Haunter Dot Art

⠀⠀⠀⠀⠀⠀⠀⢢⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣶⡆⠈⠻⣿⣿⣿⣿⣿⠋⠠⣶⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣦⣤⣤⣶⣶⣶⣾⡿⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣯⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣾⣿⣿⣿⣿⣧⠀⠛⠁⠀⠈⠿⠋⠉⠉⠉⠉⠻⠋⠀⠀⠈⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⡀⠀⠙⠿⣿⣿⣿⣿⣿⣦⣀⣠⣀⣴⡀⣠⡀⣠⡀⣴⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⡿⠟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⠛⠁⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠈⠙⠛⠋⠁⣸⡿⠃ ⠸⣿⣿⡟⠉⠉⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠙⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⠘⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀ ⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠻⣿⡿⢿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠲⣦⣤⣀⣀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⢀⣀⣠⣤⣶⣶⠟⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠲⣶⣶⣾⣿⣿⠀⢨⠙⢿⣿⣿⠏⣅⠀⢸⣿⣿⣷⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⢷⣶⣶⣾⣿⣿⣶⣶⣾⠟⣿⣿⣿⣋⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⠐⢶⣿⣿⣧⠁⠀⠋⠁⠈⠋⠀⢀⣾⣿⣿⡿⣷⣶⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣷⣤⣙⣿⣿⣷⣶⣶⣴⣴⣴⣶⣿⣿⣿⠟⣡⣿⣿⣧⣄⣀⡀ ⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿ ⣿⡿⠛⠿⠟⠉⠉⠉⠸⠋⠀⠻⡿⣿⣿⣿⣿⠻⠇⠀⠀⠈⠀⠀⠈⠉⢸⠃ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜ ⬜⬜⬜⬛⬛⬛🟧🟧🟧⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟧⬛⬛⬜ ⬜⬜⬜⬜⬜⬛⬛🟫🟨🟨🟨🟨🟧⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛🟨🟨🟨🟨🟧🟧⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟫🟧🟨🟨🟨🟨🟨🟨🟧⬛🟨🟨🟨🟨🟨🟨🟨⬛🟧🟨🟨🟨🟨🟧🟧⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜⬜ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟨⬛⬛⬜⬛🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛🟨🟧⬛⬜⬜⬜⬜⬜ ⬛🟨🟧⬛⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟧⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟧⬛⬜⬜⬜⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟧⬛⬜⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟧⬛⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨⬛🟨🟨⬛⬛🟨🟨⬛🟨🟨🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟧⬛⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨⬛⬛🟨🟨⬛⬛🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟧⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬛🟧🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬛🟨🟨🟨⬛🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨⬛🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟧🟧🟫⬛🟨🟨🟨🟧⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨⬛🟧🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟧🟧🟧⬛⬛🟨🟨🟨🟧⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨⬛🟧🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟧🟫🟫⬛🟨🟨🟨🟨🟧⬛🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨⬛🟧🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟫🟫🟫🟫⬛🟨🟨🟨🟨🟨🟧⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛🟧🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟫🟫🟫⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟫⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟧🟧⬛⬛⬛⬛⬛⬛⬛🟧🟧🟨🟧⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜

⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠿⢟⣛⣩⣤⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠿⠸⣿⣿⣿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠉⠀⠀⠀⣿⠋⠻⣿⣿⣿⠀⣦⣿⠏⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀ ⢠⠏⠀⠀⠀⠀⠀⠻⣤⣷⣿⣿⣿⣶⢟⣁⣒⣒⡋⠉⠉⠁⠀⠀⠀⠈⠉⡧ ⢻⡀⠀⠀⠀⠀⠀⣀⡤⠌⢙⣛⣛⣵⣿⣿⡛⠛⠿⠃⠀⠀⠀⠀⠀⢀⡜⠁ ⠀⠉⠙⠒⠒⠛⠉⠁⠀⠸⠛⠉⠉⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣷⡄⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣑⡙⠻⠿⠿⠈⠙⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠙⢤⡷⣤⣦⣀⠤⠖⠚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⠢⢄⡀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠷⣶⠂⠀⠀⠀⣀⣀⠀⠀⠀ ⢸⣃⠀⠀⠉⠳⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⡭⠋ ⠀⠘⣆⠀⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠘⣦⠆⠀⠀⢀⡎⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⣆⠘⣄⠸⢧⠀⠀⠀⠀⢀⣠⠖⢻⠀⠀⠀⣿⢥⣄⣀⣀⣀⠀⠀ ⠀⠀⢸⠁⠀⠀⡏⢣⣌⠙⠚⠀⠀⠠⣖⡛⠀⣠⠏⠀⠀⠀⠇⠀⠀⠀⠀⢙⣣⠄ ⠀⠀⢸⡀⠀⠀⠳⡞⠈⢻⠶⠤⣄⣀⣈⣉⣉⣡⡔⠀⠀⢀⠀⠀⣀⡤⠖⠚⠀⠀ ⠀⠀⡼⣇⠀⠀⠀⠙⠦⣞⡀⠀⢀⡏⠀⢸⣣⠞⠀⠀⠀⡼⠚⠋⠁⠀⠀⠀⠀⠀ ⠀⢰⡇⠙⠀⠀⠀⠀⠀⠀⠉⠙⠚⠒⠚⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣶⣶⣿⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⢿⣳⠞⠳⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣄⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢀⣀⠀⠀⠈⠉⠀⠀⣀⣀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣶⣿⣿⣿⣾⣇⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣼⡏⠀⠀⠀⣀⣀⣉⠉⠩⠭⠭⠭⠥⠤⢀⣀⣀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⠷⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⣀⠀⢸⡿⠿⣿⡿⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠻⠿⠟⠉⢙⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⡿⣿⠳⠀ ⠀⠀⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀ ⢀⣸⣀⡀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⢿⣿⠿⠃⠀ ⠘⢿⡿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠹⣿⣿⣿⡿⠛⣠⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠳⣄⠙⠛⠿⠿⠛⠉⠀⠀⣀⠜⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠢⠤⠤⠬⠭⠥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠖⠲⢤⡖⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⠀⠀ ⠀⡞⠉⠻⠁⢹⠀⠀⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠋⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠉⠀⠀⣿⣿⣿⠿⠋⠀⠀ ⠀⠳⢤⡀⠀⡞⠁⠀⡇⠀⠀⢀⡠⠼⠴⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠷⡏⠀⠀⣇⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢴ ⠀⠀⠀⠀⠀⠀⣸⠁⣾⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢿⣦⠀⠀⠀⢸⡀⠀⠀⢀⣠⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢀⡏⠀⠹⠿⠿⠟⠁⠀⠰⠦⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⢘⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⣼⠦⣄⠀⠀⢠⣀⣀⣴⠟⠶⣄⡀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠀⠸⡾⠁⠀⠀⠀⠉⠉⡏⠀⠀⠀⣠⠖⠉⠓⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⣀⡼⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⠤⠖⠃⡟⠀⠀⠀⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢦⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠸⡇⠈⢳⡀⠀⢹⡀⠀⠀⠀⢀⡞⠁⠉⣇⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⠴⠚⠁⠀⣀⣷⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣳ ⠀⠀⠀⠀⠀⠀⡴⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠚⠉⠉⠀⠀⠀⠀⢸⠃⣀⣠⠤⠤⠖⠋ ⣼⢷⡆⠀⣠⡴⠧⣄⣇⠀⠀⠀⠀⡴⠚⠙⠲⠞⠛⠙⡆⠀⠀⠀⠀⠀⢀⡇⣠⣽⢦⣄⢀⣴⣶⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣽⡞⠁⠀⠀⠀⢹⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢠⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠉⠁⢳⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⢦⠀⠀⠀⡠⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠀⠈⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠹⣧⠞⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⣰⣀⣀⣀⠀⠀⠀⠘⣦⣀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢦⠦⡶⡶⠿⠛⠛⠓⠒⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛🟪🟪🟪⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛⬛⬛⬛🟪🟪🟪⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪🟪🟪⬛⬛⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪⬛🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪⬛🟪🟪🟪🟪⬛ ⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛🟪🟪🟪🟪🟪🟪⬛⬛⬜⬜🟪🟪🟪🟪🟪🟪🟪⬛⬛⬜ ⬜⬜⬛⬛🟪🟪⬛⬜⬜⬛🟪🟪🟪🟪⬛⬜⬛⬜⬜⬜🟪🟪🟪🟪⬛⬛⬛⬜⬜⬜ ⬜⬛🟪⬛🟪🟪🟪⬛⬛⬜⬛🟪⬛🟪🟪🟪🟪⬜⬜⬜🟪⬛🟪🟪🟪⬛⬜⬜⬜⬜ ⬛🟪⬛🟪🟪🟪🟪🟪🟪⬛⬜⬛🟪⬛🟪⬛⬛🟪⬛⬛⬛🟪🟪🟪🟪🟪⬛⬜⬜⬜ ⬛🟪⬛🟪🟪⬛🟪🟪🟪⬛⬜⬜⬛🟪⬛🟪🟪⬛🟪🟪⬛🟪🟪🟪⬛⬛⬛⬜⬜⬜ ⬜⬛🟪⬛⬛🟪🟪🟪⬛⬜⬜⬛⬛🟪🏻🏻🏻🟪🟪⬛🟪🟪🟪🟪🟪🟪🟪⬛⬛⬜ ⬜⬛⬛⬜⬛🟪🟪⬛⬜⬜⬜⬜⬛⬛⬛🏻🏻🏻⬛🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛ ⬜⬜⬜⬜⬜⬛🟪⬛⬜⬜⬜⬜⬜⬛🟪⬛⬛⬛🟪🟪⬛⬛🟪🟪⬛🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟪🟪🟪⬛🟪🟪🟪🟪🟪⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟪🟪⬛🟪🟪🟪🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛🟪🟪⬛🟪🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟪🟪⬛🟪🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪⬛⬜⬛🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠈⡖⡤⠄⠀ ⠀⠀⢀⡀⠀⠀⠀⡐⠁⠀⠀⠠⠐⠂⠀⠁⠀⠀⠀⠀ ⠀⠰⡁⠐⢉⣉⣭⡍⠁⠂⠉⠘⡀⠀⠀⠀⠀⠂⠡⠀ ⢀⣊⠀⡄⠻⠿⠋⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀ ⡎⣾⠀⠁⣴⡆⠀⠡⢺⣿⣆⠀⢠⢱⣄⠀⠀⠀⠀⠈ ⡑⠟⠀⠀⠀⠀⠀⢀⣸⡿⠟⠀⠀⠈⢿⣿⡦⡀⠀⡰ ⠙⠔⠦⣤⣥⣤⣤⣤⡤⠆⠀⠀⠀⠀⢀⢀⠀⠈⠎⠀ ⠀⠀⠈⣰⡋⢉⠉⠁⠒⠂⢇⢠⡆⠀⠸⢴⣿⠀⠘⠀ ⠀⠀⠘⡿⠃⠀⠨⠒⢆⣸⣿⠁⠀⡠⡇⠈⠋⠀⠰⠀ ⠀⠀⠀⠛⠒⠒⠁⠀⠈⠷⡤⠤⠐⠀⠘⠒⠒⠖⠁⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠄⣀⡀⡀⠤⠐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⣀⣀⡀⠀⠀⠀⠀⢀⠀⡔⢻⣦⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠰⠛⣇⣹⡜⡄⠀⠀⠸⢠⣿⣿⣀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⡉⠤⠐⠒⠒⠒⠂⠠⠬⣁⠒⠠⢄⡀⠀⢠⠀⠐⠠⠿⢿⡇⠀⠀⠀⠀⠈⠛⠉⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡁⠒⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⣒⣀⣴ ⠰⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠌⣉⣶⣶⣦⣄⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⢁⣠⣴⣾⣿⣿⡟⠁ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠛⠿⠿⠛⠆⠤⠄⠀⣀⣀⣀⣀⣀⡀⠔⢁⣤⣾⣿⣿⣿⡿⠟⠁⠀⠀ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠀⠀⠄⠀⡀⠀⠁⠐⠒⠂⠠⠤⢤⣤⣤⣶⣾⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⢇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠉⢂⠀⢱⡀⡰⢠⡃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⡁⠂⠤⢀⣀⠀⠀⠀⠀⣀⣀⣼⣿⠀⠀⠀⠀⣮⣤⣶⣶⣦⠋⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠠⠾⠿⠿⢻⣿⠀⠀⢀⣴⣿⣿⣿⡿⠁⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢃⠤⠐⠁⠀⢰⣾⠟⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠆⠀⠀⠀⠀⢸⡟⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢰⠀⠀⠀⠀⠀⠀⣇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣆⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⢠⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀ ⠀⠸⡏⠙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠖⠋⣸⠃⠀ ⠀⠀⢻⠀⠀⠈⢳⡀⠀⠀⠀⢨⢢⠀⢠⠞⠁⠀⢠⡏⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⢻⡀⡠⠔⠊⠀⢣⡏⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠈⠓⠦⣴⣼⡏⠀⠀⠀⢠⣾⣤⣤⠶⠛⠁⢀⣿⠀ ⠀⠀⠀⠀⠀⣶⠟⢻⣿⣦⣀⣤⣾⣿⡏⠙⢲⠀⠀⣾⣿⡇ ⠀⠀⠀⠀⣸⠃⠀⢀⠀⢹⣿⣿⠃⢀⡇⠀⠘⣶⣶⣿⣿⠇ ⠀⠀⠀⠀⢰⠀⠀⠈⠻⣿⣯⣿⡿⠟⠁⠀⠀⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣦⣴⣴⣤⣶⣤⣾⣿⣿⣿⣿⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⠟⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⠏⠻⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡀⡀⠀⠀⠑⢢⢀⢄⡀⠔⠂⠐⠂⢄⠀⠀ ⠀⠀⡠⠒⠒⣬⡒⠊⠐⠁⠂⠂⠀⣀⣀⣈⠪⠂⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⠀⢇⡠⡲⠗⠁⠀⠀⢀⠔⠊⠁⠀⠀⠀⠈⠑⠢⡀⣠⠀⠀⣀⡸⠀ ⠀⠀⠀⠀⠧⠤⢄⠀⡰⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠆⠀⠑⡀⠀ ⠀⠀⠀⡰⠉⠑⠊⠰⡇⠀⠉⠢⢄⠀⠀⠀⠀⠀⢀⠇⠀⠸⠀⡔⠁⠀ ⢀⣀⠸⠀⠀⠀⠀⡆⢇⠀⠀⠀⠀⡍⠢⣀⠀⢀⠎⠇⠀⢀⠀⠙⢆⡀ ⠘⠤⢤⣊⢱⠀⠀⢡⠈⠢⡀⠀⠀⠀⢀⠌⠀⠀⠣⠤⣤⡺⢠⡀⢀⡇ ⠀⠀⡅⢀⠏⡂⠀⠈⢆⠀⠈⣅⠀⠈⢁⣀⡠⠄⢒⠞⡧⠃⠓⡗⠜⠁ ⠀⠀⢠⠖⠤⠅⠀⠀⠀⠑⢄⠈⠣⠓⠀⠒⠒⠉⢀⠔⢡⣠⠋⠁⠀⠀ ⠀⠀⠀⠣⣀⡀⠤⢄⠀⠀⠀⠈⠑⠂⠀⠀⠒⠈⠀⠀⠈⠐⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠋⡀⣰⠀⠀⢀⣀⡀⠀⢨⠃⠀⣱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠔⠩⠤⠒⠊⠁⠀⠈⠑⠉⠒⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⣿⡀⠙⠁⠀⢠⡀⣐⠓⠬⢠⢀⠉⠄⠠⠆⣄⠀⡤⢬⡀⢀

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣿⣿⣿⣄⠀⣼⠀⠀⠀⢂⣀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⡷⠋⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠣⡀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⡀⠀⠀ ⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⠀ ⠀⠀⣸⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⣤⡟⠛⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠋⠈⢿⣿⡿ ⢀⡉⠀⠀⣀⣤⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣄⠀⠀⣴⡄ ⠘⢇⠀⠰⣿⣿⢟⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢜⠿⠿⠿⠀⡀⠀⠀ ⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⣸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡞⣿⣷⣮⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡝⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠸⣸⣻⣏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⡀⠀⠀⠀⠀⠀⣾⡞⡝⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣾⣿⣶⢦⣤⣀⠸⠻⢭⣥⡻⣧⠀⡙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢠⣴⣾⣿⣿⣿⣏⣶⣾⡽⣿⣷⣟⣿⣿⣿⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⣿⡿⠘⠻⢿⣿⣿⠟⠛⠿⠿⠃⢍⣿⣿⢸⣿⣿⣿⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣟⠛⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣜⢿⣿⡿⡷⡿⣼⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠃⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣯⣾⣿⡀⠀⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣽⣿⣿⢟⣛⣳⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⢻⣾⣿⣿⣷⡽⣄⠀⠀⢀⣾⣿⣷⣄⠀⠀ ⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣦⠀⢸⣇⠀⠹⣏⢧⡀ ⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢸⣿⡄⠈⠛⠀⣶⠟⠼⠇ ⠀⠀⠀⠹⣿⣿⣷⣤⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⡿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣄⠀⠀⠈⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⢟⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⡀⠀⠀⠈⠻⢿⣿⢸⣿⣿⣿⡿⢟⣫⣾⣿⣿⠿⣛⣵⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⣾⣿⡟⠙⠚⠛⠛⠋⠉⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠘⠻⣿⣿⣷⣶⣒⣒⢢⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣏⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⣤⣤⣶⣴⣶⣶⣦⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⣧⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣻⣭⣽⡷⠟⠋⠉⠀⠀⣿⣿⣿⣿⡿⠏⠋ ⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⣀⣠⣾⣷⠶⠶⠶⣶⣦⣤⣤⣄⣀⣴⣯⣯⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⡤⣾⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠯⣇⢔⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⣀⣀⡤⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣟⣀⣶⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⣖⡄⠀⠉⠙⢿⡅⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⣻⡇⣿⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⢿⣷⠀⠀⠀⢸⡆⠀⠀⢀⣠⡾⠟⠟⠋⠉⠉⠀⠀⠀⠀⢠⡿ ⠀⠀⠀⠀⠀⢀⡟⠀⠹⠿⠿⠟⠁⠠⠴⠦⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⢹⡷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡏ ⠀⠀⠀⠀⣠⣾⠿⣧⡀⠀⢤⣄⣀⣴⡟⠶⣤⣄⠀⠀⡀⠀⠉⠋⢁⣀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠃ ⠀⠀⠀⠀⣿⡇⠀⠘⡇⠀⠀⢹⡾⠉⠀⠀⠀⠉⡭⡯⠋⠀⡤⣶⠟⠻⣷⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⢃⡎⠀ ⠀⠀⠀⠀⢯⣷⣤⡾⠇⠀⠀⠀⣷⠀⠀⠀⠀⢠⣿⠃⠀⠀⣿⣧⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣗⣫⠥⡾ ⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⣿⣇⠀⠀⠀⣯⠏⠀⠀⠀⠀⠻⣷⣤⡶⠋⡟⠀⠀⢰⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠈⠛⠶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⢻⣧⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡏⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⠵⠋⠸⡏⣎⣷⡈⢣⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣀⠀⠀⠉⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⣴⠟⠁⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡿⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣇⣠⣯⡽⣧⣇⣇⠀⠀⠀⠀⠀⠀⠀⢲⡇⡟⠀⠀⠀⠀⠀⠀⠀⢀⣷⣲⣽⢦⣄⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣿⣿⠁⠀⠀⠉⢿⡀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠀⣰⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠉⠁⣿⡄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣿⠁⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡆⠀⣏⡇⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢸⠁⣼⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⡄⠈⡟⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢀⡇⠀⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⣷⣀⣀⣀⠀⠀⠀⠘⣷⣄⣀⡀⢯⣧⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⣿⡧⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢷⠶⡶⡿⠿⠛⠛⠓⠒⠒⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠛⠉⠉⠛⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⣠⡖⢠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣷⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⢠⢿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⢸⠸⠻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⡀⣿⠀⠀⠀⠁⠀⠉⠁⢀⣀⣀⣀⣄⣤⠴⢶⣶⣿⡏⠀⣸⣃⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⠉⠛⠛⠦⠤⣄⡀⢿⡋⠉⠉⠁⠀⠀⠉⠁⠀⠀⢈⡟⢀⡼⠛⠉⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⣀⣠⠤⠖⠒⠒⢛⣛⣻⣷⡖⣀⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⢉⣠⠴⠖⠚⠉⠉⠁⠉⠻⣍⣹⣶⣦⣀⡀⠀⠀⣸⣷⠶⠶⠶⠶⢦⣤⣴⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠙⢿⣄⠈⠉⠙⠻⢿⣇⠀⠀⠀⠀⢠⠟⠀⠘⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⣠⣏⡉⠉⠉⠉⢉⡿⠟⠒⠒⠤⣄⡀⠀⠉⢦⡀⠀⠀⠀⠉⢧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣿⣿⣭⣭⡉⠑⢦⣴⠃⠀⠀⠀⠀⠀⠀⣙⣦⣠⣄⡹⢦⣀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⠘⡇⠀⠀⠀⠀⣶⠶⠞⠉⠛⠋⠘⣇⠀⠈⠳⢦⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⣧⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠳⡿⣶⣶⣤⣀⣀⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡘⢧⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣼⠀⢀⣠⣤⣄⡼⠁⣼⠀⠀⠉⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⡉⠓⠦⠼⣧⡀⠀⠀⠀⣰⡇⢠⠋⠀⠀⠀⠙⠶⣯⣀⠀⠀⠀⣿⠀⠀⠀⠀⡴⠚⠛⠳⣆⠀⠀⠀⠀⠸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣽⣶⣶⣾⣉⣉⠙⣄⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⢤⡤⠴⠛⠁⠀⠀⠀⢠⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣤⣀⣀⣀⣀⣠⣤⡴⠾⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣧⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢸⣿⣿ ⣿⣿⡄⠘⣷⣤⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣥⣶⠇⢠⣿⣿⣿ ⣿⣿⣿⣦⠈⠻⣿⣷⣄⠻⡿⠋⠙⠉⠋⠛⢿⡟⢡⣶⣿⡿⠃⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣈⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⢋⣤⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⡤⠄⠀⠀⠀⢀⠤⡀⢰⣿⡿⠛⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⡾⠀⠀⠀⢸⣶⡇⢸⠟⠁⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠤⠬⠤⠄⠉⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⢄⣀⡀⠀⠀⣀⣠⣰⣿⡶⣆⡄⣀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⣾⡏⣿⣿⣿⣿⣿⣿⣿⡷⣿⣯⣿⣿⣿⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣤⡈⢷⢹⣿⣿⣿⣿⣿⣿⠁⡿⢟⣿⣿⣿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠉⠻⣿⣿⠟⠀⠘⢸⣿⣿⡿⣡⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠀⠀⠀⢠⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⢀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠒⣶⣶⠆⠀⠀⢀⠔⠁⢠⠀ ⠀⠀⠀⠀⠘⢀⠼⠤⠀⠀⠀⠄⡠⠐⠈⠀⠀⠀⠀⡰⠟⠁⠀⢀⠔⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢜⡁⠀⠀⠀⣖⣦⠀⠀⠤⣤⠄⠐⠂⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡸⠷⢁⡀⢀⡀⠈⢉⠤⢄⠀⠈⡀⠀⠀⠀⠀⣔⡁⠄⠄⠀⠀⢀⠠⠂⠁ ⠀⠀⢠⢻⠀⠹⣿⠿⡇⠀⠡⠔⠜⠀⠀⢁⠀⠀⠀⠀⢡⠀⠀⢀⠄⠊⠁⠀⠀⠀ ⠀⠀⠀⠫⡀⠀⠐⠤⠃⠀⠀⠀⠀⢀⠀⠀⢂⠀⠀⠀⠀⢃⠀⠸⠀⠀⠀⠀⠀⠀ ⢀⠠⠐⠂⠉⠢⠀⡀⠀⠀⠀⠀⠖⠉⠉⠀⠀⢧⡀⠀⡠⠒⠀⡠⠀⠀⠀⠀⠀⠀ ⢸⡘⠀⠀⠀⠀⢢⠈⠂⠀⠀⠀⠘⢤⣄⣤⠄⠀⠈⢊⠢⣠⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠒⠒⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣾⠿⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠤⢊⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣥⠒⠉⠉⠑⠂⠠⠤⡤⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠀⠀⠀⠀⠀⠀⠀⠐⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠉⠁⣽⣿⣿⡿⠋⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⢀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣾⢙⣶⡄⠀⠀⠰⢤⣠⡤⠤⠔⠒⠂⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⣮⣞⣹⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃ ⠀⠀⠀⠀⠀⢰⠛⠿⠁⣈⣀⣀⣀⣤⠀⠀⠀⢠⠖⠒⠲⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⠔⠂⠐⠈⠈⠀⠀⠀⣠⠔⠊⠁⠀⠀ ⠀⠀⠀⠀⢠⡟⣇⠀⠉⢿⣿⣿⣿⣿⠀⠀⠀⢯⡐⠲⣠⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡟⠀⠀⠈⢿⠟⠛⢻⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠳⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠬⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠃⠢⢄⠀⠈⢣⡀⠀⠀⠀⠀⠀⢀⡽⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠔⠊⠁⠀⠀⠀⠈⠳⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠈⠀⠀⠘⡿⢆⠀⠀⣠⠔⠉⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡏⠸⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠳⢄⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⡀⠀⠀⠀⠱⡈⠣⡀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⠦⢤⣀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠤⠼⠛⠁⠀⠀⠀⠀⠘⣆⠙⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⡤⠔⠲⣶⣆⣀⡀⠀⠐⠤⠤⠔⠒⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣥⠤⢴⠚⠉⠀⠀⠀⠈⠉⠒⠂⠤⠤⢤⡤⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⢼⣿⣿⣆⠀⢀⣀⣀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⠋⠙⢿⣿⣿⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠿⢆⣀⣼⣿⣿⣿⣿⡏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣨⡙⠟⣩⣙⣡⣬⣴⣤⠏⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣤⣾⣿⣿⡇ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⠿⠿⠛⠃ ⠀⠀⠀⠀⢠⣿⣿⢹⣿⢹⣿⣿⣿⢰⣿⠿⠃⠀⠀⠀⠀ ⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠀⠀⠀⠀⠀⠀ ⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡠⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠑⢄⣴⣿⣿⣦⣀⠤⠒⠉⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⢀⣀⡀⠠⠤⠤⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡤⣄⠉⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠈⢦⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⠙⠆⣠⣤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠘⣤⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣼⠃⠀⣤⣀⡤⠾⠿⣿⣷⣴⠃⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⣵⣀⡠⠚⠙⠲⠤⣀⡴⠋⠳⠊⠙⠚⠀⠈⠳⡀⠀⠀⠈⠙⢢⡀⠀⢇⠀⠀ ⠀⠸⡉⠑⠚⠦⢌⡉⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⣰⠃⠀⠸⠀⠀ ⠀⠀⠑⡄⠀⠀⠀⠈⡇⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠚⠁⠀⠀⠀⡇⠀ ⠀⠀⠀⠈⣦⣄⠀⢀⠇⠀⠀⠀⠀⠀⣿⣿⡿⠿⢿⣿⣶⣶⣤⡀⠀⠀⠀⢀⡤⠒⠲⡦⡇⠀ ⠀⠀⠀⠀⢸⠈⠉⣡⣶⣦⣄⠀⠀⠀⠈⢿⣷⡄⠀⠀⠉⣿⣿⠇⠀⠀⡰⠃⠀⠀⢰⠁⠘⡄ ⠀⠀⠀⠀⠈⡆⢠⣿⣿⣿⣿⣷⡄⠀⠀⠈⠻⣿⣦⣄⣾⣿⠏⠀⠀⡜⠀⠀⠀⠀⠘⠀⠀⡇ ⠀⠀⠀⠀⠀⠘⢾⣿⠋⠙⢿⣿⣿⣆⠀⠀⠀⠈⠻⢿⡿⠃⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣾⣿⡏⠀⢰⣿⣷⣶⣶⣆⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣿⡿⠿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠘⠿⠿⠿⡫⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⠒⠒⠤⠤⠤⠤⢤⠔⠛⠋⠉⠓⠤⠤⠤⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠊⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⡸⢛⣷⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⢏⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣦⡀⠐⠂⠠⠴⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀ ⠀⢰⠦⣄⠈⢿⣶⡶⠤⠤⠤⠔⠒⠒⣶⠒⡫⢋⡄⠀⢸⠀⠀⠀⠀⢀⣀⠤⣤⠀⠀⠀⠀⠀⢀⡞⠉⠛⢆⠀⠀ ⢰⡟⢷⠂⠉⠚⠿⣿⣄⣀⣀⣀⣠⣴⣛⣯⠔⠋⠀⠠⠼⠦⠔⠒⠊⠁⠠⡶⢧⡄⠀⠀⠀⠀⠸⣧⠀⡀⠈⣿⠀ ⠀⠙⢮⡀⠀⠀⠀⠈⠉⡖⠛⠋⠉⠉⠁⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠞⠁⠀⠀⠀⠀⠀⡏⠿⢧⢀⠈⡆ ⠀⠀⠀⠙⢄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⣯⠀⡿ ⠀⠀⠀⠀⠀⠓⢄⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠐⠒⢖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠉⣶⡇ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣴⢦⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⠤⢤⣸⠓⠢⠄⢀⠀⠤⠔⠊⠁⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⢀⡜⠉⠉⠛⢧⠀⠀⠀⠀⠀⠀⣸⠥⣄⣀⣀⣀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⠇⠀⠀⠀⢀⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣷⣦⣀⣀⣀⡀⠤⠤⠤⠚⠁⠀⠀⠀⢸⡤⢤⡤⢤⡴⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⡷⠞⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠼⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠋⠳⣄⠀⠀⢀⢎⣔⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⠀⠀⠀⠹⣶⢛⠘⡋⠀⢠⣎⣦⠀⠀⠈⠙⠲⢤⡀⠀ ⣰⠏⠀⠀⠀⠀⠀⠀⢰⠀⠰⡤⡀⠀⢛⣋⠀⠀⠰⣄⣀⣠⣿⣆ ⠛⠒⠶⠶⢶⡶⠄⢀⣨⢦⡀⠢⠃⠀⠸⣿⠇⠀⢰⠃⠉⠉⠉⠉ ⠀⠀⠀⠰⠿⣤⣀⠛⢧⣌⡇⠀⠀⠀⠀⠀⠰⠉⠙⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣣⣞⣽⣇⠀⠈⠑⢄⠀⠐⢄⣀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠉⠠⡀⠀⠀⡆⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⢈⠁⠊⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⣀⣦⣀⣤⣤⠴⠾⣄⡀⠺⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠑⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠑⢄⣰⠉⠢⣀⠐⡀⢀⣀⠤⠐⠂⠉⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⣼⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢴⣶⣾⣿⡟⠲⢤⣀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀ ⠀⣨⣿⣿⣷⣄⠀⠈⠑⠢⠄⠛⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠁ ⠈⠉⠻⣿⣿⣿⣷⣄⠀⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⠂⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠟⠁⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣧⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠞⠁⣀⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢆⠀⠀⢀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢈⣶⣶⣾⣿⣦⣤⠄⠀⠀⢠⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣷⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣁⣴⣿⡿⠟⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠒⠤⠤⠤⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⠛⠙⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡸⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⡇⠀⠀⠀⡸⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⣀⣠⡤⠖⠚⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⠃⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⢻⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡷⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣼⣠⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣇⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⢸⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠢⡀⠀⠀⢀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡹⠀⠀⠘⢄⠀⠈⠲⢖⠈⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⢠⠞⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇⠀⡤⡀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣾⣿⣷⣶⣤⣄⣉⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⢁⣴⣾⣿⣿⡆⢇⠀⠀⠀⠀⠀⠸⡀⠀⠂⠿⢦⡰⠀⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⢁⣴⣿⣿⣿⣿⣿⣿⡘⡄⠀⠀⠀⠀⠀⠱⣔⠤⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡘⢆⠀⠀⠀⠀⠀⢃⠑⢌⣦⠀⠩⠉⠀⡜⠀⠀⠀⠀⠀⠀⢠⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣣⡀⠀⠀⠀ ⠀⠀⢰⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠱⡀⠀⠀⠀⢸⠀⠀⠓⠭⡭⠙⠋⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡱⡄⠀⠀ ⠀⠀⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢃⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣆⠀ ⠀⢸⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⠀⠀⡆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡠⠖⣡⣾⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⠀ ⠀⡏⣾⣿⣿⣿⣿⡿⡛⢟⢿⣿⣿⣿⣿⣿⣿⣧⡈⢦⣠⠃⠀⠀⠀⠀⠀⢱⣀⠤⠒⢉⣾⡉⠻⠋⠈⢘⢿⣿⣿⣿⣿⠿⣿⣿⠏⠉⠻⢿⣿⣿⣿⣿⡘⡆ ⢰⡇⣿⣿⠟⠁⢸⣠⠂⡄⣃⠜⣿⣿⠿⠿⣿⣿⡿⠦⡎⠀⠀⠀⠀⠀⠒⠉⠉⠑⣴⣿⣿⣎⠁⠠⠂⠮⢔⣿⡿⠉⠁⠀⠹⡛⢀⣀⡠⠀⠙⢿⣿⣿⡇⡇ ⠘⡇⠏⠀⠀⠀⡾⠤⡀⠑⠒⠈⠣⣀⣀⡀⠤⠋⢀⡜⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠉⡃⠈⢀⠴⣿⣿⣀⡀⠀⠀⠀⠈⡈⠊⠀⠀⠀⠀⠙⢿⡇⡇ ⠀⠿⠀⠀⠀⠀⠈⠀⠉⠙⠓⢤⣀⠀⠁⣀⡠⢔⡿⠊⠀⠀⠀⠀⠙⢦⡀⠀⠐⠢⢄⡀⠁⡲⠃⠀⡜⠀⠹⠟⠻⣿⣰⡐⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⢦⣀⢀⡴⠁⠀⠀⠀⠀⠉⠁⢱⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⢏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⡴⠁⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⠤⠖⠋⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠈⠁⠀⠀⠀⡔⠛⠲⣤⣀⣀⣀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡠⢔⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠤⠒⣀⠀⠀⠀⠀⣀⠟⠀⠀⠀⠑⠢⢄⡀⠀⠀⠈⡗⠂⠀⠀⠀⠙⢦⠤⠒⢊⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⣒⡁⠬⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢺⢠⠤⡀⢀⠤⡀⠠⠷⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⡱⠧⡀⢰⠓⠤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠈⠲⠒⠉⠉⠉⠁⠐⠺⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣱⢠⠀⡆⠀⠀⠀⠀⠀⠀⠉⠓⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⢤⣀⣘⢯⣾⢾⡷⡚⠉⠀⠀⠀⠀⠀⡘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⠉⠉⠒⠲⠮⣉⣀⠀⠀⠀⢠⡇⠀⠀⣶⣟⡆⠀⠀⠀⠀⢰⣲⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠈⠸⡇⢀⠤⡛⠛⠁⠀⠀⠠⠀⠸⠟⠋⢰⣅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⡸⠁⠀⠀⠀⠇⣇⠀⢸⠀⠰⣤⣤⣤⣤⠄⠀⢠⢺⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡈⣆⣠⠤⠤⠤⠐⠖⢲⠀⡄⢰⠁⠀⠀⠀⠀⡜⠈⠓⠋⠀⠀⢣⡀⣠⠎⠀⠀⣾⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣀⡁⠀⠀⡎⢠⠃⣇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣲⢤⣄⡠⢤⡖⠋⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⠀⣘⠛⠂⠰⢇⣘⠂⠬⣁⠒⡄⠀⢸⢷⡀⠀⠀⠀⠀⠀⠀⠉⠛⢄⠀⠀⠸⢣⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⣸⡾⢋⣀⡄⠀⠀⠀⠉⠳⣤⣡⡇⠀⢸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣠⠃⠀⡏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⢶⠆⠀⠀ ⠀⠀⠋⠃⡾⠟⠓⠀⠀⠀⠀⠀⠧⠥⠭⡝⡎⣧⡀⠀⠀⠀⠉⠐⠒⠐⠒⠊⢣⢀⣴⣶⣷⠇⠀⠀⠀⡀⠀⣼⠀⠀⡀⠉⠘⠀⠀ ⠀⠀⠀⠘⠁⠁⠀⠨⡀⠀⠀⠀⠀⠀⠀⠳⠷⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠁⠀⠀⢀⡿⣀⢿⣶⡼⠷⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠤⢄⡀⠀⠀⢀⡀⣾⣻⡟⠁⠀⠀⠀⠔⠁⠀⠉⢸⠉⠩⠍⠀⠰⡰⠦

⠀⠀⠀⠀⠰⠊⠐⠄⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⠠⠂⢉⠇⠀⠀ ⠀⠀⠀⠀⠈⢂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠈⠂⠤⠀⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠤⡈⠆⠀⠀⠀⠀⡇ ⢀⠔⠒⠤⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠐⠁⣾⣧⡡⢸⠆⠀⠀⡖⠀ ⠇⠀⠀⠀⡇⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⡄⢉⡁⠔⡊⠀⠀⠸⠀⠀ ⢆⡀⠀⣰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠐⠁⠀⠀ ⠀⠀⢫⠘⡄⠀⢸⡀⠀⠀⠀⠀⢀⣦⡀⠀⠀⡀⠁⠐⢄⠀⠀⠀⠀ ⠀⠀⠀⡄⢣⠖⠁⠱⡀⠀⠀⠀⠘⢃⢼⠑⠒⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⠀⠀⣇⡠⢃⠴⡎⠈⠢⠤⠤⠒⠁⠀⠡⡀⠀⠀⠀⢄⠀⠀⢱⠀ ⠀⠀⠀⠀⠹⡉⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠤⠒⢮⢤⢠⠀ ⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠁⠀⠀⠀⡆⠁⠀ ⠀⠀⠀⠀⠀⠘⡄⢃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠤⣓⣄⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠞⠋⠂⠈⠙⠉⠉⠉⠉⠑⣦⣶⣒⠖⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣄⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⣽⢿⣵⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣽⣷⣖⡤⣵⣿⣧⣭⠁⠀⠀⠀⠀⠀⠀ ⢀⡤⢦⣄⡈⠛⠈⠛⠋⠉⠋⠻⣿⣿⡿⣧⣀⠀⠀⠀⠀⠀ ⣾⠁⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠉⠻⣦⠀⠀⠀ ⢹⡄⠀⠀⠘⣿⣦⡀⠀⠀⠀⣠⣾⣿⢯⣯⣤⡀⠈⣷⣄⠀ ⠈⢷⡄⠀⠀⠸⣿⣿⣦⣤⣼⣿⣿⣿⢾⣿⣿⣷⠈⠇⡹⡦ ⠀⠈⢿⣷⣄⡀⠘⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⡄⠀⠙⢣⣿⠿⠿⠟⠛⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⣠⡿⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠀⠀⠶⠻⣷⣄⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠖⢉⣌⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠈⠉⠲⣿⣿⡜⡀⠀⠀⠀⠀ ⡔⢉⣙⣓⣒⡲⠮⡇⠀⠀⠀⠀⠀⠀⠘⡿⡇⡇⠀⠀⠀⠀ ⡇⠘⣿⣿⣿⠏⠀⠀⠠⣀⡀⠀⠀⠀⠀⡇⠈⠳⡄⠀⠀⠀ ⢹⠀⢻⣿⠇⠀⠀⣀⣀⠀⡍⠃⠀⠀⣠⣷⡟⢳⡜⡄⠀⠀ ⠈⣆⠀⠋⢀⢔⣵⣿⠋⠹⣿⠒⠒⠚⠁⣿⣿⣾⣷⢸⠤⡄ ⠀⡇⠀⠀⢸⢸⣿⣿⣶⣾⡏⡇⠀⠀⢀⡘⣝⠿⡻⢸⡰⠁ ⠀⢳⠀⠀⠈⢆⠻⢿⡿⠟⡱⠁⠰⠛⢿⡇⠀⠉⠀⡸⠁⠀ ⠀⠈⢆⠀⠀⠀⠉⠒⠒⣉⡀⠀⠀⢇⠀⡇⠀⠀⢠⠃⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢉⡱⠀⠀⠉⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠦⣀⣉⡉⠁⢀⣀⣠⠤⠒⠥⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣉⣀⣀⡠⠭⠛⠀⠀⠑⠒⠤⠤⠷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢀⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠘⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠸⣿⣿⡄⠀⠀⠀ ⠀⠀⣸⣿⣿⠃⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⡄⠀⠀ ⠀⢰⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀ ⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⢠⣾⣿⣿⠃⠀⠀⠹⣿⣿⣷⠀⢀⣴⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀ ⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣤⣤⣤⣄⣀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⣿⣿⠿⢋⣵⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣭⡛⢿⣿⣿⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢁⣶⣿⣿⡿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣦⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⡄⠀⠈⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⣀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀ ⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀ ⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⠛⣁⣽⠖⠲⢤⣀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠃⠀⢀⣤⣞⣿⡟⣠⠴⣚⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⡾⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠝⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠂⠀⣼⣵⣾⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣁⢆⣄⣈⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠤⠄⣰⣾⣿⠿⣫⣿⢯⡟⣿⡟⠃⣼⣿⡯⣿⣿⣿⣿⣾⣿⠿⣶⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⣾⣏⢨⣷⣾⣿⡿⠫⣴⣿⣷⣿⣿⣿⣅⢸⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢫⣿⣿⣿⣿⡿⠋⣿⡟⣿⣿⡿⡿⣃⣿⣿⣿⣦⣿⠿⣿⣿⣿⣿⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⠁⠁⠀⠋⠸⣽⠟⠘⠹⡇⢹⣿⣿⢿⣿⠀⢸⠛⠛⠋⠁⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡸⣿⡇⠀⢀⠀⠀⠐⠁⠀⠀⠀⠀⢸⣿⣿⠀⣿⠀⠀⢳⡖⠒⠒⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣬⣥⡜⢹⠀⠀⢤⣀⠀⠀⠀⠀⢸⠃⠇⠀⠁⠀⠀⠈⡇⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠙⣟⠁⠀⢸⡀⠀⠀⠈⠉⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡄⠀⣾⠉⠲⣤⣠⡤⠖⠉⠉⣩⣿⣀⡤⠶⢦⡀⠀⣸⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠉⠉⠉⠉⠹⣄⢸⣆⠀⠈⡷⣄⠀⠀⡼⢳⡄⠁⢠⠷⠶⠿⠶⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠙⢦⠀⠀⠀⠀⠈⠾⡇⠻⢷⣶⣞⢧⣸⠁⠀⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢹⢷⣶⠀⠀⢨⢿⠀⠀⢸⠀⠈⣇⣀⣀⣀⡤⠤⠤⠴⠶⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡗⠲⠦⣄⡀⠀⠀⠀⣸⢀⣀⣀⠀⢤⣸⣾⣿⠀⠀⠋⠘⢇⠀⠈⡇⠀⠘⣦⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡾⠉⠳⣄⠀⣷⡿⠉⠀⠀⡸⠀⠉⠉⠀⠀⠀⠀⠈⣆⠀⠹⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢈⣷⡟⠀⠀⠀⢠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⡞⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⣲⠏⡞⠀⠀⠀⠀⡼⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡿⣧⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡉⢿⣓⡦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⣿⠟⢹⠟⠓⢦⣀⠀⠀⣰⠋⡼⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⣷⢿⣳⡄⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣎⢿⣿⣿⣶⣤⣍⣉⡛⠒⠦⠤⠤⣀⣠⣞⡿⣰⢣⡴⠃⣀⣴⠛⠉⣹⣴⣣⠾⢅⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⣟⠳⢿⢿⣄⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣼⠛⠉⣩⡝⣛⡋⠈⠙⣿⣿⣿⠗⠦⣀⣹⠂⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⣿⣷⠃⠳⠙⣦⣹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢌⡻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢿⣿⡾⣷⡄⠀⠀⠀⢻⡀⠀⣨⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⢀⣀⠀⠉⢳⣳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣕⡦⢌⣉⠁⠙⠛⠙⢽⠀⠀⠐⠢⠌⠉⠉⠉⠀⠀⠀⠀⢀⣣⢠⠇⠀⣸⢤⣴⠒⠛⠋⠉⠉⠉⠉⠙⠛⢻⠒⠤⢄⣀⢰⡗⣲⡤⠬⢥⣀⣻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠽⠷⣶⠶⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢰⢧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⣁⣠⠤⠈⢽⣿⣿⣡⣼⡇⠀⠉⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⣠⠾⣄⡀⡞⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣁⣀⣀⣀⣘⣿⣿⣿⣿⡇⠀⠀⠩⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡠⣀⠔⢛⡆⠀⠀⠀⠀⠀⠀⠀⣀⡠⠾⣟⠢⣀⢹⡟⣿⡴⠚⠁⠀⠀⠀⠀⡰⣿⣟⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⣀⣀⠠⠤⠤⠤⠤⠤⣀⣀⣘⣃⣈⣩⣝⣋⣁⡤⠚⠀⠀⠀⠀⠀⢀⡴⠚⢻⡀⠀⠸⡀⠈⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠸⣟⣄⠀⡇⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢟⣿⣿⠟⠋⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⠈⠻⠇⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⣸⣿⣿⣷⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣵⡤⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⣄⢠⣿⣿⡟⠻⠇⣠⡾⠀⠀⠀⢠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣌⡛⣟⣿⣿⣧⣬⣛⢩⣴⠆⠀⠀⢸⣇⢠⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⣾⣿⣿⣿⣿⣿⣿⣷⣴⡛⠀⠀⢀⣾⠘⠁⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⠟⢻⢿⣿⣿⠋⠉⠉⢿⣿⣷⣔⢿⠇⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⠏⠀⡀⠀⠈⠁⠀⠀⠀⣠⡹⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⡟⠀⠀⢿⣄⠀⠀⠀⠀⠴⢿⡷⢹⣿⣿⣿⣷⡄⠀⠀ ⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠉⣿⡎⠉⠛⠛⠻⠿⢈⣿⣿⣿⣿⣿⡄⠀ ⠀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀ ⡀⣿⣿⡟⣿⡏⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠃⣿⣿⢿⣿⣿⠚ ⠀⠿⣿⡇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠸⠿⠈⠀ ⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡤⠔⠒⠚⠉⢙⣒⣒⡤⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠁⠀⠀⠀⢠⠊⠁⢠⠊⠉⠁⠀⡤⢌⢢⠀⠀⠀⠀⠀⠀⠀ ⢀⠏⠀⠠⠀⠀⠀⡇⠀⠀⢸⡶⠀⠀⠸⢷⠈⢣⠱⡀⠀⠀⠀⠀⠀ ⢸⠀⡰⠁⠀⠀⡜⠀⠀⠀⢸⣇⠇⠀⣀⡙⠓⠁⠀⠱⠀⠀⠀⠀⠀ ⢸⢠⠃⠀⢀⠜⠀⠀⠀⠀⢈⡆⠀⠹⠤⠃⠀⠀⠀⣀⣿⠀⠀⠀⠀ ⢸⣸⠀⣠⠋⠀⠀⠀⢀⠠⠬⠃⣾⡆⣠⣄⠀⣴⣦⠛⠻⡀⠀⠀⠀ ⠀⢿⣰⠁⠀⢰⠒⠖⠁⠀⠀⠀⠀⠀⠙⠋⠀⠈⠁⠀⠀⠈⢦⠀⠀ ⠀⠈⠷⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢱⣄ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⡠⠊⠑⠢⠤⠤⠭⠟ ⠀⠀⠀⠀⢸⠀⠀⢀⡔⠒⠤⣤⠬⢦⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠒⠓⠉⠀⠀⠀⠀⠉⠉⠑⠤⣔⣳⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣄⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡉⠛⠲⠿⣿⣿⣿⣿⣿⣿⣿⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⡀⠀⢰⡆⠈⠙⢿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣤⣭⣬⣥⣀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣆⢮⣫⣦⠈⠉⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⣯⠛⢮⣻⡽⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⠀⠀⣨⣭⣥⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡈⠙⠿⡿⢸⣿⣿⣿⣿⣿⣇⣤⣈⠛⠛⠉⢀⣤⣾⣿⠀⠀⠀⠀⠀⠘⣿⣿⢆⡇⣀⣠⣤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠗⣠⣾⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⠿⠋⣁⣤⠀⠀⠀⠀⠀⢻⠟⣾⠇⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⠛⠀⠀⠀⠀⠀⢀⣾⣿⠘⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⢿⣿⣿⣿⣿⣮⣁⠀⠀⠀⣠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠋⢸⣿⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⡺⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁⠀⠸⠇⠀⠈⠛⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡈⢻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⢟⣡⢻⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣶⡆⠲⢶⣶⣿⣿⣶⣶⢺⣿⣿⣧⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⠉⠉⠀⠘⢿⣟⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢢⠀ ⠀⡄⣿⢻⣿⣿⡟⣿⣿⣿⣿⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⣿⣿⣿⣿⡇⣿⣿⣿⡏⣿⣼⡆ ⢸⡇⣿⢸⣿⣿⣿⠸⣿⣿⣿⡇⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⠋⠀⢸⣿⣿⣿⡇⢿⣿⣿⡇⣿⡇⠀ ⠈⠃⣿⡼⣿⣿⣿⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⢸⣿⣿⠇⠿⠁⠀ ⠀⠀⠹⠇⢿⣿⣿⡆⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠸⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠋⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡵⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠤⢀⡀⠀⠀⠀⠀⠠⠙⠁⠀⢀⠘⣦⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀ ⠸⠀⠀⠈⠑⠠⡀⠰⢁⠀⠀⠀⡜⢣⡇⢣⡠⠔⠊⠁⠀⠀⠰⠀⠀⠀ ⠀⢃⠀⠖⠠⢀⢨⢳⢻⠀⡠⠊⠀⢸⠀⢸⠀⡀⠄⠂⠏⢁⠂⠀⣠⢣ ⠀⠈⠄⠈⠌⠢⣙⢆⠘⢾⠀⠀⠀⠀⡠⠗⢬⠂⠉⡜⠀⣌⠔⢩⠃⠸ ⠀⠀⠈⢄⠈⢢⠁⠀⠁⠀⠀⠐⠒⠚⠈⠀⠈⠤⠊⢀⡞⢪⠀⠀⠀⢸ ⣀⡀⢀⣀⣢⠀⡎⢢⢃⡇⠀⠠⣁⢧⠂⣢⠀⠀⡄⣉⣀⣉⣒⠠⡴⡸ ⠙⠢⠄⣀⠀⠠⢸⢦⡆⠀⠀⠀⠀⡤⡊⡇⡀⠈⠀⠀⡠⠔⠈⡴⣡⠃ ⠀⠀⠶⢈⣁⡀⠫⣤⠃⠀⠀⠀⠀⠐⣔⡠⠀⠐⠚⢃⠤⡠⠺⠂⠁⠀ ⠀⠀⠀⠀⢡⠌⠢⡀⠂⢤⠭⠤⢤⠔⠀⡀⠔⡉⠅⡲⠞⠂⠀⢣⠀⠀ ⠀⠀⠀⠀⠘⡄⡄⠈⠐⠂⠱⠶⠒⠒⠉⠀⠀⡠⡎⠑⠤⣀⣀⠜⡆⠀ ⠀⠀⠀⠀⠀⣨⠛⠢⢀⡀⠒⠤⣄⣀⣀⡤⠊⠀⢘⠀⠀⢡⠀⢀⠇⠀ ⠀⠀⠀⠀⠜⠀⠑⢒⠶⢹⡉⠝⠁⠀⠀⠱⡒⠂⠁⠃⠀⠀⠣⠊⠀⠀ ⠀⠀⠀⠈⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠜⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠐⠠⣀⠤⠚⠀⠀⠐⢄⠀⢀⣠⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⣤⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⢀⠤⣀⣤⣬⡇⠀⠀⠀⠀⣰⣿⠿⣿⡏⡟⠛⠛⠛⠛⠋⠉⡁⠀⣀⠀⠀⠀⠀ ⡔⠉⠘⠄⠀⢠⣿⢤⣤⣤⣾⡿⠡⣰⣿⠁⠇⢀⣀⡀⢀⣀⣨⠀⠀⠀⠀⠁⠢⡀ ⢂⠀⢀⠠⠐⣾⣿⣆⣿⣿⠿⠿⠿⠟⢁⢌⣃⣀⡀⠀⠀⠀⠀⠸⡉⠁⠢⡮⢁⠀ ⠀⠉⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⡐⣴⣵⣿⣿⣦⠀⠈⢁⠒⠄⡀⠈⠒⠀⠂⠀⠱ ⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢀⡹⣿⠻⣿⠀⠐⢆⠁⠀⡀⠜⠢⡀⠀⠀⢀⠎ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢠⠁⠀⠈⠂⠈⠀⠀⠀⠈⡇⠀⠀⠀⠐⠒⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⠀⠀⢠⡤⡀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⠇⠈⠀⢺⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠯⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣄⠀⠉⠁⠓⢤⡇⠀⠀⠀⠀⣀⠄⡴⠃⢀⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠈⠢⡴⠒⣋⠴⠋⢀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠈⢯⡥⠤⠒⠉⠀⠀⠀ ⠀⠀⣏⠑⠒⠤⣠⠎⠀⠀⡇⠀⠀⠀⣰⣯⣻⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡝⢆⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢆⠀⠀⠘⠀⠀⠀⡇⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⣹⣷⠈⢣⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⡠⠖⠉⢠⠘⣇⠌⢧⣀⠾⡇⠀⠀⠀⠀⠀ ⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢸⠀⣿⠀⠀⠁⢀⡇⠀⠀⠀⠀⠀ ⠉⠉⠓⠒⡾⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠺⠠⠧⠤⢄⣀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⢀⣶⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠤⣀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠽⠂⠀⠀⠀⠀ ⠀⠀⠀⠰⠖⠊⠁⠀⠙⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠖⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠶⣽⣶⣿⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠳⢄⣈⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣴⡄⠀⠀⠀⢸⣆⣀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠉⢒⠞⠉⠉⠉⠐⠒⠒⠒⠲⡿⠻⠛⠛⠛⣿⡄⠀⠀⡇⠀⠈⠉⣒⠺⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⠛⠛⠋⠉⠳⣄⡼⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣛⣋⠉⠉⠉⠉⠉⠒⠲⠤⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⡱⣿⠦⡀⠀⢀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡉⠒⣺⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡑⠀⡿⠀⠈⠞⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠁⠸⡇⠀⠀⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣠⠄⠒⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠉⠀⠈⠛⢥⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠖⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⢔⡏⠀⠀⠀⠀⠸⣷⠠⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠔⠋⠉⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⢠⢣⠊⠀⠀⢀⠆⠀⠀⠀⢀⠊⠀⢠⢁⡎⡸⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣅⠀⠀⠀⡼⠀⠀⢀⡔⠁⠀⣠⡇⡞⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡇⠀⢠⡞⠀⢀⠔⢹⡎⠀⡞⠀⠀⠀⠀⠀⠀⢠⡒⠒⠷⠿⠷⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠇⢀⢻⢃⣴⠁⠀⢨⠇⣸⠁⠀⠀⠀⠀⠀⠀⢸⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡈⠸⠃⡇⢰⠀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⢳⠀⠀⣸⢁⢆⡼⡡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢣⠀⣼⠰⢠⣇⠮⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⢤⡀⣃⣷⣡⢷⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠰⡇⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡴⠋⠁⠀⢠⠎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠁⠢⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡠⡶⢀⡜⡰⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠲⣄⡀⠀⠈⠳⢄⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⠁⠗⠃⢿⡟⠙⣿⡈⡄⠀⠀⠀⠀⡄⡀⣰⡟⠀⠀⠀⠀⠀⠀⠈⢯⡑⠢⠄⣀⠑⠢⢀⣀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⠐⢣⢹⡀⠀⡆⣼⣴⠗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⡴⠚⡟⠢⢄⣀⠀⠳⣄⠀⡟⢲⠒⡇⠀⠀⠀⢑⡇⡼⠛⠉⠁⡼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⢷⠀⠀⠈⠙⠒⠬⣿⣇⣸⡀⡇⠀⠀⢀⠏⢹⠀⠀⠀⣰⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠳⣸⠀⠀⠀⠀⠀⣠⠃⠀⢨⣧⡇⠀⠀⡼⠀⡟⠀⠀⢠⠇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢳⢦⡀⠀⠀⠀⠙⢆⠀⠀⣀⠔⠁⢀⡠⢛⣿⠀⠀⢰⠃⢀⡇⠀⠀⡞⠀⠀⠀⠀⠹⡢⢀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⢧⠉⣳⣤⣀⠀⠈⠳⣮⡥⠴⠚⠉⠀⢸⡏⠀⢀⡟⡀⢸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠑⢤⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢿⡁⢀⡏⠑⢢⢤⣈⠳⢄⡀⠀⠀⢸⠇⠀⡼⠀⠑⢿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⠓⠦⣄⡀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠙⢼⡀⠀⣿⠀⠈⠉⠓⠻⠶⣄⣸⠀⢠⣧⡀⠀⠈⡇⠀⢸⠈⢲⢄⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠐⠒⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⢷⡤⣿⢤⠀⠀⠀⠀⢀⡤⣧⣄⣼⣽⣽⠀⠀⢳⠀⠀⢳⡢⠧⠌⠒⠤⢄⣀⡀⠀⠈⠑⠤⢀⣀⣀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠧⠼⠼⠀⠀⠀⠀⢿⣰⡇⢸⡆⣹⠀⠀⠀⠸⡄⠀⢄⢹⠓⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⣤⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⡟⠉⠉⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣀⣠⣿⡿⠉⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠿⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠋⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⢀⣄⡈⠙⠻⠟⢁⣠⣈⠙⢁⣠⣶⣤⣾⣿⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⣤⣾⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡀⢾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣤⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠯⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠙⠋⠁⠈⠛⠋⠈⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢀⠀⠀⠀⡆⠀⠀⢀⡤⢿⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣼⠀⠀⠆⡇⢀⣿⣿⡇⠐⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠙⠯⠿⠟⠗⠚⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠐⠃⢀⣠⣤⣤⣤⣠⡤⠞⠃⠀⡰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡆⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⢾⡉⠀⠀⣀⣠⣤⡤⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢧⡟⢸⠀⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠷⢾⠋⠀⠀⠀⠀⠰⢿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠸⠶⠾⢸⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠴⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢄⡀⠀⠀⠀⠀⣠⠠⣳⠀⠀⠀⠀⢿⣿⡿⣄⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣀⣠⠤⣾⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢚⡟⠯⠟⠀⠀⠀⠀⠀⠉⠈⢿⡀ ⠀⠀⢀⣠⠞⠁⠀⠀⠀⣠⠔⠚⠉⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⣏⠓⢦⡄⠀⠀⠀⠘⣦⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃ ⢀⣴⠟⠁⠀⣀⡀⢀⡴⠋⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠹⡆⠀⢻⡆⠀⠀⠀⠸⡆⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⣾⣿⠑⣄⡎⠀⣿⠞⠁⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠹⣄⡾⠃⠀⠀⠀⠀⢹⡀⠀⠀⠈⣇⠀⣞⢳⠀⢰⠇⠀⠀ ⢻⣿⡀⣸⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢽⣇⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠉⢹⠉⢹⠟⠋⠀⠀⠀ ⠀⠉⠳⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠸⡟⠳⡀⡴⠻⣦⡶⣿⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⢳⣼⡟⣿⣆⣾⡶⠋⠀⢀⡴⠋⠀⣀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠿⠿⠥⠤⠤⠔⠋⠀⢀⡠⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠴⢋⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⡀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡠⠤⠒⠋⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠑⠒⠒⢺⣄⠀⠀⢀⡀⠀⠀⠀⢸⣇⡀⣀⣠⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠹⡄⠀⠀⠈⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⡿⣄⣀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠶⠆⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣷⣏⡴⢋⣸⠦⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣧⡴⠋⢳⡀⡞⠹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⢷⣀⡼⠛⠻⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⢀⠀⢠⣿⣷⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⠀⠀⠀⠀⠀⠀⢢⣸⣿⣷⣄⠀⠸⡄⢸⣿⣿⡆⣿⡀⠀⠘⡢⡀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣶⣤⡀⠀⠀⠀⢻⣿⣿⣿⣧⡀⣿⣾⣿⣿⣿⣿⣧⠀⠀⢃⠈⠢⡀⠀⢰⡀⢰⠀⢳⠀⠀⠀⡀⠀⠀⣠⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣦⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢷⣦⣘⡀⠀⠈⠢⣸⠐⠌⠀⠀⢇⠀⡔⡇⢀⠜⣧⡾⠃⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠻⣷⣄⡀⠀⠈⠀⠀⣆⠀⠘⠜⠀⡧⠁⣰⡟⠁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⣷⣄⠀⠀⠀⣿⣦⠀⠀⠀⠀⢀⡟⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣈⣑⣲⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣆⠀⠀⠀⠈⢿⡆⢦⡀⢸⣿⣧⢸⣆⠀⣸⠃⠀⣸⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠳⣦⡀⠀⠈⣿⣾⣿⣾⣿⣿⣿⣿⣿⣏⢀⣜⠉⠌⠀⢂⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠙⠛⠛⠓⠀⠀⠈⢿⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢈⣽⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣯⣍⣉⡁⠀⠀⣰⢿⣿⣿⣧⠀⠈⠙⢿⣿⣿⣿⣿⠏⠁⡏⠓⠒⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⡿⠟⠋⣀⡀⠀⢁⣿⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣿⣤⣼⡇⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠸⠟⡽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠃⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣠⠄⠀⠁⠟⠋⠛⠻⣿⣿⣿⣿⣿⣿⠟⠁⢠⡬⠽⠯⠭⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢏⣠⣴⠾⢋⡦⡾⠀⠀⠀⠀⡀⠀⠈⠉⠛⠛⠛⢁⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠊⢠⠃⠀⢀⠄⠺⡰⡇⠀⡰⠣⡀⣸⣮⣿⣶⣦⣄⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⡜⡠⠒⠁⠀⠋⠀⣇⡜⠀⠀⠱⡏⠙⠻⢿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⡀⠐⠁⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠉⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠈⠑⠦⠤⠤⠤⠤⠤⠀⠒⠒⠒⠒⠒⠒⠒⠢⠤⠴⠚⠉⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠉⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡶⠒⣆⠈⢣⠀⠀⠀⠀⠀⠀⠀⣸⠂ ⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⣿⣆⠘⡇⠀⣧⣀⣀⣀⣀⣀⣠⠇⠀ ⢀⡴⠉⠀⠀⠀⠓⡄⠀⠀⠠⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⣿⠤⠞⢀⡏⠀⠀⠀⠀⣸⠃⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠁⢀⣤⠴⠋⠀⠀⠀⠀⢀⠏⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠉⠀⠀⠳⡤⣄⣀⣀⡜⠀⠀⠀⠀ ⠙⢦⣀⡀⠀⣀⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣏⠁⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢰⠒⠊⠁⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⣇⠀⠀⣠⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢦⣀⠀⠀⢸⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⢸⡴⠚⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠛⠋⣰⢴⠉⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠑⣆⠀⢀⣠⠞⠙⢤⠀⠀⠀⠀⢀⡤⠞⠁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀ ⠀⠀⠀⠀⠀⠹⣢⡴⠋⣡⡖⠉⡟⠀⠀⠀⠉⠒⠒⠋⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡍⠀⣧⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣀⡤⠼⣦⣏⣀⣀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠞⠉⠀⠀⠈⠹⡙⠧⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⢗⠛⠒⠦⠤⣤⣤⣤⠤⠤⠤⠴⢇⡀⠀⠀⣀⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠓⠚⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⣷⣟⡻⣭⡩⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠸⣿⣿⣶⣄⡀⠀⠀⣶⣦⡀⢀⣾⣿⣠⣾⣿⡇⠀⡀⠀⠀⢀⣠⣴⣿⣿⠇⠀ ⠀⠀⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣴⣾⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠈⠉⠻⣿⣿⠟⠉⠁⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⣿⣿⣿⣇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣸⣿⣿⣿⣧⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⢼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⡧⠀ ⠀⠀⠙⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠉⠉⠙⠋⠉⠉⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠀⠀⠀⣮⣾⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⠀⠀⠀⠯⠭⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠱⣄⣀⠐⠀⣀⣀⣀⠠⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀ ⢰⣳⠁⠚⢿⠄⣀⡠⣔⢪⠒⠁⠼⠄⠐⠈⠵⣧⠀⠀⠀⣇⡀⠱⡀ ⠀⠈⢀⠀⠀⡜⠀⠀⠀⠀⠑⡀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡆⠹⡄⡣ ⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠀⠐⡀⠀⢊⠁⠀⠀⠀⠀⠀⠸⣀⣹⠇ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⡄⠀⠀⠀⠀⠀⠀⡘⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⢀⠔⠀⠇⠀ ⠀⠀⠀⢀⠔⠉⢂⠀⠀⠀⠀⠀⡜⠒⠀⢺⠁⠐⠂⠈⠁⠀⠜⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⠁⠢⠄⣀⡔⠀⠀⠀⢸⠀⠀⠀⢀⠠⠊⠀⠀⠀ ⠀⢀⣠⠒⠉⠀⠀⠀⢪⠀⠀⡱⠀⠀⠠⡎⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠑⠒⠒⠀⠈⠁⠀⠀⠙⢵⡵⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢂⠄⠚⠉⣀⠠⠄⢐⠲⠊⠁⠀⠀⠀⢀⠠⠄⡲⠒⠁ ⠀⠀⠀⠀⠀⢠⡪⠄⠀⠀⠃⢤⢔⠨⠒⠈⠁⡂⠀⠀⠀⢀⠄⠊⠀⠐⠁⣀⡠⠀ ⠀⠀⠀⠀⢠⢎⣆⡀⢰⣲⠄⠀⠬⢤⠀⠒⢨⣹⠇⠀⣔⠕⠈⢉⢇⠠⠒⠉⠀⠀ ⠀⠀⢠⠢⡿⠈⣞⢫⠆⠠⠈⢑⠀⢈⡤⠄⡄⠁⠀⠘⠁⠀⢠⠗⠁⠀⠀⠀⠀⠀ ⠀⠀⠘⣄⠰⡄⠀⠀⠀⠀⠉⠁⠐⠁⠘⣀⠃⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡘⠉⠈⠑⢄⠀⠀⠀⠀⠀⠠⢢⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⠀⡠⠄⠀⢄⢀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢣⠀⠀⠀⠀⠈⠎⠀⠀⠀⠒⢓⢧⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠣⡀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢹⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⡀⠈⠐⡤⢀⣈⡄⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⢀⠎⠀⢀⠔⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠪⠄⡲⠖⠁⠀⡔⠓⠊⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠄⠐⠉⠀⠀⠀⢌⢠⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⡀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠄⠸⣰⣮⡁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⡀⠀⠀⠀⡀⢀⠎⠀⠀⠀⠀⠀⠀⠰⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠢⢥⣬⠄⠀⢸⡀⠀⠀⠀⠀⠀⠀⡞⠻⣰⣄⠀ ⠀⠀⠀⢀⠄⠀⠐⠊⡤⠄⡀⠀⠀⠁⠤⢀⡀⠀⠀⣱⠀⠀⣼⡀ ⠀⢀⠔⠁⢀⠤⠐⡎⠀⠀⠐⠀⠀⢲⠄⠀⠈⢄⢸⠛⠀⠀⠀⢸ ⣰⢅⣔⡶⠁⠀⢸⠀⠀⠀⠀⠃⠀⠀⢂⡇⠀⠘⡄⠑⣄⣤⢠⠁ ⠙⠺⠋⠀⠀⠀⣈⠀⠀⠀⠀⢸⡀⠀⠈⣧⡠⢤⡅⠀⡘⢸⠅⠀ ⠀⠀⠀⠀⢀⠊⠘⠄⠀⠀⠀⡘⠀⠀⠀⠙⡿⠎⠥⠊⣠⠎⠀⠀ ⠀⠀⠀⠀⡧⠀⠀⠈⢂⡄⣀⣃⠀⠀⠀⢀⠧⠄⢐⠨⠊⠀⠀⠀ ⠀⠀⠀⢀⡜⠀⠀⢀⡇⠀⠀⠈⣢⠈⣄⠈⡅⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠮⠓⠂⠁⠀⠀⠀⠀⠷⡎⡢⣗⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣾⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⡧⢀⠀⠀ ⢷⣦⣤⡀⠀⢀⣠⣤⡆⢰⣶⣶⣾⣿⣿⣷⣕⣡⡀ ⠘⣿⣿⠇⠀⣦⡀⠉⠉⠈⠉⠁⢸⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⣀⣴⣿⣿⣄⣀⣀⣀⢀⣼⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡿⢻⣿⣿⣿⣿⡿⢿⠇⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⠰⠙⠁⠈⣿⣿⠱⠘⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⣾⡿⠁⠀⠀⠀⢿⣼⣷⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⢿⣧⡀⠀⠀⠀⠈⠛⢿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣶⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣶⣿⠟ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠈⠳⠤⠔⠒⠉⠉⠉⠑⠒⠤⠔⠉⠀⠀⢀⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀ ⢋⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⡘⢀⣤⢀⠀⠀⠀⠀⠀⢀⣤⣀⠈⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠉⠉⠒⢲⠇⠈⠛⠛⠀⠀⢀⠀⠀⠈⠛⠋⠀⢃⠀⠀⠀⠀⠀ ⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠠⢠⠤⡄⠀⠀⢠⣾⣷⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⢹⠂⠀⢀⠎⢆⠉⠀⠀⠀⠈⠂⠁⠀⠀⠀⠉⢉⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠣⢄⡸⢠⠀⠀⠀⢣⠀⠀⠀⢀⠄⠀⠀⢠⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠇⠀⠣⡀⠀⠀⢆⠀⠀⢸⠀⠀⢀⠞⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢅⣸⠀⠀⠀⠙⢤⠴⠚⠂⠀⢮⣤⣤⠎⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠂⢤⠤⠤⠤⠤⢤⡤⠤⢤⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠒⠁⠀⠀⠀⠀⠀⠈⠒⢤⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⢒⡲⠶⠚⠛⠒⠀⠀⣀⣀⠠⠤⠄⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣠⡶⠖⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⡴⠋⠀⠀⠀⣀⠤⠒⣉⡁⠤⢤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢀⠴⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠤⠒⠒⠒⠒⠒⠓⠢⢤⠔⢋⡤⠒⠉⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⡼⠁⠀⠀⣀⣀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣥⠀⠀⠀⢀⣠⣀⠀⠀⡏⢰⠋⠀⠀⠀⣀⡀⠤⠼⢗⢦⠀⠀⠀⢀⠞⣁⠴⠒⠒⣦⠀⠉⢒⡹⠝⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠛⣷⢿⣤⣀⠀⠹⣦⡿⠀⠀⠉⠉⠉⢻⠉⠀⠀⠀⢿⣤⣼⠟⠀⠀⣰⡷⠋⠀⠀⢀⣴⢋⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡦⣄⣟⠄⠸⣶⠿⢿⣴⠆⠀⡴⠉⠉⢦⡀⠀⠀⢣⣀⡠⢤⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠘⢿⠀⠀⠙⠓⠚⠁⠀⠀⠙⠤⠤⠞⠀⣀⠴⠺⣅⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⣀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⢠⠗⠋⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣀⠤⠄⠠⠤⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡠⠊⠀⠀⠀⠀⢀⣨⣔⣁⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⢀⡤⢺⡀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣇⠀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠉⢲⠤⠄⣀⣀⣳⡄⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⡰⠋⠀⠀⠀⢀⠜⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⣠⠞⠀⠀⠀⢀⡴⠋⣀⡠⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠾⠅⣠⠤⢒⡶⠊⠁⠀⠀⢀⡴⠛⠒⠊⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠇⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⢠⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠓⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⢳⡇⢰⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠶⣄⡈⠂⠔⠀⠀⠈⠀⠀⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡘⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠒⣉⣉⠛⢿⣿⣿⣄⠀⢀⣠⣤⣶⡾⠛⠋⠙⠁⣀⠔⠁⣠⣬⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐⠁⢞⣯⠎⣸⠿⠛⠉⠀⠘⢿⣟⢭⣭⡅⠀⠀⠀⠀⡠⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⢀⣠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠃⠀⠀⠀⠰⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣤⣤⣤⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠠⠔⠒⠉⠉⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⠟⠛⠛⠛⠛⠻⢿⣷⣤⣄⣀⣠⣤⡶⠦⠤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠈⢳⣆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠐⣶⣿⣿⠿⣿⠖⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣇⣿⣀⡈⠀⠀⠋⠉⠙⠛⠛⢲⣦⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⡿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣄⡉⠙⠛⠛⠛⠛⢻⡿⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⠶⠒⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠲⣤⣤⣤⣤⣴⣾⣿⡿⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠢⠤⠤⠤⠤⠔⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢸⠀⠀⠈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣧⠀⠀⢸⡀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⢀⡴⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⣰⣶⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠈⢳⡀⢀⡴⠃ ⠀⠀⠀⢀⡴⠋⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⣿⡉⠛⣷⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠛⠟⠃⡠⠂⠉⣿⣏⠀⠀ ⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠦⣄⡀⢀⡠⢾⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢰⠁⠀⣰⣿⣿⣿⣷ ⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠋⠀⠈⢧⡀⠀⠀⣀⠤⠀⠤⢄⠙⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢀⣠⣀⠀⠈⣠⣾⣿⣿⣿⣿⣿ ⣿⡷⠦⠤⠤⠤⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠻⣤⡐⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠊⠀⠈⢦⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠢⢄⡀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣠⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢠⣿⣿⡍⠙⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠻⢿⠛⠆⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣆⣘⣦⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠁⢰⣴⠀⠀⠀⠀⣿⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⠀⠈⠙⠃⣀⣀⡀⣤⡄⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠉⠁⠂⢦⣀⢀⡀⠤⠤⣥⣌⡀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠦⡀⠀⠀⠀⠈⡄⠂⠉⠀⣀⠵⢵⡒⠠⢴⡋⠉⢑⠖⠦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠲⢤⣤⣴⡥⢄⡨⠋⠀⠒⢄⡑⣄⠀⠈⠄⠀⠀⠀⠈⡝⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣆⡇⠀⠀⠊⠉⠉⡆⠈⠢⣶⣀⡀⢀⡰⠋⠀⠀⠉⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣔⠀⠠⡀⠀⢀⡇⠀⠀⠠⣇⠈⢹⠀⠀⡀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣶⣶⢆⠀⠀⠈⠉⠈⢄⠀⠀⠀⠂⠀⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠑⠦⣄⠀⠀⠀⠁⠀⠈⠀⢀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠖⠒⠊⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣤⣶⣿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⡿⢿⣿⣿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⣴⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⢿⡟⠛⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⣠⡖⠀⠀⢀⣸⡿⠁⠀⠘⠿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢔⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⢸⡇⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⣉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠊⠀⣶⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠉⢿⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠈⣧⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⠖⠀⠀⠉⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢿⣦⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢿⣧⠀⠀ ⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣿⣇⠀ ⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢯⣛⣛⣥⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢹⣿⡄ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⡇ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿ ⢸⡇⠀⠀⠀⢠⠞⠓⢄⠀⠀⢀⣴⣿⡟⢱⢆⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣿ ⣸⡇⠀⢀⡴⠁⠀⠀⢀⣷⣿⣿⣿⣿⡀⠃⠈⠀⢀⢚⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿ ⣿⡇⢠⠎⠀⠀⠀⠀⠸⠏⠘⡿⠋⠟⠃⠀⠀⠐⠃⢸⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⣿⡏ ⣿⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠁⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣿⣿⠃ ⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢇⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣾⣿⠏⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⡌⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⣠⣿⣿⡟⠀⠀ ⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠉⠙⠻⠿⣷⣤⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⣝⠻⢿⣿⣿⡿⢿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⣽⣿⣷⣤⣤⣦⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢰⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⡆ ⢸⣿⣿⡆⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣿⣿⣿⣿⡇ ⢸⣿⣿⣇⠀⠀⢀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⡄⠀⠘⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢀⣠⣴⣾⠃⠀⢀⣾⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣷⣦⣀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣾⣿⣿⣿⠃⠀⢀⣾⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣿⣷⣤⡀⠈⢿⣿⣿⣿⡿⠟⠛⣿⠿⠛⡿⠿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣴⣿⣿⣿⣿⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢻⡿⠁⢀⣾⣿⣿⣿⣿⣿⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠛⢿⣿⣿⣿⡿⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⠟⠋⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⣆⠀⠀⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣦⣴⡧⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⢹⣿⣿⡟⠀⠸⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠋⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠑⠒⠋⠉⠑⠒⠋⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡻⢿⣧⣴⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣴⣿⣿⢋⣶⣤⣄⣀⣀⣀⠀⢀⣀⣀⣤⣶⣷⣌⢿⣿⣷⠭⠛⣿⣴⣧⠀⣠⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣠⣾⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠸⠻⣿⡇⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣿⣿⢿⢸⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡀⠻⣿⡀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⢠⣿⠛⠇⣶⣾⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠂⠸⠋⢿⣿⣿⣿⣿⣿⣿⡿⠁⠁⢀⡾⠁⣾⣾⣿⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢻⡿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠤⠤⠾⠿⠷⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠻⠿⣿⠿⣿⣿⣿⠏⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠀⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⣭⣙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣉⠛⣛⣉⠁⠀⠀⢀⣤⣴⣦⣤⣀⣶⡆⣾⣿⣿⣿⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⠟⠉⠉⠙⢿⣿⣿⣇⢻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣦⡙⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣩⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣴⡾⣿⣿⡛⢋⠉⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣉⣤⣶⣤⣤⡀⠀⠀⣴⣿⠟⠁⣩⣿⣿⣿⣿⣿⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢇⣾⣿⣿⣿⣿⣿⣿⡆⠺⠿⠋⢀⣾⣿⡿⢫⣾⣿⠟⢮⣝⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣳⣾⣷⡄⠀⠈⢿⢸⣿⣿⣿⡿⣫⣶⣿⣿⣿⣷⣄⢻⡿⢋⣴⣿⣿⠟⣠⣴⡿⠷⣟⣯⣤⣶⡶⣶⣄⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠃⠈⠛⢿⣦⣀⣈⡈⢿⣿⡟⣼⣿⣿⣿⣿⣿⠿⣛⣃⣀⣘⠿⠟⢣⣾⣿⡿⠃⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣼⡿⠋⠉⠀⠀⠀⠀⠀⠘⠿⣸⠧⡄⠻⠁⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣷⣄⢻⡟⠋⠀⣼⣿⣿⣿⠋⠉⠵⠿⣿⣿⣿⣿⣿⢋⣷⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠋⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣷⡄⣶⣶⣆⣻⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣀⣠⣴⣮⢻⠇⠀⣷⡄⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣷⣤⡀⠀ ⠀⠀⠀⠀⣿⡇⠀⢰⣯⣽⠉⠉⢩⣍⣉⣉⣩⣭⣥⣭⣍⣻⣥⣭⣭⣜⠿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡸⢿⣿⣿⡿⠀⠀⠀⢹⣷⣀⣀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⢀⣼⠿⠃⠀⢸⣿⡇⠀⢸⣿⠻⠟⠿⠿⠿⠿⢿⣿⣿⠋⠛⣻⣭⣴⣶⣄⠉⠛⠿⠟⢫⣾⣿⣿⣆⣀⡈⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⡴⠟⠛⠁⠀⠀⢸⣿⡧⠀⣾⣿⡀⠀⢠⣼⡻⣿⣿⣿⣿⣿⣿⠎⣿⠿⠟⠃⣀⣴⣿⣿⠈⣙⡻⠿⠃⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡇⠀⣼⣿⡇⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⣾⡛⠻⣿⡇⠀⣿⣧⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠃⠀⢠⣤⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣠⠾⠛⢿⣿⣷⣿⣿⣿⣧⠹⠃⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⢸⣶⡅⢐⡿⠏⠀⠀⠀⢀⣴⣿⣷⡌⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀⣤⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⢻⣧⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠘⢿⣧⠀⢸⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⢰⣿⠆⢸⣿⣿⣿⣿⢿⣿⣧⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢸⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣤⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣉⠉⠻⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠋⢰⣿⣿⣧⣦⡀⣀⣴⣶⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⣄⠹⣿⣿⣧⠀⠀⠀⠈⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⢃⠔⢊⠡⠤ ⠀⠀⠹⡄⢹⣿⣿⣷⠀⠀⠀⠉⠉⠀⠐⠚⠦⣀⠀⠀⠀⠀⠀⡇⠸⢡⠞⠁⣀⣀ ⠀⠀⠀⠹⡄⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠤⠄⠒⠂⠉⠉⠁⠀⠀ ⠒⠒⠒⠒⢻⢮⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠ ⠀⠀⠰⢂⣎⣿⡟⡇⢀⣠⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿ ⠴⠥⠒⢊⡟⣿⣧⡇⡎⠻⣯⠿⢠⠀⠀⢀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⠟⠋⠉⠀ ⠀⠀⠀⠀⠇⠻⠿⠀⠀⠀⠀⠜⢁⠔⠈⣠⣿⣿⣿⠃⠀⢿⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⡄⠀⡀⠀⠀⠀⣴⣿⣿⡿⢋⣠⠟⠁⡀⠀⠀⠉⠢⣤⡤⠤⠖⠒⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⠃⠀⠀⠀⠉⠉⠉⠁⣀⢴⡮⢣⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡤⠄⠤⠰⠦⠝⠂⠁⠀⠈⢆⠸⡦⡀⠀⠀⠈⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠢⢀⡀⠀⠀⣀⠔⠈⠈⢃⠹⢮⡑⠢⡀⠀⢣⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⡆⠉⠢⣀⠑⡀⢃ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠑⣾⡘ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢳⣄⡀⠀⡇⠀⠀⠀⠀⢀⠇⢀⠴⠃⠀⠀⠀⠺⠘ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢪⠻⢄⡀⠀⠀⠀⢀⣞⠔⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⢀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⡿⠓⠶⣤⡀⠀⠀ ⠈⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⣴⣶⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⡌⠻⣦⢻⡀⠀ ⠀⠸⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣄ ⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠰⣄⠀⠀⠉⠛⠛⠿⠧⠀⠘⠛⠛⠋⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠈⢿⣿⣿⡿⠏⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⢶⣶⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣦⣤⣄⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠋⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⣼⡇⣸⠏⠀⠀⢻⣿⣿⣿⣿⡏⣸⡆⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⢋⠔⠁⠀⠀⠀⢸⣿⣿⡿⣿⡇⠛⢠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⢰⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣶⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⢿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠔⢲ ⠀⠀⠀⠀⡠⠒⠈⠉⠀⠒⠠⢀⠀⠀⠀⠀⠀⠀⠑⡀⠑⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⣄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠾⠖⠚⠁ ⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠈⢄⠀⠈⢂⠀⠀⢸⠹⣄⢀⡠⠔⠊⠉⢰⠃⠀⠀⠀⡀⠤⠤⢀⡀⢀⣀⣠⢴⣿⣛⣉⣀⡼⠤⠤⣄ ⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠐⠢⢄⡀⠀⠑⠤⣀⠀⠀⠀⠣⡀⠈⡉⠉⠉⢡⠈⠇⠀⠀⠀⣤⠏⠀⢀⡴⢏⣀⣀⡤⢖⡫⠔⠚⠉⠉⠉⠉⠉⠉⠉⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠉⠐⠒⠒⠒⡄⢣⠄⠒⠉⠀⠀⠉⠑⠒⠻⠖⠚⢉⠤⠐⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⡎⠙⢧⢸⠶⡶⢤⡀⠀⢠⠖⢉⣇⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⡀⢨⣿⣷⣤⠃⠀⠘⢳⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠗⢶⡀⠙⠿⠙⢢⣰⣴⣊⣜⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡾⠻⣧⠈⠛⠒⠢⠄⠴⡿⣻⠟⠉⠘⡄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢨⠇⢠⠏⠉⠃⠀⠀⠀⣸⠟⠁⠀⠀⠀⠈⠲⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣀⠤⠋⠀⡿⡀⠀⢠⡆⣠⡰⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡠⠴⣄⠀⠀⠀⢡⠙⠉⠁⡛⣩⠤⢤⠀⠀⣤⠔⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⣴⠯⠀⠀⠀⠉⠉⠒⢚⡆⠀⡋⠛⠁⠀⢘⡄⠐⠘⠿⢶⣤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⣴⣖⠉⡤⠚⠉⠀⠀⠀⠀⠀⠀⣀⣴⠿⣷⡗⢷⣄⠀⠀⠻⠔⠚⠋⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⣉⣉⠽⠏⠁⠤⣴⠊⠈⣳⠄⠀⠀⢀⣀⣀⠤⣾⠛⠁⣰⡏⡁⠀⢙⡿⠢⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠧⠤⠤⠤⠋⢹⠋⠁⠀⣙⠇⠀⠑⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠋⢀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢋⣉⣁⣉⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⣽⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⠈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣀⠙⣿⣿⣿⣿⣿⣿⠀⠸⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⠟⠉⣀⣤⣤⣶⠶⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⡄ ⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⣤⣭⣭⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠿⣿⣿⣿⣿⡿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀ ⠘⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠁⣀⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀ ⠀⠀⠉⠛⠿⠷⣶⣶⣶⣶⡶⠿⠟⠛⠉⠁⠀⠀⢠⣾⣿⡿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢿⣿⣿⣿⣿⣿⣷⡄⠹⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⣦⡙⢿⣿⣿⣿⣿⣿⣦⡄⠙⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣄⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⢰⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢆⣤⡞⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣾⢳⠀⠀⠀⠀⢸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡤⠴⠊⠉⠀⠀⠈⠳⡀⠀⠀⠘⢎⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠳⣄⠀⠀⡠⡤⡀⠀⠘⣇⡀⠀⠀⠀⠉⠓⠒⠺⠭⢵⣦⡀⠀⠀⠀ ⠀⢹⡆⠀⢷⡇⠁⠀⠀⣸⠇⠀⠀⠀⠀⠀⢠⢤⠀⠀⠘⢷⣆⡀⠀ ⠀⠀⠘⠒⢤⡄⠖⢾⣭⣤⣄⠀⡔⢢⠀⡀⠎⣸⠀⠀⠀⠀⠹⣿⡀ ⠀⠀⢀⡤⠜⠃⠀⠀⠘⠛⣿⢸⠀⡼⢠⠃⣤⡟⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠸⠶⠖⢏⠀⠀⢀⡤⠤⠇⣴⠏⡾⢱⡏⠁⠀⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠈⣇⡀⠿⠀⠀⠀⡽⣰⢶⡼⠇⠀⠀⠀⠀⣠⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡶⠤⣷⣅⡀⠀⠀⠀⣀⡠⢔⠕⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡇⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠙⢦⡀⠀⣀⣠⡤⠤⢤⣀⣀⠸⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣷⢠⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⡀⠀⠹⣟⣾⡧⣾⣧⠴⠚⠁⠀⠀⠀⠀⠀⠀⢠⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠓⠺⠿⢥⣭⣁⡥⠖⠂⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⡤⢤⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⢶⣠⠄⠀⠠⢸⡇⠀⠀⠀⣿⣷⣾⠃⠀⠀⠀⠀⠀⢸⣶⣿⡧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠘⡇⢀⡴⠶⢭⠛⠁⠀⠀⠀⠀⠂⠀⠀⠛⠉⠀⠀⣷⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠉⢹⠂⢀⡾⠁⠀⠀⠀⠀⢣⢸⡀⠀⢈⡇⠀⢳⣤⣤⣤⣤⣤⡴⠀⠀⢰⠟⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⢀⣀⣀⣀⣠⣤⣤⠤⡤⠀⡘⠀⡼⠁⠀⠀⠀⠀⠀⣸⠀⠓⠦⠞⠁⠀⠀⢧⠀⠀⢀⡟⠀⠀⠀⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠈⠋⠙⠁⠀⠰⠀⠀⢠⢠⡇⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢤⡀⠈⠓⠒⠋⠀⢀⣠⠞⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢣⣦⡀⠀⠈⢹⠁⢸⠀⠺⢄⣀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠛⠛⠲⠶⣟⣹⠏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠀⣨⠉⠉⠁⢀⠻⢤⣈⡁⠂⠤⣌⡙⢢⠀⠀⢸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡀⠀⠀⣸⠛⢦⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⣳⡾⠟⠁⢀⡀⠀⠀⠀⠀⠈⠙⣷⢠⣁⡟⠀⠀⢸⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⣠⠇⠀⢨⡏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⡶⠀⠀⠀ ⠀⠀⠀⠟⠇⣠⣿⠿⠧⠀⠀⠀⠀⠀⠀⢸⣎⡋⠙⢓⢶⡌⣧⠀⠀⠀⠀⠀⠙⠒⠤⠤⠀⣠⠤⠤⢾⡉⠁⣀⣄⣼⣱⡇⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠚⠡⠆⠀⠀ ⠀⠀⠀⠀⢠⡟⠉⠄⠀⠀⠄⢀⠀⠀⠀⠈⠉⠉⠉⠹⣆⣇⣹⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⢿⣿⣿⠿⠆⠀⠀⠀⠀⣆⡄⠈⣿⠀⠀⣴⣇⣤⡄⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⡴⠿⢡⡞⢻⣿⣿⣏⡙⠋⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣝⡒⠤⢤⡀⠀⠀⠀⢀⣀⢘⣟⣽⡿⠁⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢘⠀⠐⠦⠉⠀⠰⢣⠞⠓

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠒⠂⠠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡠⢠⠂⠀⠀⠀⠡⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⣷⣾⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⢨⠢⠔⡀⠀⠠⠘⠛⠛⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⠰⠀⠀⠀⠀⠡⡀⠀⠈⠀⠒⠂⠄⡀⢀⠀⡀⠀ ⠀⡴⠊⠀⠀⠀⠉⢆⠀⡔⢣⠀⠀⠀⠀⠐⡤⣀⠀⠀⠀⠀⠀⣀⠄⠀⠀ ⢸⠀⠀⠀⢠⠀⠀⠈⣼⠀⠀⠣⠀⠀⠀⡰⡀⠀⠉⠀⠀⠰⠉⠀⠁⠠⢄ ⢰⠀⠀⠀⠀⠇⠀⢀⢿⠀⢀⠇⡐⠀⠈⠀⠈⠐⠠⠤⠤⠤⠀⠀⠀⠀⢨ ⠀⢓⠤⠤⠊⠀⠀⢸⠀⠣⠀⡰⠁⠀⠀⡀⠀⠀⠀⠸⠀⢰⠁⠐⠂⠈⠁ ⠀⠀⠑⢀⠀⠀⠀⠈⣄⠖⠉⠑⢄⠠⠊⠀⠢⢄⣠⣃⣀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠠⢀⣀⠎⠀⠀⠀⠈⡄⠀⠀⠀⢠⢃⠠⠃⠐⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠯⠉⠤⢴⡃⠁⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠑⢄⠀⠀⢀⠲⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠒⠑⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣠⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧ ⠀⠀⣀⣤⣶⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣼ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣆⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿ ⣾⣿⣿⣟⢛⣛⣛⣛⣋⠭⠥⠿⣿⣿⣷⣤⠀⠀⠀⢀⣀⣀⣠⣀⡀⢿⡇⠀⣸⡇ ⣿⣿⣿⠻⢧⠙⢯⡀⠈⠉⠙⠛⠳⢦⣝⢿⣷⢠⣾⣿⣿⣿⣿⣿⣯⣬⡥⢰⡟⠀ ⢹⣯⣛⠯⢿⣾⣷⣍⡳⣤⣀⠀⠀⠀⠉⠳⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀ ⠈⠹⣿⣿⣾⣿⣿⣿⣿⣷⣭⣛⠷⢦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⢋⣵⡾⣣⣤⣦⢻⣿⣿⣿⣻⠻⣿⣿⣿⡏⠖⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⣱⣿⡟⠼⣻⣿⣿⢸⣿⣿⡇⡛⠀⣿⣿⣿⣧⡠⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢹⣿⣿⣿⣏⢿⣿⣷⣕⣧⣿⣿⣿⢿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣠⢿⣿⡟⣿⣷⣭⣻⠿⢿⠿⠷⢞⣫⣵⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⣎⢿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠻⣷⡝⣩⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⣿⣿⣿⠉⠙⢻⢟⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡧⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠙⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⣴⣶⣶⣾⣟⠟⠀⠀⠠⠃⢠⠎⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⣟⢿⣷⣶⣶⣶⣤⣤⣀⠀ ⠀⠸⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠁⡰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠈⢺⠛⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢿⣿⣿⣿⡿⢳⠃⢀⡀⠀⠀⡼⠁⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠑⠄⠀⠳⡛⢿⣿⣿⣿⡟⠀ ⠀⠀⢸⣿⣿⣿⣤⡇⠃⠀⠀⠀⢰⠃⠀⢡⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⢱⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⣿⣿⢫⡟⠸⠀⠀⠀⠀⡏⠀⠀⡎⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣄⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢦⠀⠀⢫⡹⣿⡟⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⣏⠀⠀⠀⢸⠁⠀⡸⠀⠀⣼⠟⡇⠀⠀⠀⠀⠀⠀⠘⣼⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⢧⠀⠀⢻⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠮⠀⠀⠀⡏⠀⠀⡇⠀⡰⠧⠤⠼⡀⢰⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡀⠀⠸⡄⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡟⡄⠀⡳⠀⠀⢰⠇⠀⣼⠁⡰⢁⣀⣀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠙⣌⠛⠦⡀⠱⡙⢦⡀⠀⢣⠀⢣⠀⠀⢇⠀⠈⢏⣏⠛⢖ ⠀⠀⢠⢳⠃⡇⠀⢑⠀⠀⢸⠀⡜⢉⣦⣯⡵⠶⢦⣌⠐⠜⢄⠳⣄⡀⠀⠀⠀⠈⢲⣈⣭⣵⣿⣑⠳⣄⠈⡇⠘⡆⠀⢸⠀⠀⢸⠘⡆⠀ ⠀⣠⠃⡞⠀⢱⠀⢸⠀⠀⢸⡜⢠⣿⠟⢁⠐⢿⣷⣌⢳⡀⠀⠑⠸⠯⠉⠑⠒⢢⡟⠁⠘⣿⣶⡍⠻⣬⡷⣧⠀⢳⠀⠨⡄⠀⢈⠆⢹⡀ ⡜⠁⣼⠇⠀⠈⡆⠈⡆⠀⢸⠐⣾⠃⠀⣿⡖⣶⡽⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⣶⣷⣹⣿⠀⢹⡾⢾⢀⣾⡀⠀⡇⠀⢸⠀⠀⢣ ⣠⡾⢼⡁⠀⠀⠹⡄⢱⠀⢸⠐⣻⠀⠀⣿⣏⣿⣧⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢿⣿⢿⣻⠀⠀⡷⠞⠉⣯⡇⢀⡇⠀⣸⠀⠀⠘ ⣿⡝⣾⠀⠀⠀⠀⢳⠈⢇⠸⡀⠹⡄⠀⠘⢇⣐⡨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣂⡸⠃⠀⢸⠓⠂⢰⢿⡇⢰⠀⢀⡇⠀⠀⠀ ⣷⣛⣼⠀⠀⠀⠀⠀⠣⡈⢆⢇⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠋⠁⢀⡷⢫⣗⡸⠀⡼⠀⠀⠀⠀ ⢷⣝⣾⡄⠀⠀⠀⠀⠀⠑⣌⢾⡀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⠀⠀⠁⠁⠀⠀⠀⡜⠛⣫⣷⠃⡼⠁⠀⠀⠀⠀ ⠸⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢸⣧⢿⢿⡟⡸⠃⠀⠀⠀⠀⢀ ⣧⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢠⡿⣼⡹⣾⡟⠁⠀⠀⠀⠀⠀⢸ ⠈⠁⠈⠻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣴⣟⡳⢧⣻⡽⠀⠀⠀⠀⠀⠀⢀⡯ ⣿⣶⣤⣄⣹⡽⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠀⠀⠀⢀⣠⣴⢯⡳⣞⣿⣷⣹⡇⠀⠀⠀⠀⠀⢀⣾⢳ ⣿⣿⣿⣿⣿⣿⣯⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣒⣦⢤⣤⣠⣀⣄⣠⣤⣤⣴⣶⢻⡽⣻⣮⣗⣻⢼⣻⡟⢾⡇⠀⠀⠀⠀⢀⡾⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢦⣀⠀⠀⠀⠀⠀⠹⡏⠁⠉⠓⠦⣉⡉⠛⣙⣩⠵⢚⠩⠳⣽⣽⣼⣿⣾⣷⣷⣿⣿⠆⠀⠀⠀⣠⣾⣻⣾⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⠀⢸⠁⠙⣷⣄⠀⢰⡟⠃⠀⠀⠀ ⠀⠀⠀⣠⣾⠿⠿⢿⣧⠘⢀⠄⠼⣿⣆⣸⡇⠀⢠⣦⠀ ⠀⢀⣾⠟⠁⠀⠀⢠⣿⣧⢫⢀⣴⣿⣿⣿⣧⢸⣿⢿⡇ ⢀⣾⠏⠀⠀⠀⣴⠋⠀⠈⢯⣿⣿⣿⠋⠉⣽⣿⡟⠀⡇ ⣸⡏⠀⠀⠀⡼⠁⣀⣤⢶⣾⣿⣿⣿⣶⣼⡿⣿⠃⠀⡇ ⡿⠀⠀⢀⣜⣠⠾⠋⠁⣾⣿⣿⣿⣿⣿⡟⢀⡟⠀⠀⡇ ⣧⡶⠿⠿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠉⣾⠃⠀⢸⠁ ⠁⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣹⠟⠁⠀⠀⠛⢻⣤⠏⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠋⠀⠀ ⠀⠀⠀⠀⠐⠁⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⠉⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠈⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠏⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠙⢿ ⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⢀⠎⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠘⢆⢀⡜ ⠀⢀⠔⠁⠀⠣⡀⠀⠀⡠⠁⠀⠀⠀⢸⣉⣱⠀⠀⠀⠀⢠⠀⠀⠙⢡⠂⢹⣧⣄ ⣔⠁⠀⠀⠀⢀⡨⠗⠁⠐⡄⠀⡠⠀⠤⡛⠛⠀⠀⠀⠀⠀⡇⣠⡀⢀⣴⣿⣿⣿ ⣿⣍⠉⠉⠉⠀⠀⠀⠀⠀⢈⠦⢄⡀⠀⡸⠀⠀⠀⠀⠀⠀⡎⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠆⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣄⣀⢠⣿⡓⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣏⠈⠛⠑⠀⠀⠀⠈⠢⢀⣠⠤⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⡀⠀⠀⠀⡀⠠⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⡦⢄⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠾⣿⣦⡈⣀⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⣀⣠⡴⠊ ⠀⠀⠘⣿⣷⣿⣯⣄⢀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣯⣤⣶⣿⠿⠋⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡏⠀⢢⣠⣄⡀⠀⣺⣿⡿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⠙⢿⣦⣬⣿⣿⣿⡶⠟⠉⠀⣿⣿⣿⣿⠁⠀⠐⠒⠠⡀ ⠀⠀⠀⣿⣿⣿⣄⠆⠙⡻⢿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡶⠂⢀⡀⠤⠌⠀ ⠀⠀⢠⣿⣿⣿⣿⣦⣤⠀⠀⠀⡈⠉⢹⣩⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⠃⠉⠻⢿⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟣👻👅💦

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⣮⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠈⠁⠲⢖⠒⡀⠀⠀ ⠀⠀⠀⡠⠴⣏⠀⢀⡀⠀⢀⡀⠀⠀⠀⡀⠀⠀⡀⠱⡈⢄⠀ ⠀⠀⢠⠁⠀⢸⠐⠁⠀⠄⠀⢸⠀⠀⢎⠀⠂⠀⠈⡄⢡⠀⢣ ⠀⢀⠂⠀⠀⢸⠈⠢⠤⠤⠐⢁⠄⠒⠢⢁⣂⡐⠊⠀⡄⠀⠸ ⠀⡘⠀⠀⠀⢸⠀⢠⠐⠒⠈⠀⠀⠀⠀⠀⠀⠈⢆⠜⠀⠀⢸ ⠀⡇⠀⠀⠀⠀⡗⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠎ ⠀⢃⠀⠀⠀⢀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⡃⠀ ⠀⠈⠢⣤⠀⠈⠀⠀⠑⠠⠤⣀⣀⣀⣀⣀⡀⠤⠒⠁⠀⢡⠀ ⡀⣀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀ ⠑⢄⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⠑⠢⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀ ⠀⠀⠀⠀⢀⠠⠓⠢⠤⣀⣀⡀⠀⠀⣀⣀⡀⠤⠒⠑⢄⠀⠀ ⠀⠀⠀⠰⠥⠤⢄⢀⡠⠄⡈⡀⠀⠀⣇⣀⠠⢄⠀⠒⠤⠣⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⢿⣿⡟⠀⣠⣤⣤⣀⠀⢹⣿ ⣿⡏⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣿⣿⣿⠟⠀⣸⣿ ⣿⡇⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣠⣴⣿⣿ ⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⣀⣤⣶⣿⣿⣿⣿⣿ ⣿⣷⡀⠈⠛⠛⠻⠟⠛⠛⠛⠛⠉⠉⠁⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿ ⣿⡇⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⣿⣿⡄⠘⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣿⠟⠁⣠⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⠛⠁⣠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠉⠙⠛⠛⠛⠛⠛⠛⠉⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⠸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⠇ ⠀⢻⣿⣿⠿⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠻⢿⣿⡟⠀ ⠀⠘⣟⠁⠀⢀⣠⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣤⡀⠀⣹⠃⠀ ⠀⠀⠈⠳⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡀⣀⣤⣤⣤⣤⣤⣀⠀⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⡿⣛⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢰⣿⡇⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⢿⣿⣮⣛⣡⣿⣿⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠿⢻⣿⣿⣿⡿⠹⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡤⠐⠻⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣤⣄⠀⠈⢻⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡞⣿⣿⣿⣿⣿⣿⢼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⣿⣧⣿⣿⣿⣿⣿⣿⣾⣿⢋⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⠋⢿⣿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠈⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣶⣤⡈⠙⢿⣿⠉⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣷⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⡇⠈⣿⣿⣿⡏⠀⣿⣿⡆⠈⠋⢉⣀⣀⣀⣈⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⡟⢀⣾⣿⣿⡿⢿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⠁⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⢀⣿⣿⡆⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣧⡀⠀⢀⣼⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣴⢶⣾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⢉⡶⠠⣤⣀⡀⠀⠉⠉⠛⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡇⠀⠘⢁⣴⣿⠀⠀⣠⣿⣿⣽⣦⣤⡀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀ ⠀⠀⢀⠞⠉⠙⢀⣤⣾⣿⣿⠀⣼⣿⡿⠛⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⣠⠃⠀⠀⠀⠙⢟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡀ ⠀⠇⠀⠀⠀⠀⠀⠀⠈⠺⣷⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣧ ⣸⠀⠀⡠⠀⠀⣰⢟⡛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿ ⡇⠀⠊⠀⠸⢿⠿⠆⠀⠌⣿⣿⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿ ⣧⠁⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢀⠔⠀⣼⠇ ⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⣀⠚⠿⢯⣀⣀⠀⠤⠔⠉⢀⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣯⣿⢿⣿⣿⢄⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⣷⣶⣶⣶⣶⠾⠟⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣳⣄⠀⡀⣿⣰⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠘⢷⣤⣀⠹⣿⣧⣿⣿⣿⢦⣈⠀⠀⡆⠀⢁⢀⠀⢠⡴⡇⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣷⣿⣿⣿⣿⣿⣆⠈⠳⣄⠀⢰⡀⠀⠂⡞⢠⠇⠀⠀⠀⠀ ⠀⠲⠶⣴⣾⣿⣿⣿⣿⣿⣿⡛⠦⡀⠘⣶⣬⣿⣴⣼⢀⢎⠀⠄⠀⠀⠀ ⠀⠀⠤⢴⣿⣿⣿⣿⣿⣿⣍⡉⠀⢼⣾⣿⣿⣿⣿⣿⣿⠠⠊⠀⠀⠀⠀ ⠀⠀⣶⣿⣿⣿⡿⠋⣿⣿⡷⠆⠀⢺⣿⣇⣈⣻⣿⣏⣼⠁⡀⠀⠀⠀⠀ ⠀⢸⣿⡟⠛⠉⠀⢰⣿⣿⣿⠋⢀⠈⠻⠿⢿⣿⣿⡿⠋⡠⡈⠐⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⣷⡎⠙⠃⠀⢄⠀⡩⢩⣠⣄⡡⡀⠀⠀⠀⠀ ⠈⠿⠿⠇⠀⠀⠀⠀⠈⣿⣿⡇⠐⠂⠀⠁⠖⠀⠉⠉⠻⢿⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡷

⠀⠀⠀⠀⠀⣠⣴⣾⣶⣿⣿⣶⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⣿⣿⣿⣋⣠⣿⣿⣿⣿⣿⡖⢶⣶⣤⣤⣀⣤⣶⣿⣷⡤⠶⢦⡀⠀ ⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⡿⢁⣾⡀⠀⠀⣷⠀ ⠀⠀⠻⣿⠟⠛⠛⠻⠟⠛⠋⢹⣿⣿⣿⢣⡆⠀⠈⠛⠛⠋⠀⢻⣿⣿⣶⠟⣻⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⣾⠃⠀⣠⣤⣴⣤⣤⣀⠉⠙⢁⣴⡿⠁ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⣤⣿⣿⢋⣬⡄⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⣠⠻⠿⠿⠿⠿⣛⣵⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⡇⠀ ⠀⠀⠀⠀⣠⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢀⣀⣴⣾⣿⣿⡇⣬⣭⣭⣭⣭⣭⣶⣶⣿⣷⡄⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠰⢾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢐⣛⡻⣿⣿⣿⣿⣿⣿⠻⣿⣿⠀ ⠀⠁⠀⣠⣶⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⡵⠿⢿⣿⣿⣿⢟⣄⢹⡏⠀ ⠀⠀⣰⣿⣿⣿⣿⣆⢲⣶⣶⣶⣶⣶⣶⣶⣿⢇⣷⣾⣿⡏⣟⣯⣶⣿⣿⡾⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠋ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣬⠉⠿⣛⣻⣿⣯⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣠⣶⣿⣿⣿⣿⣿⣿⠿⠿⠦⠄⠀⠀⠉⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠿⣿⠟⠛⠛⠀⠀

⣿⡿⠷⣶⣤⣄⡀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣠⣤⣶⠾⢿⣿ ⣿⡇⠀⠀⣨⣿⣿⣷⠀⢠⣿⣿⠿⠋⢉⡉⠙⠿⣿⣿⣄⣤⣾⣿⣿⣅⠀⠀⢸⣿ ⢸⣧⠀⣰⣿⣿⣿⡏⢀⣿⣿⡏⢠⣾⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⣼⡇ ⠈⣿⣴⣿⣿⣿⣿⡇⠈⣿⣿⣧⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠁ ⠀⢹⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣄⣈⠉⠉⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠛⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡎⠠⠊⠀⠠⠚⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡍⠀⠀⠀⠀⣾⣤⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠙⠡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⣤⣮⣤⣴⣶⣶⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠊⠁⣰⠙⠻⢿⣿⣿⠟⠁⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣶⣂⣀⠀⡐⠁⠈⠁⡒⠛⠋⢀⠀⢀⣿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠛⠛⡷⡀⠀⠀⡇⢠⣤⣿⣐⣿⣿⣧⣿⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣣⠏⠐⠒⠦⠤⠬⢽⣹⣿⣿⣿⣿⣟⠀⡠⠐⠒⠒⣦⡀ ⠀⠀⠀⠀⡔⠘⢄⠀⢠⡄⠀⢀⣼⠟⠉⠉⠳⣿⢇⣼⣤⣤⣴⣾⣿⣿ ⠀⠀⠀⢰⣀⣴⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣼⣿⣿⣿⣿⠋⠙⠛⠻⠷⣄⡀⢀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠀ ⠀⠀⠀⠉⠹⠛⠋⠁⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀ ⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀ ⠀⠸⣿⣿⣷⣦⣀⡴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣴⣾⣿⣿⠇⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⣠⣻⡿⠿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣥⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡜⠋⡾⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣻⣾⣭⣝⣛⣛⣛⣛⣃⣿⣾⣇⣛⣛⣛⣛⣯⣭⣷⣿⣿⡇⠀ ⠀⠰⢿⣿⣎⠙⠛⢻⣿⡿⠿⠟⣿⣿⡟⠿⠿⣿⡛⠛⠋⢹⣿⡿⢳⠀ ⠀⠘⣦⡙⢿⣦⣀⠀⠀⠀⢀⣼⣿⣿⣳⣄⠀⠀⠀⢀⣠⡿⢛⣡⡏⠀ ⠀⠀⠹⣟⢿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⢰⣿⣣⣿⣭⢿⣿⣱⣶⣿⣿⣿⣿⣷⣶⢹⣿⣭⣻⣶⣿⣿⠀⠀ ⠀⠀⠈⣿⢿⣿⣿⠏⣿⣾⣛⠿⣿⣿⣿⠟⣻⣾⡏⢿⣿⣯⡿⡏⠀⠀ ⠀⠀⠤⠾⣟⣿⡁⠘⢨⣟⢻⡿⠾⠿⠾⢿⡛⣯⠘⠀⣸⣽⡛⠲⠄⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠸⠃⠈⠙⠛⠛⠉⠈⠁⠹⠀⠀⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣀⣠⠀⠀⠀⠀⠀⠀⢠⡄⡄⣦⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⣻⣿⢷⢶⢶⢶⢆⣗⡿⣇⣷⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⣭⣭⣭⣭⣭⣻⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣷⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⢷⣶⣦⣤⣤⣀⠀⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟ ⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠛⠉⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇ ⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠉⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⢀⣾⡟⠁⠀⠀⠀⢼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⡅⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠈⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿ ⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⣿ ⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⢀⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⡀⠀⠀⢀⣿ ⣿⡇⠀⠀⢸⣿⣶⣶⣶⣤⣤⣀⠉⣻⣿⣿⣟⠋⣁⣠⣤⣤⣤⣤⣿⡇⠀⠀⢸⣿ ⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣿ ⣿⣿⣧⡀⠻⣿⣿⣿⣿⣿⠟⠉⢿⣿⣿⣿⣿⡿⠉⠻⣿⣿⣿⣿⣿⠟⢀⣼⣿⣿ ⣿⣿⣿⣷⣄⠙⢿⣿⣧⣄⣀⠀⠘⠛⠛⠛⠛⠃⠀⣀⣠⣼⣿⡿⠋⣠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⣄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣠⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⠉⠉⠉⠉⠉⠉⣁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡙⠛⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣶⣤⣼⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣶⣦⡌⠻⡿⢁⣾⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣦⡀⢸⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣆⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣴⣤⡘⢿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣁⠘⢿⣿⣿⣆⠙⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⣤⡈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠛⠛⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬜⬜⬜⬛⬛🟪🟪🟪🟪🟪⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬛🟪🟪⬛⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛⬛🟪🟪⬛⬜⬜⬜⬜⬜⬜ ⬛🟪🟪🟪⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛⬛🟪🟪🟪🟪⬛⬜⬜⬜⬜⬜⬜ ⬜⬛🟪⬛🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪🟪⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛⬛⬜⬜⬛⬛⬛ ⬛⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪🟪🟪⬛⬛⬛⬛🟪🟪⬛⬛🟪🟪⬛ ⬛🟪⬛🟪🟪🟪🟪🟪🟪🟪⬛⬛🌫️🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪🟪🟪🟪⬛ ⬜⬛⬛🟪🟪🟪🟪🟪🟪⬛⬛🌫️⬜🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛⬜ ⬜⬜⬛⬛🟪🟪🟪🟪⬛🌫️⬛⬜⬜🟪🟪🟪⬛⬛⬛🟪🟪🟪🟪🟪🟪🟪⬛⬜ ⬜⬛⬛⬛🟪🟪🟪🟪⬛⬜⬜⬜🟪🟪🟪🟪🟪🟪⬛🟪🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬛⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪⬛🟪🟪🟪🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪⬛⬛⬛🟥⬛⬛⬛⬛⬛⬛🟪🟪⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥⬛⬛⬛⬛🟪🟪🟪⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟪⬛🟪⬛🟥🏻🏻🏻🟥⬛🟪🟪🟪🟪⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟪⬛🟪🟪⬛⬛⬛⬛⬛🟪🟪🟪🟪🟪🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛🟪⬛⬜⬜⬜⬜⬛🟪⬛🟪🟪🟪🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛🟪⬛🟪⬛⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⢀⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⣰⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⢠⣿⣿⠃⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⣉⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⠀⠀⠀⢹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠉⠁ ⠀⠀⠀⠸⣿⣿⣄⠀⠀⠘⢿⣿⡵⠋⠙⢿⣦⡀⠀⠀⣤⣠⠀⣠⣿⡅⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠈⠻⣷⣄⣠⣿⣿⡼⠋⠛⣡⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠷⠶⠶⠾⣿⡿⠋⠻⣟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⣀⣤⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢛⣿⢿⣿⡟⠋⠀⠀⠀⠀ ⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡿⠋⠀⠈⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⢻⣿⣿⣟⠻⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠻⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⢸⣿⣟⠿⠀⠀⠉⠛⢿⣿⡇⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⣿⣿⡄⠀⠀⠀⠀⠀⠈⡇⢀⠠⠀⠀⠀⠁⠀⠀⡀⠀⠠⠟⠛⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⢀⡀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⠀⠔⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠿⠇⠒⠈⡄⠀⠀⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠴⠄⠀⢀⠔⠀⠀⠀⠄⠌⠀⠀⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⠀⡀⠙⠄⠀⢀⠀⣠⣾⠄⣤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡑⠁⠂⠀⣈⣥⣾⡿⢿⠀⠀⢄⠀⢀⣠⣤⣤⣴⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠋⠿⠀⠀⠀⠄⠀⠌⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠉⠀⠏⠀⠀⠈⠉⠙⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠂⠄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⣀⡰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠻⢿⣿⣮⣻⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⠀⣉⣿⡇⣿⣻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠆⢴⣧⣗⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡇⢀⣿⣛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⢻⠾⣿⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⠀⠀⡀⢱⠘⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⡀⠀⠀⠅⠈⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡈⠌⢻⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⣿⡌⠀⠈⠀ ⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠀⠀⠀⢒⣒⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⣿⡧⡇⠀⠀ ⠀⠀⡠⠒⠉⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⣿⡇⠃⠀⠀ ⣠⠀⠄⠀⠒⠀⠀⠈⠉⠀⠉⠢⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⢀⣼⣿⡟⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠆⡀⠀⠀⠀⠀⢀⣴⣿⡿⢋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠐⠈⠉⠻⠫⠐⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣷⡹⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⡉⠙⠻⢿⣿⣿⣿⣿⡌⢿⣿⣿⣧⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⡓⠀⠀⠀⡉⢻⣿⣿⣿⡸⣿⣿⡿⣸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⡀⠐⢄⣼⣿⣿⣿⡇⣿⡿⢣⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⠉⣁⣈⡿⠸⣋⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣇⠀⠀⠈⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⡀⠀⢰⣾⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠘⣿⣷⣤⣸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠈⢿⠿⠿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢙⠇⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠞⡄⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠜⢄⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠘⡌⢢⠀⢻⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⢱⠀⠱⡀⠹⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠱⡀⠘⢿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢱⠀⠀⠉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠶⠚⠉⠁⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⣀⠤⠤⠤⠔⠒⠊⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⢀⠃⠀⠀⠀⠀⠀ ⠀⢠⠖⠁⠀⠀⢀⣀⡀⠤⠤⠄⠒⠒⠒⠒⠓⠊⠉⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠁⡜⠀⠀⠀⠀⠀⠀ ⣰⡣⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⡜⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣀⠴⠚⠛⠻⣿⣿⡿⠛⢁⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡠⠖⠉⠀⠀⠀⠀⠀⠈⠓⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠄⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⣠⣀⡈⠀⠀⠑⢾⡷⠐⠈⠀⠁⠀⠀ ⢆⠀⠀⠛⠻⢁⠄⣀⡐⠂⠀⠀⠀⠘⠀⠀⠀ ⠀⠑⡀⠀⠀⠀⠀⠹⡃⢀⢀⢴⣤⡐⢂⠀⠀ ⠤⠠⣚⠖⢩⡑⠐⠉⠉⠁⠈⢄⠀⢁⠀⠀⠀ ⠈⢀⡀⠸⠈⠁⢠⣤⣤⣤⣀⠀⠈⢁⠀⣀⠀ ⠀⠘⠀⣾⣶⡄⠀⠻⣆⣠⡿⠁⡐⠀⠠⠀⡄ ⠀⠀⠘⢏⠙⢿⣆⠀⠈⠛⣠⣴⠀⣤⣤⡠⠀ ⠀⠀⠀⠀⢉⠟⠭⠀⣀⣀⠹⠿⢄⡛⠝⠁⠀ ⠀⠀⠀⠀⠩⠤⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡗⠯⢓⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠈⡟⠀⢀⣮⣹⣆⠀⠀⠀⠀⢠⠿⡬⣆⠀⠀ ⠀⠀⣇⠔⣾⠀⠀⠈⢦⠤⠤⠤⠼⠀⠀⢹⠀⠀ ⠀⢠⠷⢪⠏⣀⠴⠒⠶⣄⣀⣠⠖⠲⢤⡀⠹⡄ ⠀⡞⠀⡏⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⠀⢷ ⢸⡥⢚⡧⠚⢷⣤⠈⠉⢀⣄⡀⠉⠁⣤⣿⠦⡞ ⢸⡴⠋⠹⠄⠾⠟⠀⠀⠁⠀⠈⠀⠀⠿⠟⢰⠁ ⠘⡆⠀⢠⣂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆ ⠀⠹⡄⢸⠿⡟⠦⣍⣑⡒⠒⠒⣊⣉⡩⠛⣿⡃ ⠀⠀⠙⢾⣀⠘⢦⣀⠀⠉⠉⠉⠀⣀⡤⣎⠞⠀ ⠀⠀⠀⠀⠈⠙⠲⣾⠭⠽⠭⠭⠭⢖⡺⠁⠀⠀