀ ⠀⠐⠛⠻⣍⣀⡀⠀⠀⢀⣠⠞⠙⠧⠼⠈⠳⣄⡀⠀⠀⠀⣠⣴⣟⡀⠀⠀⠀ ⠀⠀⣠⠴⠛⢿⣭⠿⠿⢯⡅⠀⠀⠀⠀⠀⠀⣠⣭⣩⣭⣭⣿⣋⠈⠙⠂⠀⠀ ⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣿⠶⠶⠶⠤⠶⣾⠇⠀⠘⣧⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⣰⠾⠋⠀⠀⠀⠀⠀⣧⡀⠀⠀⢿⣄⣤⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢻⣇⣀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⣋⣛⣂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⡿⠟⠻⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣤⣔⣶⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡇⠀⣾⡷⠈⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣟⣽⣿⠟⡛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣄⣤⡾⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⡿⣿⣇⠐⠿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠹⣿⣷⣶⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠞⢉⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠂⡻⣷⣦⣀⣠⢴⣶⡶⣶⡾⠿⠷⡶⠶⠶⣶⣾⣿⢷⢶⡶⠶⠶⠶⣶⢶⣶⣿⣿⣿⣿⣿⣧⡀ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠻⣮⣻⣦⠀⢸⣧⣁⣤⣤⣇⣸⣅⣸⣦⣿⣸⣧⣤⣸⢇⣀⡠⢇⣬⣪⣜⣧⣾⣿⣻⣿⣁⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⣶⢻⣗⣻⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣦⡟⣷⢯⡷⠻⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢬⣿⣳⣿⠝⠉⠀⣠⣄⣤⣶⣤⣠⣄⡀⠀⠀⠀⠀ ⠀⢼⣿⣳⡯⠀⢀⣰⣿⣻⣽⣻⣞⣷⣻⡾⣽⢶⡄⠀⠀ ⢰⣿⣟⣿⠁⢀⣾⣿⣷⠟⠉⣠⣀⣀⠀⠙⢿⣟⣿⣖⠀ ⢸⣿⣿⡅⠀⣿⣿⣿⡖⣠⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⡇ ⢸⣿⣿⡧⠀⣿⣿⣿⢃⠉⠿⠿⠛⣿⣿⣿⡆⢘⣿⣿⣟ ⠘⣿⣿⣿⠄⠈⢿⣿⣿⣶⣤⣠⣴⣾⣿⡿⠃⢼⣿⣿⡏ ⠀⠨⣿⣿⣯⣂⠘⠻⢿⢿⣿⣿⣿⣟⠟⢃⣰⣿⣿⡿⠁ ⠀⠀⠈⢿⣿⣿⣾⣄⣠⢀⣀⣀⡀⣠⣴⣿⣿⡿⡟⠁⠀ ⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢠⣄⣀⡠⠀⠀⠀⠀⠀⣀⣄⡴⢈⡦⠀⠀⠀ ⠀⠘⠓⠿⠷⠿⡿⠖⢴⣮⡴⠚⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣆⡁⠀⠀⠹⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠈⠹⣿⣦⠀⠀⠀⠀ ⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀ ⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠉⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣧⡀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠘⢿⣦⡀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠛⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠙⠻⣦⣄⣀⣀⣠⣾⡿⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⠀⠈⠙⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣄⣠⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⢀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀ ⠀⠀⠀⠀⠀⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀ ⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢣ ⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿ ⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏ ⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃ ⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁ ⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋ ⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉₍ᐢ. ༝ .ᐢ₎₍ᐢ. ༝ .ᐢ₎₍ᐢ. ༝ .ᐢ₎
⠀⠀⠀⠀⠀⣴⣶⣤⠤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠁⠉⠙⠙⠛⠽⠖⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⠀⢀⣐⣦⠀⠀ ⠀⠀⠀⠀⠀⢰⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣫⡫⠦⣏⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⢸⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⢠⣶⣊⣉⣳⣀⣈⠷⣇⠀⠀ ⠀⠀⠀⠀⠀⢸⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡇⣊⠪⠎⠷⠦ ⠀⠀⠀⠀⣔⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡋⠀⠀⠀⠀ ⠀⠀⠀⣸⡕⣯⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⣎⢭⢷⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡇⢻⡃⡇⠀⠀⠀⠀⠀⠀⠀⢸⢙⡟⡏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣯⡣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠞⠿⠝⠓⠋⠛⠙⠉⠉⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⡦⣀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠋⡦⡖⠉⢵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀ ⠀⢀⡠⡢⢛⠉⠈⠃⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠚⠯⠥⠤⠼⣂⡀⡬⠂⢓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⣀⡀⠀⠀⠀⠀⠀⠀⣇⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣉⣊⠏⠑⠒⠚⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣟⣝⢗⠀⠀⠀⠀⠀⢰⣗⣩⣭⡆⠀⠀ ⠀⠀⠀⠀⠀⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢗⢡⣿⠀⠀⠀⠀⠀⠈⡕⢯⣟⡟⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣙⣿⠀⠀⠀⠀⠀⠀⠙⠮⠾⠧⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣻⡷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⡿⣽⣻⢿⡽⣟⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⢾⣻⣯⣟⣯⣿⣻⣽⢿⡅⠀⠀⢀⣠⣴⣶⣤⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣻⢿⣽⢾⠉⠁⢻⡷⣯⡿⠁⢀⣴⣿⣻⢷⣻⡾⣷⣾⢿⣽⢾⣳⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⢿⡾⣯⠀⠀⠀⢻⣽⠇⢠⡾⣟⣾⡽⣟⣯⢿⣳⣯⡿⣾⣻⣟⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⣠⡆⠀⣤⠀⣶⠙⡿⣽⢿⣆⠀⠀⢸⡿⠀⢼⣻⠏⠁⢿⠿⠙⠛⢯⣷⣟⣯⡷⣿⣽⣳⡀⠀ ⠀⠀⠀⠀⢾⣟⣧⠤⠺⡷⢾⠦⣧⣌⣙⢯⢷⡄⠀⠿⠀⣻⠃⠀⠀⠀⠀⠀⣠⣞⣷⢯⡿⣽⡷⣯⠷⠀⠀ ⠀⠀⠀⠀⠹⢾⠧⠀⠛⠀⠟⠀⠀⠙⠫⣿⣶⣤⡀⠀⠀⡅⠀⠀⣀⣴⢾⡟⠯⠟⠚⣛⠛⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣤⣶⢶⣶⣶⣤⣦⣤⣀⠀⠈⠺⣷⣻⣆⠀⠀⠀⠐⠛⣉⣤⣴⣶⢿⣻⣟⣿⣻⣷⢶⡄⠀⠀ ⠀⢀⣾⣟⣷⣻⡾⣟⠗⠉⠈⠁⠛⠙⠋⠀⠀⠙⢷⣻⠇⠀⠀⠀⠛⠉⠉⠈⢉⣿⣻⢾⣳⡿⣞⣿⣽⡀⠀ ⣀⣼⣟⣾⡽⣷⣟⣿⣣⣀⣀⣠⠤⡴⣶⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠋⠟⣿⣽⣻⣽⢷⣯⣧⡀ ⠻⣟⡾⣯⣟⡷⣿⣞⣯⡿⠝⠁⣀⣴⡟⠀⠀⠀⠀⣴⡀⣽⢿⠄⠀⠀⠠⣄⡀⠀⠀⣸⡷⣯⣟⡿⣾⡽⣿ ⠀⠀⠀⢻⣯⢿⣳⣯⠗⢁⣴⣾⣻⣽⣄⠀⠀⠀⠀⢻⡃⢸⣿⣳⣦⣤⣼⣻⣽⢿⣻⣯⣟⣷⢿⣽⡷⣟⠏ ⠀⠀⠀⠈⠛⠛⠉⠁⣴⢿⣻⡾⣽⡾⣽⣻⣧⠀⠀⣸⣧⠀⢻⣷⣻⣞⣷⢯⣟⣯⣷⣟⣾⡯⠿⠾⠝⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡷⣿⢯⣟⣿⣳⢿⣻⣟⣯⣟⣇⠀⠹⣷⣻⡾⣟⣯⣟⣾⡝⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢫⣿⣻⣞⣯⣿⣻⢾⣽⣾⣻⠀⠀⠈⠓⠿⣻⠽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⣟⡷⣯⣟⣯⣷⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣞⣿⣽⠏⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⢀⣾⡟⠒⢄⠀⠀⠀⡠⠊⣠⠔⠈⠉⢯⣂ ⠀⣾⡵⠛⠿⣭⣑⣄⣀⣠⣾⠎⠠⠠⠤⠜⡿ ⠀⠎⠓⠤⣤⢿⡿⠋⢹⠻⡹⠣⠤⠀⠠⢸⠃ ⠘⢀⣀⠰⠓⡍⢠⠀⠈⡀⠀⠢⣏⠀⠈⠁⠀ ⠀⠀⠀⡀⠸⠁⢀⠀⠀⠀⢀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠑⡀⣿⡀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢈⠝⠇⠀⠀ ⠀⠀⠀⠀⠃⢀⠌⠀⠀⠀⠀⠀⠘⡘⡄⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣶⠂⡇⠀⠀ ⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀ ⠀⠀⠌⠀⣴⠀⠀⠀⠀⠀⠀⡶⠀⡸⠁⠀⠀ ⠀⠸⠀⢠⠻⠀⠀⠀⠀⠀⣰⡁⡰⠁⠀⠀⠀ ⠀⡇⠀⠆⡈⠀⠀⠀⠀⢀⣿⠕⠀⠀⠀⠀⠀ ⢠⠁⡐⢀⡇⠀⠀⠀⠀⢈⢻⠀⠀⠀⠀⠀⠀ ⠘⡅⢩⣾⠁⠀⠀⠀⡠⠁⠊⠀⠀⠀⠀⠀⠀ ⠀⠇⠘⠏⠀⠀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡀⠀⠀⠀⢐⠃⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⡀⠀⠀⢸⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀ ⠀⢠⣾⣿⠟⠉⢉⣉⣉⠛⢦⣀⡴⠛⣉⣉⡉⠙⠻⣿⣦⡀⠀ ⢀⣿⡿⠁⣠⣾⣿⡿⠿⠿⣶⣍⣴⠿⠿⢿⣿⣷⡀⠙⣿⣧⡀ ⢸⣿⡇⢀⣿⣿⠋⠀⢀⣤⣄⡉⣁⣤⡀⠀⠹⣿⣿⡀⢹⣿⡇ ⢻⣿⡇⢸⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⡇⠠⣿⡇ ⠸⣿⡇⠈⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⠃⢰⣿⡏ ⠀⢻⣿⡄⠘⣿⣷⣄⠈⠻⢿⣿⡿⠟⠁⢀⣾⣿⠋⢠⣿⡟⠁ ⠀⠀⠻⣿⣆⠈⠻⣿⣷⣄⠀⠈⠀⣠⣶⣿⠟⠁⣰⣿⡟⠀⠀ ⠀⠀⠀⠉⠿⣷⣤⡈⠙⠿⣿⣿⣿⠿⠋⣁⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⡈⠉⣀⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠃⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢳⣄⢀⡾⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠹⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠛⢧⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⣧⡀⠀⠀⠹⣦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣤⣤⣴⡿⠛⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠙⠀⢀⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡿⣦⣀⣠⡿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⡁⢹⡏⠂⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢘⡇⠁⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡒⠒⠒⣢⣀⢀⡦⠶⣶⣶⣲⠀ ⠀⠉⢉⡽⠞⠉⠉⠲⡢⡀⠀⠀⠀ ⠀⠄⠕⠀⠀⠀⠀⠀⠈⢌⢂⠀⠀ ⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⢣⢁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠿⠟⠛⠒⠒⠒⠛⠫⠽⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡟⢋⣩⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⣛⢿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⡟⠉⣼⢿⡿⣿⡶⣝⣷⡀⠀⠀⠀⠀⣴⢿⣿⣷⣶⡝⢷⡍⠻⡷⣄⠀⠀⠀⠀ ⠀⠀⠀⡰⠋⡞⠀⢸⣇⣾⣄⣼⣿⣿⠈⡇⠀⠀⠀⢸⡇⣿⣀⣽⣿⣿⣈⡇⠀⠹⡈⢧⡀⠀⠀ ⠀⠀⡼⠁⠀⠠⠚⠉⠁⠀⠠⠀⠀⠉⠙⠃⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠨⠭⠓⠆⠀⠀⢳⡀⠀ ⠀⣸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⢀⡇⢠⠋⠀⢠⠆⢀⣠⣤⣴⣶⡖⠋⠉⠉⠉⢹⠉⠉⠉⠉⠳⣶⣦⣤⣄⡀⠀⡆⠈⠑⣄⠘⡆ ⢸⠀⠇⢀⣠⣾⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣄⡀⢸⠀⡇ ⢸⠀⡄⠈⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠉⢠⠀⡇ ⠸⣄⢸⠀⠀⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⠀⠀⡼⢀⡇ ⠀⣿⡌⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⠃⣾⠁ ⠀⠘⣷⡘⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣊⣉⣉⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⠏⢬⠏⠀ ⠀⠀⠘⣇⡈⢦⠀⠀⠀⠻⢿⣿⣿⣿⡟⠛⠛⢻⠛⠛⠻⣿⣿⣿⣿⠟⠁⠀⠀⢠⢋⣾⠏⠀⠀ ⠀⠀⠀⠈⠣⡈⠃⠀⠀⠀⠀⠙⠻⢿⣁⠀⠀⢸⠀⠀⣀⣿⠿⠛⠁⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠈⠁⠒⠒⠒⠒⠒⠊⠉⢀⣠⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⠛⠤⠤⠤⠤⠤⠞⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠠⣴⣶⣶⣶⣶⣶⣾⣿⠀⣾⡆⢸⣿⣶⣶⣶⣶⣶⣶⡤ ⠀⠈⠛⢷⣤⡀⠠⢤⣤⣼⣿⣷⣤⣤⠤⠀⣠⣶⠿⠋⠀ ⠀⠀⠀⠀⠙⢿⣷⡄⢩⣿⡿⣿⣯⠀⣴⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠀⠟⠋⣠⣈⠛⠄⠸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡇⢀⣴⣿⠟⢿⣦⣄⠀⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣾⠟⠋⠀⠀⠀⠈⠻⢿⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣤⣤⠀⠀⠀ ⠀⠀⢰⣏⣿⣏⡙⣻⣯⡕⢦⡀⠀⠀⠀⢀⣴⢚⡯⣟⠩⢛⡳⣿⢀⡀⡀ ⠀⢀⡏⣿⣉⠶⡙⢽⣿⡙⣶⣿⣦⣤⣴⣿⣧⣤⢻⡧⢜⣥⣗⠏⣿⢀⡇ ⠀⢼⣿⣧⣭⣕⡪⣥⣫⣷⣦⣼⣽⠿⢿⣿⡿⠾⣟⠲⢯⡼⣾⣧⠿⡤⣹ ⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⡿⣽⣿⠀⢸⣿⣟⣿⣿⣿⡿⠿⢿⡲⠦⠷⠟ ⠈⣷⡏⡍⠀⠄⢁⠊⡴⣿⣽⣻⡏⠀⠸⣿⣾⣹⣦⠠⡭⣙⠎⡕⠆⣿⠃ ⠀⠈⢗⠠⣌⠠⣤⣴⣟⠵⣾⣥⡇⠀⠈⣿⣏⠿⢿⣿⣦⣄⠚⠰⣾⠋⠀ ⠀⠀⠈⢿⠽⠊⠁⡿⢬⢲⣾⢰⠇⠀⠀⠿⣟⡤⠂⡍⢏⠛⠿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⢀⡞⢇⣾⠀⠀⠀⢸⢹⡔⢃⠦⠹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⣟⣤⡿⢼⡇⠀⠀⠀⢸⠀⣿⠡⢒⠀⢶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣽⡿⣼⠇⢺⠃⠀⠀⠀⢸⡇⢾⣜⢲⡀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠉⣼⢹⡏⠶⣹⠀⠀⠀⠀⢸⡆⠁⢼⣃⠅⠐⢌⡆⠀⠀⠀ ⠀⠀⠀⢰⠇⣼⡟⣼⢧⠁⡇⠀⠀⠀⠀⠸⣧⠃⢼⣯⠂⠌⠄⠸⡄⠀⠀ ⠀⠀⢀⡞⢠⣸⣷⡏⡺⢦⡇⠀⠀⠀⠀⠀⣟⡎⢲⡝⣧⠐⠬⠁⢷⠀⠀ ⠀⠀⠼⠗⠒⢻⠏⣑⢃⣾⠀⠀⠀⠀⠀⠀⣯⡗⢠⠌⡏⠓⠢⠼⢌⣇⠀ ⠀⠀⠀⠀⠀⣿⣻⣍⢳⡿⠀⠀⠀⠀⠀⠀⣷⡇⢛⡄⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⠇⣾⢘⡇⠀⠀⠀⠀⠀⠀⣷⠫⣳⢽⣳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢿⡰⣌⣹⠇⠀⠀⠀⠀⠀⠀⣯⡱⢹⡸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠒⡧⡧⢼⠂⠀⠀⠀⠀⠀⠀⢸⣇⠳⡘⢾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣹⢐⡱⣹⠀⠀⠀⠀⠀⠀⠀⢸⡔⢃⠱⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣇⢼⣹⠀⠀⠀⠀⠀⠀⠀⢸⠠⡍⢢⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠸⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⢀⣾⢻⣆⡀⠀⠀ ⢀⣤⣾⠃⠀⠙⠛⣿⠇ ⠈⠻⣶⡄⠀⠀⢸⣏⠀ ⠀⠀⢾⡷⠟⠛⠻⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣦⣀⣴⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⣻⣿⠛⣿⣟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⡏ ⠀⢹⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟ ⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⡞⠉⠉⢳⣤⠤⣤⠀⠀⠀ ⠀⠀⢰⡏⠈⠹⣷⡄⠀⡞⠁⠀⠘⡇⠀⠀ ⠀⠀⣘⣧⠀⠀⠘⢷⡀⠀⢀⣠⡾⢥⣄⠀ ⠀⢸⡏⠁⠀⠀⠀⣸⣿⡞⠋⠀⠁⠀⣬⠃ ⠀⠘⢿⣤⣶⡶⠛⠉⠘⣷⡀⠐⠁⣾⡅⠀ ⠀⠀⠀⢰⣿⠀⠀⣹⡄⣺⣿⣷⡔⣼⡇⠀ ⠀⢀⣠⡾⠛⠶⠾⠻⣿⣻⣿⠊⠉⠁⠀⠀ ⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⢧⣀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠏⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⣒⣶⠦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠲⡌⠙⢦⠈⢧⠀ ⠀⠀⠀⣠⢴⡾⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢃⡠⠋⣠⠋⠀ ⠐⠀⠞⣱⠋⢰⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣋⡥⢖⣫⠔⠋⠀⠀⠀ ⠈⠠⡀⠹⢤⣈⣙⠚⠶⠤⠤⠤⠴⠶⣒⣒⣚⣩⠭⢵⣒⣻⠭⢖⠏⠁⢀⣀⠀⠀⠀⠀ ⠠⠀⠈⠓⠒⠦⠭⠭⠭⣭⠭⠭⠭⠭⠿⠓⠒⠛⠉⠉⠀⠀⣠⠏⠀⠀⠘⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⣰⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠉⢳⡞⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⠀⣀⣴⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠆⠠⣿⡿⣿⣿⣿⢿⣿⣦⣴⣿⡿⠿⢿⣿⣷⣄⠀⢾⣿⣿⣿⣿⡿⣿⠆⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣠⣿⡿⠁⠀⣰⣿⡿⠁⠀⠀⠀⠈⠻⣿⣧⡀⠀⠘⣿⡟⠀⠀⠀⠀⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⢰⣿⡿⠁⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣴⣿⡟⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣇⣀⡀⠀⠀⠀⠘⢿⣿⣦⣀⠀⢀⣠⣾⣿⠏⠀⠀⠀⢿⣿⣦⡀⠀⠀⣀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠉⠀⠀⠀⠀⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡦⠤⠤⢧⠤⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠂⠃⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀⠀⣀⢠⡶⠊⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠁⡇⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⡰⠁⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡴⠃⠀⠀⠯⠷⡃⠀⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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