Soft-Serve Emojis & Text

⬜️⬜️⬜️⬜️⬜️📜⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️⬜️⬜️📜🟫⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️📜📜📜📜🟫⬜️⬜️⬜️ ⬜️⬜️🟫🟫🟫🟫🟫🟫🟫⬜️⬜️ ⬜️⬜️️📜📜📜📜📜📜📜⬜️⬜ ⬜️📜📜📜📜📜📜📜📜🟫⬜️ ⬜️🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜️ ️📜📜📜📜📜📜📜📜📜📜📜 ️📜📜📜📜📜📜📜📜📜📜🟫 ⬜️🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜️

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣾⣿⡿⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣠⠀⠀⠀⠀⢸⣿⠀⠉⠉⠁⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⣾⣿⠀⠀⢠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⢠⣿⡀⠀⠀⠹⣿⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠈⢻⣧⠀⠀⠀⠘⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⢀⣀⣤⣤⣽⣛⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠸⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⣠⣴⣶⣶⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡿⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⠎⠛⠉⠉⠉⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡶⠶⠦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⠤⠿⠶⣤⡀⠀⠀⠀⠀FUCK ALL YOU BITCHES DONT ⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠈⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀ ⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀CALL ME A PIECE OF SHIT!! ⠀⢀⡔⠟⠓⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠆⠘⠚⢔⡄⠀ ⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀ ⣼⠂⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿ ⢹⡆⠀⠀⠀⠀⠬⠀⠀⠂⠀⠀⠀⠠⠀⢄⠀⠘⠉⠉⠐⠤⠀⠀⠀⠀⢀⡐ ⠀⠚⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠀ ⠀⠀⠈⠩⢦⣤⣠⣄⣤⣠⣠⡤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣠⢤⠠⠞⠈⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⢈⡡⠄⠀⠀⠀⠀⠀⠂⠠⢄⡁⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡈⠢⡀⠀⠀⠀ ⠀⠀⡠⢃⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⢂⠀⠀ ⠀⡐⣀⣊⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣑⣀⢣⠀ ⢰⠀⢿⡟⠉⠉⠀⠀⠈⠉⠉⠙⢶⣶⣶⡶⠚⠉⠉⠉⠉⠉⠉⠉⢹⡿⠀⡆ ⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⠁⠀⢸ ⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸ ⢃⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⢸ ⠘⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠇ ⠀⠱⠀⠀⠀⠀⠀⠀⠙⠳⢒⡤⠤⠀⠀⠤⠤⣐⠾⠋⠀⠀⠀⠀⠀⠀⡞⠀ ⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠈⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠐⠼⢟⣲⡐⠈⣻⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠐⠀⢀⠀⠀⠀⠀⡉⠉⠉⢠⡘⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⡀⠈⠐⠀⠄⠀⠀⠀⠀⠀⣀⣀⢈⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣠⠌⠉⠓⠒⠀⠀⠀⠀⠐⠊⠊⠇⠿⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠯⣷⡀⡜⢡⠆⠰⠂⠀⠀⠀⠀⠒⠦⠄⠌⠙⠲⢻⠉⡿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣾⠟⢠⠇⢩⠃⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠹⣄⠀⡈⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⡋⠁⠀⠀⠀⠀⠀⠀⣰⠓⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡆⠳⣌⢸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡟⠱⠡⠃⠐⠂⡄⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠆⢹⣴⣀⣳⣷⣶⠾⠟⠛⢷⣄⠀⠀⠀⠀⠀ ⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⣉⡙⡛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⢣⡑⠈⢻⡆⠀⠀⠀⠀ ⠀⢸⡇⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⡀⢰⢠⠀⡆⠀⠆⠀⡄⢄⢶⠼⣿⠀⠀⠀⠀ ⠀⠹⣷⡀⠘⡟⡆⡄⡀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠐⣶⠄⡇⠾⠘⠀⢉⡄⢠⢧⢧⢸⠀⣰⡟⢀⠀⠀⠀ ⠀⢀⣼⣷⡄⠀⣡⠁⢀⠈⡀⠀⠈⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⠘⠢⠘⠊⢈⣡⠴⠋⡀⠋⡰⠃⡄ ⢸⠕⢋⡽⠻⣶⣅⣇⠈⠰⠁⡇⠄⢰⠀⠀⠀⠀⠠⢠⣴⠠⠀⠃⠀⠀⢀⣀⣤⠔⡨⢔⡾⢣⠞⢠⠞⢀⡜⠁ ⠀⠈⠁⠀⠚⠉⠉⠛⠛⠛⠓⠒⠒⠶⠦⠤⠤⠤⠤⠶⠶⠒⠒⠊⠭⠉⠍⠂⠈⠋⠀⠋⠐⠁⠘⠁⠀⠊⠀⠈

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀ ⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀ ⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀ ⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀ ⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠛⠓⠒⠲⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⢰⢗⣯⣲⡀⠀⠀⢀⣴⣾⣯⣗⢦⡀⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣹⠀⠀⣾⢸⣿⣿⣿⣷⠙⣆⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⣿⢎⡻⣿⠞⠀⠀⠘⠾⣿⣿⣿⠟⣠⠞⠀⠢⡀⠀⠀⣸⠃ ⠀⠀⣀⣀⡀⠀⠹⡄⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢡⢆⢆⠀⠰⠀⣰⠏⠀ ⢀⣤⣧⣸⠛⠓⢦⣹⠞⢳⣭⣍⠙⠛⠓⠀⠁⢄⠀⠀⠊⢂⣠⡴⠟⠁⠀⠀ ⢸⣸⠋⠙⠣⣄⠀⠙⠦⣺⠀⠈⡷⠶⠦⠤⠤⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀ ⠸⣨⠓⢄⡀⠈⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠫⣷⣤⣉⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠳⢤⣁⡀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⡶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⠛⢷⡀⠀⠀ ⡟⠀⠀⣸⡷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡤⠤⣿⡀⠀ ⣷⠀⣼⠋⠀⠀⢹⡀⠀⠀⠀⢠⣶⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠀⠀⠈⢻⡄ ⠘⢧⡇⠀⢀⣤⠾⠛⠻⢶⣤⡟⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣦⡀⠀⠀⣸⡏⣇⠀⠀⠀⣷ ⠀⢸⡇⢀⠏⠀⠀⠀⠀⠀⡿⠁⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡷⠿⠝⠛⠻⠿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢻⡀⠀⣾⡤⠛⠒⠲⣤⡇ ⠀⠀⣷⢸⠀⠀⠀⡤⠖⠚⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢸⡇⣼⠃⣇⠀⠀⠀⠈⢱ ⠀⠀⠘⣿⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢋⡤⠖⠒⡖⠒⠀⠀⠀⠀⠙⣏⠓⠲⢤⡀⠀⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠿⠁⠀⠈⢳⡆⠀⠀⢠ ⠀⠀⠀⢸⡄⠀⠈⠀⣀⣀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⡾⠋⠀⣠⠜⠁⠀⠀⢀⣀⡀⠀⠈⠓⠆⠀⢙⡧⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⠃⠀⣀⣄⠀⠀⢠⡏⠁⠀⠀⡴ ⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⢳⣄⢀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠉⠁⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡀⢰⠋⠀⠀⠀⠈⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠳⣽⡄⠀⠀⠀⠀⣀⡴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⡴⠟⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠿⠦⢤⠶⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣇⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠛⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣴⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⠀⠈⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀ ⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀ ⢠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⡌⢀⠔⠊⠉⢹⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⡴⠚⢹⣿⣶⣾⡀⠀⠀ ⣇⠋⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⡜⠀⠀⢰⣿⣿⣿⡇⠀⠀ ⡿⣦⣤⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣥⣤⣶⣿⣿⣿⣿⠇⠀⠀ ⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠸⡈⣿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⢋⠆⠀⠀⠀ ⠀⠑⣌⠻⢿⣿⠏⢀⡠⠞⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠎⠀⠀⠀⠀ ⠀⠀⠈⠲⣄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡦⠤⢀⣀⣀⠀⣀⣀⡀⠤⠒⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠒⠒⠒⠒⡄ ⠀⠀⠀⠀⠀⠸⣸⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡇⠸⢶⣾⣿⡇⡇ ⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⢰⠋⠀⠉⢢⠀⠀⠀⡇⠀⣼⣿⣿⡧⡇ ⠀⠀⠀⠀⠀⠀⠀⠱⠄⠠⠃⠀⠀⠀⠘⢆⡠⠜⠀⠀⠓⠓⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⡀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠁⠢⠤⠄⠒⠉⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⢀⣠⣦⣶⢿⣛⢯⠯⣝⠮⣝⡹⣏⢿⡻⢿⣳⣤⣀⣀⣰⣴⣾⢿⡿⣿⢷⣄⠀⠐⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣁⣶⣷⢿⣫⣓⣮⢓⡮⢇⡻⣬⢛⡼⣣⡝⡶⣹⢣⣓⢮⢻⠿⣿⣹⢮⣗⣻⡼⢯⣿⣷⡄⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢠⣶⣿⡿⢛⣽⣿⣿⣿⣿⣿⣿⣷⡭⢏⡶⢣⡝⡞⣥⢻⣬⡓⣏⠾⣹⢻⣿⡼⣧⣿⣿⣿⣿⣿⠄⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣜⣧⣿⡿⣾⣷⣶⣿⣼⡭⢧⣫⠽⣿⣿⣿⣿⣿⣿⣿⡀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣿⡿⠏⠀⢺⣿⣿⣿⣟⠻⣿⢿⣿⣿⣿⣿⡾⢏⣾⣿⣿⣿⣿⣿⣿⣿⣷⣧⡻⣜⣿⣿⣿⣾⣿⡟⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⡇⠀⠀⣸⣿⣿⣿⣿⣦⡹⣸⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡼⣿⣿⠿⠋⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢰⣿⣾⡇⠀⠀⠘⢯⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡟⢻⡟⣽⣿⣿⣿⣿⣿⡵⣻⣆⠀⢀⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣞⣷⡀⠀⠀⠀⠹⠿⣿⣿⣿⣿⡿⢹⠁⠀⠸⣿⣿⣿⣿⣷⣌⠀⣿⣿⣿⣿⣿⣿⢞⡵⡏⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⢮⣝⣿⡷⣶⣤⣤⣤⣼⡟⢋⠅⢢⠙⣧⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠮⣝⣷⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣿⣟⢾⡹⣏⠷⣎⢷⡹⣖⠏⢄⠊⡄⠃⡜⠻⣆⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⡟⣾⡗⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⣀⣤⣾⣿⣯⠷⣭⢻⡜⣧⠟⢡⠘⡠⢃⠌⡒⣀⠣⢈⡙⣷⣦⣝⣻⡿⠿⣿⣿⣿⣛⢧⣛⣾⡏⠀⡰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⠒⠒⠒⠔⠉⣀⣴⣶⣿⡻⣝⣾⣿⣿⣍⠩⡉⠔⣈⠢⠑⡄⢣⠘⡰⢀⠆⡡⠐⢯⣻⡜⣯⣛⢿⡻⣝⣶⣯⣷⡿⠟⠀⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⣠⣤⣀⣾⡷⣦⣤⣶⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⣷⣬⠒⡀⠆⡑⡈⠆⡱⢀⠣⡘⠤⢉⠌⢷⡝⣶⡹⣎⢷⣹⣛⣿⠟⠁⣀⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⣱⣦⣾⡿⣹⢻⣧⡽⣽⠟⠿⣿⣿⣿⣿⣿⣿⡿⠞⠋⠉⠀⠉⠻⢦⣕⣠⢁⠒⠤⢁⠆⢡⠘⡠⠊⠤⣙⠳⠽⣎⣷⡷⠛⠁⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⣶⣿⢻⣱⡭⢇⡯⢽⢿⣧⣌⠂⣽⣿⣿⠟⠛⠁⢀⣡⠖⠃⠒⠄⡀⠀⠀⠉⠛⠓⠾⠦⢮⣤⣧⣴⣭⣴⠴⠾⠚⠋⠉⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⠏⢸⣿⣼⣧⣛⢿⣿⡘⡉⢄⣿⡋⡐⢿⠁⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⢀⣀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⢊⣵⣄⣀⣴⣾⣿⣿⣿⣏⠢⢈⣿⣶⢾⠟⢡⠐⣺⠆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⢫⣴⠟⡉⢌⡶⠛⠛⠛⢋⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⡿⣿⠟⠉⠈⠻⢦⣘⣴⠏⢀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⢹⣿⣿⣿⣿⠟⣀⠔⠒⠂⠤⠤⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠢⣙⠛⠛⣁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣯⣭⣷⣾⣿⣾⢿⡿⣿⣾⣯⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣭⡷⢾⡿⡟⡿⢻⠍⢧⠳⢌⢣⢓⡱⢎⠷⣛⠿⣻⠷⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡷⢟⣯⢮⣵⣿⣼⣳⣎⡱⣊⠌⣞⢢⡍⣎⠱⣊⠼⣡⢎⣧⣛⣴⣭⣫⡟⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣽⠯⣝⡚⠈⢸⣿⣿⣿⠀⠛⣟⠤⢫⢌⠳⣜⢢⠛⣆⢳⣝⠋⠁⣿⣿⣿⡏⠹⣷⣛⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣯⣾⡟⡱⠮⡽⣷⠾⣿⡿⢿⡰⡛⢯⡃⢇⠚⡹⢄⢣⡙⢌⠞⣎⣳⣸⣿⣿⣿⢇⡴⣯⢓⡜⣿⡝⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣧⣿⠿⣡⢑⡘⠬⡙⠹⡋⢟⠯⢹⠑⠢⡁⠎⡰⠐⡊⠦⣑⠊⡌⠭⡱⠭⢇⠯⡝⢯⡹⢉⠎⠲⣌⡻⡞⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣻⣿⢏⡳⣕⢪⠰⡡⢌⠱⡈⢆⡘⢄⡉⠒⠤⢑⠠⡑⣈⠒⠤⡉⠴⣁⠖⡡⢊⠴⢈⠆⡌⠰⣈⠡⣈⢓⢽⡹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⣿⡟⡼⡰⢎⠥⢃⠔⢨⠐⣐⠢⢐⠂⡌⢡⠒⢌⠰⡐⠤⠉⡔⢡⠒⢄⠢⡑⢢⠐⡡⢂⡘⠤⢐⠢⡐⢨⠊⢧⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⡧⣿⡱⡒⢍⠲⢈⠆⡘⢤⢊⠔⢢⠁⠎⡰⠀⠎⡐⠢⡁⠆⡱⠈⡔⡈⠆⡱⢐⢂⠡⠒⠤⡐⠌⢢⠐⡁⠆⣹⢼⡞⢿⣿⣿⣿⣿ ⣿⣿⣿⡆⣿⡔⢡⠊⡔⢂⣬⣵⡣⡚⠬⡁⢎⠒⡠⠑⡌⠰⣁⠢⢑⠠⢃⠔⡈⢆⠡⢂⠌⢢⢉⠒⡤⣍⣦⡂⠅⡚⣜⢾⣿⢸⣿⣿⣿⣿ ⣿⣿⣿⣷⡏⡰⢁⢶⣸⣿⣏⠏⢱⠉⡰⢈⠰⡈⢰⢁⡈⢁⡀⠇⡈⢆⠁⡎⢰⠈⡆⢁⠎⡰⡈⠶⢁⠿⢾⣹⣷⣸⡸⢿⣿⢾⣿⣿⣿⣿ ⣿⣿⣿⢱⣽⣲⣿⣿⣿⣷⣼⣬⣂⣡⡐⡁⠆⡑⢂⠆⢌⠰⡀⢃⠌⢂⠥⠘⠄⠒⣈⣐⣨⣐⣌⣶⣬⣶⣿⠿⣿⣷⣿⣿⣿⢺⣿⣿⣿⣿ ⣿⣿⣿⣎⣿⡿⣿⣿⡷⣮⣝⣹⢛⡟⠻⠿⢷⣾⣶⣾⣶⣷⣶⠷⣚⠷⢚⠷⣻⠿⡛⠟⣛⢛⡫⢭⣭⢳⡾⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⡞⣿⡵⣫⢟⣧⢻⡜⣫⡜⡹⡜⢢⠔⡠⠄⡤⢀⢄⠢⣐⠠⢃⡜⣄⣲⡱⣫⣜⢧⣟⡷⣯⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡸⣷⣱⢎⡜⢣⠞⣡⢚⡱⢌⡳⡘⢥⠚⡄⠣⣌⠲⣄⣋⠶⣜⡖⣧⢻⡵⣺⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⢛⣿⣿⣶⣧⣘⢤⢃⡔⢢⡑⣌⣂⢣⡬⡵⣬⢳⡼⣍⣟⡲⣝⡞⣧⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⡳⣟⡿⣻⢵⢪⣳⢚⡧⣝⠶⣭⡳⣝⣳⢭⣳⢳⡞⣲⡽⣮⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣎⡿⣽⣎⠷⣭⢻⡼⣭⢻⢶⡹⢧⣏⡷⣭⣷⣻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣳⣯⣞⡵⣛⣾⣹⣳⣟⣾⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡳⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣟⣛⡿⠿⠿⠿⠿⠿⣟⣛⣛⣻⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀ ⣣⠔⠚⠻⣄⣡⣞⣄⣠⣆⠀⢼⣼⣄⣀⣀⣠⣆⠜⡘⡻⠟⠙⣲⠦⣈⢳⡀⠀⠀ ⡇⠒⢲⡤⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠤⣖⠬⠓⠂⠉⣿⠇⠀⠀ ⠙⠲⠦⠬⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡄⠀⠀⠀⠀⠀⣞⠀⢀⣲⠖⠋⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⢢⠃⠀⠀⠀⠉⠙⠻⠛⠁⠀⠀⠀⢀⡜⠒⢋⡝⠁⢀⣀⣤⠂⠀ ⠀⠀⠀⠀⠀⡇⠷⠆⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠤⠟⠉⠀⢰⠱⡾⣧⠀⠀ ⠀⠀⠀⠀⠀⠹⢄⣀⣀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢠⣤⡀⣼⢾⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⡏⠀⡡⠣⢖⣯⠶⢄⣀⣿⡾⠋⢸⢀⡶⠿⠲⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣹⠃⣀⣤⠞⠋⠀⠉⠢⣿⣿⡄⠀⣿⠏⠀⠀⠐⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⢡⡾⠋⠀⠀⢀⡐⣦⣀⠈⠻⣇⢸⢁⣤⡙⡆⠈⡏ ⠀⠀⠀⠀⠀⠀⣠⠎⢁⠔⡳⡟⠀⠐⠒⠒⠋⠀⠠⡯⠙⢧⡈⠻⣮⠯⣥⠧⠞⠁ ⠀⠀⠀⣀⠴⠋⠀⢶⠋⢸⡝⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⠀⠙⡆⠘⠦⢄⡀⠀⠀ ⠀⠀⣸⠅⢀⡤⢺⢸⠀⢸⡃⠤⠀⠀⠀⠀⣀⡤⢚⣋⣿⢄⡀⢇⡀⠀⠀⣝⡶⠀ ⠀⠀⢿⠀⡏⠀⠘⠞⠀⢸⡵⣦⠤⠤⠖⣿⠥⠞⠉⠀⢸⠖⠁⠀⠙⠢⣑⠶⣽⢂ ⠀⠀⠸⠤⠃⠀⠀⠀⠀⠀⠉⢳⠂⠈⡽⠁⠀⠀⠀⢀⡼⠒⠓⢤⠀⠀⠀⠙⠚⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡎⠀⠀⠀⠀⢠⠎⣠⠀⠀⠈⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡶⠗⠋⣱⠄⠀⠀⠀⣧⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠦⣤⣷⠂⢀⡸⠁⠀⡼⠁⠀⠀⠀⠈⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⢀⣀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠢⠤⠤⣄⡤⠼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢦⣄⣉⣑⠢⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠃⠀⠀⠀⠀🇹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠔⠁⣠⡾⠃⢐⡩⠐⡊⣵⡻⣏⢿⡹⢯⡝⣯⣛⢿⡽⣫⢻⢯⣿⡹⢯⢿⣿⣽⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⡾⡿⢁⣴⢟⡴⣋⣼⣳⡝⣮⢮⡝⣧⠏⣶⢹⣎⡿⣵⢫⢷⡹⣿⣭⣛⣦⣳⣷⣄⠀⢵⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠇⢀⣼⢯⡽⣵⡻⣝⢮⡳⣝⣾⣳⠽⣎⢷⡹⣎⢷⣎⠷⣮⡝⣷⢫⡞⣵⢫⣷⣯⣶⣙⡞⣿⣦⠈⠹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⢀⣾⣿⣹⢾⣝⡳⣝⣮⢷⣽⣷⣫⠿⡽⣎⢷⣏⣾⣿⡝⣶⡹⢾⣏⢾⡱⣏⢿⣞⡽⣻⢾⣵⣯⣷⡀⢳⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠀⢀⣾⡿⢶⣻⡾⣭⣟⡼⣮⠟⢹⣷⢫⡿⣽⢎⡿⣞⡾⢹⣟⢶⡹⣏⣟⢮⡳⣝⠾⣿⡜⣧⢻⢮⢷⣻⢷⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⢻⡽⣯⢿⡵⣻⢞⡵⢀⣾⢞⡯⣽⡞⣭⢿⣽⠇⢹⣯⢻⡷⣭⣟⡮⢷⣭⢻⣽⣿⢾⡽⣾⢷⣻⢿⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⣼⡿⣭⢿⣹⢯⣷⡿⠕⠉⠀⠀⣿⢞⡽⢧⠿⣜⣯⡿⠃⢫⣯⢷⡟⣞⣿⢼⡳⣎⠷⣾⣏⢾⡹⣞⣳⢯⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⣽⣏⢾⣽⣿⢿⣿⣿⣶⣄⠀⠘⣯⡻⣭⣛⢷⠟⠀⠀⠀⢻⡾⣝⣾⣻⢮⢷⣭⢻⡼⣛⣮⣷⢿⣟⢿⣳⡿⢤⡀⠀ ⠀⠀⢀⠜⢹⣿⣽⣳⢯⣿⡿⠉⣲⣿⣿⡟⣿⡆⠀⠙⣿⣶⣭⢿⠀⢀⡤⠀⠀⣿⣣⣿⡽⣏⡾⣎⢷⣹⢯⡷⣏⡿⣞⢯⡷⡇⠘⣟⣧ ⠀⢠⠎⠀⣼⣟⡾⣽⣿⣿⡇⠀⣿⡿⣟⣿⡿⠀⠀⠀⠈⠉⠙⠛⠂⣾⣿⣿⣿⣾⣿⢧⡿⣽⢺⡽⣧⢻⣯⢷⡿⣹⣞⣻⡼⡇⠀⠘⣾ ⢠⠃⠀⣰⣟⣾⣽⣳⣟⡏⠻⠀⠙⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⣿⢻⣿⣻⣽⣳⢏⣷⣻⣞⣯⣽⣳⣭⢷⣻⡇⠀⠀⠱ ⡎⠀⢰⣿⣹⡞⣷⢯⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡹⣻⣿⣿⠀⣿⣿⣾⡽⣟⡾⣵⣻⡼⡶⣏⡾⢧⣳⢿⠀⠀⠀ ⣇⢠⣿⡷⠉⠟⠛⠻⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠯⣘⠋⠀⠛⠋⠀⠐⠾⣿⣳⢯⡷⣿⡽⣹⣏⢷⣻⠇⡀⠀ ⠻⣿⡟⠀⠀⡔⠛⠒⠒⠺⠷⣤⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠈⠈⣻⡟⠉⣿⣳⣟⣳⡞⣿⡄⠙⠓⠄ ⠀⠈⠳⣀⡜⠀⠀⣠⣤⣤⡴⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠚⠿⠒⣺⡏⠀⣼⢿⡽⣯⡷⣽⢯⡇⠀⠀⠀ ⠀⠀⠀⠈⢆⠀⣰⣿⢿⡽⡇⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠻⠄⢄⣠⡈⠉⢹⣦⣤⣴⣾⠏⠀⡔⠁⣼⡿⣹⣿⡞⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠹⣌⠛⣿⠷⠀⣿⠟⡷⢄⣀⠀⢀⢀⣀⣠⡜⠀⣰⣾⣟⣿⣻⠀⠐⣿⡽⠛⠁⢀⠞⠀⣸⣟⡷⣏⣷⣻⢷⣻⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠈⠳⡀⠀⣰⣷⣤⣧⣤⣬⠍⠉⠉⠀⢺⠀⠠⣿⣳⣟⠾⠃⠀⠴⠋⠀⡠⠔⠁⠀⣠⣿⢾⣹⡽⢾⡽⣯⢿⡇⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⣶⠃⠈⣿⠿⠍⠀⠀⠈⢀⣠⣼⠀⠀⠛⠋⠁⠀⢠⡀⠐⠒⠉⠀⢀⣤⣾⣿⣽⣞⡷⠿⠯⣿⡽⣯⣷⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⢠⠃⠀⠀⡇⠑⣒⡲⠖⠛⠉⠀⢸⠀⠀⢀⣀⣀⣀⣔⠳⣔⣤⠤⠖⠛⠉⠉⠀⣀⣀⣤⣤⣴⣿⢻⣷⣻⡆⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⣠⠃⠀⠀⡔⠛⠋⢣⠀⠀⠀⠀⠀⣸⢀⠖⠉⠀⠀⠀⠉⠉⠉⠙⠀⣀⣤⣶⢾⣟⡿⣽⡯⣷⣻⣼⣻⢞⡷⣿⡀ ⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⡎⠀⢀⡀⠈⡆⠀⠀⠀⢀⢿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⣻⢿⢮⡷⣞⡽⣞⣿⣵⣻⢶⢯⣻⣽⣳⣧ ⠀⠀⠀⠀⠀⠀⡹⠋⠀⠔⢹⠉⠈⠉⠚⣊⣅⠀⢀⣰⠃⠘⡄⠀⠀⠀⢀⡔⢿⣿⢿⣞⣯⣽⢻⣿⣞⡽⣞⡽⣻⡶⣏⡿⣏⣷⣳⢯⣟ ⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠠⠁⠘⣤⡺⠃⠀⣠⢳⡀⠀⠀⠀⢇⠈⠙⢆⠹⣷⢯⣟⢾⣻⡾⣭⣻⢽⣻⣳⡽⣛⣮⢷⣻⣞ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡜⠁⠀⠀⢫⠉⠳⢤⣄⠤⠘⣦⠀⠘⢷⣿⣻⣞⣯⢷⣻⢷⣯⣳⢯⣷⣹⣻⡼⣛⣦⡙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⢿⣶⣄⣴⣿⠟⠋⠁⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⢳⡽⣎⡟⣾⣻⣯⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣿⡿⢿⣿⣶⣶⣦⣤⣠⣤⣶⣾⣿⠿⠿⠟⢻⡿⣧⢟⣳⣿⣾⣷⣿⣿⡿⣷⣶⣄⣤⣶⣿⢿⡿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⡿⣵⣫⢿⣿⢧⣿⣟⡳⣟⣧⣛⣿⣿⣿⣼⢏⣾⢳⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣶⢫⣟⣻⣿⣿⣯⢳⣛⡶⣛⣾⣿⣟⣿⡿⣎⣯⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡿⣼⣣⣿⣿⣿⣟⣿⣣⣿⣿⣿⣿⣿⢿⣸⣻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠙⠛⠛⠉⢿⣾⣳⢭⣯⣷⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡷⠶⠿⠛⠓ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠉⠉⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⢠⣤⣿⣷⣤⣦⣤⡄ ⠀⠀⠀⠀⢿⣧⠀⢀⡀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⠀⢁⣿⡇⠀⠀⠀⠀ ⢠⣴⣶⡾⢿⣿⡟⠛⠛⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣀⡀⠀⠀⠀ ⠈⠁⠀⠀⠀⢻⣧⡀⢀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣧⣮⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠙⠛⡿⠷⠀ ⠀⠀⠀⢀⣤⣶⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠙⢿⣦⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠁⠀⠈⠉⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣾⡿⠿⠛⠉⢿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⢀⣬⣽⣿⣿⣿⣿⣿⣿⣾⡾⢿⠿⠿⠿⠟⠛⠛⣿⡿⢯⢿⣿⣄⠀⠀⠈⢻⣷⡄⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣟⠋⠁⣠⣿⣿⡹⡽⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⢽⡺⣟⣿⣆⠀⠀⠀⠻⣿⣄⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠘⢿⣷⣰⣿⣿⣼⣷⣟⣾⣻⣷⣤⣤⣀⣤⣤⣾⣿⢏⣷⣯⣷⣭⣿⣿⣧⣠⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⠀⣠⣿⠿⠛⠉⠉⠉⠛⢿⣷⡽⣏⣿⣛⣯⢿⣹⣺⣿⠿⠛⠉⠉⠉⠙⠻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣶⢻⣼⢳⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣳⡽⣺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢻⣜⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣻⢼⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣏⡾⣭⠷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠉⠉⠙⠻⠿⣷⣶⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢖⣒⣒⣒⣲⣒⡦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⡯⠝⠚⠉⠁⠀⠀⠀⠀⠈⠉⠙⠓⠬⣝⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⡭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⠀⠀⠀⠀ ⠀⠀⢰⢣⠟⠀⠀⠀⠉⣿⣏⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠀⠀⠀⠘⣎⢧⠀⠀⠀ ⠀⢀⡟⢸⠀⠀⠀⣀⣤⠿⣽⣛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣰⣾⢿⣻⡧⠦⣤⣀⠀⠀⠉⣸⡇⠀⠀ ⠀⢸⠇⢸⠀⣰⠟⠉⠀⡠⠀⠈⠙⢮⢻⣧⣢⠀⠀⠀⢩⣾⢟⡵⠋⠀⣀⣀⠀⠉⠳⡄⠀⢰⣿⠀⠀ ⠀⢸⠆⢸⢰⣿⠀⠀⣾⣿⣿⡆⠀⢸⣷⣹⣿⠀⠀⠀⠹⠏⣿⡇⠀⣰⣿⣿⣷⠀⠀⣿⠀⠸⣿⠀⠀ ⠀⢸⡎⢸⡆⢻⡄⠀⠙⠛⠋⠁⠀⣸⣿⠳⡌⠀⠀⠀⠐⠟⣏⣷⣀⠀⠙⠋⠁⠀⣰⠿⡇⢨⣿⠀⠀ ⠀⠘⣿⠾⣧⣀⣭⣶⣦⣤⣤⡴⠾⢻⣿⡀⠐⠀⠀⠀⠀⢀⣿⣟⣺⣷⠶⠶⣶⣯⡧⡾⠻⣿⡏⠀⠀ ⢠⣾⠋⠀⢉⠉⣿⢿⣍⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⡾⣽⡆⠀⠀⠈⠻⣄⠀ ⣿⠈⠀⠀⠀⢠⣿⠈⢿⡻⡖⡶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⢴⡶⢶⠞⣿⡿⠁⢻⡄⠐⠀⠀⡀⣽⡀ ⠹⢦⣔⣀⣢⣿⢣⠀⠀⠙⢷⣙⡶⢲⡘⣶⡳⡜⣆⠳⣜⢢⠳⡜⣥⡿⠋⠀⠀⡜⣷⣄⣂⣥⣾⠟⠀ ⠀⠀⠈⠉⠀⠙⢧⡒⡄⢀⠀⠉⠛⢿⣿⣧⣹⣜⣮⣳⣌⣧⡽⠞⠉⠀⠀⢠⢸⣴⠟⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⡆⢤⡀⢀⠀⠈⠉⠉⠉⠉⠁⠀⠀⢀⠠⢤⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢥⣎⣔⣢⣰⣀⣦⣐⣡⡾⠼⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⣴⣦⣤⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⠀⠀⠀⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠛⠛⠛⠻⢿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠘⢷⡀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠈⣧⡀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠉⠉⢁⣴⣿⣿⣿⣿⣶⡀⠈⢉⣿⣧⡖⠋⠉⠉⢉⣿⣿⣿⣟⠾⣾⣿⠀⠀⢸⣧⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⢿⡄⠀⠀⣴⣿⣿⣿⣿⣿⠀⣿⣿⡀⠀⠈⢻⡀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣘⣿⣿⣿⣿⣿⡿⠃⠴⠿⣋⡜⠓⠦⣤⣿⣿⣿⣿⣿⣿⣸⡏⣿⠇⠀⠀⢸⣧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡁⠠⠒⠊⠁⠀⠀⠀⠀⠈⢙⠛⠛⢻⣱⣯⣿⡿⠀⠀⠀⢸⣿⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⢀⣿⠃⠀⠀⠀⢸⣿⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⢴⣿⠀⠀ ⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣀⣀⣀⣀⣤⣤⣦⡶⠶⠶⠶⠶⣾⠿⢿⣶⣿⣤⣤⠴⠾⣿⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡴⠛⠉⠳⣾⠟⠁⠈⢹⠛⠲⣶⣴⣆⠀⢀⣼⠀⠀⠀ ⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣾⠁⠀⠀⣰⠏⠀⠀⢠⡇⣀⠄⠉⠙⢿⣧⣾⡏⠀⠀⠀ ⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡇⠀⠀⣸⡟⠀⠀⠀⢰⡿⠋⠀⠀⣰⡏⠁⠈⢳⡀⠀⠀ ⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⠃⠀⠀⢀⣾⠇⠀⠀⢰⣿⣧⣀⡀⢀⣿⠀⠀ ⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠸⣸⠂⠀⢰⣿⡇⠀⠀⠀⣿⣿⣟⠻⠿⠛⣿⡆⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⢀⠏⠀⠀⠸⠿⠷⢄⣤⢸⣿⠁⢿⣶⣶⣶⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣴⠀⠀⠉⢩⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⢸⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣶⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣧⠀⠀⠀⠀⠻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣿⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣀⣼⡿⢿⣆⠹⣷⣄⠀⣠⣴⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠐⠒⠿⢿⣏⠀⠀⠈⣷⠿⠿⠿⠟⠛⣉⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠤⠴⠿⠋⠀⠀⠀⠙⠻⠶⠶⠖⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀

huge freaking fart!!!!!111!111!! 💩💨

(ෆ̥● ꄃ ●ෆ̥) '` (ू ͒•‧̫•ू⑅ ͒) (͒˶˙•●̫•˙˵)͒ ٩̋(ˊ ᵒ̵̶̷̤᷄ꇴᵒ̴̵̶̷̤᷅ ˋ)۶ ♡(ؔᵒ̶̷ᵕؔᵒ̷̶) ˘̴͈́ᵜ˘̴͈̀ ต( ິᵒ̴̶̷̤ ﻌ ᵒ̴̶̷̤ )ິ ૮꒰˶ᵒ̴̶̷᷄౪ᵒ̴̶̷᷅˵꒱ა ⁌꒰๑⃙⃘ˆˑˆ๑⃙⃘꒱⁍ ⋆͛*͛ ͙͛(๑•﹏•) ₍˄·͈༝·͈˄₎◞ ̑̑ෆ⃛ ꒰•·̫•꒱ྉ ˚‧(๑σ̴̶̷̥́ ₃σ̴̶̷̀ू)·˚ ꒰ •ॢ •ॢ⑅꒱ ꒰⁎ॣ●̷॔ ̴̧̇●̷꒱५₃ ( ᵒ̴̶̷̤ꈊᵒ̴̶̷̤ )✧ ·◌̊ˈ*(⁰̶̶̷ ˙̮ ⁰̴̷̷๑ॢ) Ϛ⃘๑ɞ̴̶̷ .̫ɞ̴̶̷ू꒜ ৎ •ु·̫•ूॽ♡ ꒰* ुര  ̫ രू꒱ ต( ິᵒ̴̶̷̤́ᆺ⃘ᵒ̴̶̷̤̀ )ິต દ⑅•ﻌ•૩ (  ु́•̶̤ ‧̫ ⁃ ૂ̀ )

⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣄⠀⠀⠀⠀⠀ ⠀⣴⠊⠛⠦⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠈⠳⡄⠀⠀⠀ ⠸⣿⠀⠀⠀⠉⢹⣆⠀⠀⠀⠠⡶⠖⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠈⡆⠀⠀ ⠀⠈⣧⠀⠀⠀⠀⠉⠓⠂⠐⠋⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⣤⢀⠀⠈⡇⠀⠀⠀⢹⡂⠀ ⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠁⠈⠁⠉⠻⢷⠶⠴⢭⡄⠤⡀⠀⠀⠀⠀⠀⢿⡇⠀⠈⢢⠀⣸⡇⠀⠀⠀⠐⠁⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⡀⠀⠀⠀⠀⠀⠀⣠⡚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢮⡀⡀⠀⠀⠀⠉⢳⡄⠀⡘⠛⠋⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡅ ⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣠⡴⠖⠤⠴⠤⠶⠀⢄⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣤⠞⠵⠁ ⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢰⡺⠀⠀⠀⢀⡾⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⠀⠀⠀⠀⠀⢱⠀⠀⠘⠛⢧⡀⠀⠀⣀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠖⠶⠶⠵⠃⠀⠀⠀⢺⢈⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢆⠀⠀⠀⠀⠀⠸⣄⠁⠀⠀⠈⠻⠒⠚⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⡀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢻⡁⡀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⡾⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠹⠄⠀⠀⠀⠈⢯⠀⠀⠀⣠⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⢸⡇⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⡄⠀⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣸⡁⠀⢀⠾⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡣⠀⣸⡿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣬⠛⠁⡆⠉⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢧⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣸⣤⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠖⠒⠒⠂⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠞⠛⠉⠉⠁⠁⠀⠀⠀⠈⠉⠉⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠋⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⠀⠀⠘⢷⡀⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡦⠀⠀⠈⢳⡀⠀⠀ ⠀⠀⣾⠁⠀⠀⠀⠈⠙⠋⠁⠀⣠⠴⠒⠒⠒⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠒⠦⣄⠀⠈⠙⠋⠁⠀⠀⠀⠈⢷⠀⠀ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠘⡆⠀⠀⢰⠃⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢿⡀ ⢸⡏⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢹⠀⠀⣏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⠀⠀⣇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⡇ ⢸⡇⠀⠀⠀⢀⣤⣶⣿⣷⡀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⢠⠇⠀⠀⠸⡄⠀⠀⠀⠙⠿⠿⠿⠟⠃⠀⠀⢀⣾⣿⣶⣤⡀⠀⠀⠀⢀⡧ ⢸⡇⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⠀⢸⡇ ⠀⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣾⠆ ⠀⢹⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡏⠀ ⠀⠀⢷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡾⠀⠀ ⠀⠀⠈⢷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡾⠁⠀⠀ ⠀⠀⠀⠈⢻⡄⠉⠛⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠛⠉⢠⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣤⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣤⣴⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠐⠀⠀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⡐⠊⠲⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠁⠀⠁⠐⠲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠪⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⠄⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠆⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠒⠒⠚⠈⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠂⠒⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣀⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⣿⣿⡉⠛⠿⢿⠃⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢻⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⢷⣀⡾⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠿⠿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣠⠖⠋⠀⠀⠀⣰⣴⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠏⠀⠉⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣾⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣯⡼⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⠴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠤⠤⠤⠤⠤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⠛⠛⠛⠛⠛⠃⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡘⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⢿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡾⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠉⠉⠀⣴⣾⣷⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣠⡤⠤⠠⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢸ ⠛⠓⠐⠒⠒⣲⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⠁⠀⡆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠛⣄⠀⠀⠀⠀⠘⣆⠀⠙⢤⣀⠀⠈⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣦⣀⣀⣀⣀⣈⡶⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣠⠔⠛⠒⠒⠢⠤⠖⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣾⣷⣎⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢰⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢏⣶⣶⣦⣥⣿⣿⣿⣿⠠⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣰⣛⣛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠫⢀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣟⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⢠⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁ ⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀ ⣿⣿⣿⣿⣷⣬⣛⠿⢿⣿⣿⣿⣿⠿⠿⢛⣭⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣤⣤⣤⣤⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣷⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡶⠶⢶⣦⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠷⠷⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢁⣴⣿⣶⣜⢿⣆⠀⠀⠀⠀⠀⠀⢠⣾⠿⣫⣾⣿⣿⣿⣶⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢸⣿⣿⣿⣿⣧⢻⣆⠀⠀⠀⠀⠀⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⣿⣿⣿⣿⢘⣿⠀⠀⠀⠀⢀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠸⣿⣿⣿⣿⣿⢈⣿⠀⠀⠀⠀⠀⢿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣄⠙⢿⣿⡿⣯⣾⠃⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣴⡿⠃⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠈⠻⢷⣦⣴⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣟⣛⣯⣥⣤⣾⠿⠋⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⢠⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠉⠉⠉⠀⠀⣄⠸⡄⠹⣄⠀⠀⠀⠀⢳⠀⠀⠀⣰⣿⡟⠀⠀ ⠀⠀⠀⢠⣶⠿⢿⣦⣄⡀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠸⣆⠹⡄⠹⡆⠀⠀⠀⠎⠀⢀⣴⣿⠏⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⢰⣿⠿⠿⢿⣶⣦⡀⠈⠻⣷⡿⠿⣷⣤⡘⠛⠛⠿⠻⠿⠿⠿⠿⣷⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠹⣆⠙⠦⠀⠀⠀⢀⣤⣾⡿⠟⠁⠀⠀⠀⠀ ⢠⡶⠿⣿⣿⣷⣼⣿⠀⠀⠀⠀⠙⢿⣦⣼⡟⠀⠀⠈⣿⣿⠿⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠈⣀⣀⣴⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⣰⣿⠟⠻⢿⣿⣧⡀⠀⠀⠀⠀⠙⠿⣦⣄⠀⣸⡿⠁⠀⠀⢹⣷⣤⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣠⣤⣤⣴⣾⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣦⣿⡏⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠈⠻⢿⣇⣿⠀⠀⠀⠀⣿⡝⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠛⠻⣿⣦⡀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣧⢰⡟⠁⠹⣦⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢩⡿⣿⣆⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣷⣬⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢻⣿⠛⠛⠓⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣤⣤⣤⣤⣤⣶⣶⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⢀⠉⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠭⠍⣴⠟⣸⣿⠋⣉⣠⣀⣀⠁⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⠀⠀⠀⢸⣷⣆⣞⠁⣼⠟⠀⠀⠛⢁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣾⣿⣆⣀⣾⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠉⠛⢿⣿⣿⣿⣿⣿⣿⠿⠿⠀⡄⣰⣿⣠⠉⠈⣾⡏⣦⢠⣀⣾⣿⠁⠉⠀⠸⡀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⣿⣻⣿⣿⠀⠀⢠⣼⣿⡟⠩⢀⣾⣧⣤⣿⣿⣿⣿⡇⢆⣤⠶⠿⢿⣯⣑⣰⡟⠒⠃⡴⢀⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠇⠀⠀⠀⢠⣿⣿⣯⣿⣿⣇⣼⡏⣿⡏⠀⣤⠸⢃⣿⣿⢺⣿⣿⣫⡾⠋⠀⠀⠀⣾⣿⣼⡏⠠⠀⡞⢡⠟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣼⣿⣿⣿⣿⣿⣿⣯⣤⡄⣫⣄⣾⣿⣏⣼⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣅⠂⢀⡘⣡⠯⣤⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢷⡀⠀⠀⠀⠙⠋⠙⠋⠉⠛⠛⠻⠻⠿⢿⣿⣿⣿⣿⣥⣾⡟⠁⠀⠀⠀⠀⠀⢸⣟⢻⣶⣌⡼⠃⢠⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠛⠀⠀⠀⢠⡰⠿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠦⢭⣳⠄⢠⣿⣿⣧⣰⠟⢻⣶⣔⠒⠧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢯⡹⠦⡀⠤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⡟⠒⠀⢉⣞⣾⡿⠃⣰⢏⠀⠀⠀⡈⠿⣦⣠⣤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⣷⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⣿⣷⣤⣀⠀⠺⡟⢰⡶⠅⠚⣻⠄⡀⠀⠘⠛⣰⣥⣤⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣼⣷⣼⣧⣶⣄⣙⡀⠀⣠⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠘⠛⠋⢷⡀⠀⠁⠀⠉⠉⠉⠀⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿ ⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⢾⣿⠿⠃⠀⠀⠀⠀⠀⢄⠀⠀⠀⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⣿⣿⣿⣿ ⠀⠀⠀⠨⠽⢿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣠⣀⣀⠒⢂⡉⣼⡄⣈⡁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢹⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿ ⣀⠀⠀⠀⠀⠰⠈⠿⢌⡛⠛⢻⣿⣿⡟⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠿⠛⠛⠻⠿⠿⠿⠿⠿⢷⣦⣶⣾⣦⡀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿ ⢛⣦⣄⠀⢀⠀⠀⣤⡀⠁⠠⣦⣙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿ ⣿⣿⣿⣿⣾⡃⠀⠙⠛⣶⠀⢔⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⣿⣿⣿⣿⣿⣿⣿⣦⣀⡁⣶⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⢈⡠⠄⠀⠀⠀⠀⠀⠂⠀⠀⡁⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣌⡑⠠⡈⠢⡀⠀⠀⠀ ⠀⠀⡠⠃⡴⠃⣤⠶⠶⣤⣄⣀⠀⠀⡠⠛⠉⠉⠉⠉⠓⢄⠈⠢⠈⢂⠀⠀ ⠀⡰⠀⡎⠀⠀⠁⢀⡴⠦⡀⠀⠀⡜⠀⠀⢀⣀⠀⠀⠀⠀⢳⣀⠁⡀⢣⠀ ⢠⠁⠀⠀⠀⠀⠀⠸⣔⣴⠃⠀⠀⠁⠀⢰⠁⠀⡆⠀⠀⠀⠈⡿⣄⠐⠀⡆ ⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢷⡄⠈⠢⠘⠀⠀⠀⠀⡼⠟⠙⣆⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⡀⠀⠀⢀⡠⠞⠁⠀⠀⢹⠀⢸ ⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣸⠀⡸ ⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠇ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡜⠀ ⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁⠀⠀⢹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠒⠒⠒⠒⠒⠲⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣄⠀⠀⢀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡆⡙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⢿⣿⣿⣶⣼⡇⠀⢰⣶⣿⣿⣿⠿⣿⣿⣃⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣿⣿⡇⡄⠘⠛⠉⠁⠀⠀⠨⠿⣿⡄⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣷⠃⠀⠀⠀⠀⠀⠀⣠⣄⣿⣿⡆⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢨⢰⠛⠁⠀⠙⠓⣦⣀⠀⠀⢠⠏⢻⠀⠀⠀⠀⠀⣀⣾⠟⢋⠉⢹⣷⡆⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⣿⣿⣶⠿⢶⣼⣦⡴⠶⣾⣿⣿⡟⢀⠀⣰⣿⣹⡇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠽⣦⡄⠀⠀⠀⠈⣉⣠⡴⢿⣻⣿⣦⣤⣀⣉⣀⡴⠞⣿⠻⣷⣿⠁⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣟⡲⠶⢒⣛⣭⣽⠾⠛⠉⠉⠙⠳⢯⣭⣽⣿⣿⣯⣾⠿⡋⠀⣿⡀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⢋⣩⣤⣶⣿⣿⣆⠙⣿⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⣿⣏⢟⣿⣿⠏⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⣀⣀⡤⠤⠴⠦⠤⣄⣀⣀⡀⠀⠀⢀⣀⣠⣴⣶⡯⠵⣿⠿⣿⣽⣿⣿⠃⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢹⣄⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠭⢿⣀⣀⣸⣀⣠⣿⣜⣿⠿⣛⣡⣤⣤⣴⣿⠏⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣙⣆⠀⠀⠀⠻⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣩⣭⣽⠿⠛⠛⠛⠙⣣⣿⠏⠀⠀⠀⣴⢊⡼⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⣿⣷⠄⠀⠀⠙⢷⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡶⣿⡿⠋⠀⠀⠀⠈⠻⡏⠀⠀⠈⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠛⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⢙⣧ ⠀⠀⣰⣀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣾⣿⠛⣻ ⠰⣤⣿⣿⢳⣦⣀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣶⣦⣴⡴⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⣿⡧⠼⠼⠟ ⠀⠘⠺⠷⠿⠿⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠿⣿⣯⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣻⣿⡿⠿⠿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣬⠋⠩⣤⣴⣾⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠿⣄⠀⠘⠟⠛⠛⠿⢦⣄⡀⠀⠀⠀⣼⣏⣤⠀⠈⠷⠤⠛⠃⠀⠀⠀⠀⣟⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⣽⣿⡄⠀⠀⠹⣮⡛⢦⡄⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣍⠳⢦⣄⣀⣀⣀⡤⠤⠴⠶⠶⢿⣿⣷⡆⠀⠀⠈⠙⢦⡉⠉⠉⠉⠉⠉⠉⢉⣀⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⣀⣀⣀⣀⣤⣤⣴⠿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠓⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠉⠁⠒⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠁⠀⠐⣿⣿⡿⠿⠆⠀⠀⢠⣬⣷⣤⡄⠀⠀⠀⠀ ⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢄⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢳⡈⢆⠀⠀ ⠀⠆⠀⠀⠀⠀⠀⢠⠔⠂⢩⣿⣿⣯⠉⣿⠚⢉⣽⣶⣺⡇⠘⡆⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠻⠿⠟⠰⠗⠑⠺⠿⢿⣿⡇⠀⣷⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠹⠃⠀⣹⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠋⢉⠝⢿⠟⠺⠽⣠⠀⡆⠀ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⢠⠇⠀⡷⠀⣸⠛⢅⠀ ⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⣼⠁⢰⣿⠲⣺⠀ ⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢹⠄⠉⣝⠀ ⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⡜⡇⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠘⡀⠀⣠⡼⠓⣽⣤⡴⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠃⠀⠈⢀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣤⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣿⣶⣽⣧⡀⠀⠀⠀⠀⣴⡾⣿⣿⣿⣷⣦⣉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⣿⣿⣿⡏⣧⠀⠀⠀⢰⡿⢰⣿⣿⣿⣿⣿⣿⣦⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢻⣿⣿⣿⡗⣿⠀⠀⠀⠸⣷⡸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣌⠻⠿⣿⣷⠇⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⠟⠁⣠⡾⠃⠈⠑⢤⡀⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠽⠷⠶⠟⠋⡀⢀⠀⠀⠀⠹⡄⠀⠀⢠⣿⠇⠀ ⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢧⠱⡈⢧⠀⠀⠀⠇⠀⣠⣿⠋⠀⠀ ⠀⠀⢀⣿⠀⣼⡿⠿⠶⣦⣄⠘⢿⡶⠷⢦⣌⠛⠛⠛⠷⠶⠶⠶⠄⠀⠙⢄⠀⠀⠀⠀⠈⢧⠙⠆⠀⢀⣀⣴⡾⠟⠁⠀⠀⠀ ⢠⡞⢛⣿⣷⣿⣇⠀⠀⠀⠹⢷⣿⠁⠀⢨⡿⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢀⣀⣤⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⢸⣄⣿⠋⠈⠙⠻⢦⣄⠀⠀⠀⠙⢷⣦⣟⡅⠀⠀⢹⡿⠶⠶⠶⢶⡶⠶⠶⠶⠶⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠛⢿⣧⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣼⡁⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣟⣻⣤⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⠛⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀ ⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⡆ ⢸⣿⠃⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⡈⠀⠀⣿⣧ ⣾⣿⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⡇⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠇⠀⠀⠀⡸⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⣿ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣾⡿ ⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢰⣿⠇ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⣿⡟⠀ ⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀ ⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⠟⠁⠀⢀⣿⡟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⣿⣶⣶⣾⣿⣿⠃⣿⣿⣿⣿ ⣿⣿⡿⢿⣿⣿⠁⠀⣿⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿ ⣿⡟⠀⢿⣿⣿⣆⠀⣿⣿⠁⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿ ⣿⣷⡄⠘⣿⣿⣿⣧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿ ⣿⣿⣿⡄⢻⣿⣿⡿⠿⠛⠛⠂⠤⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⡇⢸⣿⣿ ⣿⣿⣿⣇⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿ ⣿⣿⣿⠟⠋⠉⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿ ⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿ ⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿

⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀ ⠸⠀⠀⠘⡀⠀⠀⠀⢀⠔⠁⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⢃⠀⠀⠡⠀⠀⠠⠁⠀⠀⠈⠙⣿⣶⣶⣦⠀⢠⣤⣤⣤⣤⣄⡀⠀⠣⠀ ⠀⠈⠆⠀⠀⠡⢀⠃⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠈⠁⣿⣿⡇⠉⠁⠀⠀⢃ ⠀⠀⠈⠄⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠸ ⠀⠀⠀⠈⢆⠀⠀⠐⡄⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢂⠀⡠⠜⠁⣰⣤⠀⠀⠀⠛⠋⠛⠻⢷⡄⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠫⣀⣴⣾⣿⠛⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁ ⠀⠀⠀⠀⠀⠠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⠁⢤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⢀⡠⠃⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⢞⢦⡀⠀⠀⠀⠘⢷⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢞⢲⡀⠀⠀⠀⠀⠀⠀⠈⠺⣐⢀⠀⠀⠈⢞⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣷⣀⠀⠀⠀⠀⠀⠀⠱⣝⣦⣄⠀⠀⠀⠀⠀⠀⠘⠲⡁⡀⠀⠀⠉⢾⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠻⣾⡳⡀⠀⠀⠀⠀⠀⠈⠹⡺⡐⡀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⢽⡾⣄⠀⠀⠀⠀⠀⠀⠘⢪⠮⠢⠀⠀⠑⢷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢵⣄⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠈⠳⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠚⢾⣦⡀⠀⠀⠀⠀⢀⣀⣩⣖⣶⡶⣽⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣦⡀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠙⢟⢦⣄⢀⣶⡿⣿⡿⠟⠉⣩⠿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠻⣄⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡳⠛⠁⠀⠀⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠜⢲⡀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⢻⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢂⡙⢦⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠐⣌⢳⣆⠀⠀⠀⠀⠀⠀⠙⠳⢄⣤⣶⣿⡿⠂⠀⠀⠀⠀⠀⠀⣬⣟⣛⣿⣷⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣦⠀⠀⠀⠀⠀⠒⣽⡧⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⡷⣀⠀⠀⠀⠀⠘⠪⣺⢦⡀⠀⢀⣾⡏⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢻⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢯⣶⡀⠀⠀⠀⠀⠈⠻⣷⣄⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠘⢿⣢⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⣀⣀⣀⣀⣸⣿⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣻⣺⣿⣿⣿⣻⠃⠀⠐⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢀⣶⣶⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣀⠀⠀⠀⠀⣴⣿⣿⠛⠊⢉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠓⠛⠛⠿⠿⣻⣷⣄⠒⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠀⢰⣿⡿⠁⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣷⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣶⣿⡟⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠄⠀⣸⣿⠠⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⣂⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡿⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢵⣅⣾⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣟⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⡾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢠⣤⣠⣴⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠷⣺⣾⣿⣧⣶⡤⣤⢤⢴⢴⢶⡶⣶⣒⣖⣲⣲⣿⣷⣶⣾⣿⣿⣿⣿⣿⣙⣟⣿⣻⢿⣿⣓⣽⣿⣭⣯⡶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠛⠻⠳⠟⠿⠛⠛⠛⠛⠛⠙⠙⠙⠋⠋⠙⠚⠒⠉⠈⠉⠉⠙⠋⠉⠙⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⡷⠛⠉⠉⠙⢶⡄⠐⠃⣿⡟⠃⠉⢀⣶⠿⠿⠷⠿⠟⣴⡄⠀⠀⡠⣠⡶⠂⠀⠛⠛⠛⢻⡟⠛⠛⠀⠀⡆⠀⠀⠀⣤⡄⠀⠰⣆⠀⠀⠀⠀⠀⠀⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣟⠀⠀⠀⠀⠀⠈⣿⡀⢸⡇⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⡻⡒⢉⣴⠿⠙⣤⠶⠦⡄⠀⠀⠀⣿⠀⠀⠀⠀⣾⣿⡄⠀⢸⠽⡇⠀⠀⠹⣦⠀⠀⣀⣶⢟⣧⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀⢠⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⣴⡶⠦⠶⠦⠤⠀⠀⠀⣴⡾⠛⠓⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠙⡇⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⣧⡿⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡧⡇⠹⣇⠀⣯⡇⠀⠀⠀⠀⠙⣿⠏⠀⢰⠏⠔⠈⠀⠈⠹⢦⡀⠀⣯⠀⠀⠀⠀⠀⠀⠀⢳⣟⡇⠀⠀⠈⡇⠘⡿⠀⠀⠀⠀⡿⠀⠀⣰⠶⢗⣦⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠨⢛⢀⠇⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⡿⣦⡀⠀⠀⠀⠉⠙⣧⠀⠀⠀⣟⣇⠀⠀⠀⣵⡇⠀⠻⣧⣿⡂⠀⠀⠀⠀⠀⣿⠀⠀⢸⡎⠀⠀⠀⠀⠀⠂⠪⣧⣸⣿⡄⠀⠀⠀⠀⠀⠀⣇⡇⠀⣤⡮⠋⠀⢽⣇⣀⣀⣀⣯⡀⣟⠇⠀⠀⠀⠳⣄⠀⣿⡆⠀⠀⠀⠀⠀⠐⣟⠔⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⢧⡀⠀ ⢠⣿⠀⠀⠀⠀⢀⣼⡷⠁⣽⡇⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠫⢷⣀⠀⢀⣤⡧⠃⠀⠀⣼⡿⠀⠀⠀⣿⠇⠀⠀⠩⣿⡅⠀⠀⠀⠀⠀⢸⡇⠀⠘⡷⡀⠀⠀⠀⠀⠀⠀⣮⠛⣽⣧⠀⠀⠀⠀⠀⡠⡏⣿⡏⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⣯⢸⡏⠀⠀⠀⠀⠀⣇⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠉⠉⠛⠛⠋⠉⠉⠴⠖⠗⠐⠒⠛⣿⣧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠕⢦⡀⠀⠀⠀⣗⣿⡀⠀⣼⡏⠀⠀⠀⠀⠛⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠯⣶⣒⣒⣐⣮⠏⠀⠈⠻⣟⡤⣤⣤⡾⠋⠀⡯⠻⣆⠀⠀⠀⠀⡟⠀⠀⠀⠀⢼⡇⢹⡣⡀⠀⠀⠀⣜⠌⣿⠇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⠛⠛⠛⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠀⠀⠀⢻⡅⠀⠀⠀⠀⢿⠀⠘⠧⠵⠟⠋⠀⠀⠙⠛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠉⠉⠀⠀⠠⠗⠚⠋⠁

⠀⠀⣠⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠈⣇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣤⣤⣤⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⠀⠀⢳⠀⠀⠀⠀⠈⣆⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠛⠛⠀⠀⠘⣿⠿⣿⣿⣿⣿⠿⣿⣿⡆⠀⠀⠀⠹⡀⠀ ⠀⠀⠀⠈⢇⠀⠀⠀⠀⠘⣆⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠳⣄⠖⢲⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⡴⠋⠀⠀⣱⣄⡀⠀⠀⠀⠀⠈⠛⠋⠉⠛⠻⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⠚⠁⠀⢀⣴⣿⣿⣿⣿⠒⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣠⣶⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⠀⠀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⣰⣦⣴⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⢀⡉⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠙⣆⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⣻⣿⣿⣿⡛⠛⠲⣿⣀⠴⠶⠶⣶⣤⣤⣤⣿⡆⠀⢹⡆⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⢠⣿⣧⠀⠀⣴⣿⣿⣿⡇⣿⣧⠀⠀⢿⠀⠀ ⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠬⠿⠿⠿⠿⠏⠐⣛⡥⠉⠓⠾⢿⣿⣿⣿⣧⣿⡿⠀⠀⢸⡆⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⠷⠛⣿⠇⠀⠀⢼⡇⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋⠀⠀⠀⣸⡇⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣄⣠⡀⣀⣠⣄⠀⠀⠀⢻⠇⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⢀⡴⠛⢯⣿⠛⠙⡿⠦⣭⣠⡀⠀⣼⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠀⠀⣼⠁⠀⢰⣀⡄⠈⠻⣷⢼⡇⠀⠀ ⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⢸⠇⠀⠀⣸⠏⠀⢀⣾⠁⠀⠹⡄⠀ ⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⣿⠀⠀⣴⡏⠀⠀⣾⣿⠷⣶⠾⣧⠀ ⠀⠀⠀⠀⠈⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠆⠀⠟⠀⠀⠿⠓⢠⡄⣿⠙⢷⣴⣶⡿⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠆⠀⠀⣼⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⣶⣶⣶⣶⣶⣦⣤⣼⣧⠀⠀⠀⠀⠀⠀⢀⣿⠀⣇⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⡄⠀⠀⠀⣀⣤⡿⠛⢧⣹⣦⣀⣴⣾⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⣈⣉⣿⠆⠀⠀⠿⣍⣉⡩⠴⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠂⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿ ⢈⣿⣿⣿⣿⣿⣿⣯⡀⠀⠈⠻⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠛⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⢿⡻⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⠉⠀⠐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⣶⣤⣀⢀⠀⢀⣤⣾⡟⠦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠉⠉⠹⣿⡀⠛⠉⠙⢧⡀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠐⠀⠒⣤⣀⣝⡀⣀⣠⡞⢉⣧⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⣀⡈⣥⡺⠿⣬⣭⣾⣿⡟⡄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣛⢭⣿⣷⠸⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠐⠒⠒⠒⠂⠤⢤⡒⡚⣻⣹⢿⣃⣠⠇⠀⢀⠀⠀ ⠀⠀⠀⣵⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢉⣽⠏⠀⠰⠋⠢⡀ ⠀⢠⠀⠘⡆⠀⠀⠑⠦⣄⣀⣀⣀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⡤⢼ ⠈⠻⠽⣢⠇⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠻⠇⠉ ⠀⠀⠀⠁⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⢰⣿⣷⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠀⠀⠀⠀⡘⢻⠽⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠁⠫⠑⠚⠓⣤⡀⠰⣧⡈⠒⠋⠉⢹⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠩⢗⠀⠀⠒⣒⣿⠷⠀⠉⠫⠀⠨⠭⠽⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⠀⠀⠀ ⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀ ⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⡄ ⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⠈⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣿⣿ ⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢀⣿⣿ ⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⣿⡏ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢀⣿⣿⠃ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀ ⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢼⣿⣿⣷⣦⣄⣀⡄⠀⣀⣤⣶⣿⣿⣿⠄⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⡇⠀⠿⠟⠋⠉⠙⣿⣇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⢠⣤⣿⣦⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣜⠁⠀⠈⠑⣦⣄⣀⡎⢹⠀⠀⣀⣠⣼⡏⠁⢀⣿⡆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠙⠛⣋⣽⣿⣿⣉⡙⠛⢋⣤⣶⣿⣽⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣟⣶⣶⣒⣫⡽⠞⠋⠉⠛⠯⣽⣿⣾⣿⡾⣟⠀⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢉⣥⣶⣿⣿⡧⠹⣷⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠘⣆⠀⠠⠈⠉⠀⠀⠀⠀⠉⠉⠑⠺⠿⣿⣉⣉⡇⣠⣷⣾⠿⢛⣡⣤⣴⡿⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣦⡀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣭⠽⠟⠛⠋⢉⣷⡿⠁⠀⢀⣾⠟⠳⣄⠀⠀ ⠀⠀⠀⠀⠘⣿⡟⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠏⠀⠀⠀⠀⠹⠀⠀⠈⠳⣄ ⠀⢀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⢰⠀⣠⣶⡾⢿ ⠰⣼⣿⣲⣤⡀⣹⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⡷⠶⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⡤⠧⠏ ⠀⠙⠛⠛⣱⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⣷⠿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⡋⠋⠽⠽⢷⣤⣀⠀⠀⠀⢠⡏⡀⠘⢤⡸⠿⠛⠋⠙⣶⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠉⠀⠀⠀⠀⠀⢽⣷⡀⠀⠸⣝⠳⣄⠀⠀⠀⣀⣀⣠⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡓⠦⠤⠤⠤⠒⠒⠚⣻⣿⣷⠀⠀⠈⠙⢎⡉⣉⣁⣀⣀⡤⠶⠿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⣄⣀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣀⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⣀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢳⡀⠀⠀⠀ ⠀⢀⡞⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⡄⠀⠀ ⠀⡜⠁⣾⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⢶⣦⣄⡀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣷⠀⢳⠀⠀ ⢸⠁⠘⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⣇⠀ ⡏⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠛⠛⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡟⠀⠀⠀⢻⠀ ⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀ ⡃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⠁ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣗⡒⠤⠤⢄⣀⣀⣀⣀⣠⡤⠤⠖⣺⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣄⣀⣀⣀⡀⠀⣀⣀⣀⣠⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡾⠟⠛⠛⠛⢃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀ ⠀⠀⠀⠀⢠⠋⠟⠀⠀⣠⣤⠀⠀⠛⠋⣽⣍⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⢀⣀⣀⣀⣲⠀⠀⠸⣿⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠓⠀⠒⡆⠀⠘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⣾⡿⠀⠀⠀⠀⡇ ⠀⠀⠀⠹⠀⠀⠆⠀⠀⠀⠐⢹⠀⠀⢠⣤⣤⣶⣾⣿⠟⠋⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠁⠀⠈⢂⠀⠀⠰⡀⠑⠄⡈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀ ⠀⠀⠀⠀⠀⠎⠉⠈⢭⠉⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠤⠐⠁⠀⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⣶⣾⢿⡿⣿⣟⡿⣿⢿⡿⣿⣟⡷⣶⢶⣦⣤⣄⣀⡀⢀⣴⣶⡶⣶⢶⣦⡀ ⠀⠀⢸⣟⣷⢯⣿⣻⢷⣯⢿⣯⢿⣽⣷⣻⢿⡽⣟⣾⣽⣻⢿⡅⢸⣿⣳⡿⣯⣟⣿⠆ ⠀⠀⣸⣿⣼⢿⣧⢿⡿⣼⣿⣻⢿⣼⢧⣿⣟⣿⢿⣻⣼⣟⡿⡇⢸⡿⣧⣿⣻⢿⣼⠄ ⢠⣾⣿⣳⣯⣿⢾⡿⣽⣟⣾⡽⣟⣯⣿⢾⣽⡾⣟⡿⣾⣽⣻⡅⢸⣿⣽⢾⣻⣯⣿⠂ ⠈⢿⣞⣷⣟⡾⣿⡽⣟⣾⢯⣟⣿⣳⣯⡿⣞⣿⡽⣟⣷⣯⢿⡅⢸⣿⣞⣿⣽⣞⣿⠄ ⣠⣿⣟⣾⣽⣻⢷⣟⡿⣽⣻⣟⣾⣽⣳⣿⣻⢷⣟⣿⣳⣯⢿⡃⢸⣷⢿⣞⣷⣯⣿⠄ ⢻⣟⣾⣽⢾⣻⣟⣾⣟⣿⣳⣯⣟⣾⣟⣾⡽⣿⣞⣯⣷⣟⣿⡃⢸⣿⣻⢾⣻⡾⣽⠆ ⢠⣿⣻⢾⡿⣽⣾⣻⢾⣳⣟⣷⣯⡷⣿⣞⣿⣳⣯⣟⣾⣽⠾⠇⠸⣿⣽⣻⢷⣿⣻⠇ ⣿⣿⣹⢿⣹⡿⣾⣹⡿⣏⣿⡾⣷⣿⢷⣏⣷⡿⣷⣏⡿⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀ ⠙⣷⢿⣻⣽⢿⡽⣷⣟⡿⣞⣿⣳⣯⡿⣯⢿⣽⡷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠋⠙⠃⠋⠙⠙⣷⣟⡷⣟⣿⣻⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⣟⣿⣳⢿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣯⡿⣞⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣾⣽⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣽⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣾⡽⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠂⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢀⡀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣷⣦⡀⠈⠓⢄⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⣴⠟⠁⢀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠋⠉⠉⠉⠉⠛⠿⣦⡀⠀⠙⢤⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⢠⠾⠁⠀⠸⡿⠋⠁⠈⠙⠛⠿⠿⠶⠗⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⣦⠀⠀⠱⡄⠀⢳⡀⠀⠀⠀ ⠀⢀⡾⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⡄⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⠀⠀⠘⠀⠀⠱⡀⠀⠀ ⠀⡜⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⠋⡀⣀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⡴⠋⠈⢳⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠘⡄⠀⢳⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣥⣾⠏⠀⠀⠀⠀⣇⠀⠀⠀⢸⡁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⣿⢻⣧⡀⠀⠀⠀⣇⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠘⢿⣦⡀⠀⠈⢷⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⠎⠙⣷⠀⠀⠀⢹⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠁⠀⠀⢹⣇⠀⠀⠈⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠁ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣼⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠙⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡾⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠁⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣶⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣷⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⡟⠛⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⢃⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠘⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣀⣀⢰⡟⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠐⠤⣄⣈⠉⠳⢦⣀⢩⣿⣿⣿⣦⡀⠀⠀⠀⣰⠁⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡳⡀⠀⠈⠻⢿⡟⠉⠻⣿⣦⡀⣰⠇⣠⣾⣿⣟⠋⠉⠉⠁⢹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠘⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⣦⣴⠉⠛⠟⠃⠘⠿⡿⣿⡿⠃⠀⠀⢀⣸⣷⡶⠷⠀⠀⠀⠀⠀⢸⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠄⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇ ⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣇⠰⠀⠀⠀⠀⢻⠛⠓⠶⣤⣄⠀⠀⠀⠀⠙⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟ ⠀⠀⠀⢀⣾⠟⠉⠉⠉⠛⢿⣦⠀⠀⠀⠀⠸⡄⠀⠀⠈⠛⣷⣄⠀⠀⠀⠈⠳⣍⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⠀⠀⠀⢺⡏⠠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠈⠷⣤⡀⠈⠉⠛⠛⠶⠶⣤⠤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃ ⠀⣤⣴⣿⢀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢀⠈⠻⣷⣦⣄⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⠀ ⣰⡿⠋⢹⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠳⣤⣀⣉⠙⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀ ⣿⡇⠁⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡗⠀⠀ ⠸⣷⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀ ⠀⢿⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠯⠀⠀⠀⠀ ⠀⠀⢿⣆⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣦⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⣷⣍⠛⠳⠶⠶⠶⠶⠶⢟⣿⣿⡟⠻⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡦⣤⡤⣶⡾⠟⠋⠁⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠙⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣶⣖⢂⢒⡐⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⠵⠒⣩⠟⠛⠙⠂⠀⠀⠉⠒⢤⣾⣖⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠄⣀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⠁⠀⠀⠈⠱⡄⠀⠀⡠⠃⡜⠀⠀⠀⠀⢀⣾⠗⠋⠛⢆⠀⠀⠀⣠⣤⣤⡄⠉⢢⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠱⠀⢠⠃⢠⠃⠀⠀⠀⠀⢸⠋⣠⣤⡀⠘⡆⠀⢰⡿⠋⠉⠳⣄⠈⣆⠀⠐⡄⠀⠀⢀⠔⠂⠐⠲⢄⠀⠀⠀ ⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⢃⠆⠀⠀⠁⠀⠀⢄⣀⣹⠀⣷⣼⣿⠀⢻⠀⢿⣖⣹⣷⡀⠈⡆⠈⠀⠀⢰⡀⠰⠃⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠈⣆⠤⠤⠤⠤⠾⣼⡀⠀⠀⠀⠀⠀⢀⡀⠂⠙⠻⡓⠋⢀⡏⠀⠀⢿⢿⡽⠃⠀⡜⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡠⠁⠀⠀ ⠀⠀⢀⠔⡩⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠊⠁⠙⢕⠂⠀⠘⡖⠊⠀⠀⠀⠀⠑⡤⠔⠊⡉⠐⠀⠀⢀⣰⡼⠤⠤⠤⢄⣰⠁⠀⠀⠀ ⠀⡰⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣲⠖⠤⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠒⢧⡀⠀⠀⠀⠀⠘⣷⣀⠉⠑⠒⠂⠒⢐⣦⠖⠋⠀⠀⠀⡗⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠸⣿⣷⣦⣤⣤⣤⣾⠇⠀⠀⠀⠀⡴⠛⠉⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⢠ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⢀⠞⢄⠀⠀⠀⠀⠀⠘⢾⣿⣻⣿⣿⡟⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢎⠀⠈⠢⡀⠀⠀⠀⠀⠈⠛⠿⠿⢛⠁⠀⠀⠀⠀⠈⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⢤⡀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠉⠓⠦⣀⣁⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠈⢿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢛⣛⡛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡟⠁⠀ ⠀⠀⢸⣿⣿⡀⠀⡔⠉⠀⡴⢏⠉⣠⠿⡟⢦⡀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⢀⡖⠉⠹⣿⣷⣄⠀⠑⢄⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀ ⠀⠀⠈⣿⣿⡇⠀⣇⠀⣰⠃⢸⡞⢁⣼⣿⠀⢳⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠘⣆⠀⣰⠇⣿⡎⢳⣄⠀⢣⠀⠀⠀⣸⣿⣿⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⠀⠈⠀⣿⡶⠋⣴⡟⠁⣿⣓⡾⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠈⣿⣥⣴⡟⣿⡀⠙⢦⡾⠀⠀⢀⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣧⡀⠀⠈⠳⣾⣿⣿⣶⡿⠟⠁⠀⣠⣿⣿⣿⠿⠿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⡦⠞⠀⠀⢀⣼⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣦⣄⣀⣀⣈⣉⣉⣀⣀⣤⣾⣿⣿⠟⠁⠀⠀⠙⢿⣿⣿⣦⣄⣀⣈⣉⣉⣁⣀⣀⣤⣴⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢅⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠈⠉⢉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠁⠀⠈⠁⠈⠁⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⣨⠗⠦⣤⣀⣀⠀⠀⠀⠀⢀⣀⣠⢖⣴⣯⡅⠀⠀⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠠⠭⠶⠀⠨⠩⠿⠿⠿⠛⢻⠟⢋⠴⠿⠟⠛⠥⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⠋⠙⠳⣤⡀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀⣠⡴⠟⠛⣷⠀⠀ ⠀⠀⠈⠳⢤⣀⢈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣀⣠⡴⠋⠀⠀ ⢀⣠⣤⣄⣄⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣡⣤⡴⣦⣀ ⢹⣅⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢀⣠⠏ ⠀⠈⠙⠉⢋⣉⣇⠀⠀⣾⣷⠄⠀⡀⠀⠀⠀⡀⠀⢴⣿⡆⠀⢀⣿⡙⠋⠋⠀⠀ ⠀⠀⢤⠶⠋⠉⢈⣦⡀⠈⠉⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠀⣠⣎⠈⠉⠛⢷⡀⠀ ⠀⠀⠻⣤⣤⠶⠋⠀⠈⠑⠠⠄⣀⣀⣀⣀⣀⣀⡀⠤⠐⠉⠀⠈⠻⠶⠖⠶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⡀⠀⡠⠤⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠁⠀⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠤⡀⠀⡠⢄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⣀⣀⣈⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠀⣎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⣸⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🩷 qui s'en soucie vraiment 💙 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿ ⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣤⣤⣶⣶⣦⠀⠀⠀⠀⢠⣴⡾⢿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢋⣥⣴⣶⢶⣦⡁⠀⠀⠀⢀⣴⣟⢶⣶ ⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠛⠛⠛⠀⠈⠀⠀⠀⠀⋠⠛⠩⠤⠤ ⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠞⠃⠀⠀ ⣾⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠒⠚⠛⠛⠀⣼ ⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠖⠀⢰⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿ ⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠻⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿ ⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿ ⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢤⡄⢀⣤⠀⠀⣠⣤⡄⢠⡄⣤⣤⣄⠠⣤⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣷⣼⠃⠀⠸⣏⡐⣶⢸⡇⣿⢤⣿⠸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠈⠁⠉⠀⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀ ▶︎ •၊၊||၊|။||||။‌‌‌‌‌၊|• 0:10 💗💙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢶⡲⠛⠽⠯⠽⠯⠿⠹⢖⡶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⠟⣋⣁⠄⡐⢀⠂⠄⠂⠄⡐⠠⠀⠄⣈⣙⡫⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣞⠟⣣⡾⠛⣉⣉⡛⢶⡄⠌⢠⠉⡐⠠⢡⡾⢛⣩⣉⡛⢷⣝⠫⡗⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⡇⡁⢦⣏⢰⡏⠉⣿⣿⡆⣻⡌⠀⢆⠠⣁⡿⢰⠋⠹⣿⣿⡄⣻⡤⢈⢫⠷⡄⠀⠀⠀ ⠀⠀⢠⢿⣸⢃⠸⢸⣇⠿⠧⠼⠿⣻⡧⢸⢃⠛⣀⠤⡘⡧⢼⣧⠼⠿⠻⠧⣸⡇⠜⣀⡿⡸⡄⠀⠀ ⠀⢠⡟⢦⡹⢌⡸⣔⢶⣲⡖⣦⠔⡠⢂⠍⡎⡘⡄⠦⡑⢍⠰⣀⠦⣴⢲⣶⣲⠬⡍⢆⢯⡱⣛⡄⠀ ⢠⡿⣘⢣⡜⢪⠴⡌⢎⡡⠜⡄⣊⠱⣈⠒⠤⡑⢌⠰⡁⢎⠰⡐⢢⠌⡱⠢⣅⠳⣌⠳⣌⠶⣡⠿⡀ ⣸⠵⡩⢊⡜⣡⠞⡘⣤⣵⣮⣶⡶⢃⠉⡍⢩⠉⠍⡩⢉⠍⢩⠐⢷⣾⣴⣵⣨⠱⡌⣧⢩⠘⢕⡚⣇ ⣟⠼⣁⠧⣊⣽⣾⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠊⠘⣿⣿⣿⣿⣿⣷⣧⣣⢚⡌⣝⢺ ⣿⠸⣉⢯⡙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡜⢫⡜⡌⣿ ⣷⡡⣏⠦⣙⠼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠧⡙⣥⢺⢄⣻ ⢱⣇⢸⢎⡱⣊⢽⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡟⡸⣑⠦⡏⣸⡇ ⠈⣟⡄⢫⠖⡥⢎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡜⡱⠜⡼⢠⣷⠀ ⠀⠘⣽⡌⢳⡜⡢⢕⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡘⠲⣍⡝⢡⢯⠃⠀ ⠀⠀⠘⣾⡄⢳⡍⠚⣴⢩⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⢱⢢⡍⢳⡜⢠⣿⠃⠀⠀ ⠀⠀⠀⠘⢿⡦⣙⢣⡓⢮⡘⢭⢛⡿⣿⡀⠀⠀⠀⠀⠀⠀⣿⢿⡛⣍⡚⢥⢎⡹⢆⣱⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣣⡙⢦⡙⢦⢋⡶⠱⡌⡟⠯⣍⠻⡻⢱⠩⣖⢱⠸⣘⠣⢎⣵⡮⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢵⡼⣂⡅⠊⠝⠛⠼⠳⠬⠳⠗⢋⠋⠱⢈⣅⢧⡻⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⠶⣞⣖⣦⣤⣥⡖⣶⠮⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⡤⢤⡀⢠⡀⠀⠘⠡⠀⢀⡀⣀⡄⣄⡄⣄⠀⠀⠀⠀⠀⢀⠀⢸⢹ ⠀⠀⠀⠀⠀⠤⢠⡀⢿⣿⣿⣿⣿⠇⢀⣠⣤⣀⣀⣤⣄⡁⢿⣿⣿⣿⣿⠇⢀⡀⠀⠀⠇⠀⡂⠈ ⠀⠀⠀⠀⠀⠰⠈⠁⠈⠻⣿⡿⠋⠀⣾⣿⣶⣿⣿⣶⣝⣷⠈⠻⣿⡿⠋⠀⠈⠡⠆⠀⡇⢀⠂⠀ ⠀⠀⢀⣠⣤⣤⡄⠀⣠⡀⢰⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠀⢠⠌⢀⡄⠀⣠⣤⣄⣀⢇⡎⠀⠀ ⢀⡀⠸⣿⣿⣿⡏⠀⠘⣴⣺⡗⠃⠀⠀⠈⠻⣿⣿⠟⠁⠀⠒⢾⠇⡞⠃⠀⢿⣿⣿⣿⠏⠀⠀⠀ ⣾⣿⣦⣌⠙⠛⠀⠀⠀⠙⠈⠁⠀⠀⢀⣀⣀⣉⣁⣀⣀⠀⠀⠚⠸⠏⠀⠀⠈⠛⠋⠁⣠⣴⣿⡆ ⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣠⣶⣾⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣶⣦⣄⣀⣀⣀⣤⣶⣾⣿⣿⣿⣷ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀ ⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀ ⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀ ⠀⢠⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣷⡀⠀ ⠀⢸⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⢀⣴⣾⡿⣛⠛⠃⠀⠀⠀⠀⢸⣿⣿⡂⢰ ⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡷⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⢸ ⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢈⡼ ⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠐⡇ ⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⢀⣐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⡇ ⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠙⠻⣿⣷⣶⣶⣶⣶⣶⣶⣿⡿⠏⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⢐⡽ ⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠉⠹⠟⠛⠻⠿⠛⠁⠀⠀⠀⢀⣤⣾⣿⡿⠃⠀⠀⠀⡼⠃ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⠟⠋⠉⣩⣽⣟⣻⣙⠛⡛⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠃⠀⢔⣿⠟⠛⠉⠁⠱⡆⠀⠀⠠⡔⠒⠒⢤⠀⠉⢿⣿⣿ ⣿⣿⣿⡅⠀⠀⢡⢡⣶⣿⣿⠛⣶⣤⠀⠀⠀⣤⣤⣦⣤⠁⠀⠘⣿⣿ ⣿⡿⢩⡵⢶⡾⣵⣉⣉⡽⠋⠙⠻⠋⠀⠀⢻⡟⠋⢉⣉⣉⣭⣻⡿⣿ ⣇⡇⣿⠤⣾⠳⢦⣄⣀⠀⠤⠴⡶⢆⣀⠀⠈⢳⣦⣈⠉⢩⣇⢀⣿⣿ ⣿⣿⡺⠀⠘⢷⣦⣽⣍⠙⠓⣶⢯⣭⣄⣀⣶⣋⣁⣠⡵⣾⣿⠈⣽⣿ ⣿⣿⣿⡄⠀⠈⠳⣼⠉⠛⢿⣿⣦⣤⣼⣧⣬⣯⣤⣼⣷⣿⣿⠀⢾⣿ ⣿⣿⣿⣿⣦⣀⡀⢈⠛⢦⣼⡁⠀⠈⡏⠉⢻⡟⢻⠟⣿⣿⡟⠀⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣛⠿⣧⢄⣛⠛⠻⠿⠧⠿⠿⠿⠟⠛⣃⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⠛⠓⠲⠶⠴⠐⠢⢒⡈⠡⠐⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣤⣶⣿⣿

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⬜️⬜️⬜️⬜️🌫️🌫️🌫️🌫️🌫️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️🌫️🥛🥛🥛🥛🥛🟫🟫🟫🟫 ⬜️⬜️🌫️🥛⬜️⬜️🥛🥛🥛🟫🥠🧇🟫 ⬜️🌫️🥛⬜️⬜️🥛🥛🥛🟫🥠🧇🟫⬜️ 🟦🌫️🥛🥛🥛🥛🥛🥛🟫🧇🥠🟫🟦 🟦📘🌨️🌨️🌨️🌨️🌨️🌨️🌨️🌨️🌨️📘🟦 🟦📘🧊🧊🪟⬜️🪟🪟🧊🧊🧊📘🟦 ⬜️🟦🟦🟦🟦🪟⬜️🧊🟦🟦🟦🟦⬜️ ⬜️⬜️⬜️⬜️⬜️🟦🪟🟦⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️⬜️⬜️⬜️🟦⬜️⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️⬜️⬜️🟦🧊🟦⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️🟦🟦🧊📘📘🟦🟦⬜️⬜️⬜️

⬜️⬜️⬜️⬜️⬜️⬜️⬜️⬜️⬜️⬜️🟥⬜️🟥 ⬜️⬜️⬜️⬜️🟪🟪🟪🟪🟪⬜️🟥🟨🟥 ⬜️⬜️⬜️🟪💟💟💟💟💟🟥⬜️🟨🟥 ⬜️⬜️🟪💟⬜️⬜️💟💟💟🟥🟨⬜️🟥 ⬜️🟪💟⬜️⬜️💟💟💟🟥⬜️🟨🟥⬜️ 🟦🟪💟💟💟💟💟💟🟥🟨⬜️🟥🟦 🟦📘🫐🫐🫐🫐🫐🫐🫐🫐🫐📘🟦 🟦📘🧊🧊🪟⬜️🪟🪟🧊🧊🧊📘🟦 ⬜️🟦🟦🟦🟦🪟⬜️🧊🟦🟦🟦🟦⬜️ ⬜️⬜️⬜️⬜️⬜️🟦🪟🟦⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️⬜️⬜️⬜️🟦⬜️⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️⬜️⬜️🟦🧊🟦⬜️⬜️⬜️⬜️⬜️ ⬜️⬜️⬜️🟦🟦🧊📘📘🟦🟦⬜️⬜️⬜️

🍑𓂸🥜 🅽🆄🆃🆂

⠀ ⢠⠔⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠑⡶⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⠷⠶⠒⠚⠉⠉⠉⠓⡄ ⠀⠀⠀⠀⡼⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⡴⠲⢤⠇⠀⠀⠀⠀⣆⡸⠂⠀⠀⠐⠀⠀⠀⢶⣤⣀⣀⡤⠞⠁ ⠀⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢈⡷⠒⢆⠀⠀⠀ ⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀ ⢰⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀ ⠀⠙⠲⠞⠓⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠳⠤⠖⠃⠀⠀⠀⠀⠀⠀(๑ > ᴗ < ๑)(˵ •̀ ᴗ - ˵ ) ✧

⡈⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⡈⡇⢈⣴⣦⢶⣴⣴⣦⢶⣴⢦⣶⡴⣦⡶⣴⣦⢶⣴⣤⡀⠀⠠⡀ ⠁⡇⣿⣟⣾⠗⢀⢸⣾⢿⣽⣻⣾⠻⠝⠛⢉⡈⠛⠻⢾⣿⠀⠀⠀ ⠀⠀⣿⣾⠷⠞⣹⡿⣯⢿⡞⠋⣡⣴⣾⢿⣟⡿⣟⣷⣄⠹⠀⠀⠀ ⠀⠀⣿⣯⣤⣼⡿⣽⡛⢁⣴⣿⣻⣽⡾⣯⡿⣽⣟⣷⣻⡆⠀⠀⠀ ⠀⠀⣿⣽⣻⢯⡟⠃⣴⣿⣻⢾⣽⣳⡿⣽⣻⣽⡾⣯⣷⢿⠀⠀⠀ ⠀⠀⣿⣳⡿⠏⣠⣿⣟⣷⣻⣯⣟⣷⣿⣻⣽⣷⣻⢷⣯⣿⠀⠀⠀ ⠀⠀⣿⣽⠃⣴⣿⣳⢿⣞⡿⣿⠆⠀⠀⢠⣿⣞⣯⣿⣳⡏⠀⠀⠀ ⠀⠀⣿⠃⣼⣻⢾⣽⣯⣿⠟⠁⠀⣠⣄⣸⣿⢾⣽⣞⣯⠅⠀⠀⠀ ⠀⠀⡇⣸⣷⣻⣯⣷⣻⣿⡀⣠⠞⠹⣿⣿⢯⣿⣞⣯⠏⢸⠀⠀⠀ ⠀⠀⢁⣿⣽⣯⢿⣽⡟⢿⠗⠉⠀⢠⣿⣽⢾⣯⣟⡿⢀⣾⠀⠀⠀ ⠀⠀⢸⣟⣾⡽⣯⣿⠀⠀⠀⣠⣶⣿⣻⢾⣟⣾⡽⢀⣾⣻⠀⠀⠀ ⠀⠀⣿⣟⡷⣿⣻⣿⣤⣤⣤⣬⣿⣷⣻⣯⢿⠞⢠⣾⢯⣿⠀⠀⠀ ⠀⠀⣿⣽⣻⢷⣟⣿⣻⣟⣿⣻⣟⡾⣷⡻⠋⣰⣿⢯⣿⣽⠀⠀⠀ ⠀⠀⢻⣷⣻⢿⣾⣳⡿⣾⡽⣷⣻⡽⠛⣠⣾⢿⡽⠿⢾⣽⠀⠀⠀ ⠀⠐⡌⢳⣿⣻⡾⣽⣻⢷⣟⠏⢃⣤⣾⢿⡽⡟⣁⣤⣾⣿⠀⠀⠀ ⠀⠀⣿⢦⣈⣑⠛⠛⣋⣁⣤⡾⣿⡽⣾⣻⡏⠛⣡⣾⣟⣾⠀⠀⠀ ⠃⠀⠙⢿⣯⣟⣿⣻⣯⣿⣽⣻⣷⣟⣯⣷⣷⣶⣿⣳⡯⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠚⢛⣉⣉⣉⣉⡀⠀⢀⣈⣉⣉⣉⡛⠓⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⣿⣿⠷⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠲⢾⣿⢿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣋⠵⢊⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣑⠦⣝⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣿⡿⣚⣱⣿⡷⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠿⠿⢾⣿⣾⣟⢿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡵⠋⠉⣼⡿⠛⢁⣤⣶⠶⣶⣦⣌⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢁⣴⡶⠶⢶⣤⡈⠙⢿⣧⠉⠙⢦⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⡞⠁⠀⢸⡿⠁⢠⣿⠋⠉⢳⣤⣹⣿⣆⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣰⡿⠛⠲⣤⣄⣸⣿⣄⠈⢿⡇⠀⠀⠳⡀⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠃⢀⡞⠀⠀⠀⢸⡇⠀⣿⣷⣀⣀⣼⣿⣿⣿⣿⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⣇⠀⢀⣿⣿⣿⣿⣿⠀⢸⡟⠀⠀⠀⢹⡀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠁⠀⣸⠀⠀⢀⣠⡼⠷⠶⠛⠛⠛⠛⠛⠛⠻⠿⠿⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡿⠿⠿⠛⠛⠛⠓⠚⠛⠶⠾⢧⣄⡀⠀⠀⡇⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣾⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀ ⠀⣸⢇⠁⠀⣠⠔⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠶⠶⠶⠶⠖⠒⣶⠒⠲⠶⠶⠶⠶⠤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠦⣄⠀⠀⠀⠘⣇⠀ ⠀⡿⠈⠀⡴⠃⠀⠀⠀⠀⣿⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⣿⠀⠀⠀⠀⠱⡄⠀⠀⢿⠀ ⢸⡇⠃⢰⠃⠀⠀⠀⠀⣰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⠀⠀⠀⠀⠸⡄⠀⢸⡇ ⢸⡇⠀⠈⢧⢀⣀⣤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣤⣀⡀⢠⠃⠀⠘⡇ ⢸⣶⠀⠀⠀⠈⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠁⠀⠀⠀⠀⡇ ⢸⡗⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⢤⡇ ⠸⡇⣇⠀⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠀⢸⢸⡇ ⠀⣷⢸⠀⢳⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡞⠀⡏⣾⠀ ⠀⢹⡎⣇⠈⣇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣿⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢰⠃⣸⢡⡏⠀ ⠀⠀⢿⡸⡄⠸⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⠏⢠⠇⡾⠁⠀ ⠀⠀⠘⣧⠹⡀⠹⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⠎⢀⡎⣼⠃⠀⠀ ⠀⠀⠀⠘⣧⠱⡀⠹⡄⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⠎⢀⠞⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⡹⣄⠙⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⡟⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣠⠏⢠⢎⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣜⢦⡈⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⡴⢣⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣇⠀⠀⠀⠀⣀⡧⠀⠀⠀⠀⠀⣸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠫⠽⢿⣓⣒⣶⣿⣶⣒⣚⡿⠿⠝⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡲⢤⣀⠀⠀⠀⠀⠉⠒⠦⠭⣉⣀⡀⠀⠀⠀⢀⣀⣀⡤⠤⠒⠉⠀⠀⠀⠀⢀⡤⢖⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣝⣒⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⣒⣫⡵⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢬⣭⣍⣉⣒⣒⡒⠒⢒⣒⣒⣈⣩⣭⡥⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⣀⣤⠾⠛⢻⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⠟⠉⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠈⢻⣿⣏⠉⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡿⠟⢻⣿⡿⠀⠀⠈⣿⣿⣦⡀⠀⠀ ⢀⡀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⢼⣿⡇⠀⠀⠀⣿⡏⢻⣧⠀⠀ ⢸⣿⣿⣶⣶⣤⣸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⣧⠀⢻⣷⡄ ⠈⠻⠯⠛⠛⠻⠿⠿⠟⠀⠀⠸⠿⠿⠷⠦⠀⢤⡿⢻⠀⡼⠇⠑

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠛⠛⠉⠉⠉⠛⠛⢷⣶⣤⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠛⠛⠛⠻⢶⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣆⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀ ⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⣿⣿⠁⢀⣾⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⣿⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⢠⣿⣿⡇⠀⠙⠛⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀ ⠀⠀⣠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣅⠀⠀ ⠀⢠⣿⠇⠀⠙⠻⣷⣦⣄⣀⡀⠀⣀⣀⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⠻⣶⣦⣤⣤⣤⣤⣤⣴⣶⡿⠛⢿⡇⠀⠀⠀ ⠀⣿⡏⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣿⠀ ⢠⣿⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠳⣄⠀⠀⢹⣇ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠘⡆⠀⢸⣿ ⠈⣿⡄⠀⠘⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠁⠀⣾⡇ ⠀⢻⣷⡀⠀⠈⠛⠆⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠓⠀⠀⠀⠀⠀⣼⡿⠀ ⠀⠀⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀ ⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄⠀⠀⠀⢀⣠⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠀⢀ ⠀⠀⠀⠀⠀⣀⣭⣿⡿⠿⣿⣶⣶⣦⣤⣤⣤⣤⣼⣿⣿⣶⣶⣿⣿⣋⣁⣀⣀⣠⣤⣤⣤⣴⣾⣿⣟⣛⠁⠀⠀⠀⡠⠀ ⠀⠀⢀⣴⡿⠛⠉⠁⢀⣾⡟⠁⣼⣿⣿⣿⡏⠉⣩⣭⣿⣻⣿⣿⣿⣍⠉⠙⣿⣯⣿⡏⠻⣿⣌⠉⠙⠛⢷⣦⣄⡐⠁⠀ ⠀⣰⣿⠋⠀⠀⠀⢠⣾⠏⠀⢰⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡄⠘⢿⣦⠀⠀⠀⠈⣻⣧⠀⠀ ⠀⠛⢿⣿⠀⠀⢀⣿⠇⠀⢠⣿⣿⣿⣿⡇⠀⠀⠸⢿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣷⠀⠈⢿⣇⠀⠀⢰⣿⡿⠇⠀ ⠀⠀⠰⣿⣤⣤⣾⡏⠀⠀⣾⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠈⣿⣇⣠⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠁⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⢸⣿⡟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣷⣶⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣸⣿⣿⣿⣿⣧⣤⣴⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠟⠁⠀⠉⡉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣤⣴⣶⡿⢿⣦⡀⣀⣤⣾⣶⣄⡀⣀⣴⣿⢿⣧⡀⠀⢀⣤⣶⣄⡀⠀⣠⣾⣷⣶⣬⣀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠙⠛⠛⠛⠁⠈⠙⠛⠛⠛⠁⠈⠛⠻⠿⠛⠉⠉⠛⠿⠿⠟⠁⠀⠈⠝⠛⠋⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⢀⡴⠖⠒⠀⠀⠀⠀⠀⠀⢰⣦⡀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⠀⠈⢠⣶⣶⣤⠀⠀⠀⠀⣤⣀⡀⠉⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣄⣀⣀⣀⣾⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⣆⠀⠀⠀⡀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠘⠦⠞⠋⢀⣠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣀⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⡼⣷⠼⣆⣼⢇⣿⣄⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠙⠢⠐⠉⠉⣴⣾⣽⢟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠤⢴⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠻⣿⣶⣦⣭⣉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠉⠉⠇⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣦⣀⠀⠀⣀⡴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⠛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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