Sit Applejack Emojis & Text

⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡞⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⠉⠦⣀⠀⢀⡰⢃⠡⠒⢠⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠤⢉⠰⡈⠅⠏⠒⠒⠓⠫⢠⡊⠡⢉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⢬⣴⠌⠃⠡⠄⠀⠉⠀⠢⠀⠀⡈⠋⡳⡌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣎⢰⠃⠀⢣⡀⠀⠀⠀⠈⠐⢀⠈⠂⠀⠄⡐⣹⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣯⢾⠇⠀⠀⠙⠀⠢⠈⠤⢀⠀⠠⠈⠂⡈⠑⠙⣫⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢹⡜⡸⢧⠞⠒⠠⡈⠀⠑⠀⠐⡴⣀⣀⠤⣺⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠆⢛⣬⠏⢰⠏⢹⣷⡄⠀⠀⠲⡏⢀⣷⡧⣅⡊⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⠸⢬⠀⢘⣶⣷⣿⡇⠀⠀⠀⣿⣷⣿⡷⡇⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⠸⣌⢊⢻⢿⡿⠃⢠⠉⠩⠘⠿⠻⢉⡇⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡘⢆⡀⠉⠀⠀⠣⠤⠒⠃⠀⣠⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠹⡖⢤⣄⣀⣤⠤⠖⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠑⢄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠘⡀⠀⠀⡇⠀⠈⢀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⠂⠌⣴⠃⠀⠉⢑⢎⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⠅⠀⠠⠀⢠⠎⠈⢇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠊⠀⡀⠄⠀⠀⠀⠈⡗⡎⠒⠁⢻⠀⠀⠈⣇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠀⠔⠁⡀⠈⡠⠂⣩⠗⡇⢻⠀⠀⠘⣇⠀⢀⠈⢇⢳⠉⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⡌⠀⠐⠀⠀⢃⣰⠁⠀⢹⢸⠀⠐⠀⢸⡄⠀⢀⠘⢮⡆⠀⠈⢇⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠑⠄⠀⢬⠀⠀⠈⣏⡆⠀⠐⠀⢳⡀⠀⢀⠈⢧⠀⢠⠼⠤⢀⡰⠿⠂ ⠄⠈⠀⠀⣠⠚⠉⠉⠉⠓⠄⢘⣇⠀⠂⢀⠘⣇⠀⠀⡀⠘⢦⠁⠀⠀⠀⠈⠢⡀ ⠈⠢⡀⢰⠃⠀⠀⠀⠀⢀⣀⣤⢾⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⢦⣀⣄⣤⣤⠤⡼ ⠀⠀⠀⠈⠒⠒⠞⡒⠓⠂⠇⠀⠈⠑⠒⠒⠒⠒⠋⠒⠒⠚⠐⠚⠀⠀⠀⠀⠀⠀

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

🟨🟨🟨🟨🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🟨🟨🟨🟨⬛🟨🟨🟨🟨🏻🏻🏻🏻🟨🟨🏻🏻🏻🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨🟧🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬛🟨🏻🏻🏻🟨🟨🟨🟨🏻🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬛🟨🟨🟨⬛🟨🟨🟨⬛🟧🟨 🟨🟨🟨🟧⬛🟨🟨🟨🟨⬛⬜⬜⬜🟩🟩🟩🟩🟩🟩🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜🟩🟩🟩⬜⬜⬛🟨⬛🟨🟨🟨🟨⬛🟨🟨 🟨🟨🟨🟧🟨⬛⬛⬛⬛⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟩🟩🟩🟩🟩🟩🟩⬜⬜⬛🟨🟨🟨🟨⬛🟨🟨🟨 🟧🟨⬛🟧🟨🟨🟨⬛⬜⬜⬜🟩🟩⬜⬜⬜🟩🟩🟩🟩🟩⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛🟩🟩🟩🟩🟩⬜⬜🟩🟩⬜⬜⬛🟨🟨⬛🟨🟨🟨🟨 🟧🟨⬛🟧🟨🟨🟨⬛⬜⬜🟩🟩⬜⬜⬜⬜⬜⬛⬛🟩🟩⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛🟩⬛⬛⬛⬜⬜⬜⬜🟩🟩⬜⬜⬛⬛🟨🟨🟨🟨🟨 🟧🟨🟧⬛⬛⬛⬛⬜⬜🟩🟩🟩⬜⬜⬜⬜⬜⬛⬛⬛🟩🟩⬛🟨🟨🟨🟨🟨🟨⬛🟩⬛⬛⬛⬛⬜⬜⬜⬜⬜🟩🟩⬜⬛🟨🟨🟨🟨⬛🟨 🟧🟨🟧🟨🟨🟨⬜⬜⬜🟩🟩🟩⬜⬜⬜⬜⬜⬛⬛⬛⬛🟩⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟩⬜⬜⬛🟨🟨⬛🟨🟨 🟧🟧🟧🟨🟨🟨⬜⬜🟩🟩🟩⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛🟩⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟩⬜⬛⬛⬛🟨🟨🟨 🟧🟧🟧🟨🟨🟨⬜⬜🟩🟩🟩⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜🟩⬜⬜🟨🟨🟨🟨🟧 🟧🟧🟧🟨🟨⬜⬜⬜🟩🟩⬛⬛⬛🟩⬛🟩⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛🟩⬛🟩⬛⬛⬛⬛⬜⬜⬜⬜🟩🟩⬜🟨🟨🟨🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩🟩⬛⬛🟥🟩🟥⬛⬛⬛⬛🟩⬛🟩⬛🟨🟨🟨🟨🟨⬛⬛🟥🟩🟥⬛⬛⬛⬛⬛⬛⬜⬜⬛🟩🟩⬜🟨🟧🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩🟩⬛🟥🟥🟥🟥🟥⬛⬛🟥🟩🟥⬛⬛🟨🟨🟨🟨🟨⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛🟩⬛🟩⬛🟩🟩⬜⬜🟨🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩🟩⬛🟥🟥🟥🟥🟥⬛🟥🟥🟥🟥🟥⬛🟨🟨🟨🟨🟨⬛🟥🟥🟥🟥🟥⬛⬛⬛🟥🟩🟥⬛⬛🟩🟩⬜⬜🟨🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩⬛⬛⬛🟥🟥🟥⬛⬛🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨⬛⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥⬛🟩🟩⬜⬜🟨🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩⬛⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛🟩🟩⬜⬜🟨🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩⬛⬛⬛⬛⬛🟩⬛🟩⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟩⬛🟩⬛⬛🟥🟥🟥⬛⬛🟩🟩⬜⬜🟨🟧🟧🟧 🟧🟧🟧🟨🟨⬜⬜🟩🟩⬛⬛⬛⬛⬛⬛🟥🟩🟥⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟥🟩🟥⬛⬛⬛⬛⬛⬛🟩🟩⬜🟨🟨🟧🟧🟧 🟧🟧🟧🟨🟨🟨⬜🟩🟩🟩⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛⬛🟩🟩⬜🟨🟧🟧🟧🟧 🟧🟧🟧🟨🟨🟨⬜🟩🟩🟩⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛🟩🟩🟩⬜🟨🟧🟧🟧🟧 🟧🟧🟧🟨🟨🟨⬜🟩🟩⬜⬛⬛⬛⬛⬛🟥🟥🟥⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟥🟥🟥⬛⬛⬛⬛⬛🟩🟩🟩⬜🟨🟧🟧🟧🟧 🟧🟧🟧🟧🟨🟨🟨⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟧🟧🟧🟧🟧🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜🟨🟧🟧🟧🟧 🟧🟧🟧🟧🟨🟨🟨⬜⬜⬜🟩⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟧🟨🟨🟨🟨🟨🟧🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜🟨🟨🟧🟧🟧🟧 🟧🟧🟧🟧🟨🟨🟨🟨⬜🟩🟩🟩⬛⬛⬛⬛⬛⬛🟩🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛🟩🟩⬜⬜⬜🟨🟧🟧🟧🟧🏽 🟧🟧🟧🟧🟧🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩⬛⬛⬛⬛⬛⬛🟩🟩🟩🟩⬜🟨🟨🟧🟧🟧🟧🏽 🏽🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩⬛⬛⬛⬛🟩🟩🟩🟩⬜🟨🟨🟨🟧🟧🟧🏽🏽 🏽🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩⬜⬜🟨🟨🟨🟧🟧🟧🟧🏽🏽 🏽🏽🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟧🟧🟧🏽🏽🏽 🏽🏽🏽🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🏽🏽🏽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠖⠛⠛⣿⠀⠈⢻⣦⡀⠀⠀⠀⠀⢠⣄⠀⣸⠃⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡶⠛⠉⠁⢈⣷⡴⠖⠚⢻⠀⠀⠈⣧⢻⣄⠀⠀⢀⡏⢻⢠⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠟⠁⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⢷⡀⢸⠁⢸⡿⠀⢸⣇⡴⣷⣤⠀⠀⣀⡤⠞⠋⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠟⢋⣩⠽⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⢸⡇⠀⣼⣮⠞⠉⣼⡤⠚⠁⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠖⠉⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠈⠀⢠⡿⠋⠀⠼⠋⠀⠀⢀⡴⢋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⣠⠴⢾⡇⠀⠀⣶⠞⡷⣶⣤⣤⣤⣂⡄⣀⠀⠀⠀⠹⣆⣿⡀⣠⣟⣥⡄⠀⠀⠀⣠⡾⠟⠛⠉⢁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⢰⡏⠀⠀⢷⡀⠀⠹⡄⢣⢿⣿⣦⣬⡏⠛⠛⠁⠀⠀⠀⢻⣿⣇⡏⡿⠀⣿⠀⠀⠈⠁⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⢧⠀⠀⠀⠹⣄⠀⠙⠦⣳⣟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡇⢠⡿⠖⣶⠠⠴⠾⠛⠒⠒⣶⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣷⣌⢧⡀⠀⠀⣼⠀⠀⠀⠀⠉⠀⠀⢀⣠⠂⠀⠀⠀⠀⠀⢹⣇⢸⡇⠈⠀⣠⢏⣀⡤⠤⠖⠚⣋⡥⠖⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣦⣚⢧⣂⣀⣧⣀⣤⠤⠖⠉⣽⡆⠀⠀⠀⠀⠀⠘⣿⠟⠀⠠⠾⣿⢓⣦⠙⢦⡴⢚⣡⡤⠴⠶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢿⣮⡙⠲⣄⠁⠀⣿⠀⠀⣼⠃⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠞⠛⠉⠀⠀⠈⣿⠿⠖⠒⠶⠦⣄⡀⠀⠈⠉⠲⢤⡀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠙⣟⣄⠈⢳⣰⡏⢀⣾⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠛⠓⠀⣿⢸⡄⢠⡟⣰⠟⠁⢀⡼⢻⡄⠀⢀⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡙⠧⠤⠴⠋⣸⡷⢋⡾⠃⣀⡴⠋⠀⠀⢿⠦⡼⠁⠀⠀⣶⣀⣀⣨⣧⡀⠀⠀⢀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠉⢀⣾⡵⠊⠁⣀⣀⣠⠴⣿⡾⠁⠀⠀⣰⠏⠉⠁⠈⢧⠙⣆⠀⠈⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⡟⠀⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣠⠖⠉⠁⣀⣤⠞⣿⠁⠀⠀⣼⣇⠀⠀⠀⠀⠈⣇⠘⣇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡼⠀⠀⣠⠞⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠁⠀⣠⠞⠉⠀⢸⣿⣿⡆⠀⢧⣻⠀⠀⠀⠀⠀⢸⡄⢸⡄⠀⠀⠈⣧⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⠞⢀⣠⠞⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⠋⠙⣿⡆⠈⣧⢨⣿⡑⠂⠙⠳⣦⠀⠀⠀⢸⡇⠘⡇⠀⠀⠀⢹⡆⠀⣰⠟⠀⠀⣀⠴⣫⡤⠖⠉⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⣓⣖⡿⠃⠀⣼⢿⠂⠀⠀⠀⢀⡿⠀⠀⠀⢸⠇⢀⡇⠀⠀⠀⢸⡇⢰⡏⠀⣠⢞⡵⠋⠁⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢳⡄⠀⢀⡾⠁⠀⠀⢀⣟⣀⣸⠃⠀⠀⠀⢸⡇⢸⡇⢸⠁⡞⠀⠀⠀⠿⣧⣄⣠⣤⣤⢤⣤⣴⡶⠶⠶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠶⠟⠃⠀⠀⠀⠈⠉⠉⠿⠶⠶⠶⠶⠾⠏⠈⠻⣿⣀⢧⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠾⠛⠓⠲⠾⢷⡙⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⡶⠂⠀⠀⣿⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⣶⢶⣞⡡⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠳⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⡝⢧⠉⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣽⠀⠀⠀⠀⠀⠀⡇⡇⠀ ⠀⠀⢀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣇⠀⠀⠀⡃⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡧⣇⠀ ⠀⠀⣸⠀⣠⠔⠋⠉⠉⠉⠑⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠀⠀⠀⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⡇⣷⠀ ⠀⠀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⢻⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣧⣿⠀ ⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⡀⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⢸⡇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⣿⠀ ⢀⡟⠀⢀⣀⣤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⢰⡟⢀⣼⡴⠚⠋⢻⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡷⡿⠀ ⣼⡥⠞⠉⠀⠀⢀⣠⡴⠶⠒⠛⠛⢲⣤⡀⠀⠀⢻⡁⢠⠀⢠⣯⡴⠋⠁⠀⠀⠀⠀⠹⠄⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⣿⡀ ⠏⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⡶⠋⠀⠈⠓⢤⡀⢳⡏⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡄⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⠁ ⠀⠀⣰⡿⠃⠀⠀⢀⣴⠞⢁⡞⠁⢀⡤⠂⠀⠀⠙⢾⡷⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠿⡄⠀⠀ ⢀⣾⠟⠀⠀⠀⣴⡿⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢷⠀⠀ ⠈⠏⠀⠀⢠⣾⠟⠀⠀⣼⠁⣀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣖⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠘⣇⠸ ⠀⠀⠀⣰⣫⠏⠀⠀⠀⣿⣤⡿⠋⠐⠚⢿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⣿⣿⡆⠙⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⡀⠀⢹⡄ ⠀⠀⢰⢿⡏⠀⠀⠀⢀⣧⣾⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⢀⣿⣿⣿⠀⠈⢻⣟⠛⠃⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠈⣧ ⠀⢀⡏⡼⠁⠀⠀⠈⠉⣹⡏⠀⢸⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⣾⣿⣿⣿⡀⠀⠈⢿⡦⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸ ⠀⠸⢀⠇⠀⠀⠀⠀⠀⣿⡙⠀⢸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⡿⣿⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠸ ⡄⠀⢨⡄⠀⠀⠀⠀⠀⣸⠇⠀⠘⣍⠈⢀⡇⣀⣠⠤⣤⡀⠀⠀⠘⣯⠃⠈⠀⣹⠏⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣄⡇⠀⠀⠀⠀⣰⢏⡠⠴⠄⠉⠉⠋⢸⡁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣉⡉⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠁⠀⠀⢀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⡉⠳⣤⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠃⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠘⣿⠟⠁⠀⠀⠀⠀⣰⠃⠀⢀⠄⠀⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⠖⢶⣶⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣀⡾⠃⠀⠀⣾⠃⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢧⡀⠀⢀⣀⣴⠟⠀⠀⠘⣿⡇⠸⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣶⡿⠋⠀⢀⡾⡛⠀⣼⢡⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠬⠓⢚⣩⠞⠁⠀⠀⠀⠀⢿⣇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢻⡟⠋⠀⠀⣠⠞⡱⠁⣼⠃⢸⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⢳⠀⢀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⢻⣿⣿⣯⣉⠀⠉⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢦⡀⠀⣿⡟⢮⣝⠻⣦⡆⠀⠀⣤⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡇⠀⠉⠙⣿⡇⠀⠙⢷⣌⠻⣆⠀⠘⣷⣄⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⠀⠉⠳⣄⣠⣴⣾⣯⣍⡙⠛⠻⢿⣷⡶⣤⣿⡇⠀⠀⠀⠻⣆⠹⣧⠀⢻⣿⡄⠚⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⡀⠀⠀⠙⢿⣿⠈⢻⣏⠉⠳⣤⡀⠈⠻⢦⡉⠋⣦⠀⠀⠀⢹⣇⢻⡆⢸⡇⢿⡄⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⢧⠀⠀⠀⠀⠙⢧⡀⢻⣆⠀⠈⢷⡄⠀⠀⢻⣄⠘⣧⡀⠀⣀⣿⣾⣷⣼⣧⣼⣷⣶⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠸⡀⠀⠀⠀⠀⠈⢿⡄⢻⡆⠀⠈⣷⠀⠀⠀⣻⣤⣴⣿⣿⣿⣿⡟⠋⠉⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠀⢳⡀⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⣹⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠓⢄⣤⣶⣿⣿⣿⠁⣹⣷⡿⠟⠉⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⣿⣿⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣤⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⡀⠀⠀⠠⣶⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣆⠀⠀⣸⡟⣠⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠻⣿⣿⣿⡟⠀⠈⠻⣿⣿⣿⣿⣧⣼⣿⠞⠁⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⡿⠿⣿⣿⡉⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢙⡿⠁⠀⠀⠀⠈⠉⠙⣿⠹⠋⠁⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀ ⢹⣿⣿⣿⠄⠀⢸⡟⣧⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠟⠁⠀⠀⠀⠀⠙⠁⣰⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀ ⠀⠻⣿⡿⠀⠀⠈⣧⠹⣧⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠴⠒⢒⣶⠏⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠊⠿⣿⣦⡀⠀⠠⡤⠤⠤⠤⠤⠴⠖⢲⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⣄⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣏⣿⠀⢰⡈⠉⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠙⠂⠀⠀⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⢠⡷⣿⡆⠈⢿⣶⣄⡀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⢧⡀⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠹⣇⠀⠀⠻⣿⣿⣷⣾⣽⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠙⣦⡀⠀⠈⠛⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣠⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⢷⡈⢷⡀⠀⠈⠀⠈⠙⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⢳⡄⠹⣆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠹⣦⡈⢷⣄⠀⠀⢀⣼⣿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣞⣷⣄⠙⢧⣠⣼⣿⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠐⠒⠒⠚⠛⠓⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

▓▓▓▓▓░▓▓▓▒▒▒▒▒▒▓▓▓▓▓▓▓ ▓▓▓▓░░░▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓ ▓▓▓░▐▌░▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓ ▓▓▒░░▌░░░░░▒▒▒▒▒▒▒▒▓▓▓ ▓▓▒▒░░░░░░░░▒▒▒▒▒▒▒▒▓▓ ▓▓▒░░░░░░▀▀███▒▒▒▒▒▒▒▒ ▓▓▒░░░░░▌▄████▌░░▒▒▒▒▓ ▓▓▒▒░░░░███▄█▌░░░▓▓▓▓▓ ▓▓▒▒▒░░.’.░▀▀▀▀░░░░▓▓▓▓▓ ▓▓▒▒▒▒░░░░░░░░░░░░▓▓▓▓ ▓▒▒▒▒▒▒░░░░░░▐▄░░▓▓▓▓▓ ▓▒▒▒▒▒▒▒░▓▓▓▓▓▓▓▓▓▓▓▓▓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⢀⣠⣤⣤⢤⡤⢤⢤⣤⣀⣀⣸⠁⢄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢯⣿⠲⡯⢤⣏⣠⠞⣱⢋⡞⠁⠀⢈⣿⠀⠈⣇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⢋⡷⣇⠘⣇⡏⢰⠃⡜⠀⠀⠀⢺⡀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⡜⢀⠏⠓⢿⠀⣸⣀⣇⣀⡤⠀⢤⣝⣦⡀⠈⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢰⠁⢸⣀⣤⠞⠛⠉⠁⣿⣼⣿⣄⣀⣿⡆⠉⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⣠⠾⣿⡷⣤⠀⠀⠀⣧⢿⣿⣿⣹⣿⡷⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡾⠁⠀⠛⣷⣌⣳⡄⠀⠹⡌⠻⣿⣿⠿⠋⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠘⢿⣾⡏⠀⠀⠑⠀⠀⢠⠤⠴⢚⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⡤⠖⠊⠉⠉⠑⠲⣄⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡋⠼⠀⡆⠀⠀⢀⣏⣒⡶⠟⣉⢹⡄⠀⠀⠀⠀⠀⢀⣼⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠵⠖⢲⢿⣇⣠⢴⡟⢁⡏⢻⣄⡤⠤⠤⢤⡾⠈⣠⣔⣚⣛⠫⢍⡙⠲⣄⠀⠀⠀⢹⡀⢹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢈⣠⠴⠋⢀⠞⠀⡏⡇⠀⢀⣴⠃⠹⣞⠉⠀⠀⠈⠙⢦⡙⢦⠀⢳⡀⠀⠀⣧⠀⡏⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢧⢀⡴⠃⠀⡸⢀⡇⡔⡾⢸⠶⡄⢸⠀⠀⠀⠀⠀⠀⠳⡄⢳⡀⢧⠀⠀⢸⠀⢃⠸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢧⡀⠀⡰⠃⡼⠐⡄⣯⣾⡶⢸⢿⠀⠀⠀⠀⠀⠀⠀⢹⡀⢣⢸⠀⠀⠘⠀⢸⠀⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠙⠺⣅⡞⠁⡀⠹⠷⠤⠼⠊⡼⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⢸⠀⠀⢸⠀⢸⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠓⢦⡇⠀⢀⡀⠀⠀⣳⣄⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣼⠀⠀⢸⠀⡏⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡼⠀⠀⢸⠉⠉⠉⠻⣝⢦⡀⠀⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⡜⢠⠇⢠⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾⡄⠀⠀⠀⠘⢦⠙⢦⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⡿⠀⢠⠇⢸⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡇⢹⡀⠀⠀⠀⠈⢇⠈⢧⠀⠀⠀⠻⡀⠀⠀⠀⠀⢸⢸⡇⠀⢸⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢰⠃⠀⢧⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠀⢳⡀⠀⠀⠀⡏⡾⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣼⠀⠀⠸⡄⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⣸⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⡞⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣠⠾⠤⠤⠤⠔⠃⠀⠀⠀⠓⠒⢺⠁⠀⣀⣀⣀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠋⠁⠀⢰⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠊⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜⬜⬜🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏽🏼🏽⬜⬜⬜🏽🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽🏼🏼🏽⬜⬜⬜🏽🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🏽🏼🏼🏼🏽🏽⬜🏽🏽🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏽🏼🏼🏼🏼🏼🏽🏽🏽🏼🏼🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨⬜⬜🏽🏼🏼🟨🟨🟨🟨🟨🟨🟨🏼🏼🏼🏼🏼🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨⬜🏽🏼🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🏼🏼🏼🏼🏽🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🏻🟨🟨🟨🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🏼🏼🏼🏽🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🏻🏻🟨🏼🏼🏼🏽🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🟨🟨🏼🏼🏼🏼🏽🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏼🏼🏼🏽🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟨🟨🟨🏻🟨🟨🏻🏻🏻🏻🏻🟨🟨🟧🟧🟧🏼🏽🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟨🟨🟨🟧🏽🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟧🏼🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟧⬛🟨⬛🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟧⬛⬛🟨🟨⬛🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟧🟨🟧🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟨🟧🟨🟨🟨⬛🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟧🟨🟧🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨⬛⬜🟨🟧🟨🟧🏼🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟧🟧🟨🟨🟨🟨⬛⬛⬛⬛🟨⬛⬜🟨⬜🟨🟧🟨🏼🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟧🟨🟨🏼🏼🏼🏼🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🏻🟨🏼🏼🏼🏽⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🏻🏻🟨🏼🏼🏼🏽⬜🟨🟨🟨🏻🏻🏻🏻🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🏻🏻🏻🟨🏽🏼🏽🟨🟨🏻🟨🟨🟨🟨🟨🟨🏻🏻🟨⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🏻🏻🏻🟨🏽🏽🟨🏻🏻🟨🏻🏻🏻🏻🏻🏻🟨🟨🏻🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🏻🏻🏻🏻🟨⬜🟨🏻🏻🟨🏻🟨🟨🟨🏻🏻🏻🏻🏻🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🏻🏻🏻🏻🟨🟨⬜🟨🏻🟨🏻🟨🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🏻🟨⬜ ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🏻🏻🏻🟨🏻🏻🟧🟨🏻🏻🟨🟨🟨🏻🏻🏻🏻🟨🏻🏻🏻🟨🏻🏻🟨 ⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🏻🟨🏻🏻🟨🟨🟧🟨🟨⬜⬜⬜🟨🏻🏻🏻🏻🟨🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜🟧🟨🟨🟨🟨🏻🏻🏻🟨🟨🟥🟨🏻🟨🏻🟨🟩🟧⬜⬜⬜⬜⬜🟨🏻🏻🏻🟨🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜🟧🟨🟨🟨🏻🏻🏻🏻🏻🏻🟨🟥🟨🏻🟨🟩🟥🟩🟧⬜⬜⬜⬜⬜🟨🏻🏻🟨🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜🟧🟨🟨🟨🏻🏻🏻🏻🟨🟨🟨🟥🏻🏻🟨🟥🟨🟥🟧⬜⬜⬜⬜⬜🟨🏻🏻🟨🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜🟧🟨🟨🟨🏻🏻🏻🟨🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜🟨🏻🟨🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜🟧🟨🟨🟨🟨🏻🏻🟨🏻🏻🟨🟨🟨🟧🟨🟨🟨🟨🟧⬜⬜⬜⬜🟨🏻🏻🟨🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜🟧🟧🟨🟨🏻🏻🏻🟨🏻🏻🟨🟨🟧🟨🟨🟨🟧⬜⬜⬜⬜⬜🟨🏻🟨🏻🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟧⬜⬜⬜⬜🟨🏻🏻🟨🏻🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟨🟨🟧🟧🟧🟧🟧🟨🟨🟧⬜⬜⬜⬜⬜🟨🏻🟨🏻🏻🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟧🟧⬜⬜⬜🟨🏻🟨🏻🏻🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟧🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜🟨🏻🟨🏻🏻🏻🏻🏻🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟧🟨🟨🟨🟧⬜🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜🟨🏻🟨🏻🏻🏻🏻🏻🟨🏻🟨⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟧🟨🟨🟨🟧⬜🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜🟨🏻🏻🟨🏻🏻🏻🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟧🟨🟨🟨🟧⬜🟧🟧🟧🟧🟨🟨🟨🟧⬜⬜⬜🟨🟨🟨🏻🏻🏻🟨🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟧🟨🟨🟧⬜🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟧🟨🟧⬜🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜⬜🟨🟨🏻🏻🏻🟨🟨⬜🟨⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟧🟧⬜🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜🟨🏻🏻🏻🏻🟨🏻🏻🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜🟨🟨🟨🏻🟨🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜🟨🏻🟨🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧🟨🟨🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜🟨🟨🏻🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟧🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟨🟨🟨🟨🟨🟧🟨🟧⬜⬜⬜🟧🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

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

⢀⣤⠖⠀⠀⣀⡠⠤⠤⣈⢳⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠑⠀⠒⠉⠀⠀⢀⠀⠠⠍⢷⣀⠙⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⣀⠀⠒⠀⢁⣀⠄⠀⠀⠀⠀⡸⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣏⠉⠉⣝⡡⠔⠂⠈⠉⠉⠀⢀⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢽⣛⡆⠘⠁⣀⣤⡤⣀⠀⠀⠀⢁⠜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢿⠇⠀⣼⣿⣿⣀⠙⡎⡀⢰⠁⣰⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⡋⣠⠀⢟⡻⠟⡃⢂⠇⠀⢯⡠⡾⠁⢀⣀⡤⠶⠬⠍⡑⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢎⡀⠀⠑⠒⠒⠁⠀⠀⠸⣚⣲⡔⢉⡼⢒⡟⠐⢄⠈⠄⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠜⢉⡟⢤⡚⢆⠀⠀⡄⢰⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠐⡓⠺⡄⡜⣰⠀⠃⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⢀⣰⠀⢀⠏⠁⢸⠀⠃⠀⠸⣄⠣⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠈⢹⠃⠀⠸⡉⠈⡆⠈⠙⡆⠘⡄⢀⠰⠀⠻⣉⡡⡾ ⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢸⡘⠀⠀⢇⠀⢸⠀⠀⠸⡀⠙⢌⠢⡑⠄⣀⡠⠃ ⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⡎⠇⠀⠀⢸⠤⠼⡀⠀⢀⡇⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠸⣄⣀⣠⠜⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⢠⠴⠖⠉⠉⠉⠢⡀⢢⠉⠃⠶⣤⣀⢤⣄⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠋⠒⠒⠀⠤⣀⠀⠀⠱⡈⡄⠀⠀⢠⡟⠁⠘⣦⠀⢰⢠⢊⠕⣵⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⠇⠀⠀⠀⠐⠂⠠⠄⡈⠂⣄⡥⠓⠀⠀⠜⠀⠀⠁⠸⡄⢸⢁⠆⠀⠀⢠⠟⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠁⠀⡠⠄⠲⠤⣄⡀⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡟⣎⠘⠀⠀⠠⡏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢸⠁⠀⠀⠀⣟⣭⠲⠃⠀⣴⠶⢦⡀⠀⠀⠀⠀⠁⣸⠁⢸⡆⠀⠀⠘⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⢸⠀⠀⠀⢤⡾⣌⠀⠀⢸⣓⡰⢦⡙⢦⠤⠀⠀⠐⡇⠀⢀⡃⠀⠀⠀⠀⠰⡿⠔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠈⣆⠀⠚⠋⣷⣸⠀⠀⢸⣿⣇⠀⣷⢈⠛⠯⠔⢰⠃⠀⢸⡿⠙⡆⠀⢀⠏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢄⠈⢆⠀⠀⣹⠟⠀⠀⠀⠻⣿⣿⣼⢺⡒⠀⢀⡞⠀⢀⢧⡁⠀⠇⣠⢤⡀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⠑⣌⢧⡐⣠⠀⠀⠀⠀⠁⠀⢁⠀⣠⠎⠀⢀⠎⢎⡏⠀⡶⠁⢀⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡈⠳⣍⠓⠒⠀⠠⣦⢴⡏⢁⡴⠃⠀⢀⠎⡜⢸⠁⠀⠁⢀⡾⠋⠂⠀⣀⡀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣄⠈⢢⡀⠀⠀⢹⢸⣧⠏⠀⠀⡰⠃⡜⠀⣏⠇⠀⠴⢫⣀⣴⡿⠛⠉⠀⠀⠀⠈⠉⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠄⣀⠀⠱⣣⠀⠱⡀⠀⣾⢸⡏⠀⢀⠞⠀⡜⠀⣸⠁⠀⠀⡠⠜⠛⠻⣄⠒⠒⠒⠢⢄⡀⠀⠀⠀⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢡⡶⠒⠵⢀⠿⡆⠀⢣⢠⡿⢌⠀⠀⡎⠀⡸⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡎⠿⠳⣦⡀⠀⠈⠢⡀⠀⠀⢩⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡈⠳⠆⠀⠞⠁⡇⠀⢸⡞⠀⢸⡀⢸⠀⢠⠃⢀⡏⡀⠀⠀⠀⠀⠀⠀⡄⠹⣼⠆⠈⢓⡄⠀⠀⠐⡄⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⣤⡄⠀⢀⣧⠶⡏⠀⠀⢰⣧⢸⠀⢸⠀⢸⠁⡇⠀⠀⠀⣠⠀⠀⠀⠘⣶⢀⡀⠈⣶⠀⠀⠀⢱⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣾⡀⢸⠀⠸⣼⣝⣞⡆⠁⠘⠄⠀⠀⠘⠁⠀⣿⠀⠙⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠋⠳⣄⣣⠀⠙⠺⢣⡯⠀⠀⠈⠒⡄⠀⠀⠀⡟⠀⣿⠀⠀⠀⡘⠀⢠⠃⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡀⢠⡇⠀⠀⠀⠙⢃⡆⠴⡏⠁⠀⠀⠀⢰⠀⠀⠀⠀⣧⡰⠆⠀⠀⡰⠁⡠⠃⢰⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢰⡆⠀⠀⠀⢈⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠀⠀⡰⢁⠔⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⣜⠃⠘⣃⡀⠀⠀⣄⣵⠀⠀⠀⠀⣸⠀⢀⠜⡰⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠶⠞⠃⠀⠀⠈⠁⠀⠉⠀⠐⢦⣤⢰⠞⠁⠀⠎⡌⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⢸⠀⠻⣥⣀⣀⣀⢀⡀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⣸⡈⢄⠀⠀⠉⠀⢀⡀⠀⡀⠈⣉⠓⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠀⠀⠛⠈⠁⠀⠀⠀⠉⠫⡎⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣇⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢀⣀⣀⣀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⢿⡟⡓⠌⠃⠀⡁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⣎⣅⠓⠉⢟⣿⣟⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠉⠹⣵⠀⢋⡿⣙⣰⠀⠀⠀⠀⡀⠄⠒⠒⠢⢄⠀⠀⠀ ⠀⠀⠀⠪⢠⡀⣰⣟⠏⣇⠀⠀⣀⣀⣀⡀⠀⠀⢊⠣⡀⠀ ⠀⠀⠀⠀⠀⡰⠁⡈⠀⢦⠀⠠⢿⠁⠈⠙⢄⠀⠁⡄⣷⠀ ⠀⠀⠀⠀⠀⢀⡀⠙⠦⠊⠀⠟⠚⠀⠀⠀⠈⣴⠀⠀⡇⡆ ⠀⠀⠀⠀⠀⠀⢂⠃⡒⠒⢗⢄⠐⢆⠀⠀⠀⣿⠆⢠⡠⠃ ⠀⠀⠀⠀⠀⢀⠂⢀⠐⠀⠀⢡⠀⠈⢂⠀⢀⣿⣠⠞⠁⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠇⠀⠰⠀⠀⠈⡆⠸⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠀⠒⠈⠀⠁⠀⠈⠓⠐⠂⠁⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿⬜⬜⬜⬜🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🏿⬜🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🟫🟫🟫🟫🟫🏿🏿🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🏿🟫🟧🟫🟫🏿🏿🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🟫🏿🟫🟧🟧🟧🏿🟫🏿🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🏿🟫🟫🟧🟧🟧🟧🏿🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🟧🟧🟧🟧🟧🏿🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🏿🟫🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿🟫🟫🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🟫🟫🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🟧🟧🟧🟧🟧🟧🟧⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🟧🟧🟧🟧⬛⬛⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🟨🟧🟧🟧🟧⬜⬜🟩🟩🟩⬛🟧🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🟨🟧🟧🟧⬛⬜⬜🟩⬜⬛⬛🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🟫🟫🏿🟨🟧🟧🟧🟧⬜🟩⬜⬜⬛⬛🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜🏿🟫🏿🟨🟨🟧🟧🟧🟧⬜🟩⬛⬛⬛⬛🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜🏿🟫🏿🟨🟨🟨🟧🟧🟧⬜⬜🟩⬛⬜⬛🟧🟧🟧🟧⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🏿🏿⬜🟨🟨🟨🟧🟧⬜🟧⬜🟩⬛⬛🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🏿⬜🟨🟨🟨🟧⬜🟧⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧⬜🟨🟨🟨🟨🟨🟨🟨🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟧🟧🟧🟩🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜🟧🟧🟧🟥🟥🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟧🟧🟧🟧🟥🟥🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟧🟧🟧🟩🟧🟧🟩🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟥🟥🟧🟥🟥🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟥🟥🟧🟥🟥🟧🟧🟧🟨🟨🟨🟨🟨🟥🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟥🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜🟧🟧🟧🟧🟨🟨⬜🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟥🟥🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🟨⬜🟨⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜🏿🏿⬜⬜⬜⬜🏿🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏿🏿🏿🏿⬜🏿🏿🏿🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🏿🏿🟫🏿🏿🟫🟫🟫🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🏻🏻🏻🏻🏿🟫🟫🟫🟧🟫🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜ 🟨⬜⬜🟨🏻🏻🏻🏻🏻🏿🟫🟧🟨🟧🏿🏿⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🏿🟧🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🏻🏻🟨🟨🟨🟨🟨🟧🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🏿⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🏻🟨🏿🏿⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟨🟩⬜⬜⬛🟨🟨🟨🏻🏻🏻🟨🏿⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟨🟨⬛🟩⬜⬜🟨🟨🏻🏻🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟨🟨⬛🟩⬜🟨🟨🟨🏻🟨🟧🟧🟧⬜⬜⬜🟨🟨⬜⬜⬜ ⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🏻🟨🟧🟨🟦🟨🟧⬜🟨🏻🏻🟨⬜⬜ ⬜⬜⬜⬜🟧🟧🟧🟧🟨🏻🟨🟧🟨🟦🟥🟦🟨🟧🟨🏻🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟥🟥🟥🟨🟨🟨🟥🟨🟥🟨🟧🟨🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟧⬜🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🏻🏻🏻🟨🟨🟧🟨🟨🟨🟨🟧⬜🟨🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟧🟧🟧🟨🟨🟨🟧⬜⬜🟨🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧⬜🟧🟨🟨🟧⬜⬜⬜⬜🟥🟥🟥⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧⬜⬜🟧🟨🟨🟧⬜⬜🟨🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟨🟨🟧⬜⬜🟧🟨🟨🟧⬜⬜🟨🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧⬜⬜⬜🟨🟨🟨⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⣿⢗⠦⣄⠈⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡤⢄⠀⠀⣀⢤⣶⣿⣁⠉⢻⠀⠙⣌⢣⠀⢷⡸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢀⠀⠑⢿⡙⣗⠢⢌⠙⢯⡛⢢⠀⠈⣇⢧⢸⢱⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⠘⡀⠀⠈⠳⡜⣆⠈⢧⠀⠙⡌⣣⣤⣼⡿⠾⣶⣷⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠸⡀⢣⠀⠀⢀⣷⢸⡀⣸⣤⢶⣿⣿⣿⣿⣷⡀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣀⣵⣾⣿⣿⣴⣿⡉⠀⢀⣽⣿⡟⢿⣿⣿⣄⠈⢻⢏⠲⡀⠀⠀⠀⠀ ⢀⣠⣾⣿⣿⠿⠿⣿⣿⣿⣿⣆⠈⠻⣿⡇⠀⠻⠿⣿⢶⠿⠃⠀⠹⡄⠀⠀⠀ ⢻⣿⡏⠁⣿⡆⠀⠙⢿⣿⣿⣿⣷⣠⠞⠀⠀⠐⠂⡜⢄⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠛⠃⠀⢸⠹⣄⡀⠀⠉⠛⠛⠋⠁⠀⠀⢀⣩⠟⠁⠈⠢⡀⠀⠀⠀⠘⢆⠀ ⠀⠀⠀⠀⠈⣦⠟⠿⣤⣀⣠⠀⠀⠀⠒⡖⠉⠀⠀⠀⠀⢀⡬⠢⣀⠀⠀⢈⠇ ⠀⠀⠀⠀⠀⣿⡆⢳⣄⠀⠙⣇⠀⠀⠀⠱⡀⢀⡠⠔⠊⠁⠀⠀⠀⣀⠔⠋⠀ ⠀⠀⠀⠀⠀⣏⢧⠀⠙⢿⡺⠾⠆⠀⠀⠀⠈⠣⡀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⢦⠣⡀⠀⠙⠳⢶⡄⠀⠀⠀⠀⠙⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣯⣧⡙⢄⠀⠀⢸⡇⠀⠰⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣿⣎⣳⣤⣿⡇⢀⣀⣣⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🏻🏻🏻🏻🏻🟨⬜🟫🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟫🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🏻🏻🏻🏻🏻🏻🏻🟫🟧🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟫🟧🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟧🟫🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🏻🏻🏻🏻🏻🟨🏻🏻🟧🟧🟧🟫🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🏻🏻🟨🏻🏻🟨🟧🟧🟧🟫🟧🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🏻🏻🏻🏻🏻🟨🟧🟨🟨🟧🟧🟧🟧🟧🟫🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧🟫🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟫🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟫🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟫🟧🟧🟧🟧🟧⬛⬛⬛⬛🟧⬛🟧🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟫🟧🟧⬛⬛⬜⬜🟩⬛🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟫🟧🟧⬛⬛⬜⬜🟩⬛⬛🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟫🟧🟧⬛⬛⬛⬛🟩⬛🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜🟫🟧🟧🟧🟧⬛⬜🟩🟩🟧⬜🟨🏻🟨⬜⬜⬜⬜⬜🟨🏻🏻🏻🏻🏻🏻🟨⬜⬜ ⬜⬜⬜🟫🟧🟧🟫🟧🟩🟩🟩🟧⬜🟧🟨🏻🟨⬜⬜⬜⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜🟫🟫🟫🟧🟧🟧🟧🟧🟧🟨🏻🏻🟨⬜⬜⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟧🟧🟨🏻🏻🏻🟨⬜⬜⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟧🟨🏻🏻🟨⬜🟫🟫🟫🟨🏻🟨🟨🟨🏻🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟫🟨🏻🏻🟨🟫🟧🟧🟧🟫🟨⬜⬜⬜🟨🏻🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜🟨🏻🏻🏻🟫🟨🟨🟧🟧🟧🟧🟧🟧🟫⬜⬜⬜⬜🏻🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🏻🟨🟧🟧🟧🟧🟧🟧🟧🟧🟫⬜⬜⬜⬜🟨🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟧🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟫⬜⬜⬜⬜🟨🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟧🟧🟫🟧🟧🟫🟧🟧🟧🟫⬜⬜⬜⬜⬜🟨🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟫🟧🟫🟫🟫🟫🟧🟧🟧🟫⬜⬜⬜⬜🟨🏻🏻🏻🏻🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟫🟧🟧🟫🟫🟧🟫🟧🟧🟫🟫⬜⬜⬜🟨🏻🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟫🟧🟧🟫⬜🟫🟧🟫🟧🟧🟫⬜⬜⬜⬜🟨🏻🏻🏻⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟫🟧🟧🟧🟫⬜🟫🟧🟫🟧🟧🟧🟫⬜⬜🟨🟫🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟫🟧🟫🟧🟧🟧🟫⬜🟫🟧🟫🟧🟧🟧🟫⬜🟨🏻🏻🟫🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟧🟧🟧🟫⬜🟫🟫🟫🟧🟧🟧🟫🟨🏻🏻🏻🏻🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫⬜⬜⬜⬜🟫🟫🟫🟫⬜🟨🟨🟨🏻🏻🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🏻🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨⬜🟨🟨🟨⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗⢤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠖⢏⣉⣉⣹⠀⠀⢹⢦⡀⠀⠀⡰⣆⢠⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠋⠁⢀⡴⠚⠉⠀⠀⠁⠀⠘⡎⣷⣄⠀⠇⢸⡎⢀⡇⣤⣄⠀⠀⢀⡤⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢛⡠⠶⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶⠀⢸⠀⢸⣾⠞⢹⡤⠚⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡗⠉⠀⠀⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣧⠀⢀⡾⠁⠐⠋⠀⢀⣴⣋⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⡔⠉⢻⠀⠸⡏⢍⣿⣖⠺⡷⠤⠆⠀⠀⢹⣾⡀⣾⠖⡆⠀⠠⠔⠋⠁⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⣇⠀⠈⠣⡀⠙⢌⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⡼⠀⣧⢤⡄⡠⠴⠮⠥⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣜⣆⠀⢀⡅⠀⠀⠈⠉⠀⢀⡴⠀⠀⠀⠀⢸⡇⡇⠈⠁⣼⣁⣤⠤⠒⢊⠥⠒⠊⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣷⣬⣳⠤⠴⠤⡖⠊⢁⣿⠀⠀⠀⠀⠈⡿⠁⠀⢚⣏⠵⠈⢲⣊⠥⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣌⠑⢆⢠⠇⢠⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⡏⠉⠉⠉⠑⢦⡀⠀⠈⠓⣄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡾⠳⠀⡏⠇⢈⡟⣴⠋⠀⡼⣄⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢫⡻⠤⠔⢃⡶⢋⡞⢁⠤⠊⠀⢸⠦⡌⠀⠀⣖⣀⣨⣦⡀⠀⢀⣎⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⡾⠊⣁⠠⠤⢒⣻⡟⠀⠀⡴⠃⠀⠀⢳⠙⡄⠀⠀⢳⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡎⠀⢀⡜⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠊⠀⣠⠖⠋⣼⣤⠀⢸⢳⠀⠀⠀⠀⡇⠸⡀⠀⠀⣇⠀⠀⠀⣠⠋⠀⠀⢀⠞⢀⡠⠋⡜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡾⠓⢶⠀⢻⢙⣖⠈⠛⠦⡄⠀⠀⢸⠀⡇⠀⠀⢸⡀⢀⡼⠁⠀⣠⣖⡡⠔⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠝⠶⠟⠀⢸⢿⡀⠀⠀⢠⠃⠀⠀⡜⠀⡇⠀⠀⠈⡇⡾⠁⡰⡻⠊⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣱⣄⣠⡏⠀⠀⠰⠧⣴⠁⠀⠀⢀⡇⢷⣸⠀⡁⠀⠀⠛⠲⠴⠒⠒⠒⣲⣦⣑⢲⡦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠲⠧⠤⠤⠤⠤⠔⠒⠊⠉⠁⢀⡄⠈⠹⡌⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢤⣜⠡⠊

⠀⠀⠀⢀⣀⡤⢴⢚⡛⠛⠛⠛⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠴⠟⢛⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⢠⡾⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡞⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⢋⣴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢸⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡷⠋⡞⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡶⠋⠉⠀⠀⠀⠀⠀⣸⠀⢸⠋⢹⠀⠀⠀⣀⣠⣤⠞⠉⠀⡼⠀⠀⣀⣤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⣼⠃⠀⠀⠀⠀⣀⡴⣿⣡⡾⣉⡤⠤⢤⣀⡤⠀⠀⣠⠇⠀⡼⢀⡏⢀⡴⠞⢉⡼⠁⠀⢀⡼⢁⣴⠞⠉⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⢀⡤⣾⠋⢀⣿⣫⣾⣿⣷⣄⠀⠘⣧⢖⠋⠁⠀⣼⣷⡼⣴⠟⠀⠀⡾⠀⠀⢠⣾⡵⠋⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣟⣠⠶⠟⣿⣤⡿⠀⠸⣳⣿⡇⠀⠘⣿⡆⠀⠛⠋⠁⠀⢺⠏⢻⠟⠁⠀⠀⣼⣵⠶⣦⡿⠋⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠈⣿⣿⠇⠀⠀⣿⣿⠿⣦⣴⣿⡇⠀⠀⠀⠀⢀⡞⠀⣾⠀⠀⢀⡾⡿⠁⢀⡟⠀⠀⠀⣴⣏⣡⣤⣤⣤⣤⡤⠤⠤⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⠟⠋⠀⠀⠀⠈⢻⣷⣿⣿⡟⠁⠀⠀⠀⣠⠞⠁⢸⣿⡦⡤⠚⢹⡇⠀⣼⡥⠖⢶⡈⠉⠀⠀⠀⠀⣠⡿⠛⠳⢶⣦⣀⠈⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣆⠉⣠⠆⠀⠀⠀⠉⠋⠉⠀⢀⣠⣴⣞⣉⡄⢠⣿⣿⡇⡿⠀⣸⠀⠰⠋⠀⢀⡞⠀⣀⣠⠤⠖⠛⠉⠀⠀⠀⠀⠉⠻⣷⡤⣄⣀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠧⢤⣀⣀⣀⣀⣀⣠⣤⠴⠋⠉⣹⠏⣠⣿⣿⣿⡷⣧⣾⠇⠀⠀⠀⣠⠿⠴⢟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡌⢿⡛⢾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⢃⣴⣿⣿⡿⢫⡷⠛⠟⠀⠀⠀⠺⢧⠀⠀⣠⡟⠛⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⢧⠀⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⠃⢸⠁⠀⠀⠀⠀⢀⣠⣿⡴⢻⡅⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⠻⣿⠇⠀⣼⠀⠀⠀⠉⠉⠉⠀⢹⡇⠀⣧⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣿⡏⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⣄⠺⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⠀⠀⠀⠘⣿⡆⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢿⠁⠀⠘⣆⢸⡇⠀⠀⠀⠀⠀⢠⡇⠀⠇⢠⡇⠀⠀⠀⠀⠀⠀⠘⣧⢸⠀⠀⠀⠀⠀⠀⣿⡇⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⢙⣾⡇⢰⡀⠀⠀⣠⡞⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠓⢾⠈⠛⠀⢿⡻⡋⠉⢧⠀⠀⠀⠷⢶⡀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢀⣿⣷⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢿⠀⠀⠀⠸⣇⢳⠀⠈⣇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠸⠏⢸⠀⢀⠀⠀⠀⢸⣿⡏⣧⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠀⠀⠀⠀⢹⠈⣇⠀⢸⡆⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡄⢘⣇⠀⠀⢸⣿⣿⠘⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠘⡆⣿⠀⠘⣇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠸⣿⠘⡿⣆⠀⠀⣿⣿⣆⠀⠙⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢻⣆⡇⠙⢦⡀⢻⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣷⠇⠀⢠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠳⣄⣿⢿⣿⣧⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠷⣌⠙⠻⠿⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣧⣀⣠⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡃⠀⠀⠀⠀⠀⢀⣼⠃⠀⠺⢤⣤⣤⣤⣤⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⢲⣶⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠿⢉⣀⣀⣀⣉⡉⠉⠛⠿⣟⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣤⡀⠀⠀⢀⣴⠟⠥⢤⣀⠀⠀⠀⠈⠉⠉⠙⢲⣖⡨⣽⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠀⠙⠻⣶⡋⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠉⢻⡶⣍⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⢠⠀⠀⠙⢿⣄⣀⣀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠹⣌⠑⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠘⡆⠀⠀⠀⠃⠀⠀⠉⠛⠲⢤⣀⠰⣤⣙⢄⡀⠀⠀⠀⠀⠹⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⠀⢳⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡙⠳⣜⣯⠛⠧⣄⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⡀⠳⠄⢀⠈⠙⡾⠉⠀⢀⡼⠛⠶⣍⢻⡆⠀⢹⡏⢻⡶⠤⣤⣌⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣄⠀⠀⣉⣙⡇⠀⠀⡎⠀⡴⠓⣿⣧⠀⠀⠀⣷⣾⣿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡟⣇⠀⠀⠀⢣⡀⠀⢇⠘⣇⣀⣿⣿⡆⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡘⣧⠀⠀⠀⠙⢤⡘⣆⠘⢿⣿⣿⠇⠀⠀⠀⠠⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠻⠋⢉⣉⠩⠙⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⣨⢧⡀⠀⠀⠀⠉⠚⠧⠬⠟⠋⠀⠀⠀⠰⣤⣤⠟⠁⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⣠⠶⠏⠀⠀⠀⠒⠒⠢⢭⡑⠲⣕⢤⡀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡈⢷⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣤⣴⠚⠙⣄⠀⣠⡴⠚⠉⠀⠀⠀⠀⣸⢿⢷⣶⣤⣤⣄⣈⠉⠐⢄⠀⠈⠢⡈⠳⡙⣤⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣖⠻⣄⠀⠀⠉⠉⠉⠉⠉⠉⢳⡀⡟⢷⡀⢻⡍⠁⠀⢀⣠⠴⠶⢚⣉⠽⠛⢙⣿⡗⠷⣔⣄⠙⢦⡀⠑⣄⠀⠘⡄⢱⠘⣞⢏⠾⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠳⣷⢀⠻⣦⣷⡄⠀⠈⠙⣶⣎⣁⢀⠤⠊⠁⣸⡇⠀⠈⠳⣟⡀⠙⡄⠘⣆⠀⠹⡀⢷⠸⡜⡆⠙⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⠈⠛⠂⠀⠀⠀⠀⢹⠆⣀⣤⡾⢃⡇⠀⠀⠀⠙⣵⡀⠸⡄⠸⡆⠀⡇⠘⡄⢣⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡾⢛⡵⠋⠀⢸⠁⠀⠀⠀⠀⢹⣇⠀⢱⠀⢡⠀⢸⠀⡇⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⢀⣠⡶⣷⠋⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⣿⠀⢰⣇⢸⠀⢸⠀⠃⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⢤⣀⣀⡆⠀⠀⠈⣆⣉⣭⡶⠛⢧⠀⠀⠀⢸⢥⣀⠀⠀⠀⠀⠀⢸⡆⡎⢹⠈⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⢹⠀⠀⠀⢹⡄⠀⢳⠀⠈⣧⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⣿⣿⢸⡄⡄⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⢸⡀⠀⠘⡆⠀⠀⠀⠀⠸⡄⠀⠀⠀⣾⢁⣿⢸⡇⡁⢸⠀⠀⢸⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⢸⡇⠀⠀⢳⠀⠀⠀⠀⠀⣷⠀⠀⢰⣿⣾⣇⢸⡇⡇⢸⠀⠀⢰⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀⠀⠘⠋⢸⣿⠐⣇⣧⠸⠀⢨⢸⡟⣇⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⣿⣸⣿⣿⠀⠀⢸⠀⣧⠘⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⢿⣧⡂⢸⡆⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⢿⡀⠹⣿⣌⣇⡀⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⡀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣼⠒⢺⠃⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⠳⣷⠀⠈⠻⣿⢳⣤⡙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣏⣀⠀⠀⠀⠀⢀⣀⡴⠇⠀⠉⠓⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠳⠏⠙⠻⠿⠶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⢤⣤⣤⣠⢤⢤⢤⠀⡀⡀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⠝⠛⠝⡻⡌⠬⠸⠀⠦⣣⡚⠃

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜ ⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🏽🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜ ⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🏻🏻🏻🟨🟨🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜ ⬜⬜⬜🏽🏽🏽🏽🏽🏽🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🟨🏻🟨🟨🏽🏽🏽🏽🏽🟧🟧🟧🟧🏽🏽⬜⬜ ⬜⬜⬜🏽🏽🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🟨🟨🏽🏽🏽🟧🟨🟨🟧🟧🏽🏽⬜ ⬜⬜⬜🏽🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🏽🟧🟧🟨🟨🟨🟧🟧🏽⬜ ⬜⬜⬜🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟧🟨🟨🟨🟨🟨🟧🏽⬜ ⬜⬜🏽🏽🏽🏽🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟧🟨🟨🟨🟧🟨🟧🏽⬜ ⬜⬜🏽🏽🏽🟨🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟧🟧🟨🏽⬜ ⬜⬜🏽🏽🏽🟨🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟧🟨🟧🏽 ⬜⬜🏽🏽🏽🟨🟨🟨🟨🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟧🟨🟧🏽 ⬜⬜🏽🏽🏽🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟧🟨🟧🏽 ⬜⬜🏽🏽🏽🏽🟨🟨🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧🏽 🟨🟨🟨🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟧🟨🟧🏽 🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🟨🟨🟨🟨🟨🟨🟨🟧🟧🟨🟧🏽 ⬜🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🟨🏻🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟧🏽 ⬜⬜🟨🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨🏻🏻🏻🏻🏻🟨🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🏽 ⬜⬜🟨🟨🏻🏻🏻🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🏽 ⬜⬜⬜⬜🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟧🏽🏽 ⬜⬜⬜🏽🏽🟨🟨🟨🏻🏻🏻🏻🏻🏻🏻🟨🟨🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🏽🏽🏽 ⬜⬜⬜⬜🏽🏽🏽🟨🟨🟨🟨🟨🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛🟨🏽🏽🏽⬜ ⬜⬜⬜⬜🏽🏽🏽🏽🏽🟧🟨🟩🟨🟨🟨⬛⬛⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬜⬜⬜🟩🟩⬛⬛⬛🏽🏽⬜ ⬜⬜⬜⬜⬜🏽🏽🏽🏽🟧🟨🟩⬛⬛⬛⬛⬛⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬜⬜⬜🟩🟩⬛🟨🏽🏽🏽⬜ ⬜⬜⬜⬜⬜🏽🏽🏽🏽🟧🟨🟩⬛⬜⬛⬛⬛⬛⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛⬛⬜⬜🟩🟩🟨⬛🟨🏽⬜⬜ ⬜⬜⬜⬜⬜🏽🏽🏽🏽🟧🟨🟩⬛⬜⬛⬜⬛⬛⬛⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬛⬜⬜🟩🟩🟨🟨🏽🏽⬜⬜ ⬜⬜⬜⬜⬜⬜🏽🏽🏽🟧🟨🟩⬛⬛⬛⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬛⬛⬛🟩🟩🟨🟨🏽⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏽🏽🏽🟧🟨🟩🟩⬛⬛⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛⬛⬜⬛🟩🟨🟨🏽🏽⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🟧🟨🟩⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛🟩🟨🟨🟨🏽⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🟧🟨🟩🟩⬛⬛⬛⬛⬛⬛🟨🟨🟧🟧🟧🟧🟨🟨🟨⬛⬛⬛⬛⬛⬛🟨🟨🟨🏽🏽⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🏽🏽⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🏽⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣤⣤⣤⡖⡶⢊⠟⡝⡶⠒⠒⣧⠀⠎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⢳⣼⡈⣯⠏⡜⠸⠀⠀⢰⠁⠀⢸⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠎⡈⠙⢻⣀⡇⣤⣤⡄⠠⣷⠤⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢸⢀⣷⣶⡉⠀⠀⣟⣿⣷⣶⣿⣀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡼⠋⠘⢿⣙⣦⠀⠹⡘⢿⣿⠿⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠤⣀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠈⢻⣿⡀⠀⠁⠀⢰⠒⢒⣽⣇⠀⠀⠀⠀⠀⢀⡴⣋⠔⠂⠉⠉⠉⠒⢄⠑⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠬⣡⣆⣀⣠⡷⠚⣫⡔⡼⣄⠀⣀⣀⢠⠾⢋⣀⠤⣤⠤⢀⡀⠀⠀⢣⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣋⠭⠋⡐⢁⢿⠉⢀⡼⠙⣦⠛⠉⠉⠲⣝⢦⡈⢆⠀⠀⡇⢸⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢣⡠⠊⠀⡜⡸⠀⢿⡹⠂⣸⠀⠀⠀⠀⠈⢆⠱⡈⡆⠀⢸⠘⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠑⢄⡜⡠⠃⠰⣾⣛⡱⢻⠀⠀⠀⠀⠀⠈⡆⢃⠁⠀⢨⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢤⡆⠀⡈⠁⢘⣆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢡⢸⡄⠀⢸⢰⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⠀⢀⡍⠉⠉⠫⡳⣄⠘⠉⢣⡀⠀⠀⠀⠀⢸⢸⡇⠀⡆⠘⣠⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⢣⠀⠀⠀⠱⡈⢢⠀⠀⠱⡀⠀⠀⠀⢸⣼⠆⠠⣡⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⠀⣇⠀⠀⠀⢡⠈⡆⠀⠀⢱⡀⠀⠀⡼⠿⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠇⠀⢸⠀⠀⠀⡸⠀⡇⠀⠀⠀⢃⠀⢰⣡⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⣸⣀⣀⣸⠀⠀⠀⣇⣀⡇⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠒⠒⠒⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠚⠉⠙⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠙⢾⣭⡞⠀⠀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠛⢦⣀⣼⠁⠀⠀⠀⠈⢻⡇⠀⠀⣠⠶⠞⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⡇⢀⠞⠁⠀⠀⢠⣾⠖⡻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣧⠏⠀⠀⠀⠀⠀⢀⡴⢶⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⡶⠋⣩⡿⠛⢢⡀⠀⠀⡾⠉⠙⠒⢦⣄⠀⢰⡟⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠹⣤⡾⠁⠀⠀⠀⠀⠈⠳⡏⠀⠀⢸⠀⢧⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⣧⣾⣯⠶⢦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⢸⠀⣸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠸⣿⡿⠁⠠⢾⣿⠀⠀⠀⠀⠀⠀⣠⣖⣛⠛⠳⣤⠏⢀⣤⠏⢀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡀⢹⡀⠀⠀⣼⣿⣧⠀⠀⠀⢀⡾⠉⠉⣿⣷⡀⠘⣿⡭⠏⢀⡾⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣮⣳⡀⣇⢸⣾⣿⣿⠏⠀⠀⠀⣸⣅⣠⠖⢿⡿⡇⠀⠀⢀⣴⣯⡤⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣉⣽⣿⣿⡿⠋⢀⣀⣀⠀⢹⣿⣿⣿⣿⡇⠀⢀⣀⡀⡿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⢡⣄⡙⠢⠀⠀⠠⠀⠠⠿⠛⠛⠛⠒⠲⠞⠓⣾⠃⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢯⣿⠢⠤⠤⢤⡤⠤⠤⢞⡷⠆⠀⠀⠀⣰⠏⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠉⠀⠀⠀⣏⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠻⣝⠒⠄⠀⠀⠀⣴⠞⠁⠀⠀⢠⡼⠃⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣬⡙⠒⠒⠒⠊⠁⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣀⡀⠀⠀⠀⣠⡏⠉⠙⠓⠒⠒⠛⢻⡍⠀⠀⠀⠀⠀⣶⡶⠶⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⡀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⠋⠀⠀⠀⠀⠀⠀⣀⡠⠽⠷⣤⠤⠤⢔⣃⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⠦⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⣸⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠲⠤⠤⣼⠁⠀⠀⠀⠀⠀⠀⠸⢧⣄⣀⣤⣞⠁⠀⠀⣠⡞⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢿⠞⢁⣤⣶⡮⢷⣯⠞⠋⠉⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⣦⣀⣀⡠⠶⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣄⣀⣀⣀⠈⢇⠀⠀⠀⢀⡤⠔⠒⠤⠤⣀⠈⠷⠞⠁⠀⠀⠈⠙⢦⡀⠀⠀⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠚⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠙⠗⠋⠉⠛⠻⢦⣀⠀⡎⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⢀⡼⢻⠒⠦⡀⢻⡱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⢷⡇⠀⠀⠀⣀⣀⠀⠀⠀⢳⡀⠀⠀⢰⡏⠀⣸⠀⠀⠙⢼⠃⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⠁⠀⢻⡄⠀⠀⢷⠀⠀⠘⠧⠴⠃⠀⢀⠀⠁⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠘⡄⠀⠀⡇⠀⠀⠸⡴⠚⠉⠒⢦⣀⠀⡟⠢⠄⠴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠿⠶⠤⣄⣀⠀⠀⠹⢦⡀⢠⡇⠀⠀⠀⠀⠀⢀⣇⡤⠀⠀⠀⢀⣤⡞⠋⠀⠀⠀⠀⠻⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⢾⡟⣿⠁⠀⠀⠀⠀⠀⣼⡏⢠⠴⠒⠊⠉⠈⠙⠓⠦⣄⡀⠀⢀⡼⢧⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⢡⠏⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡋⠀⠀⠉⠓⠦⢤⣤⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⣈⠙⠶⣀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠬⠥⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠙⢦⡀⠀⣀⠤⠚⠋⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠳⣮⣁⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠶⠒⠒⠓⠒⠒⠲⠲⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⣀⣤⡶⠚⠛⠋⠉⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠉⠀⠀⠀⠀⠀⢀⣠⣶⣿⣭⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⢷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣠⣴⠶⠾⠛⠉⠉⠉⠁⠀⠉⠉⠉⠙⠻⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠀⠈⢻⣆⠀⠀⣠⣾⠟⢁⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠘⣧⠀⠀⢻⣦⣰⠟⢁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢻⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀ ⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀ ⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⠶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⡀⠀⠀⠀⣿⠞⣛⣋⣉⣉⣙⣛⣓⣢⠄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠉⠉⠛⠛⠷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠇⠘⣇⠀⠀⢠⣿⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⠷⣶⣤⣀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⢻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⢸⠇⠀⢀⣴⠖⠒⠒⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣄⠀⠀⠈⣿⡀⠀⠀⢀⣤⣼⣧⡀⠀⠀⠈⢳⡌⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣾⣿⣆⠀⠀⠀⠀⠀⠀⢾⣧⠄⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠸⣧⠀⢀⣾⣿⠟⠛⢿⣿⣋⠀⠘⣷⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⣿⠀⠀ ⢸⣿⠈⣿⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣿⠀⢸⣿⡟⠀⠀⠈⢻⣿⣟⠓⢻⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⣿⠀⠀ ⢸⡏⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⣠⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⡇⠀⠀⠀⠀⢻⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠹⣶⠀⣿⠀⠀ ⣾⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⡿⣿⡿⠛⠿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⠀⠀ ⢿⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠙⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⣤⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⢿⣶⡄⠀⠀⠀⠈⠇⠀⠀ ⢸⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠈⡷⠶⠿⠟⠻⣷⡀⠀⠰⠾⣯⣥⣤⣴⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠻⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⣀⣠⣤⡤⠴⣶⡄⠀⠀⠀⠀⠀⠀⣰⣿⣷⣄⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣆⠀⠀⠀⠀⢻⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⢀⣠⠴⠋⠁⠀⠀⠀⢀⣴⣾⠟⠛⠿⣿⣷⣤⣀⣠⣴⠟⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣆⠀⠀⠀⠈⣷⡈⢿⣦⡀⠀⠀⠀⠀⣾⣏⣀⣠⡶⠶⠋⠁⠀⠀⠀⠀⣠⡴⠉⣼⠇⠀⠀⠀⠈⠙⠿⣿⣿⠃⠀⠀⠀⠙⠛⠀⠀⠀⠀⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡄⠀⠀⠀⠈⢿⣄⠙⢻⣦⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢰⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠐⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠛⣷⣄⠈⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠉⠛⠳⠶⠦⢬⡍⠉⠛⠛⠛⠛⠛⢋⣽⠟⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠁⠀⠀⠀⠀⠙⢿⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠛⠉⢿⣆⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠐⠦⠤⣤⣤⣤⣴⠶⠟⠛⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠰⣿⣋⣥⣄⣠⡤⠔⠻⢧⡀⣠⣤⡾⣿⣽⣿⡶⠢⢴⣶⡓⢦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣿⣯⣤⣍⣙⣿⣴⡶⠶⣿⣿⣶⣄⢀⣽⣷⣤⣴⣿⣿⡿⠛⠁ ⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠿⠛⠛⠛⠛⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢀⣀⣤⣶⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⣠⣼⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠀⣀⠀ ⠀⣀⣤⣶⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⢢⡀⠀⢸⣇⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⡽⠁ ⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠻⣄⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⣤⡶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⣴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠻⣷⣄⣀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣶⣶⡶⠶⠿⠟⠛⠛⠉⠉⠀⠀⠀⢀⡀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿🏿⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿🏿🏿⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿⬜⬜🏿🏿🏿🏿🏿⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿🏿🏿🏿⬜⬜🏿🏿🏿🏿⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🟧🟧⬜ ⬜⬜⬜⬜⬜⬜🟧🟧🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏻🟧🟧 ⬜⬜⬜⬜⬜🟧🏻🏻🟧🏿🏿🏿🏿🏿🏿🏿🏿🏿🏻🏻🏻🟧 ⬜⬜⬜⬜🟧🏻🏻🏻🟧🏿🏿🏿🏿🏿🏿🏿🏿🏻🏻🏻🏻🟧 ⬜⬜⬜🟧🏻🏻🟧🏻🏻🟧🏿🏿🏿🏿🏿🏿🏿🟧🏻🏻🟧🟧 ⬜⬜⬜🟧🏻🟧🏻🏻🏻🟧🏻🏿🏿🏿🏿🏿🏻🏻🟧🏻🟧⬜ ⬜⬜⬜🟧🏻🟧🏻🏻🏻🟧🏻🏻🏿🏿🏿🏻🏻🏻🏻🟧⬜⬜ ⬜⬜🏿🟧🏻🏻🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜⬜ ⬜🏿🏿🏿🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜ ⬜🏿🏿🏿🟧🟧🏻⬛🏻⬛⬛⬛🏻🏻🏻🏻🏻⬛⬛🏻⬛⬜ ⬜🏿🏿🟧🏻🏻🏻🏻⬛🏿🏿⬜⬛🏻🏻🏻⬛🏿⬜⬛🏻🟧 ⬜🏿🏿🟧🏻🏻🏻🏻🏿🏿🏿🏿🏿🏻🏻🏻🏿🏿🏿🏿🏻🟧 🏿🏿🏿🟧🏻🏻🏻🏻🏻🏿🏿🏿🏻🟧🟧🟧🏻🏿🏿🏻🏻🟧 🏿🏿🏿🏿🟧🏻🏻🏻🏻🏻🏻🏻🟧🏻🟧🏻🟧🏻🏻🏻🟧⬜ 🏿🏿🏿🏿🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜ ⬜🏿🏿🏿🏿🟧🏻🏻🏻🏻🏻🟧🏻🏻🏻🏻🟧🏻🏻🟧⬜⬜ ⬜⬜🏿🏿🏿🟧🏻🏻🏻🏻🏻🏻🟧🟧🟧🟧🏻🏻🏻🟧⬜⬜ ⬜⬜⬜🏿🏿🏿🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜⬜⬜ ⬜⬜⬜⬜🏿🏿⬜🟧🟧🟧🏻🏻🏻🏻🏻🟧🟧🟧⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟧🏻🏻🏻🏻🏻🏻🏻🟧⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟧🟧⬜🟧🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜⬜⬜⬜⬜ ⬜⬜🟧🏻🟧🏻🟧🏻🏻🏻🏻🏻🏻🏻🏻🟧⬜⬜⬜⬜⬜⬜ ⬜🟧🏻🟧🏻🏻🏻🏻🏻🏻🟧🏻🏻🏻🏻🟧⬜⬜⬜⬜⬜⬜ ⬜🟧🏻🏻🟧🟧🏻🏻🏻🟧🏻🏻🏻🏻🟧⬜⬜⬜⬜⬜⬜⬜ 🟧🏻🟧🟧🟧🏻🏻🏻🏻🟧🏻🏻🏻🟧🟧⬜⬜⬜⬜⬜⬜⬜ 🟧🏻🏻🏻🏻🏻🏻🏻🟧🏻🏻🏻🏻🟧🟧⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜🟫⬜🟫🟫⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫⬜⬜🟫🟫⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟫🟫🏻🏻🏻🟫🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟫🟫🏻🏻🏻🏻🏻🏻🏻⬜⬜⬜⬜⬜⬜ ⬜⬜🟫🟫🟫🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜⬜⬜⬜⬜ ⬜⬜🟫🟫🟫🏻🏻🏻🏻🏻🏻🏻🏻⬜⬜🏻⬜⬜⬜ ⬜⬜🟫🟫🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜⬜⬜ ⬜⬜🟫🟫🏻🏻🏻🏻🏻🏼🏻🏻🏻🏻🏻🏻⬜⬜⬜ ⬜⬜⬜🟫🏻🏻🏼🏼🏼🏼🏼🏼🏼🏻🏻⬜⬜⬜⬜ ⬜⬜⬜🟫🏻🏻🏼🏼🏼🏼🏼🏼🏼⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🏻🏼🏻🏼🏼🏼🏼🏼🏼🏻⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🏻🏻🏻🏼🏼🏼🏼🏼🏼🏻⬜⬜⬜⬜⬜ ⬜⬜⬜🏻🏻🏻🏻🏼🏼🏼🏼🏼🏻🏻⬜⬜⬜⬜⬜ ⬜⬜⬜🏻🏻🏻🏻🏼🏼🏼🏼🏼🏻⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏻🏻🏻🟩🏼🟩🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏼⬜⬜⬜⬜⬜🟩⬜⬜⬜⬜⬜⬜⬜🏼⬜🏼 ⬜🏼🏼🏻🏻⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏼🏼🏼 ⬜🏼🏼🏼🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏼🏼🏼⬜ ⬜⬜🏼🏼🏻⬜⬜⬜⬜⬜⬜🏼⬜⬜🏼🏼⬜⬜⬜ ⬜⬜🏻🏼🏻⬜⬜⬜🟫⬜🏼🏼🏼🏼🏼⬜⬜⬜⬜ ⬜⬜🏻🏻🟫🟥🟥🟫🟫⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟥🟥🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏼🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏼🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏼🏼🏼⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏼🏼🏼⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏼🏼🏼⬜⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏼🏼🏼⬜⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏽🏼🏽🏼⬜⬜⬜🏼🏼🏼⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🏽🏽🏽🏽⬜⬜⬜🏼🏽🏼🏽⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏽🟫🟫⬜⬜⬜🏽🏽🏽🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟫🟫⬜⬜⬜🟫🟫🟫🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟫🟫⬜⬜⬜⬜🟫🟫🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟩🟥🟫⬜⬜⬜⬜🟫🟫🟩⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🟫⬜⬜⬜⬜🟫🟫🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟫🟫🟫⬜⬜⬜🟫🟫🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜🟫🟩🟫🟫⬜⬜⬜🟫🟫🟩🟫⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🟥🟫⬜⬜⬜⬜🟫🟥🟥🟫⬜⬜⬜⬜ ⬜⬜⬜🟫🟥🟫🟫⬜⬜⬜⬜🟫🟥🟥🟫⬜⬜⬜⬜ ⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜ ⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜ ⬜🏽🟫🟫🏽🏽🏽⬜⬜⬜⬜⬜🏽🏽🟫🟫🏽⬜⬜ 🏽🏽🏽🏽🏽🏽🏽⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽🏽🏽 🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽🏽

⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟧🟧🟧🟧🟧🟥🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🟥🟧🟧🟧🟨🟨🟨🟧🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟥🟥🟥🟧🟧🟧🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟧🟧🟧🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟧🟧🟧🟨🟨🟨🟨⬛⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟧🟧🟧🟨🟨🟨🟦⬛🟪🟪🟪⬛🟦🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦⬛⬜🟪⬜⬜🟦🟦🟦🟦🟦🟦🟩🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦⬛🟥🟥⬜⬛⬛🟦🟦🟦🟦🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦⬜🟥🟥⬛⬛⬛🟦🟦🟦🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟦⬜🟥🟪⬛🟪🟦🟩🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜🟪🟪🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦⬜🟪🟪🟪🟦🟦🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦⬜🟪🟪🟪🟪🟪🟪🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟦🟦🟪🟦🟦🟦🟦🟦⬜🟪🟦🟦🟦🟦🟦🟦🟪🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟦🟦🟦🟪🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟦🟦🟦🟪🟪⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟩🟩🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟩🟨🟨🟨🟨🟩🟩🟩🟦🟦🟪🟪⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟩🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟨🟧🟧🟧🟨🟨🟨🟩🟩🟦🟦🟪🟪⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟧🟧🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟦🟪⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟪⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟥🟥🟥🟧🟧🟨🟨🟩🟦🟦🟪🟪⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜🟦🟥🟥🟧🟧🟨🟨🟩🟦🟦🟦🟪⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜🟦🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟪⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟥🟦🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟪🟪⬜⬜⬜ ⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟥🟦🟦🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟪🟪⬜⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟥🟦🟦🟥🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟪🟪⬜⬜⬜ ⬜🟦🟦🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟧🟧🟨🟨🟩🟩🟦🟦🟦🟪⬜⬜⬜ 🟦🟦🟦🟦🟦🟦🟦⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟥🟥🟥🟧🟧🟧🟧🟨🟨🟩🟩🟦🟦🟦🟪🟪⬜⬜ 🟦🟦🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟧🟧🟧🟨🟨🟨🟩🟩🟦🟦🟦⬜🟪🟪⬜ ⬜🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟧🟧🟧🟨🟨🟨🟩🟩🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜🟦🟦🟦🟦⬜🟦🟦🟦🟧🟧🟧🟧🟨🟨🟨🟩🟩🟩🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜🟦🟦🟦🟦⬜🟦🟦🟦🟧🟧⬜🟧🟨🟨🟨🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟧⬜⬜🟧🟧🟨🟨🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦 ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦⬜⬜🟧🟧🟨🟨🟩🟩🟩🟩🟦🟦🟦🟦🟦⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦⬜⬜⬜🟧🟨🟨🟨🟩🟩🟩🟦🟦🟦🟩⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜🟨🟨🟨🟩🟩🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜🟨🟨🟨🟩🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜🟨🟨🟨🟩⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦⬜⬜🟦🟦🟦🟦🟦⬜🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜🟥🟥🟥⬜🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🟥🟥⬜🟦⬜🏻🏻🟥🟥🟥🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟥🟥🏻🟦🏻🏻⬜🟥🏻🏻🏻🏻🟦🟦🟨🟨🟨🟦🟦🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟥🟥🟥🟦🟦🟦🏻🏻🟨🟥🟥🟥🟥🟦🟦🟦🟨🟦🟦🟦🟨🟨🟨🟨🟨⬜🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟥🏻🟥🟥🟦🏻🏻🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🟥🏻🏻🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🏻🏻🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🏻🏻🏻🏻🟨🟨🟨🟨⬛⬛🟨🟨🟦🟦🟦🟨🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🏻🟥🟥🟥🟨🟨🟨⬛🟦⬛⬛🟨⬛🟦🟨🟨🟨🟦🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🟥🟥🏻🏻🟨🟨🟨⬛🟦🟦⬛⬛🟨🟨🟨🟨🟨🏻🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🟥🏻🏻🏻🟨🟨🟨⬛⬛⬜🟦⬜⬛⬛🟨🟨🟨🏻🟥🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🟥🟥🏻🏻🟨🟨🟨⬛⬜⬛🟦⬜🟨🟨🟨🟨🟨🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🏻🏻🟥🏻🏻🟨🟨🟨⬛⬛⬛🟦⬜⬛🟨🟨🟨🟨🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟥🟥🟦🟥🟥🟨🟨🟨🟨🟨⬛⬛🟦⬜🟨🟨🟨🟨🟨🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟦🟦🟦🟥🟨🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟥🟦🏻🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟥🟥🏻🏻🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟥🏻🏻🟥🏻🏻🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟩⬛🟨🟨🟨🟨🟨🟩🟨🟨🟨🟩🟨🟨🟨🟨🟨🟩🟩🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟥🟥🏻🟥🟥🏻🏻🏻🟥🏻🏻🟨🟨🟦⬛⬛🟩⬛⬛🟨🟨🟦🟩🟩🟨🟩🟩🟨🟨🟩🟩🟩🟩🟨🟨🟦🟦🌫️🟦🟩⬜⬜⬜⬜⬜⬜ 🟥🟥⬜🟥🏻🏻🟥🏻🏻🏻🟥🏻🏻⬛🟦🟦🟦🟩⬛🟩🟩⬛🟨🟦🟦🟩🟨🟩🟩🟩🟨🟨🟩🟩🟩🟩🟦🟦🟦🟦🟦🟩🟩⬜⬜⬜⬜⬜ 🟥⬜⬜🟥🏻🏻🟥⬜🏻🟥🏻🏻🏻🟦🟦🟦🟦⬛🟩⬛⬛⬛🟨🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🌫️🟦🟦🟩🟩🟩⬜⬜⬜⬜ 🟥⬜⬜🟥🏻🏻⬜🟦⬜🟥🏻🏻🏻🟦🟦🟦🟩🟩⬛🟨🟨🟨🟨🟨🟦🌫️🟦🟦🟦🟦🟦🌫️🟦🟦🟦🌫️🟦🌫️🟦🟦🟨🟨🟩🟩⬜⬜⬜⬜ 🟥🟥🟥🟥🏻🏻🟥⬜🟥🏻🏻🟥⬜🟦🟦🟦🟦⬛🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🌫️🌫️🟦🟦🌫️🌫️🟦🟦🟦🟦🟦🟩🟨🟩🟩⬜⬜⬜⬜ 🏻🏻🏻🏻🏻🟥🟥🟥🟥🏻🏻🟥⬜⬜🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟩🟨🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟨🟩🟩⬜⬜⬜⬜ 🏻🏻🏻🏻🏻🟥🟥🟥🟦🏻🏻🟥⬜⬜⬛🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩🟩🟩🟨🟩⬜⬜⬜⬜ 🏻🏻🏻🏻🟥🟨🟥🟦🟦🟦🟥🟥⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟨🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩🟩🟩🟨🟩⬜⬜⬜⬜ 🟥🟥🟥🟥🟨🟦🟨🏻🟦🏻🟥⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟨🟩🟩🟩🟨🟩🟩🟨🟨🟩🟩🟩🟩🟨🟩⬜⬜⬜⬜ ⬜⬜🟥🟥🏻🟨🏻🏻🏻🟥⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟨🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩🟨🟩⬜⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🏻🏻🟥🟥🟥⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜🟨🟨🟨🟨🟩🟩🟨🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩🟨🟩⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟩🟩🟨🟩🟩🟨🟩🟩🟩🟩🟨🟩🟩🟨🟩🟩⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟨🟩🟨🟩🟩🟨🟩🟩🟩🟩🟨🟩🟩🟨🟩🟩⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟩🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟨🟩🟩🟩🟩🟨🟩🟩🟩🟩🟨🟩🟩🟨🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟩🟨🟨🟩🟨🟩🟨⬜⬜⬜🟨🟨🟨🟨🟨🟩🟩🟩🟨🟩🟩🟩🟩🟨🟩🟩🟩🟨🟩🟩🟩⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟩🟨🟨🟩🟩🟨🟨⬜⬜⬜🟨🟨🟨🟨🟨🟩🟩🟩🟨🟩🟩🟩🟩🟨🟩🟩🟨🟨🟨🟩⬜🟩🟩 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟩🟨🟨🟩🟨🟨🟩🟨⬜⬜⬜🟨🟨🟨🟨🟨🟩🟩🟩🟩🟨🟩🟩🟩🟦🟩🟨🟦🟨🟨⬜🟦⬜🟩 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬛⬛🟨🟨🟨🟨🟩🟩🟩🟦🟨🟨🟦⬜🟦🟩🟨🟩🟩🟩⬜🟩⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬛🟩⬛🟨🟨🟨🟩🟩🟦🟦🟦🟩🟨🟦🟩🟩🟩🟩🟩🟩🟩⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩⬛⬛⬛🟨🟨🟨🟨⬜⬜⬜⬛🟩🟩⬛⬛🟨🟩🟨🟩🟦🟨🟩🟩🟩🟩⬜🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟩🟩⬛⬛🟨🟨⬜⬜⬜⬛⬛⬛⬛🟩⬛🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣋⣉⡥⠀⠨⠭⠤⢬⣉⠉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠓⠦⣌⡓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠙⠶⣍⠳⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⠳⣄⢠⡶⠤⠤⠤⣬⣉⣙⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⢷⡹⣄⠀⠀⠀⠀⠈⠉⠓⠦⣌⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠉⠉⠙⢻⣧⣤⠴⣒⣚⣛⣛⣒⣲⠦⣄⡀⢸⣿⣤⣄⣀⡀⠀⠀⠀⢻⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡆⢀⡴⢞⡵⠞⠋⠁⠀⠀⠀⠀⠉⠙⠾⣝⢦⡀⠉⠉⠛⠻⠿⣶⣤⣀⢻⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠷⢫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣆⠀⠀⠀⠀⠀⠉⠛⠿⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣤⠟⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡆⠀⠀⠀⠀⠀⠀⠀⢸⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⡴⠖⠒⢒⡎⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⠀⠀⢷⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠋⠀⠀⠀⡼⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢀⡴⢋⡤⠖⢢⡘⢧⡀⠀⠀⢸⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢒⣋⣉⣉⣉⣉⣉⣉⡺⠀⢧⣀⡀⠀⢸⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⣠⠏⣰⠋⠀⠀⣀⠹⡄⢳⡀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢭⣟⡛⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⠋⡼⠁⠀⠀⠀⢸⡄⢹⡀⣇⠀⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣤⠤⠄⠀⠀⠠⠤⠼⢣⡏⢰⠃⠀⠀⠀⠀⠸⡇⠀⡇⢸⠀⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⢡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣾⠾⠿⠿⠿⣿⣯⣭⣛⠛⠑⠋⠀⠀⠀⠀⠀⢸⠃⠀⡇⢸⠀⡟⠸⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣼⣡⡤⢤⣄⣀⡀⠀⠉⠙⠻⢷⣦⣄⣠⡖⣠⠀⠁⠀⢰⠃⡾⠀⠙⠓⠲⢤⣉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⣯⣴⣶⣤⣤⣄⡉⠓⠦⣄⡀⠀⠈⠙⠿⣾⣏⠀⠀⢀⡏⣰⠃⠀⠀⠀⠀⠀⠈⠙⢦⣝⢷⣄⠀⠀⠀⠀⠀ ⠀⣸⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣛⣩⣥⠖⠚⠛⢛⣲⠶⠮⣝⡓⢦⣄⠀⠀⠀⠀⠀⠀⣰⢃⣾⣿⣿⠿⠛⠋⠙⠛⠻⢶⣤⣉⠲⣄⠀⠀⠈⠛⢿⣦⡘⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢦⠀⠀⠀⠀ ⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣫⢶⣿⡿⠋⠀⢀⡴⠚⣉⣤⣶⣶⣶⣿⣷⣮⣻⢦⡀⠀⠀⣼⢃⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠙⣦⡀⠀⠀⠙⢿⣦⠈⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣧⠀⠀⠀ ⢰⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣫⢞⣵⡿⠋⠀⢀⡴⠋⣠⣾⠿⠟⠻⢿⣿⣿⣿⣿⣿⠷⣝⢦⡼⣳⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡁⠙⢦⡀⠀⠀⠹⣷⡄⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡆⠀⠀ ⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣾⣳⣾⠏⠀⠀⣰⠋⣠⡾⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠙⢧⡴⠃⠸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠳⣄⠀⠀⠈⢿⡄⠹⡄⢳⡀⠀⠀⠀⠀⠀⣴⣷⡜⡇⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⡟⣸⡿⠁⠀⢀⡼⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧⠀⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣿⣿⣷⡄⠘⢦⠀⠀⠀⢳⡀⢹⡈⢧⠀⠀⠀⣠⣾⠟⢸⣇⡇⠀⠀ ⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡞⣼⡟⠁⠀⢀⡞⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢣⠀⠀⠀⢧⠀⣇⠸⣄⣠⣾⠟⠁⠀⣸⢸⡇⠀⠀ ⠘⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⢱⡿⠀⠀⠀⡞⠙⣾⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣿⡀⠀⢧⠀⠀⠘⡆⢸⠀⣿⣿⡁⠀⠀⢀⡏⢸⠁⠀⠀ ⠀⢷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⣿⠁⠀⠀⣸⠁⣸⣿⣿⣷⣤⣀⣤⣴⣾⣿⣟⠉⢉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⣻⠿⢿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣧⠀⠈⡇⠀⠀⢳⠘⡆⣿⢹⣷⠀⠀⣼⠡⡎⠀⠀⠀ ⠀⠸⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⢠⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢽⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⢸⠀⡇⣸⢀⣿⠀⣰⠇⡼⠀⠀⠀⠀ ⠀⠀⢻⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡿⠀⠀⠀⡾⠀⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⠀⠀⣞⢰⠃⣿⣾⠏⣰⠏⣸⠁⠀⠀⠀⠀ ⠀⠀⠈⣇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⠀⠀⠀⡇⠀⣼⣿⣿⣿⣇⠀⢈⣿⣿⣿⡿⣿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠖⢀⡆⠀⠙⠿⣿⣿⣿⡿⠁⠀⠀⡼⠀⣜⠛⢻⢷⣿⡁⣰⠏⠸⠧⠤⣄⠀⠀⠀ ⠀⠀⠀⠘⣆⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡆⠀⢠⡿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣫⠞⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠇⠀⠀⠐⣟⡋⠁⠀⠀⣠⢾⣵⣟⠻⢷⣦⣸⠉⠻⣿⡛⠛⠛⠲⣍⢳⡄⠀ ⠀⠀⢀⡤⠼⠇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡽⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠀⠀⠻⠉⠉⠉⠉⠉⠀⠉⠻⣷⡎⢹⣿⣧⠀⠉⠃⠀⠀⠀⢸⡎⣷⠀ ⢠⡞⣣⠴⠚⠋⠻⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢳⡀⣇⠀⠀⢿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡼⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢿⣏⠈⣿⠆⠀⠀⠀⠀⠀⢸⠇⠹⡀ ⢏⣼⠁⠀⠀⠀⠀⠘⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡳⡽⡄⠀⠀⠙⢿⣿⣿⣿⡿⣷⡀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡩⠞⠁⢰⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⣿⠀⣿⠀⠀⠀⠀⠀⠀⡾⣠⡌⢳ ⡞⣧⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⠀⠀⠀⠀⠀⠀⠈⢳⡹⣝⢦⡀⠀⠀⠀⣀⡤⠞⠙⢷⡀⠀⠀⠙⢮⡉⢙⣒⣒⠀⠀⠀⠀⠀⠀⣒⣚⡭⠵⠚⠉⠀⠀⡀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⠱⡿⣠⠈ ⢷⡜⢦⡀⠀⠀⠀⠰⣄⡀⠀⠙⢮⡳⢦⡀⠀⠀⠀⠀⠀⢻⡹⡖⠛⠙⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⢄⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡾⣺⢱⠃⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣴⠋⠀⠀⠀⠀⠀⣼⣏⣴⠀⠀⠀⣼⠃⢀⡼⢻⡆ ⠀⠙⢦⡝⠶⣤⣀⡀⠹⡝⠳⢤⣀⠙⠳⣭⡳⢤⣀⠀⠀⠀⢷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⢣⠏⠀⠀⠀⠀⢀⣠⠔⢋⣠⠾⢻⡎⡳⠤⣤⡤⠴⢞⣋⣍⣾⠀⠀⣼⡥⠞⠋⠀⢸⠀ ⠀⠀⠀⢉⡻⠇⣈⡭⠿⠻⣆⢰⣮⣽⣓⣒⣛⣤⠼⠛⠀⠀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣓⠦⣀⠀⠀⠀⠀⠀⣀⠜⡱⠋⠀⢀⣠⠴⠚⣉⡤⠖⠋⠁⠀⠀⠈⠛⠒⠒⠓⠒⠋⠉⣟⢹⡀⠘⠉⠀⠀⠀⢠⠏⣰ ⠀⢀⡴⢋⡴⠞⠉⠀⠀⠀⠈⠳⣭⡳⢤⣀⠀⠀⠀⠀⠀⢀⡼⣹⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠭⣝⣒⣒⣫⣵⡪⠤⠒⣋⡭⠄⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣧⠀⠀⠀⢀⣴⠋⡴⠃ ⢀⡞⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣮⢩⣗⣒⣒⠚⣭⠶⠋⠓⠢⢤⣍⣙⠒⠲⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠐⠒⠚⠉⠉⠀⠀⠀⠈⠁⢀⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⠓⠶⠒⢋⡤⠟⠁⠀ ⢸⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣆⢀⡾⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢶⡦⢤⡤⣤⣤⡤⠤⠤⠤⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀ ⢸⣇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⡾⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠹⣆⢳⡄⠀⠀⠀⠀⠀⠀⠈⠳⢥⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣎⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡌⢧⡀⠀⠀⠀⠀⠀⠀⢀⣤⢟⡙⣇⠀⠀⠸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠧⣭⠳⢦⣄⣀⠀⠀⠀⠀⣀⣤⠞⣡⠞⠹⣆⢛⠦⣄⣀⣤⠤⠖⣋⣤⣿⢃⡟⠀⢀⣰⢇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⢀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⠦⣭⣉⣉⣉⣉⣩⠶⠛⠁⠀⠀⠈⠙⠓⠶⠤⠴⠒⣾⣟⡋⠀⠘⠓⢚⣉⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⠀⠐⣏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣤⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⠈⣇⢀⣠⣤⣤⣴⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠉⠛⣿⣿⡿⣧⣤⣀⠀⠀⠀⠉⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⢸⣿⡿⣶⣍⠻⢷⣎⡰⠄⠀⠀⣤⡙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠙⠓⠤⣼⣽⡇⠈⠻⣷⣄⠙⢿⣦⠠⠀⠘⣿⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠻⢦⣄⠀⠀⠀⠀⠀⣀⣤⢶⣿⣿⣿⣿⣼⣀⣀⠀⠀⢸⣿⡇⠀⠀⠈⠻⣷⡀⠹⣷⡀⠀⠹⣿⣧⡴⢟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠙⢷⣤⣤⣶⡿⢿⣶⣦⣤⡉⠉⠙⠻⢿⣿⡻⠶⣼⣿⣧⠀⠀⠀⠀⠘⢿⣄⠹⣷⡀⠀⣿⡽⣧⡈⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠙⢿⣿⡇⠈⢿⣧⠈⠛⠷⣦⡀⠀⠈⠻⢷⣌⠛⠛⢤⣄⠀⠀⠀⠈⣿⣆⢹⣧⠀⢸⣇⢹⣧⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣷⠀⠀⠀⠀⠀⠹⢿⣄⠂⢻⣧⠀⠀⠈⢿⣆⠀⠀⠀⠙⣧⡀⠸⣿⡀⠀⠀⠀⠘⣿⣜⣿⣄⣸⣿⢈⣿⣄⣠⣥⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢻⣧⠀⠀⠀⢻⡇⠀⠀⠀⠘⢷⡄⠈⢓⣢⣤⣴⣶⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠌⢻⣆⠀⠀⠈⣿⡀⠀⠀⣀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠨⣿⡇⠘⣿⠀⠈⠁⣹⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣧⠀⠀⠙⢦⡀⣀⣴⣾⣿⣿⣿⡗⠀⣿⣧⣽⣿⠟⠛⠁⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠙⢿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣋⠁⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⣿⡏⠀⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⢀⣾⡟⣠⠟⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠿⣿⣿⣿⡿⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣿⣻⠞⠁⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣿⣿⣿⣿⣿⠿⢿⣿⣿⡉⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⣻⣿⠃⠀⠀⠀⠀⠀⠈⠉⠙⣿⡏⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⠀⠀⠈⣿⠹⣷⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣴⡿⠃⠀⠀⠀⠀⠀⠰⠚⠁⢀⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⠀⠀⠀⢹⡇⢻⣧⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣾⠃⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀ ⠀⠀⠈⠻⠿⠋⠀⠀⠀⠈⣿⠘⢹⣧⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠚⠉⠁⢀⣴⠿⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣶⠙⢿⣿⣷⣄⠀⠀⠀⠤⠤⠤⣤⠤⠤⠤⠤⠶⠶⢶⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣹⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⠇⠀⠐⠉⠛⠛⠷⠶⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⡸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠈⠙⠶⡄⠀⠀⠀⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣷⠀⠘⣷⣄⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⠀⠀⠙⣿⣿⣶⣄⡀⠀⢀⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⣠⠴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⢿⣆⢠⠀⠈⠻⣿⣿⣿⣿⣾⣦⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡌⢻⣦⠀⡀⠀⠈⠻⢿⣦⣀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⣀⣀⣤⠴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⢷⡄⠻⣧⡀⠀⠀⠰⠄⠙⠻⢿⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡎⣻⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡇⢹⣧⡀⠻⣧⡀⠀⠀⠀⠀⠈⠠⢸⣿⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡙⢷⣄⠈⢻⣆⠀⠐⠀⠀⣄⣾⣿⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣬⡟⣧⡀⠙⢿⣄⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣮⣿⣦⣠⣝⣷⣿⣿⣯⣾⡀⢀⣀⣀⣀⣀⣨⣿⣀⣀⣀⣀⣀⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠟⠻⣿⣿⡟⠉⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⣠⠴⠖⠛⣙⣒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⣦⠀⢈⣽⠁⠀⣠⠟⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣼⣿⣶⣋⠤⠒⠈⢉⣽⠀⠉⢢⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣥⡵⠞⠉⠁⣰⠁⠀⢀⠀⠈⠙⠲⢄⡀⣤⠀⢀⣤⣄⠙⢦⣀⣾⡿⠟⠉⠀⣀⡜⣀⠞⠙⠀⠀⠀⡇⡿⠶⢦⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿ ⠟⠀⠀⠀⠀⣿⠀⢀⠀⠱⡄⠀⢦⠀⠻⣿⣤⣿⣿⣿⡞⡉⠙⠋⠀⠠⡶⠋⠉⠙⠳⣄⣀⣀⠔⠀⡦⠖⡚⢹⠃⠀⠀⠀⠀⣀⣴⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⠀⢸⠃⠀⢱⠀⠘⣆⠀⣹⡿⠛⠉⠉⠛⢷⡄⠀⠀⠀⡇⠀⣀⣀⡀⠈⢧⠐⡀⠀⠀⢰⠁⣾⡀⠀⠀⣴⠟⠉⢻⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⠣⡄⢧⠀⠘⣧⡀⢈⣿⠋⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢣⣾⣿⣶⣿⠤⠬⢿⢽⡀⠀⢰⠀⢇⢳⡀⠀⠣⣄⡀⣸⡿⣿⠿ ⠀⠀⠀⠀⠀⢹⣦⡈⠪⡁⠀⠀⠈⢹⠃⠀⣴⠛⣿⣉⣷⠀⢀⣸⢄⠴⠊⠁⠀⠈⠇⠀⠀⡞⠀⠈⢳⠀⠳⢼⣄⠙⠦⣤⣤⠽⢋⡴⠋⠐ ⠀⠀⢀⣀⡀⠀⠙⢤⣁⣬⠷⠤⢤⣿⠀⠀⣿⣀⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⡇⠀⠀⠀⢣⣀⣀⣀⣙⠒⠒⠒⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⢹⡆⢀⡞⠉⠀⠀⠀⠈⢻⣦⡤⠛⠉⠀⢶⠀⠀⠀⠀⠀⢀⡤⠚⣁⣤⣶⣼⣄⡇⠀⠀⠀⢸⡿⢷⡶⠤⣽⣶⠀⠀⠀⠀⠀⠀ ⠶⠤⠤⠶⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⠳⢤⠤⠔⠊⣁⢠⣾⣿⣿⣿⣟⡛⢻⠀⠀⠀⣼⡇⠀⠉⠓⢦⡙⢦⠀⠀⠀⠀⠀ ⠊⠀⠀⠀⢀⡟⠀⠀⠀⣰⠟⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠹⣦⡀⢹⣿⠟⠛⠧⡄⠰⣿⢸⠀⠀⢰⣿⠃⠀⠀⠀⠀⠹⣦⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠃⠀⠀⠀⣏⠐⠋⠀⢀⡿⠛⣩⠟⠀⠀⠀⠀⠀⠙⢿⣿⡏⢧⣠⣤⣤⠾⢡⠏⠀⣠⡿⠃⠀⢀⣤⢤⡀⠀⣿⢿⡀⠀⠀⠢ ⠀⠀⠀⠒⢦⠀⠀⠀⠀⠙⠦⣤⣤⡾⠁⡼⠛⠋⠉⠉⠓⢦⡀⠀⠀⠙⠳⠤⣍⣈⠤⠔⠁⢀⡴⠃⠀⠀⠀⣸⡁⠠⠷⢀⡟⣸⡇⠀⠀⠀ ⠦⣄⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣀⠀⢀⣀⠠⢾⠁⠀⠀⠀⢠⣿⣷⣄⣤⡼⠿⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢖⣶⡶⠚⠁⠐⠒⢦⡈⣧⠈⠛⣿⢶⣶⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁⠘⠉⠀⠀⠀⢀⣠⣴⡷⣿⠤⠚⢹⠉⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠏⠁⠈⠿⠁⡠⢿⢀⡠⠴⠛⣲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⢣⠀⠀⠀⠞⠁⠋⠀⠀⠀⠚⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⠤⣤⣤⢾⣯⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡄⠀⢀⣼⠟⠁⠀⠀⠀⠈⣆⡠⠖⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣿⡗⠿⢷⣀⠀⠀⢶⣤⣄⣠⣤⣟⠉⠉⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠈⠳⠶⣾⡿⠛⠛⠿⢻⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣶⣿⣍⣤⢀⠀⠀⢨⣧⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣷⣦⣮⣤⣀⣸⣿⣿⣽⣿⣿⡀⠀⠘⠿⣇⠀⠀⠀⢠⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠉⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡖⣀⠀⣿⣄⠀⢠⠏⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠆

⠀⠀⣰⡟⡽⣌⢧⣹⠜⣃⠻⣌⠧⣍⢿⡧⡹⣌⣿⡻⡹⣌⢧⡙⢮⡱⣍⢎⡳⢭⢻⡷⣍⢮⡱⣍⢮⣱⣫⣧⣤⡴⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⣴⡟⡼⣑⢎⡶⡡⠊⠀⠘⡌⢷⡘⢾⣗⡱⣾⢏⠶⡱⢎⠶⣙⢦⠳⡜⢮⡱⣋⠶⡹⣟⡦⣳⣼⢞⡳⣋⠶⡱⢎⡵⢪⣍⢻⡹⢶⣄⡀ ⢰⡟⡼⡱⢎⡞⡠⠀⠀⠀⠀⠘⠨⡝⣎⣷⢹⣯⢋⡞⣱⢋⡞⡱⢎⡳⣙⢦⠳⣍⢞⡱⢻⡵⢯⡱⢎⡵⣩⢞⡱⢫⡔⢧⢎⢧⡙⢮⣍⢻ ⣿⡜⣱⡙⣞⡐⠀⣰⠀⠀⠀⠀⡅⡟⡴⣹⢟⣾⠱⣎⠵⣫⢜⡱⣋⠶⣩⢎⡳⡜⢮⡱⢫⡝⢦⡙⣎⠶⡱⢎⡵⢣⢞⡱⢎⠶⣙⠶⣌⢳ ⡟⣮⡵⣙⠆⠆⠠⡅⠀⠀⠀⠀⠸⠱⢃⠑⠈⣟⡷⣌⢳⡱⢎⡵⣩⢞⡱⢎⡵⣙⢦⡙⢧⡚⣥⢛⡬⢳⡙⢮⡜⣣⢎⡵⣋⠞⣥⢛⡬⢣ ⢳⣩⢛⣾⠸⠀⢰⡇⠀⠀⠀⠀⠀⠗⠀⠀⠀⠘⣷⣜⢣⡝⣎⠶⡱⢎⡵⢫⢴⣭⡶⠿⠞⠛⠻⠯⠿⢳⣟⣦⡝⢦⣋⠶⣩⠞⡴⢫⡜⣣ ⡇⣎⠳⡆⠂⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡙⢦⢫⡕⣫⣜⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⠳⣥⢛⡜⣣⠞⡥ ⡷⣌⢳⣃⢁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣧⠳⡜⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢿⣆⠯⡜⣥⢛⡜ ⣷⢌⡳⢼⡘⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢻⣮⠕⣎⠳⣜ ⢹⣮⡱⢣⢧⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣧⣛⢬⠳⡜ ⠀⠙⢷⣍⡎⢧⢂⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡁⣿⡜⣎⠳⣍ ⠀⣠⡾⢫⡜⣣⢛⣴⣀⡙⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡆⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⡜⣬⠳⡜ ⣸⢏⡸⢇⡾⣁⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⢹⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⣀⣶⣿⣿⠿⠏⠉⢉⣿⣿⡿⠏⢹⡿⢿⣿⣿⣿⡸⣆⠿⣸ ⣏⢮⡱⢫⠴⣩⢞⣿⣿⡿⢟⠀⠰⠈⢦⣤⣴⡎⠉⣽⣿⣿⠉⢿⣿⣿⣿⣿⣿⡟⢹⢹⣦⣤⣴⡏⢉⣿⠇⠀⠸⠶⠔⣿⣿⢯⡱⢎⣣⠏ ⡎⢶⡩⢇⡻⣔⢫⠼⢿⡇⠀⡀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢻⠀⢈⣿⠟⠛⠛⣿⡇⢸⢆⠻⣿⣿⣿⣿⠏⠀⠀⢠⠘⠀⣿⢏⠶⣙⡞⠁⠀ ⡝⢦⡙⢮⡱⢎⢧⢛⠞⣿⠀⠁⠀⠀⠠⠀⠉⠛⠛⢉⠐⢹⠀⣸⡟⠀⠀⠀⢹⣧⢸⠀⠂⢀⠉⢉⠀⠊⠀⠀⢦⠇⢠⣿⢎⡳⢯⠴⣶⢺ ⡝⢦⣋⢧⡙⣎⠮⣍⢧⣿⣷⠒⡀⠀⠀⠀⠁⠀⠀⠁⠀⡘⢀⡿⠁⠀⠠⠄⡀⠻⣎⡀⠀⠀⠀⠀⠀⠀⠀⣘⠛⢢⡾⢿⣌⡳⣍⣞⣴⠟ ⣾⡱⢎⠶⡹⣌⠳⡜⣎⡆⢻⢿⣅⡀⠀⠀⠀⠀⠀⠀⣀⣵⠟⠁⠀⠀⠀⠀⠀⢀⠙⠷⣄⣀⡀⠀⠀⣀⣠⣽⠷⠛⠀⠈⠙⠛⠛⠉⠀⠀ ⡮⣝⠻⡾⡵⢾⡟⡜⢦⡹⢆⠡⡉⠛⠓⠲⠶⠖⠒⠛⠉⠁⠀⠀⠈⠀⠀⠀⠀⠋⠀⠀⠈⠉⠉⠉⢉⡩⡩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣬⢳⡱⣙⢾⡹⣜⢣⡝⣎⢳⡀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠑⡄⠀⠀⠀⠀⠀⠀⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣵⢩⠞⣷⡬⢳⡜⣬⢣⡛⣦⣁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢄⠊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣾⣰⢫⢗⠾⣖⣳⢏⡞⢯⣬⡂⡌⢂⡄⠤⠀⠀⠀⠀⠀⠀⠀⠠⢀⣐⠨⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣭⠿⣞⠳⣬⡟⡼⣘⠧⣎⠽⢿⣄⠀⠁⠉⠀⠀⠀⠀⠈⠉⠀⠁⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⣥⢛⡬⢳⠼⣟⠴⣩⠞⣬⢛⢦⡛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢫⡷⣌⠳⣜⢣⢏⣽⡎⡵⣋⠶⣩⢖⡹⡜⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠉⠉⠙⠛⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⢀⠀⠀⡔⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠒⠠⢀⢂⢸⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠎⠀⠀⠀⠀⠀⠀⡠⠐⠀⢄⣉⣪⡀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠁⢀⠀⠀⠀⠀⠈⠫⡁⠀⣀⣀⣀⣀⠀⠈⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢈⠎⢀⠍⠉⠐⠠⠤⢀⠜⡡⠄⠀⠠⢄⠈⠑⠀⠑⠀ ⠀⠀⠀⠀⠀⠀⢌⠀⣼⠀⠘⠒⠠⠤⠤⠐⠈⠀⠀⠀⠀⠁⡐⠑⡄⠀⠀⠁ ⠀⡀⠆⠀⠀⠀⠀⠀⢰⠑⡠⠞⠉⢶⡀⠀⠀⢀⡤⢥⠀⠠⠁⠀⠛⠀⠀⠀ ⠀⡇⠖⠀⠀⠀⠀⠴⣮⣿⢻⣦⠀⠀⡇⠀⢀⢾⡀⢸⣷⡇⠀⡘⠀⠀⠀⠀ ⠀⡇⡶⠡⠀⠀⠀⠀⠘⠙⠻⣷⡇⢠⠃⠀⣸⣾⠏⠼⠉⠀⢠⠁⠀⠀⠀⠀ ⠀⢹⠁⢃⠑⡀⠀⠀⠀⡧⡀⠀⠀⠀⠀⠀⠐⠀⡀⠀⢀⠔⠁⢀⠴⠁⠀⠀ ⠀⢸⢸⠀⢂⠘⠄⠀⠀⢰⠈⠂⢄⣀⣉⡁⠤⠚⡠⠔⠁⣠⠔⠁⠀⠀⠀⠀ ⠀⡇⠘⡆⠈⡄⠘⡀⠀⢸⠠⡄⠀⠐⡘⢎⠑⡍⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀ ⠜⠀⡆⡇⠀⠰⠀⢡⠀⢸⢡⠘⡀⡀⠑⠅⢂⠰⠊⠀⠘⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠃⠀⡄⠀⢸⠀⠸⠀⡆⠃⡑⠠⠐⠀⠑⢅⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⡔⠀⠀⡌⢀⠃⡇⠀⡄⠀⠈⠉⢳⡲⠀⠀⢀⠌⢹⠀⠀⠀⠀⠀ ⠠⢄⣤⠊⠀⢀⠜⡠⠊⠀⠁⠀⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠑⠌⠉⠩⠁⠀⠀⠀⠠⠋⠈⠑⠒⠂⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⠿⠛⠋⠛⠙⠿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠞⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠀⠀⠀⠐⠒⠤⢤⣀⠀⠀⠘⡆⠀⠀⡇⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣘⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣀⡀⠈⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠈⠁⠒⠉⠙⠷⡤⠤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣧⠞⠉⠈⡟⠙⠒⠢⢄⣀⠀⠀⣀⠀⣷⡖⠉⢁⣀⣀⣀⡀⠀⠈⠉⠓⠤⡀⠈⠣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⢠⡇⠀⢀⡞⠁⠀⠀⠀⠀⠈⠉⠉⢁⡼⠀⠛⠋⠁⠀⠀⢀⠈⠙⠦⡄⠀⠀⠈⠀⠀⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣼⡇⠀⠀⠻⠒⠶⠤⠤⣤⡤⠤⠒⠉⠀⠀⠀⢀⠀⠀⠀⠈⠀⢠⠃⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡷⢄⠀⢀⣠⡤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠀⠀⢀⡞⠀⠀⢸⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⣴⠟⠃⠀⠀⠉⣷⡀⠀⠀⠀⠀⢠⣴⡞⢻⣧⠀⢀⡞⠀⠀⠀⡄⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠠⠹⡀⠀⠀⠀⠀⠀⠀⢰⣦⣬⣿⡿⠛⣷⣄⠀⠀⠀⢺⡇⠀⠀⠀⢠⣿⡅⠀⠘⣿⣶⣮⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⡄⢳⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣤⣿⣟⣧⠀⠀⢸⠇⠀⠀⠀⣞⣽⣿⡆⣐⣾⣿⠛⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⢰⠐⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⠹⢿⣿⣻⠀⠀⡞⠀⠀⠀⣰⣿⣿⠿⠁⠺⠟⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⢱⠀⠳⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢃⠀⢣⡀⠘⢆⠀⠀⠀⠀⠀⠘⡟⠦⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢸⡀⠀⢣⠀⠈⢦⠀⠀⠀⠀⠀⡇⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠠⠴⠋⠀⣀⠔⠋⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢸⡇⠀⠀⢧⠀⠀⢧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠻⡍⢿⣛⠒⢤⣠⠔⠋⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⢹⠀⠀⠘⡆⠀⠈⢇⠀⠀⠀⢸⡈⠓⣄⠀⠀⠀⠱⡀⢙⠢⠀⠙⡄⠀⣠⠎⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠀⢀⡇⢸⠀⠀⠀⢱⠀⠀⠸⡀⠀⠀⢸⠳⡀⠘⡆⢀⠀⠀⠱⢌⠀⠡⠀⠹⡴⠃⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠸⠀⢸⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⢸⠀⢷⠀⢹⠈⣇⠀⠁⠀⠁⠀⠣⣄⣧⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠘⡆⠈⡇⠈⠑⠂⢄⠈⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⡤⠎⠀⠀⢀⡞⠀⠀⠀⢰⠃⠀⢰⠁⡆⠀⠳⠀⡇⠙⠀⠒⠒⠻⢦⡀⢀⡀⠘⠀⠀⠀⠀⡴⠻⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢀⡎⠀⢠⠇⠀⡅⠀⠃⢸⡇⠀⠀⠀⠀⠀⠀⢷⡖⠃⠀⠀⠀⢠⠞⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣄⣀⡠⠖⠁⠀⠀⠀⢀⠞⢀⡴⠋⠀⠠⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣗⠒⠲⠦⠴⠮⠥⠖⠉⠀⠀⠀⠀⠀⢀⡤⠟⠲⢤⣀⣀⣀⡀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟩🟩🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜🟧🟩🟩🟧🟧🟧🟧🟧⬜⬜⬜ ⬜🟧🟧🟧🟧🟩🟩🟧🟩🟩🟧🟧🟧⬜⬜🟧🟧🟧🟧🟩🟩🟧🟩🟩🟧🟧🟧⬜ 🟧🟧🟥🟥🟥🟧🟩🟩🟧🟥🟥🟥🟧🟧🟧🟧🟥🟥🟥🟧🟩🟩🟧🟥🟥🟥🟧🟧 🟧🟥🟥🟥🟥🟥🟩🟩🟥🟥🟥🟥🟥🟧🟧🟥🟥🟥🟥🟥🟩🟩🟥🟥🟥🟥🟥🟧 🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧 🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧 🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧 🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧 ⬜🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧⬜🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧 ⬜⬜🟧🟧🟥🟥🟧🟧🟥🟥🟧🟧⬜⬜⬜🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧⬜ ⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜🟧🟧🟥🟥🟧🟧🟥🟥🟧🟧⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟩🟩🟧🟧🟧🟧🟧⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟧🟧🟧🟩🟩🟧🟩🟩🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟧🟥🟥🟥🟧🟩🟩🟧🟥🟥🟥🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟥🟥🟥🟥🟥🟩🟩🟥🟥🟥🟥🟥🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟧🟧🟥🟥🟥🟥🟥🟥🟥🟥🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟧🟥🟥🟧🟧🟥🟥🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⢤⡤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡤⠖⠲⡍⣇⠀⠳⠀⠀⠀⠈⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢦⣀⠀⠈⢻⡆⠀⢃⠀⠀⠠⠀⠀⠀⠰⠀⠀⢠⢿⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⢤⡀⠹⠀⠘⡄⠀⠀⠀⠀⠀⡘⠀⢀⣾⠎⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢣⠀⣀⣀⡀⢀⠃⠠⠾⠋⡀⠀⡰⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⢳⡖⠟⠉⠁⠀⢉⠟⠒⢦⣤⠞⢻⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡯⡀⠀⠱⡆⠀⠀⣠⠎⠀⠀⣰⠃⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⠈⢢⣀⣁⡠⠴⣷⣶⣾⡿⠇⠀⢸⠀⢷⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡖⠋⠀⢠⠒⢉⣿⣩⣧⠀⠀⠀⡿⠀⠀⢀⡞⠀⡿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⢀⣼⡄⠘⢿⣿⣿⣀⣀⡾⠁⠀⢀⡀⠀⣴⠃⠠⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣶⡿⠛⠃⠀⠀⣇⣾⣹⣇⠀⢀⣴⣻⣷⣾⢷⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠓⠒⠦⢤⣠⣻⣿⣧⣿⣴⣿⡟⣿⣿⣿⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣠⠤⣿⡄⠹⠿⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠧⠤⠔⠻⣷⠄⣀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠈⣯⣉⠁⠲⣌⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠒⠒⣊⣉⡩⠽⢿⡉⠀⢀⣠⠤⡖⠚⢻⡟⠒⣦⣞⢣⡴⠚⠳⣌⠱⣄⠈⢢⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣿⣉⣀⣀⡤⠔⠚⠋⢉⠉⢉⡄⠀⡟⠲⠁⠈⠉⢠⢿⢿⠀⠀⠀⢹⣆⠸⡀⠈⢇⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣴⠦⠒⠋⠠⠊⠁⣰⠁⠀⠀⣸⢧⣾⣿⣿⣧⠀⠀⢸⣿⠀⡇⠀⠘⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣎⠉⢓⠒⢺⠀⠀⠀⠀⠀⠈⠀⢠⡾⠋⠀⢠⡵⠃⢰⠀⠐⠿⣼⣿⣿⣿⣿⠀⠀⣸⢸⠀⡇⠀⢠⠱⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢱⣀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠁⠀⢺⠀⠀⢾⢻⣿⣿⣿⣿⠀⠀⡏⢸⠀⣇⠀⠈⣧⠳⡈⠳⣀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⡀⠻⣆⢰⡈⢳⣄⠀⠀⣆⠀⠀⣆⠀⠀⠀⠀⢀⣸⡆⠀⠀⠤⠙⡟⠻⡟⠀⠀⣇⢸⠀⠸⡄⠀⠸⣷⡘⢦⡈⠑⠲⣶ ⠀⠀⠀⢸⠀⠀⠀⠉⡏⠙⠛⠉⠈⠙⠒⣇⡈⠑⢾⡶⠒⠒⠋⠙⣲⠿⡖⠒⠒⠀⠀⢴⠃⠀⠀⢹⢸⠀⠀⠹⡄⠀⠹⡌⠢⣌⠓⣴⠏ ⠀⠀⠀⢸⠀⠀⣠⣴⡇⠀⠀⠀⠀⠀⠀⡇⠀⠉⢹⣿⡂⠉⠉⠿⣅⠀⠙⣖⠂⠈⠉⣏⡀⠀⠀⠘⣎⣇⠀⠀⠘⢆⠀⠘⣦⡈⠛⠁⠀ ⠀⠀⠀⠀⢷⣾⣿⡿⠀⠀⠀⠀⠀⠀⡾⢽⠭⣭⠿⣿⡗⠒⡈⠉⢸⠀⠀⠈⢦⠄⠀⠀⢛⡄⠀⠀⠹⣼⣄⣀⣀⣠⠷⠒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠠⣟⣿⣒⣚⣹⣿⡟⠉⠀⠀⢸⠀⠀⠀⠈⣖⠂⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡿⠠⠄⢺⣿⡟⠁⠐⠐⡾⠀⠀⠀⠀⠸⡆⠀⠄⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠂⠈⢸⡟⠀⠀⠐⢶⠇⠀⠀⠀⠀⠀⡗⠀⠤⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣷⣦⣀⣸⣿⣶⣄⢀⠎⠀⠀⠀⠀⠀⣸⣤⣀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠙⢻⡟⠛⠛⠛⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⠁⠀⠀⠀⣠⡤⠖⠋⠉⠉⠉⠉⠒⠦⣌⣷⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠙⠲⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣹⣇⠀⠀⠈⢷⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢷⣄⠀⠀⠀⠀⣀⡀⠤⠐⠂⠈⠀⠀⠀⠀⠀⠀⠈⠉⠑⢒⡾⠋⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢯⣉⠉⠉⠁⠀⠀⠀⣀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣍⣿⠓⠒⠒⠋⢩⡟⠁⣀⡤⠴⠒⠒⠊⠉⠉⠙⠀⠀⠀⡼⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⣿⣷⣄⠀⠀⢠⣿⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠛⣻⡆⠀⠘⠁⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⣿⣿⡇⠀⠀⢀⣴⣿⣿⡿⠋⠪⣿⣧⡴⠂⠀⢀⡴⠛⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣽⣿⠁⠀⠀⣾⣿⣿⣿⣿⣦⡤⢈⢹⠦⠤⠀⢸⠁⠀⢰⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠽⠁⠀⠀⠈⡿⢿⣿⣿⣿⠟⢁⡜⢸⠀⠀⠀⣿⠀⠀⣴⣿⠁⠀⠀⠀⠀⢀⣠⠔⠒⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠤⠤⢻⠀⠀⠘⢦⡬⠭⠤⠔⠋⡠⠊⠀⠀⠀⢹⡖⢨⡾⠁⠀⢀⡤⠶⡾⠋⣉⣁⠀⠉⠑⠢⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠘⡟⢻⣛⣷⡴⠋⠀⣰⡷⠋⢩⡟⠉⠲⣄⠀⠈⢆⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠁⣿⠤⢤⣾⠋⢀⣴⡋⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠁⠀⣸⠃⠲⣯⠀⠹⣆⠀⠀⠀⢱⠀⠀⡇⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠴⣿⠀⠀⡟⠀⡄⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢻⠀⣼⡥⠾⡇⠀⢀⠀⢰⠀⢠⠀⠸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⠀⠀⠀⠀⡇⠀⠘⡀⢸⠀⠸⣧⡀⠻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠙⠶⢤⣤⠀⠀⠀⢰⠶⠛⠻⡄⠀⠀⠿⢦⡄⠀⠀⣷⠀⠀⡇⢸⡀⠀⢹⡟⠦⠬⠟⢀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⢸⠀⠀⠀⠸⡆⠀⠀⠹⡄⠀⠀⠀⠹⡄⠀⢹⡄⠀⡇⠀⢇⠀⠀⠻⣄⣀⠤⢚⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣾⢸⠆⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀⠀⠀⢳⠀⠀⠻⣄⠘⣄⠈⠣⡀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⢸⡄⠀⠀⢹⠀⠀⠀⠀⠈⡇⠀⠀⠙⠳⢬⣓⣤⣈⣑⣦⠶⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⢸⢇⡟⠀⠀⠀⠀⠈⣧⡤⠤⢼⡀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠤⠴⠋⣼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣠⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⠠⠤⡗⢢⡀⠀⢀⡀⡐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⢉⡤⠓⠉⠁⠀⢳⡄⠈⣥⠁⢣⡀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠍⠋⠏⠀⠀⠀⠀⠀⠈⢿⣇⠁⢸⠋⠗⠁⡠⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠀⠂⠁⠰⢩⣶⣒⠶⠄⠈⡾⣰⡗⡄⠄⠊⡩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢦⣂⠈⡂⠁⠛⠋⢀⠀⠀⠸⡟⠠⢋⣀⡉⠭⡢⠤⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠙⣾⠖⡚⢲⠈⡱⠀⠀⠀⠋⢀⠿⠊⢲⠑⠂⣐⠒⠠⡀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⣤⠌⡷⢈⣎⠜⢠⠀⠀⠀⠀⢀⠁⠀⠸⠀⠀⠀⠁⠀⠈⢂⠀⠘⡆⠀⠀⠀ ⠀⠀⠫⠦⠵⢪⡣⠂⣁⣿⠃⢀⠇⠒⡦⠀⠣⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⠊⡡⠒⣯⠀⣶⠀⠀⠐⠂⠀⢡⠀⠀⠔⠀⡠⢃⠔⡑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⣈⣭⡇⣢⠉⠈⢱⠀⠀⠀⠀⠈⡀⠎⡠⠞⢊⠕⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠥⡠⠇⠀⠨⠄⠀⠀⠇⢤⣈⠀⠑⠒⢒⡒⠦⠔⡦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠰⡀⠸⠘

⠀⠀⢀⣀⣀⣀⡀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⢿⣟⡞⠎⠃⠀⠃⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢁⣄⠓⢸⣿⡤⣟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⢻⣦⠈⠜⠛⢋⣰⠀⠀⠀⠀⢀⠄⡒⠐⡂⢄⠀⠀⠀ ⠀⠀⠀⠛⡰⣀⣰⢖⣏⢆⠀⠀⠰⢂⣡⠀⢀⠀⢂⢱⡀⠀ ⠀⠀⠀⠀⠀⡘⠨⠀⠀⢾⠠⢮⢁⠀⠈⠘⠄⠀⠀⠆⡵⠀ ⠀⠀⠀⠀⠀⢇⡀⠁⠦⠂⠣⠿⠛⠀⠀⠀⠈⢸⠀⠀⡇⠃ ⠀⠀⠀⠀⠀⠈⢬⠁⠒⠒⢗⠄⠐⠀⠀⠀⠀⣆⠀⢦⢀⠄ ⠀⠀⠀⠀⠀⢀⠂⠠⢡⠀⠀⢂⠀⠈⠄⠀⠀⡟⠰⠜⠁⠀ ⠀⠀⠀⠀⠠⠂⠀⠀⠀⡆⠀⠸⠀⠀⠈⡄⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⠤⠀⠂⠀⠁⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡠⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⣀⡠⠒⠭⢀⠀⠐⠪⢵⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢡⠈⠣⠠⠄⡀⢑⢄⠀⠀⠩⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢆⠂⠀⢤⠄⢠⢕⢯⠓⡤⣀⣱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡷⡀⠺⡀⡥⣋⣷⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣵⡀⠀⠒⠼⠋⠀⢠⡴⠁⢀⡀⠀⢀⡠⠆⠉⡀⠖⠰⣍⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⢜⠄⠀⠒⠂⢪⡗⡘⡈⠁⣄⠒⠛⢻⠋⢥⡢⠠⡀⠔⣹⡾⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⢸⠁⠀⠈⢱⢄⢊⠀⠀⢳⠡⠱⢰⠁⣴⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⡀⠒⣠⡰⠟⠀⢘⠀⠀⠈⣆⠇⠈⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⢃⢰⠈⡄⠀⠱⠀⠀⢿⢰⡂⠀⡄⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠈⡼⠀⠀⠀⠀⡇⠸⢻⢸⡁⢰⠷⣥⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠃⠀⠀⠃⠀⡄⠀⠀⠀⠀⠘⣿⢷⡘⠸⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⡌⠀⠀⠀⡜⠚⠀⡀⠠⠆⠀⠀⠘⠇⠙⠷⡵⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠂⢄⠤

⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🏻🏻🏻🟨⬜🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🏻🏻🏻🟨🟨🟨🟨🟨🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🏻🏻🟨🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🟨🏻🏻🏻🟨🟨🏻🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🏻🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🏻🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🏻🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟨🟨🟨🟨🏻🟨🟨🟧🟨🟨🟧🟧🟧🟧🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧🟧⬛⬛⬛⬛🟧⬛🟧🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧⬛⬛⬜⬜🟩⬛🟧🟧🟧🟧🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧⬛⬛⬜⬜🟩⬛⬛🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟧🟧🟧⬛⬛⬛⬛🟩⬛🟧🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧🟧⬛⬜🟩⬜🟧🏻🟧🟧🟧🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟧🟧🟧🟧🟧🟩🟩🟧🟧🟧🟧🏻🟧🟨🏻🟨⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🏻🟧🟧🟨🏻🟨⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🏻🟨⬜⬜⬜⬜🟨🟨🏻🏻🏻🏻🟨🟨🟨🟨⬜ ⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🏻🟨🟨⬜⬜⬜🟨🟨🏻🟨🟨🟨🟨🏻🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟨🟨🏻🟨⬜🟧🟧🟧🟨🏻🟨🟨🟨🟨🟨🏻🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟥🟨🏻🟨🟨🟧🟧🟧🟧🟧🟨⬜⬜⬜🟨🟨🟨🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🏻🟥🟨🟨🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🟨🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🟨🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟧🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🟨🏻🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🟨🏻🟨🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🟨🏻🟨🟨🏻🟨 ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜🟨🏻🟨🏻🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜🟨🟥🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧🟧⬜🟨🟨🟨🟥🟥⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🏻🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜🟨🟨🏻🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨⬜🟨🟨🟨⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣩⣽⣿⣿⣿⣿⣿⣿⣋⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⣹⣿⣿⣿⣿⣿⣯⣿⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣴⣿⣿⡟⢾⡟⠻⣟⠛⠛⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠀⢿⣿⠿⡿⡿⢷⣀⣿⣄⠈⠳⡄⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⢸⡿⡄⢳⠹⡄⢻⣿⠘⢦⠀⠹⡆⠀⠸⣦⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⡆⠀⣼⢧⠇⢸⡄⢡⠀⣿⣇⠘⣆⠀⢹⠀⠀⢹⡳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣿⢿⣧⣞⣀⣸⠀⣸⠀⢸⣿⣄⣹⣄⣨⣷⣶⡾⠃⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠋⠙⠛⠳⠶⣤⣤⣄⣤⣤⣤⣤⡶⠖⠚⠛⠛⠷⢶⣄⣹⣮⣿⠟⣉⣙⣿⡛⠛⠋⠉⢹⣏⡉⠻⣽⣟⡿⠃⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠛⠛⠛⠻⠷⢦⣄⠀⣿⡿⣿⣿⣀⣰⣿⣿⡇⠀⠀⢠⣿⢋⣿⣦⢸⣿⠀⣴⠟⠉⠀⢀⣀⣠⣭⣽⣽⣿⡶⠶⠶⡶⠶⠶⠛⠛⠉⠉⢹⡆ ⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠘⠷⣦⣄⡀⠀⠀⠀⠀⠙⢷⣿⣠⣿⣿⣿⣿⣾⣿⠃⠀⠀⢸⣿⣿⣭⣿⣿⣿⣾⠃⠀⣠⠾⠋⠉⠉⠀⠀⠈⠉⣹⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃ ⠀⢰⡾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⡷⠂⠀⠀⠀⢻⣟⢿⣿⠿⢿⣿⣿⢈⠉⢉⣸⣿⣿⣿⢿⡿⣿⠃⢠⡞⠁⠀⠀⢀⣠⣤⠤⠶⠟⠋⠁⠀⠀⠀⠀⣠⣴⡾⠛⠁⠀ ⠀⠘⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠹⡄⣿⢷⣄⠀⠀⢮⣇⣹⡿⠉⢀⣤⣾⣷⡿⣠⠏⠀⠀⠀⠀⠈⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢶⠀⠀ ⠀⠀⠀⠈⠛⠛⠶⢦⣤⣤⠀⠀⠀⠈⠛⠲⠶⠶⠒⡿⠁⠀⠀⠁⢻⣆⣈⣿⠳⠶⠬⠿⠶⠛⣿⡍⣇⢻⡃⠋⠀⢠⢶⣤⣄⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⣀⣠⡶⠀⠀⠀⠸⣷⠶⠶⣿⡀⠠⣿⡿⣿⠀⠀⠀⠀⠀⠀⢿⣷⣼⡌⢷⢲⣦⣾⣈⡧⠈⠉⠉⠉⠀⠀⠀⠀⠰⢶⣶⠾⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠷⠶⠒⠒⠛⣽⡏⠀⢀⣠⣤⡖⠀⠀⠀⠈⡛⠛⢹⡇⢿⡀⠀⠀⠀⠀⠀⣸⠁⡇⢱⡈⠛⠛⣿⠉⣁⡀⠀⠀⠘⢷⣦⣄⣀⠀⠀⠉⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠘⠿⠤⠤⢴⣾⠟⠁⠀⣸⠃⣤⢷⡀⠀⠀⠀⣰⡏⠀⣇⠀⠙⠦⠼⢻⣀⣈⣻⡷⠦⢤⣤⡿⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠶⠶⠻⢿⣇⢈⢷⣷⣄⣠⣾⣽⡇⣴⡟⢧⠀⠀⢀⣾⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⠖⠒⣿⠙⠻⣿⣾⠛⠛⣿⣫⠞⡏⣿⣦⣑⣦⠞⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠤⠴⠞⢻⡨⠀⠈⠙⢷⡾⠋⠀⢀⣧⡷⡝⠳⣤⣀⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⡦⠞⠙⣿⣶⣉⢱⡏⣿⠀⣲⣼⣿⢧⠙⠶⣄⡉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⣼⣷⡞⣿⡇⠀⠬⢿⣿⣿⣿⠍⠉⣿⡼⡷⣤⣬⡝⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢀⣷⣿⢉⡟⢻⡦⠤⠭⣿⣏⣩⣀⣴⡟⠻⣏⢻⣷⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⢛⣯⡟⠁⣼⣀⣤⣤⣼⣀⣉⣁⣽⣷⠀⠹⣾⣿⠷⢤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⠛⠷⢴⡇⠀⠀⠀⣼⠀⠀⠀⢹⣿⣷⢤⡿⣿⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡰⠋⢀⣴⢿⠃⠀⠀⠀⣿⠀⠀⠀⢸⣇⠙⣦⡀⠘⣆⢰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢀⡴⠟⠁⡟⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⣤⠈⣷⣤⡈⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢃⣀⡴⠞⠉⠀⠀⣴⡇⣠⠶⢦⠀⣿⠀⣤⣄⠀⣿⡌⢷⣿⡈⠻⢦⣀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠷⠚⠛⠋⠉⠉⠉⠉⠉⣿⡴⠫⣼⡾⣿⣿⡿⣹⣌⢳⣻⡇⠘⣿⠷⠶⠶⠿⠷⣶⣌⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⠸⢻⠃⠻⡿⠃⢿⠣⠀⠿⣷⠶⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠾⠶⠞⠳⠦⣬⣤⡤⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬛🟥🟥⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛🟥⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟨🟥🟥⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟨🟥🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬛🟥🟥🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬛🟥🟥🟨🟨🟨🟨⬛🟨⬛⬜ ⬜⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛🟨🟨🟨🟨🟩🟨🟨⬛ ⬛🟨🟥🟨⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬛🟨🟨⬛⬜⬜⬜⬜⬛🟨🟨🟥🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬛⬛⬛⬜⬜⬜⬜⬜⬛🟨🟥🟨🟨🟨🟥🟨🟨🟨⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛🟨🟨⬛🟧⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛🟧⬛⬛🟨🟨⬛🟧🟧⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬛🟧⬛🟨🟨⬛⬜⬛🟧🟧⬛ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬜⬛⬛⬜⬜⬜⬛⬛⬜

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫⬜🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫⬜🟫🟫⬜🟫🟫⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟧🟫🟫🟧🟧🟫🟫🟧🟫🟫🟧🟫⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟧🟧🟧🟧🟫🟫🟧🟧🟨🟨🟧🟫⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟧🟧🟧🟧🟫🟧🟨🟨🏻🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟧🟧🟧🟧🟧🟨🏻🏻🏻🏻🏻🏻🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟧🟧🟧🟧🟧🟧🏻🏻🏻🏻🏻🏻🏻🏻🟨🟨⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟧🟧🟧🟧🟧🟧🟨🟨🏻🏻🏻🏻🏻🏻🏻🏻🟨⬜⬜ ⬜⬜⬜⬜⬜🟫🟧🟫🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🏻🏻🏻🏻🏻🟨⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟧🟨🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🟨🟨🏻🏻🏻🟨⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟨🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟨🟨🏻🟨⬜ ⬜⬜⬜⬜⬜⬜🟫🟨🏻🟨🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛🟧🟧🟧🟨🟨🟨 ⬜⬜⬜⬜⬜⬜🟫🟨🏻🏻🟨🟧🟧🟧🟧🟧🟧⬛⬜🟩⬛🟧🟧⬜⬜🟨 ⬜⬜⬜⬜⬜⬜⬜🟨🏻🏻🏻🟨🟧🟧🟧🟧🟧⬜🟩⬛⬛🟧🟧🟧⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟨🏻🏻🏻🟨🟧🟧🟧🟧⬜⬜🟩⬛🟧🟧🟧⬜⬜ ⬜⬜⬜🟨🟨🟨🟨⬜⬜🟨🏻🏻🟨🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜ ⬜⬜🟨🏻🏻🏻🏻🟨⬜⬜🟨🟨🟥🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜ ⬜⬜🟨🏻🏻🏻🏻🏻🟧🟧🟧🟥🏻🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🟨🟨🟧🟧🟧🟧🟧🏻🏻🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🟨⬜🟧🟩🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🟨⬜🟧🟥🟥🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🏻🟨⬜🟧🟥🟥🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🏻🟨⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟥🟥🟥⬜⬜🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜🟨🏻🏻🟨⬜⬜🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜ 🟨🏻🏻🏻🟨⬜⬜🟧🟧🟧🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨⬜⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣒⣋⣉⡉⠉⠉⠙⠓⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠴⣻⡿⠛⠉⣁⣤⠴⠒⠒⠂⠉⠉⠁⠈⣙⡲⢤⣄⠀⠀⢀⣴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣴⡾⢏⡴⠋⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠈⠛⢶⡞⠁⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣵⠞⠁⢠⠟⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢀⣀⣀⣤⠏⠀⠀⢰⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠟⠁⠀⣰⡏⠀⠀⠀⠀⠀⣰⡿⠀⠀⢠⡴⠋⠁⠀⠀⠈⠀⠀⠀⢸⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⣿⡇⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⡶⡟⠙⠻⡄⡾⢤⣄⣀⣀⣀⣀⣀⣠⠴⠚⠀⢀⡟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⡿⡯⡅⠀⠀⠙⡟⠀⠀⣩⣉⣉⣩⣥⣶⣗⡄⣴⣯⠀⠀⣠⠶⠋⠉⡿⠀⠀⠀⠀⢀⣠⠴⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⣾⠁⡇⣷⠄⠀⠀⠀⡷⠒⠋⠉⠁⣴⣿⠘⠛⠒⠀⢹⠹⣦⠞⠁⠀⢀⠞⠁⣠⠴⣲⠿⠋⠁⠀⣰⠟⠁⢀⣠⡴⠖⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠻⣆⣷⡿⠀⠀⠀⠀⠑⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⣾⠀⢷⠀⢀⡴⣫⠖⠋⢁⡾⠃⠀⠀⣠⢞⣥⠶⠚⠉⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⠉⠤⠀⣦⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢰⡿⡄⢸⣠⡿⠋⠀⠀⣴⣋⣀⡀⣤⡾⠟⠉⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢶⠞⢻⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⡟⠀⣇⠘⡇⠀⠀⢀⣾⠋⠁⣼⠉⠁⠀⠀⢀⣠⣶⣯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⣤⠤⠤⠤⢤⡴⠚⠋⠀⢀⣼⡏⠀⠀⢿⠀⡇⠠⠴⡿⠑⢀⡼⣃⣀⢀⣠⡶⠯⠭⠽⠦⣤⣀⠈⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣀⡴⢛⡱⡇⠀⠀⢼⡀⡇⢀⡞⠀⣠⠟⠛⠉⣹⠀⠀⠀⠀⠀⠀⣀⡼⠯⠳⣤⣄⣀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠖⠒⠒⠛⠛⠛⠛⠒⠒⠲⢦⣄⠀⡞⠁⠀⠀⠉⣹⠟⢁⡇⠀⠀⣿⣿⣿⠏⠀⠈⠁⠀⣠⣞⣁⣤⠤⠴⠒⠲⡉⠉⠳⡄⠐⠌⢯⣿⡗⢶⣿⡄⠀⠀⠀⠀⠀⠀ ⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⣰⠏⠀⣸⠃⢀⡼⠫⠞⠁⠀⠀⣠⡴⠚⠉⠛⣷⣄⠈⠀⢤⠀⠙⣄⠀⠘⡄⠘⡀⢯⢻⡄⠙⢷⠀⠀⠀⠀⠀⠀ ⠹⣄⡀⠀⠀⠀⠀⠀⠀⣠⡶⡟⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⠀⣠⣧⠶⠋⠁⠀⠀⠀⠀⠀⣨⠟⢀⣠⣶⠋⠈⢳⡀⠀⠑⡄⠘⡄⠀⢹⠀⢳⠘⡏⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠓⠒⠶⠴⠴⠚⠋⠀⡇⠀⠀⠈⢹⡇⠀⠀⠀⠀⠹⣾⠉⠀⠀⠀⠀⠠⠴⠒⠒⠚⢛⡏⠉⠀⡿⠀⠀⠀⢻⡄⠀⢹⡄⢹⡄⠀⡇⠈⡄⢹⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣸⣇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠈⠀⢰⠇⠀⠀⠀⠀⣧⠀⡄⢧⠈⡇⠀⡇⠀⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣦⠀⠀⢀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⡄⡇⠸⠀⠃⠀⡇⠀⡇⠸⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⡾⠀⠀⠀⢳⣄⣠⠤⠴⠛⠙⣷⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⢸⣷⡇⠀⡇⠀⠀⡇⠀⡇⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠘⢦⠀⠀⠀⠛⣧⠀⠀⠈⠀⢻⡀⠀⠀⠀⢸⣿⡇⠀⢸⢸⠀⡇⠀⡇⢸⡆⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⠀⠈⣳⠂⠀⠀⠹⡄⠀⠀⠀⠀⣧⠀⠀⠀⠽⠃⣯⠀⢸⣼⠀⡇⠀⡇⢸⣿⡌⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⡄⢸⣟⡄⢰⠀⡇⠘⣇⠻⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢹⣇⢸⡟⣷⣸⠀⠁⠀⢹⡄⠉⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⣼⡇⠈⢿⣧⢸⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣼⡼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠙⢦⣹⣦⣄⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢀⣧⠇⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠉⠻⢮⡙⠳⠿⠷⠦⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢸⡏⠳⠶⠶⠒⠛⣹⠃⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⡀⠀⠀⢀⣀⣠⠟⠁⠀⠀⠀⠀⠀⠻⠦⠤⠤⠤⠤⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣴⣶⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣸⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⠷⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⢿⣿⣿⣿⣿⢿⠀⢠⣿⣿⣿⠟⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⠟⠘⠀⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠻⠿⠿⠟⠋⠀⠀⢸⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⣧⣀⡀⡴⠋⢹⣯⣤⣶⣾⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠠⣴⣶⣤⣤⣤⣤⣄⣀⠀⠀⠠⢴⣄⠀⠀⣿⠏⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⣶⣤⣙⢷⣾⡟⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡟⠈⠀⣶⠆⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⠿⠛⠋⠁⢀⣀⣠⣤⡴⠾⠿⠛⠛⠛⠛⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⢻⣷⡀⠀⠀⢸⡿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⢤⣤⣤⣤⣤⣴⣶⡶⠾⠛⠛⠛⠉⠉⠀⠀⣠⣤⣶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⣠⣤⣾⠟⠋⠁⠀⠘⣿⣧⠀⠀⢸⣧⠙⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠋⠉⠀⠀⠀⣀⣀⣴⠆⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⣴⡾⠟⣍⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠘⣿⡀⠈⢿⣦⠀⠀⠀⠀⠀⣿⡇ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢋⠀⠠⣤⣿⡿⣿⣿⣏⠉⠁⠀⠀⠀⢰⣿⠁⠀⠀⣠⣾⠟⠋⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⢻⣧⠀⠘⠷⠀⠈⢿⡆⠀⠀⠀⠀⣿⠃ ⢸⠁⠀⠀⠀⠀⠀⢀⣴⡿⠋⣿⠀⣙⣿⡿⠛⠁⠀⣹⣿⣿⣷⠀⠀⠀⠀⣿⡇⠀⣠⣾⠟⠁⠀⠀⠀⢀⣴⣶⠾⠿⣿⣷⠶⣦⣄⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⡟⠀ ⣸⠀⠀⠀⠀⣠⣾⡿⠃⠀⢸⣟⢠⣿⠋⢀⣶⣦⣾⣿⣿⣿⣿⠀⠀⠀⢸⡿⢀⣴⡿⠁⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀ ⠛⠀⠀⢀⣾⡿⠋⠀⠀⠀⢿⣿⡟⠁⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⢼⣷⡿⠋⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀ ⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⣿⠀⠙⠋⠛⢿⡿⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⢠⡏⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⢹⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀ ⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠘⣿⣌⠃⢀⣠⡾⠃⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠄⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣷⠤⠤⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⠀⠀ ⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⣈⡴⣀⢆⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⣼⡟⢸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠘⠻⣷⣤⣀⣀⣠⣴⠞⠁⠠⡾⠛⠛⠻⠿⣶⣄⠀⠀⠀⢿⣿⡿⣿⡏⢿⣿⠇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠴⠾⠃⠀⠉⠛⠛⠉⠀⠀⠀⠠⢿⣆⠀⢀⣶⠬⠁⠀⠀⠀⢹⣿⡳⢭⠁⣼⠇⠀⠀⠀⠀⠀⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠘⠻⠿⢶⣿⣤⣄⣀⣀⣠⡴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣤⣤⣶⣶⣀⡀⠀⠀⠀⠀⣠⣿⠃⣸⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣼⡿⠁⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⠁⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣴⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⢀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣤⣀⡀⠀⠈⠉⠒⠒⠘⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠻⢿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⢻⣮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢠⣤⣀⡀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢸⣟⠛⠿⠿⠷⠦⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⢠⠀⠀⠀⢸⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢠⡾⠀⠀⠀⣾⡇⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠛⠛⠷⠦⣤⣀⣤⡴⠿⡛⠁⠀⠀⠀⢀⣼⡇⠀⠀⣸⡟⠀⠀⠀⠀⠙⡻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣀⡀⠙⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢔⠅⣊⣵⡿⣞⠛⢲⣼⣈⡷⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢃⣾⣿⡿⠋⠜⢀⣟⡷⡁⠀⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠏⠘⡿⢄⢁⡁⠀⠉⠡⢀⡟⠁⠀⢀⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⢠⠁⣸⢮⣍⡀⠠⢴⢊⡧⠖⡊⣑⡻⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠞⠀⡇⠀⢳⡔⠂⠆⡮⡇⡬⠥⡶⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠘⢆⡇⠀⠈⠁⡜⣰⠘⢟⣱⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠰⢱⡀⠐⣠⠃⠹⣤⣤⠏⢻⣳⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⢠⡞⠈⣩⠋⠳⢀⢰⠀⠀⠈⣄⠙⢍⡉⠁⠒⢄⠀ ⠀⣀⡀⠀⠀⠀⢀⢼⠜⠀⠁⡇⠀⠀⡔⡙⡄⠀⠀⠱⡁⢀⢣⠑⠀⠀⠃ ⢜⡄⠈⠀⣠⠎⣰⣋⣉⣀⣠⡟⠀⢀⠗⠈⠘⠩⢰⠀⠘⡄⠁⠂⠀⠀⡀ ⠈⠚⠛⠈⠑⠊⠀⠀⣠⠞⠁⠀⢠⠏⠀⠀⠀⠀⢸⠀⠀⠰⠀⡠⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣃⠀⠤⠴⠃⠀⠀⠀⠀⠀⠈⣆⠀⠀⡗⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠃⠀⠀⠀⠀

⡉⠻⡟⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡠⣒⠨⢭⠴⡢⡀⠀⠀⠀⠀⠀⠘⣿ ⡵⠚⠁⡜⠀⢄⠁⠢⢄⡄⣠⣤⢱⣠⡿⠛⣉⣐⡰⠙⠀⠰⠷⣢⠀⠀⠀⠀⢨⣿ ⠁⠀⠀⡇⢰⠀⠆⠱⠈⣷⠿⠛⢵⡄⠀⢹⠀⣀⠉⢖⠌⠘⢡⢹⠀⢀⡤⠲⣿⣿ ⠀⠀⠀⣏⠢⢆⠸⠢⡽⠁⣠⡤⡀⠘⡄⣈⠜⠳⡓⠚⡛⠄⠰⣰⠣⡈⠢⢤⢛⠟ ⠀⠀⢀⠘⢥⡬⠆⢤⡇⢸⡘⠿⠓⠈⠉⠀⢀⠠⠐⡒⠀⠀⢣⡈⠁⣒⠛⠂⠁⠀ ⢄⡀⠜⢠⠋⠀⠀⠀⢻⠁⠀⠉⢄⡀⠄⡂⣥⣾⣿⠷⡄⠀⣸⠙⠫⢝⢅⠀⠀⠀ ⠁⠀⢠⠃⠀⢰⢹⠇⢸⡀⡄⠀⠀⠘⣦⣽⡏⠑⢂⣟⠇⢠⡟⠀⠀⠀⢳⡇⠀⠀ ⠀⠀⢢⠀⠀⠘⠦⠤⠋⠜⠂⠐⠢⡄⠈⠙⠬⠭⠅⠊⡠⠋⠀⢸⡁⠇⣸⣼⠀⠀ ⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⡤⠒⠤⡐⣎⠣⡤⣤⠪⠃⠂⠉⠁⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠀⢀⠔⢺⡟⣪⠊⢀⣄⡀⠀⠀⠀⠀⠀ ⠳⡆⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣰⠋⠄⠀⠔⠘⠉⠀⠚⠂⣄⡀⠀⠀⠀ ⠀⠙⠦⣀⣀⣷⠀⠀⠀⠀⠑⢄⡀⢀⡴⠋⠀⠘⣀⠠⠀⠠⢀⠀⠀⠈⠏⠀⠀⠀ ⠀⠀⠀⠠⠿⠉⠣⢄⣐⣶⣴⣾⠉⠁⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⣴⣮⣄⡀⠈⣇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀ ⠀⠀⠂⠰⣿⣷⣶⣿⣿⣿⢦⢄⢹⡄⢀⠎⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢨⡿⣿⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠀⢀⡬⠟⢛⣉⠃⢄⡱⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡀⠀⡴⠋⠰⠈⢌⢁⣂⡠⠴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⢀⣾⢇⠄⣰⢲⡄⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠤⠤⠀⡀⠀⡀⠈⣺⠃⠨⠀⠘⢿⡷⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⡀⠈⠡⠄⠵⡈⣌⢢⢈⡆⠀⠀⢒⡊⠁⢠⠓⢁⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⡈⠀⣆⡈⢯⠪⢽⡄⠛⠒⣄⣀⣏⠑⠠⠟⡭⠿⣿⠻⠑⠠⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⣿⠟⣸⣿⡃⠀⢀⢻⣗⠨⠔⠂⠄⡆⠀⠀⠀⠀⠀⠸ ⠀⠀⠐⣠⠀⠀⠀⠀⠀⢀⡧⢀⡿⠿⡏⠀⠞⠋⠛⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠍⠈⠁⠀⠐⠀⠆⠀⡌⠀⠘⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠢⣠⣐⣀⠀⠀⠀⠰⡁⠀⢰⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡠⠄⠒⠠⡀⢣⡐⢂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠞⡒⢖⡦⡤⢀⠑⢵⣸⠀⡐⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⠖⡹⠉⠳⣈⠒⠉⠁⠀⠈⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢩⠂⠕⢕⡞⠅⠀⠠⠐⠒⠀⣀⠂⡸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢐⡄⢢⣷⡤⠀⢁⣠⣞⢺⡷⢂⡗⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣜⣳⠿⡻⠇⠀⢏⠿⡿⠟⠁⡼⢀⡟⡇⠀⢀⠔⢂⠭⣀⠙⢕⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠑⠤⢀⣀⠀⠤⠐⢀⣡⡯⢴⠁⠔⣡⡨⠐⠒⠢⡑⢄⢡⠀⢱⡄⠀ ⠀⠀⠀⡔⠒⠄⣠⠁⠀⠀⣰⢿⣗⣲⠎⡌⡜⡡⠂⠁⠀⠈⠪⢆⢻⠀⠘⣿⠀ ⠀⠀⠀⠁⠀⣀⢸⠀⠀⠘⡦⠼⢛⢝⡉⠺⡌⠀⠀⠀⠀⠀⢀⠗⠁⡐⢡⢸⠀ ⠀⠀⠀⡀⠀⠑⠉⡀⠀⡀⢋⡉⠄⣪⡟⠠⡰⠀⠀⠀⠀⠙⢤⠔⠈⡠⢂⣾⡆ ⠀⠀⠀⢃⠀⢠⠀⡇⠀⢰⠺⣒⠊⢁⠀⠘⢀⠃⠀⠀⠀⠀⢀⣦⠊⣠⡾⣡⢿ ⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⡆⠀⠉⢣⠑⠠⣀⠀⠑⢄⠀⠀⠸⡿⠛⡁⢔⢣⠃ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢡⠀⠀⠈⠀⠀⢠⠑⡀⠀⠡⡀⠀⠈⢣⢔⣵⢡⣤ ⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⢰⠀⠀⢸⠀⠰⡀⠀⠐⡄⠀⠀⢇⣜⡣⠟ ⠀⠀⠀⠀⠀⣤⣴⣇⣀⣀⣠⣷⣶⣥⣤⣤⣼⣶⣤⡇⠀⠀⠘⣀⠀⠑⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠊⠉⠁⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⠴⠒⠛⠒⠯⠥⣄⣀⠀⠀⠀⠉⠉⠙⠛⢿⢶⣴⡋⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠈⢇⠹⡆⠀⢀⣀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣀⣀⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢸⡀⡇⠀⠘⠛⠁⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⢀⣴⣋⠥⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠱⡀⠀⠀⣸⢃⡇⠀⠀⠀⢾⣿⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣧⡴⠚⠋⠙⠃⠀⠀⠀⠀⠁⢀⣠⠷⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠏⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡈⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠇⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⣩⠴⠛⠋⠛⠲⢦⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠏⣠⣿⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢏⡟⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⢠⡏⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣀⣀⣠⣤⠶⣿⣿⣿⣿⡆⠀⠇⠀⠘⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⣀⣀⣠⣤⣤⣴⣶⠚⠁⠀⠀⠀⠈⠉⢹⣿⣷⠾⠛⠋⠙⡿⢿⣄⡴⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡟⣿⣿⡿⠿⠷⠶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⣇⣼⡿⣶⣶⠂⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣧⣿⠃⠀⠀⠀⢸⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢻⣿⣷⡾⠿⢩⠻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣽⣟⡛⠂⠸⢠⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠖⢋⣁⡆⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸⣿⣿⠿⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⢸⠀⠀⢰⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⠴⠗⠒⠶⠄⠀⢀⣠⣾⠏⠀⡜⠀⠀⡼⠀⣼⣇⣀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⣿⣿⣿⣿⣶⣄⣀⣤⢤⣘⣁⣀⠀⠀⠀⢤⡶⠟⠊⠁⠀⢀⡇⠀⠀⡇⠀⣿⡏⠉⠙⠛⠓⠲ ⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠶⣄⠀⢀⣀⣀⣰⡏⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢸⣿⢷⣄⠀⠀⠀⠀ ⣅⣀⡀⠀⠈⣿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⣷⣿⣿⣿⠟⣧⠀⠈⠉⡉⠀⠀⢹⠃⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⡿⢿⠀⠙⣦⠀⠀⣚ ⠀⠀⠉⠙⠓⠿⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠙⣏⡸⠃⣰⣿⡷⢦⣄⣑⡄⣠⣿⠀⠀⠀⠀⠀⢰⠃⠀⢰⠃⢰⠇⠈⠳⣄⡇⢐⠋⠉ ⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⣿⡇⢰⡿⠹⣧⠀⠈⠉⠣⡀⢹⠀⠀⠀⠀⠀⡸⠀⠀⣸⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠈⡆⠀⠀⠀⠀⠀⡇⠻⡇⢸⡇⠀⣿⣆⠀⠀⢠⠟⣿⠀⠀⠀⠀⠀⡇⠀⠠⡇⠀⢿⡇⠀⠀⡼⠷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠲⣶⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⣀⠀⠀⠈⠻⡺⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡠⠔⣒⣿⣿⣿⣿⣷⣄⡀⢱⡈⢻⡆⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⠖⠉⣠⣾⣿⡿⢿⣧⠉⠉⠉⣿⡶⣧⣀⡿⠋⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⠁⣴⣿⣿⣿⣿⡗⢻⣹⠀⠀⡽⢿⣷⡈⠈⠀⢨⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣴⢿⣿⣻⡿⠃⡤⠬⠁⠀⠸⣇⣾⡏⠑⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⡾⠁⠀⠱⣿⣧⡄⠁⠀⠀⠀⠀⠀⣀⣱⠄⠀⣿⠋⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⠃⠀⠀⢠⠏⠀⢻⡀⠻⠷⡄⠀⠀⠀⠀⣠⡾⡿⠀⣀⣠⠴⠖⣫⣵⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⢀⡏⠀⢀⡼⢿⣶⣤⣄⡀⠀⠒⢻⠏⢰⣷⠟⠋⢉⣇⣉⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠇⠀⢸⠁⠀⠙⣿⡀⣠⠖⢀⡏⢠⡏⡟⠀⠐⣟⢠⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠸⡄⠀⢸⠀⠀⠀⠸⣿⠁⠀⣸⠀⡾⣯⣱⣤⠉⢁⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠻⣆⢸⠀⠀⠀⠀⡇⠀⡸⢹⢰⡇⠈⢿⣊⣽⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠻⣆⠀⠀⠀⡇⢀⡇⠘⣾⡇⠀⠀⢙⡷⣿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡇⢹⣄⡀⠀⢀⣾⠁⠀⠘⠿⣶⣶⠿⠁⠈⢿⢾⣟⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣧⡾⠈⠛⠛⣽⠋⢿⡆⠀⠀⣠⠀⠀⠀⠀⢸⡆⠈⠻⣍⠉⠉⠛⠒⠦⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡟⢁⡠⠤⡾⠃⠀⠀⠉⠓⢒⣿⠀⠀⠀⠀⠀⢿⠤⡀⠈⠳⡦⢄⡀⠀⠀⠙⢧⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡼⠋⠉⠀⢸⡇⠀⠀⠀⢀⡶⠋⠸⣆⠀⠀⠀⠀⠘⣆⠈⠢⠀⠹⡄⠉⠢⡀⠀⠈⠃ ⠀⣠⢛⠋⠑⡆⠀⠀⠀⣠⠖⢉⣾⠯⠄⠀⠂⠐⠚⢻⡄⠀⠀⠘⣧⠈⠃⠝⠦⠤⢤⣀⠀⠈⢷⡄⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⠰⡇⢸⠀⠀⠀⠀⣠⡞⠁⣠⣚⣁⣀⣀⣀⣀⣴⣿⠟⠁⠀⠀⣴⠟⠀⠀⠀⠈⠐⠂⣿⠀⠀⠈⢳⠀⠀⠀⢣⠀⠀⠀⣀⠌ ⠀⠘⠢⠽⣿⠖⣛⣡⠴⠚⠉⠀⠀⠀⠀⣠⠿⠋⠁⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⢸⣠⡴⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⡄⢠⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣀⣠⠤⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣷⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡄⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⠋⠙⡇⠀⠀⠀⠀⠘⡄⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣰⠛⠉⠉⠓⠂⠀⠀⣿⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠙⠓⠦⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣤⣶⣦⣄⡀⠛⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠙⠻⣇⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡟⣵⣶⡶⢤⣈⠻⣦⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡞⠁⠀⠀⠀⠘⢹⡇⠀⣿⣷⣍⢷⡘⣧⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⢣⡀⠀⠀⠀⢘⣿⠟⢋⣉⡙⠓⠀⠀⠀⠀⠈⣷⢶⣿⣼⣿⣧⢷⢸⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠻⣦⡀⠀⣾⢃⡾⠻⣧⣝⢦⠀⠀⠀⠀⠀⠈⠣⣟⠿⠿⣟⣼⠟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠁⠀⡏⢸⡀⣠⡿⣿⣯⣇⠀⢀⡴⠊⢩⠀⠈⢉⣩⠿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⣿⢸⡿⣿⣷⣿⣿⡟⠀⠈⠒⠂⢀⣠⠶⠋⠁⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⣳⣙⠿⢟⣽⠃⠀⣄⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⣠⣿⣀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠙⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡙⠛⠟⠛⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⠛⢦⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠈⠳⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠳⣦⣤⡤⠴⠶⠒⠉⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⡠⠊⠉⢩⠉⠙⠶⣄⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋ ⢀⡞⠁⠀⢠⠏⠀⠀⠀⠈⢳⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀ ⡼⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⣧⡀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣠⡾⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⡉⠉⠉⠀⠀⠀⠈⠉⠉⠳⠶⣄⡀⠀⠀⣀⡴⠋⠴⠶⠒⠚⠒⠒⠒⠶⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣈⡽⠶⠋⠉⢀⣀⣀⡤⠤⠤⠤⠤⠤⣀⣀⡀⠈⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⣠⠞⠋⠉⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠁⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠙⠳⢦⣄⡀⠀⠀⠀⢀⣾⢠⡾⠁⣤⢚⣥⠴⠚⠛⠉⠉⠙⠛⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠙⠛⠛⠛⣋⣥⣾⣥⣾⠖⢉⡤⠖⠒⠛⠒⠦⣤⡀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠻⣾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇⠘⢇ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠙⢦⡀⠀⠀⢀⡼⠁⠀⢸ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡞⠛⢤⠀⠹⣷⡄⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⡀⠀⠙⠛⣻⠟⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠻⡀⢻⣳⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⢸ ⠀⠀⠀⣠⡶⠛⢿⡀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⢿⠘⡿⣇⠀⠀⢸⢷⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⣿⡇⠀⠘⢷⡀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⠀⡼⠀⠐⠹⣆⠀⣼⠀⠙⢦⡀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀ ⠀⠀⠀⠹⣇⠀⠀⠈⢿⣄⠀⠀⠀⣿⡀⠈⠧⠤⢤⣠⡖⠁⠀⠀⢀⣨⡿⠟⠲⠶⣦⣙⠳⢦⣄⣀⠀⠸⣟⠷⣄⡀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⣀⣀⢀⣀⣀⣠⢴⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠻⣦⠀⠀⠀⠙⢦⡀⠀⢻⡇⠀⠀⠀⣄⡀⠻⣷⣦⣴⣟⣥⣄⣀⠀⠀⠈⠻⣦⠀⠈⠉⠙⠓⠛⠶⢌⣿⡷⢤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⡥⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠈⠻⣶⠟⢿⡀⠀⢀⡘⠻⢶⣾⣿⣿⠉⣀⣨⣽⣷⡄⠀⠀⠙⣧⠀⠀⠀⠀⠀⢠⣾⠏⠉⢷⣍⠉⠙⠒⠲⢶⣶⣶⣶⡶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢠⡾⠋⠀⢸⣧⠀⠀⠹⢷⣶⣿⠋⢠⣾⡏⠁⠀⠹⣿⡄⠀⠀⢹⣆⠀⠀⠀⢠⡿⣱⡶⠋⠉⢿⣦⠀⠀⠀⠘⣿⣟⣹⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⢠⣾⡄⠀⠀⠀⠀⢸⠏⢀⣿⠿⣷⣄⣀⡼⠛⢻⠀⠀⠀⢿⠀⠀⢀⡾⢹⡏⢷⣄⣀⣼⣿⡀⠀⠀⠀⢹⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢸⡏⠻⣆⠀⠀⠀⣿⠀⢸⣿⣀⣉⣿⣿⡇⠀⢸⠀⠀⠀⠘⡆⠀⢸⡇⣾⣀⣬⣿⡏⠀⢸⠇⠀⠀⠀⢸⣇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⢣⡀⠙⢷⣄⠀⠘⢦⡀⢻⡿⣿⣿⡟⠀⠀⣼⠀⠀⠀⠀⣷⠀⣸⡀⢹⠟⢿⡿⠀⠀⡾⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠳⣄⠀⠙⢷⣀⠀⠉⠛⠧⣼⣏⣀⣀⣠⢏⣀⡠⠶⠞⠛⢉⡉⠉⠻⡷⢾⣅⣀⣶⣁⣀⣠⠴⠞⠉⠁⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⣦⡀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠲⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠤⠤⠴⠂⠀⠀⠀⠀⠀⢀⣾⠉⣷⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠃⣹⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⡿⠲⠦⢤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠶⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡝⠶⣤⣀⣠⣤⡶⠿⣦⣄⣼⠃⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⠟⣡⣶⠾⣿⣿⣿⣏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠋⣴⠋⠀⠀⠀⠙⣷⡀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⡾⠁⠀⠀⠀⠀⠀⠘⣧⡞⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣼⣧⠞⠁⠀⠀⠀⠀⣴⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡤⠶⠒⢖⡻⣧⡀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣼⠟⠛⠳⢦⣤⡀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣧⢀⡾⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠟⢋⣤⠶⠛⠋⠉⠉⠉⠛⠳⠤⣤⡤⠞⣻⣇⣴⠞⠁⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⣷⠀⠀⠀⠈⢻⣿⠃⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠟⣡⠾⠋⠀⠀⠀⠀⢀⣠⣤⣴⣖⣺⣿⠀⠀⠙⠏⠀⠤⠈⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠏⣰⠋⠀⠀⠀⠀⢰⡿⣯⣀⣞⠁⠀⠀⠘⣧⡴⠞⠛⠛⠛⠻⢶⣄⠀⠀⠀⣠⣏⣀⣠⣴⣿⡀⠀⠀⠀⢀⣘⣧⠀⠀⢹⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⢸⡇⠀⠀⠀⠀⠀⠈⠻⢤⣉⠙⠳⠶⢦⣴⣯⣀⡴⠶⠒⠒⠺⣟⡛⠀⣠⡾⠋⠉⣵⠏⠈⢹⡇⣰⡄⠀⢸⠉⠻⣷⠦⣼⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣿⠈⢿⡄⠀⠀⠀⠀⠀⠙⢾⡍⠀⠀⠀⢈⣷⠄⠀⣿⠇⠙⣦⡇⠀⠀⠻⣦⠀⢀⣠⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠀⣠⠶⠶⢦⣽⡆⠀⣾⠉⠀⠀⠀⢹⡄⠀⠈⠁⠀⠀⠀⣻⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⣈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣰⡿⢾⡋⠙⠒⠖⠋⣁⣴⣶⣦⣸⡿⠤⠾⠷⠶⠶⠶⠟⠉⠛⠲⠶⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠳⠦⣍⣉⡙⠒⣒⣒⡪⠽⠟⠁⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⡿⠿⠒⢀⣀⡀⠭⠽⠒⠤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢫⣴⢒⠟⠁⠀⠀⠀⢀⠴⠂⠈⠙⠦⣤⠞⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠖⠉⡴⠋⠀⠀⠀⢀⡔⠁⠀⠀⣀⡀⢤⠏⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠃⠀⣸⠁⠀⠀⠀⢠⡿⠀⢀⠖⠉⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⡾⢷⡀⣎⠀⠀⠀⠀⠀⠀⣠⠏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⣠⣿⣿⠀⠀⠙⡏⠉⢁⣀⣈⣻⣿⣇⢠⡎⠀⢀⡤⠒⢲⠀⠀⠀⠀⣠⠤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⣠⡏⢸⣷⠀⠀⠀⡗⠋⠉⣠⣿⣍⠛⠁⢸⢻⡴⠋⠀⡰⢃⡠⢖⡿⠋⠀⣠⠞⢁⣠⠴⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡟⢹⡼⠋⠀⠀⠀⠁⠀⢰⣿⡿⠃⠀⠀⣸⠀⣇⢠⡾⠗⠉⡰⠋⠀⣠⣾⠵⠚⠉⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡂⢹⠋⠀⢀⡾⠛⣳⠞⠋⠀⠀⣠⣖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢥⠤⠤⢤⡤⠒⠉⢀⣼⠃⠀⢣⢸⠀⢴⡟⠁⣰⣃⡀⢀⡴⠮⠽⠧⣌⡉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡼⠁⠠⣴⣯⠿⠀⠀⣸⣼⣀⠎⠠⠞⠉⢉⠇⠀⠀⢀⣀⠤⡞⠉⢲⣤⣌⡻⣄⠀⠀⠀⠀⠀ ⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⢳⡼⠁⠀⠀⣰⠃⢰⠀⢀⣿⡿⠋⠀⢀⡠⠶⢷⣒⠋⠉⠉⠠⡀⠘⠄⢀⠹⣿⡍⢻⡄⠀⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣸⠇⠀⠀⠀⡇⢀⣧⠴⠋⠈⠀⠀⠀⣻⠀⣀⡴⠛⢳⡀⠁⠄⠱⡀⠘⡄⠆⢳⢻⠀⠁⠀⠀⠀⠀ ⠀⠀⠉⠒⠲⠴⠖⠊⠀⡇⠀⠀⢹⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠖⠒⠚⣻⡉⠁⡇⠀⠀⢳⡀⠘⡀⢳⠀⠃⢰⠸⡞⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠼⣇⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠞⠁⠀⢰⠃⠀⠀⠀⡇⢠⢳⠸⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡆⠀⠈⣆⠀⣀⡠⠴⢯⠀⠀⠀⡎⠀⠀⠀⠀⢹⣼⠘⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠉⢣⠀⠀⠚⣇⠀⠀⠉⢳⠀⠀⠀⣸⣿⠀⢡⡇⠀⠀⢠⣇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⡷⠂⠀⠸⡄⠀⠀⠈⡆⠀⠀⠋⢹⠀⢸⡀⠀⠀⠘⣿⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢀⠃⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⢸⡆⢸⣷⢠⠀⠀⢸⡘⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⡸⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⢷⣸⠈⢿⡆⢆⠀⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣧⠃⠀⠀⠀⢀⠇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠻⣇⠀⠛⢬⣦⣄⡳⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢰⣿⣀⣀⣀⣠⡾⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠓⠉⠙⠛⠓⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⢀⡾⠀⠉⠉⠀⠸⣅⣀⣀⣀⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠛⠋⠉⢉⣛⣒⣶⡦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⣀⡴⠖⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠰⠚⠋⠉⠉⠉⠉⠉⠉⠛⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⢤⡀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠙⣧⡀⠀⠀⠀⠀⢀⡤⠖⠃⣀⣠⡤⠴⠖⠒⠒⠒⠲⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⡀⠈⢳⡀⠀⣠⡶⢋⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠋⠀⠀⠀⢹⡄⠀⢻⣶⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⣰⠇⠀⠀⠀⠀⠸⣇⠀⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀ ⠀⢀⡿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡒⠶⠶⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣼⠹⡆⠀⠀⣿⡭⠶⠶⠶⠶⠿⣯⣤⣀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢩⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠑⠀⢰⡏⠀⣠⡤⠤⠄⠀⠀⠈⠉⠛⠷⣤⣀⠀⠀⢻⡀⠀⠀⣀⣼⡀⠀⠀⢻⡟⠳⣤⡀⠀⠀⠀⠀⢸⡇⠀ ⢠⣿⣧⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⠘⣇⠀⣸⣿⠛⠻⣿⣅⡀⣷⠀⠀⠙⢷⣄⠀⠀⠀⡇⠀ ⣸⠇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⣿⡏⠀⠀⠹⣿⣏⢹⡇⠀⠀⠀⠙⢷⡀⠀⡆⠀ ⡟⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣴⣿⡿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠛⢀⣿⡇⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠻⣤⡇⠀ ⣧⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠃⠀⠀⠉⠻⣿⣶⡄⠀⠀⠀⠀⢤⠀⢿⣇⡀⠀⠀⠀⠈⣉⡥⠴⢶⣦⠀⠀⠀⠹⠀⠀ ⢹⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡇⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠘⠓⠚⠋⠻⣦⠀⠘⠿⠷⠶⢾⡋⠁⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⡤⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠋⣀⣀⣠⢤⣄⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠸⣷⠀⠀⠀⢹⡿⣆⠀⠀⠀⠀⠀⣀⡴⠚⠉⣁⡤⠞⠁⠀⠀⢀⢴⡾⠛⠛⠿⣷⣤⣤⡶⠋⠀⢠⡀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⠀⠀⠀⢻⡌⠳⣄⡀⠀⠀⠻⠒⠒⠋⠉⠀⠀⠀⠀⡶⠃⣼⠃⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠁⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠹⣦⡈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠉⠓⠲⠦⠭⠉⠛⠛⠛⠛⣻⡿⠋⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⡶⣿⠉⠀⠀⠀⠀⠙⠶⠦⠤⠀⠀⠀⣠⡴⠞⠋⠉⢻⣆⠀⠀⢀⣤⣤⣄⣀⢀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣗⣛⠻⣿⣤⣬⣷⣾⣍⠉⣿⣏⣁⣿⣿⡾⠃ ⠀⠀⠀⢀⣀⣤⣤⡶⠾⠛⠛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀⣤⡴⠾⠛⠋⠉⠉⠀⠀⠉⠙⣿⣧⣤⣽⣿⣿⠿⠿⠛⠛⠉⠋⢀⠀ ⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠐⣄⠀⢻⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⠁⠀⢀⣀⣤⠤⠤⠤⠀⣸⠁ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢈⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠒⠚⠋⠉⠉⠉⠀⠀⢀⣠⠴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⡀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⣤⣤⠴⠶⠶⠚⠛⠉⠁⠀⣀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⡛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣾⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣮⠀⡟⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣇⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣰⠃⠙⢷⡀⠀⠀⣀⣤⠴⠒⠛⠋⠉⠉⠉⠉⠉⠉⠛⠒⠦⣤⣀⠀⠀⠀⠀⣠⠞⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢸⠏⠳⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠲⣤⠞⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣿⠀⠀⣹⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠻⣆⣀⡏⠀⠈⢳⣄⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⢄⣼⠃⠀⠀⠀⠀⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠈⠀⠀⠀⠈⢿⡀⠀⢀⡞⠈⠱⣤⡴⠚⠛⠉⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⣸⠃⢸⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢀⠀⠀⠀⠹⣦⡞⢁⡼⠟⠁⠀⠀⠀⢀⣀⣠⣤⡴⠚⠋⣼⠀⠀⠀⠀⠀⢰⠇⠀⣬⣧⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⠋⠀⠀⠀⠀⠈⣻⠟⠀⢀⣠⡴⠚⠋⠉⣁⣠⠴⠟⠀⢠⣧⣄⠀⠀⠀⠀⠀⠀⣰⠟⠋⢧⠀⠹⣷⡄⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠸⠃⢠⡶⠋⠙⠒⠒⠚⠉⠉⠀⣀⣠⣾⣿⡿⣿⡷⠀⠀⠀⠀⠸⢿⡌⠀⠸⡆⠀⢹⣽⡀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⡾⠁⠀⣠⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⢘⡿⣷⡿⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⡇⣴⣿⡿⠋⢻⣼⣿⣿⡇⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⡇⠀⠸⣿⢻⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⣻⡟⠙⢧⣀⣤⣿⣿⣿⠀⣀⠀⠀⢀⣤⠞⠁⠀⠀⠀⢸⠃⠀⠀⡿⢸⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⢳⢧⠀⠀⠀⠀⢠⡄⠈⢧⡀⠀⠀⠀⢿⡇⠀⠀⠉⠛⠛⣻⡿⠚⠁⢀⡴⢋⡠⠀⠀⠀⠀⢀⡏⠀⠀⠀⡇⣼⠀⠀⢀⡟⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⣆⠀⠀⠀⠀⠀⠻⣆⠈⢧⡀⠀⠀⠀⠹⣆⠀⠀⣠⠾⠉⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⣷⡏⠀⠀⣾⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⣸⡷⣌⡳⣤⣀⠀⠀⠈⠻⠟⠁⠀⠀⢀⡞⣰⠟⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣸⡼⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⣰⠟⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⢀⢟⣾⠃⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡿⠃⠀⠀⡿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠁⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⡼⠁⠀⠀⣸⠁⢰⠃⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⣿⠍⣿⠃⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣰⠃⠀⡿⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠙⠶⣤⣤⣀⣠⠖⠋⠁⠀⠀⣿⢰⡿⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡼⠁⠀⣰⠁⠀⠀⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⠞⠀⠀⢠⠏⠀⠀⠀⢀⣤⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡶⢤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⢸⡇⠀⠀⣼⠁⠀⠀⠀⠀⢠⣟⠀⠀⣠⠞⠁⠀⠀⣰⠏⠀⠀⠔⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣠⣾⣇⠀⢰⠃⠀⠀⠀⠀⢠⣿⡿⣆⡾⠁⠀⠀⢀⡴⠃⠀⣀⣠⠾⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠄ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣶⡿⠁⠀⠀⠀⠀⢀⣠⢾⣿⣿⣿⢦⠘⣿⠀⢾⠀⠀⢀⠀⠀⣸⡇⢰⡏⠀⠀⠀⠠⠟⣀⣀⣨⠿⠀⢀⡀⠀⠀⠀⠐⣿⠓⠶⠤⠄⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⢴⡾⠋⠀⢀⣀⣤⡤⠞⠋⠁⣸⣳⣆⣸⣾⣄⣼⣧⢺⠀⠀⠹⡄⠀⢸⡇⠸⠀⢠⠤⠄⠀⢀⡈⠉⠀⠀⠀⠀⢹⠲⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠁⠀⡀⠀⠀⠀⢠⡏⠈⠳⣾⣿⠿⠻⠟⡻⣇⠀⠀⠙⢦⡀⢳⡀⠀⠘⠷⣤⣤⡼⣿⣿⣓⠤⠤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣇⠀⠀⠀⢸⡇⣠⡼⠛⠈⠀⠀⠀⠙⠻⣆⠀⠀⠀⠙⠲⢽⣦⣤⣀⣀⣠⣾⡿⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⣟⢷⣣⡂⠀⠸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠉⠉⣡⡴⠟⠁⠀⠀⣀⡬⠿⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⢠⣌⠓⠛⠁⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠖⠚⠋⢉⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠦⣄⡨⠗⠀⠀⠀⠀⠀⢸⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠈⡟⢧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⠂⠀⠛⠂⠀⠀⠀⡼⢸⡇⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⣠⡴⠚⣿⡀⠀⠀⢀⡇⢸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⠶⠒⠚⠋⠉⠉⠉⠓⠒⠶⠦⣄⣀⠀⠀⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⢾⣿⠀⣠⡾⠋⠀⠀⣇⠉⠒⠚⠉⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀ ⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⡼⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣶⡏⠀⠀⠀⠀⠈⠓⠲⠖⠚⢩⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀ ⡖⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠈⠓⢤⣸⡇⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⢤⣀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣤⠞⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢄⡀⠀⠀⠈⠙⠳⠦⠤⣠⣇⣀⣀⣀⡀⠴⠿⠋⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠊⠁⠀⠀⠀⢀⣴⣳⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⠤⢤⣤⣤⣤⣤⡤⠤⠔⠚⠋⠀⠀⠀⠀⠀⠀⣰⠛⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠶⠚⣉⣠⡔⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠟⠻⠛⠛⠟⠻⢿⣿⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠬⠽⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⠉⠀⠀⠀⠀⠀⠒⠲⠦⣤⣄⡀⠀⠀⠀⠀⢷⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⠀⢧⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣷⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠒⠲⢤⣄⠀⠀⠈⠓⣾⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠐⠛⠛⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠙⢶⣤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠳⣿⠀⣠⠴⠒⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣄⣀⡤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠢⢤⣄⠀⠀⠀⠹⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢹⡞⠁⠀⠀⣸⠇⠀⠀⠀⠙⠳⢤⣄⣀⣀⡤⠏⣰⠛⣇⢀⣠⡤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠙⠲⣄⠀⠙⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠀⠀⣿⠁⠀⢀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣰⠏⠀⠛⠉⠁⠀⠀⠀⠀⡄⠀⠉⠻⢦⡀⠀⠀⠀⠈⠁⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣸⣿⠀⠀⠀⠻⡶⠤⣤⣤⣀⣀⣀⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡿⠀⠙⣆⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣤⣴⠿⢻⡀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⠲⠄⢀⣤⡿⠟⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣛⡒⠀⠀⠀⣰⠏⠀⠀⠀⣾⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⣴⠟⠙⠀⠀⠀⠀⢙⣷⡆⠀⠀⠀⠀⠀⠀⢰⣾⡟⠛⢿⣶⠀⠀⣰⠏⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢰⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣬⣛⣿⣿⠿⢿⣄⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⣰⣿⡁⠀⠈⠽⣿⣦⣼⡇⠀⠀⠀⠀⣸⠁⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠈⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⢿⣿⣿⣇⠀⣼⣯⣳⣄⠀⠀⠀⢹⡗⠂⠀⠀⠀⢰⡟⣿⣳⣄⠀⣀⣹⣿⣞⡗⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⢸⡘⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠾⣫⢾⣿⣿⣷⢿⡄⠀⠀⢺⡇⠀⠀⠀⠀⣿⣴⣿⡟⡿⠀⢾⣭⠿⠃⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⢸⡇⢣⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠃⠘⠻⣿⣟⣸⠃⠀⢀⡟⠀⠀⠀⠀⣤⣿⣿⣿⠻⠁⠘⠻⠋⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠈⡇⠘⣇⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡆⢸⠀⠘⣄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠸⡇⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠳⣤⡀⠀⠀⠀⠀⠐⠚⠛⠓⠀⠀⠀⢀⣤⠊⠀⠀⠀⣠⠞⠋⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⣧⠀⠀⠘⡆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⡀⠄⠠⠞⠋⠀⢀⣠⠴⠋⠀⠀⠀⣠⣴⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⡿⡆⠀⠀⢹⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠉⢿⡉⢹⡟⠓⠶⢤⣀⣠⠶⠋⠁⠀⠀⣀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡏⠀⢀⡇⣧⠀⠀⠀⢷⠀⠀⠀⢣⡀⠀⠀⠀⠀⢸⠐⠶⣄⠀⠀⠀⠀⠈⢧⠀⠙⡷⡄⠀⠙⣧⠀⠀⠀⣠⠞⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⠀⣸⠀⣿⠀⠀⠀⠘⡇⠀⠀⠈⣇⠀⠀⠀⠀⢸⢦⠀⠈⢳⡀⠀⠀⠀⠈⢧⠀⢦⠹⡆⠀⠘⣆⠀⣼⠋⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⢠⡇⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠀⢸⠈⣧⠀⠸⣇⠀⣀⠀⠀⡈⠳⣄⠀⠘⡄⠀⠹⡾⠁⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠁⠀⠀⠀⠸⠁⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⣸⠀⠹⡆⠀⢸⡆⢹⡀⠀⠈⠀⢌⠁⠀⠘⢦⡀⣿⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇⠀⠀⢀⡇⠀⠀⢷⠀⠀⡇⠀⠙⠳⢤⣀⠀⠓⠀⠀⠀⠉⢳⣄⠀⠀⠀⠠⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡼⠀⠀⠀⠀⢸⠇⠀⠀⢸⠇⢰⠀⢸⡇⠀⡇⠰⣖⡂⣐⣀⣑⣤⡀⠀⠀⠀⠀⠹⡆⠀⠀⠸⠀⠀⢀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠐⠒⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⡼⠀⠀⢠⡏⠀⣿⠀⠀⡇⠀⡇⠀⠈⠉⠉⠉⠉⠉⠙⢶⠒⠢⣤⠀⠀⠀⠀⠀⠀⢠⠏⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣸⠃⠀⢀⡾⠀⠀⡇⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡎⠇⠀⠀⠀⠀⢀⡴⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⣰⠃⠀⣠⡾⠁⠀⢀⡇⠀⠀⠈⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠓⢶⣯⣥⣀⣀⡀⠀⢀⡤⠞⣁⣤⠾⠋⠀⠀⠀⠘⠁⠀⡀⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠉⠉⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠈⠙⠳⠶⠶⠶⠴⠀⠈⠁⠀⠀⠉⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⣄⠀⠀⠀⠀⠀⣠⡤⠤⠒⠒⠒⠒⠒⠒⠲⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠖⠤⢄⣀⠀⠀⠀⠀⠀⠈⣧⠚⠳⣖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⠁⠉⠉⠉⠉⠉⠁⠒⠦⢄⡀⠀⠀⠀⠀ ⠀⡸⠀⠀⠀⠈⠙⢦⡀⠀⢀⡴⢻⣤⠴⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠈⡶⠋⠀⠀⢷⡀⢀⣠⠟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⢸⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⣟⠉⠀⠀⠀⢘⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⣾⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢀⠞⠀⢙⡆⠀⠀⠀⠀⠀⢀⠄⠀⡇⣰⠓⠠⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠄⠂ ⣿⠀⠀⢸⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⠁⠀⢀⠞⠀⠀⠀⠀⠀⠀⡜⠀⣼⡴⠃⠀⠀⠀⠀⠀⠈⢇⠈⠉⠉⠉⠀⠀⠀⠀⠀⢆ ⣿⡆⠀⠀⣇⠀⡇⢠⠟⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⠔⠃⠀⠀⠀⠀⠀⠀⢰⠃⣼⠟⠁⠀⣀⠤⠒⠒⠀⠀⠸⡄⢀⠀⠀⠀⠀⠀⠀⠀⠈ ⢸⡇⠀⠀⠸⡀⣧⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣯⠞⠁⠀⣰⡾⠗⠛⠋⠉⢻⡻⣿⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⠀⠀⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡼⡏⠀⠀⠀⠀⠀⠀⢷⢹⡀⢳⡀⡆⠀⠀⠀⠀⠀⠀ ⠀⠹⣇⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠵⠸⡄⠀⠀⠀⠀⢀⡿⢸⡇⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠁⠙⠦⣄⣀⡤⠞⣁⠜⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢦⣀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠉⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢻⠻⡀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢁⣼⡥⠖⠛⠓⠆⠀⠀⠀⣀⠤⠒⠂⢉⠁⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡆⠹⡄⠀⠀⠀⠀⠀⣤⣶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠔⢉⡀⠀⠀⠀⠚⠀⠀⢠⠄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠘⠆⠀⠀⠀⠀⠈⠉⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡔⠚⡁⠘⡄⢀⣼⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⢣⠀⢹⣽⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠉⠉⠛⠓⠒⢶⠒⠒⠊⠉⠀⠙⠄⣀⣀⠼⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⢦⣄⠀⠀⠀⠘⢷⣄⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣀⠀⠙⠳⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠒⠒⠛⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠾⠡⠤⢤⣈⣉⡙⠻⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡶⢦⣄⣠⠞⠉⠐⠂⢤⡀⠀⠀⠀⠈⠛⢿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢀⠀⠈⢷⣀⣀⡀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠙⡟⠺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠘⡆⠀⠀⠃⠀⠉⠙⠲⢄⡐⢤⣷⡄⠀⠀⠀⠘⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣆⠹⣄⠀⠀⢄⡠⠔⠒⣤⣝⠿⣯⠙⢲⣤⣄⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣧⡀⠀⠒⢺⠀⠀⠜⢁⠬⣷⡍⠀⠘⣦⣿⠉⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡻⡄⠈⠉⢆⠀⢇⠻⣄⣿⣿⠀⠀⠙⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⠹⡄⠀⠀⠑⢜⣆⠹⣿⠟⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠤⢄⡨⡉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡛⣆⠀⠀⠀⠈⠉⠁⠀⠀⣀⣨⠿⡇⠀⣀⡤⠖⠋⠉⠙⣶⣾⣍⣀⣀⠀⠀⢀⠉⠀⢌⠻⣧⣀⡘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣌⢧⡀⠈⠉⠙⠋⠉⠹⡙⡟⣆⠹⡉⠁⢀⣠⠤⢒⡺⠟⢛⣿⡗⠦⣠⡑⢦⠑⢄⠀⢣⠰⠹⡿⡲⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠷⣄⠀⠀⠀⠀⠀⠙⠧⠈⣷⠷⡄⠀⠘⠛⠡⡄⠀⢁⡼⡇⠀⠈⢿⡄⢡⠈⢆⠀⠆⢃⢱⢳⠘⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠧⣺⠏⢰⠃⠀⠀⠈⣷⠀⢣⠘⡀⢠⠸⠘⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠈⠦⣄⣀⣀⣤⣾⠎⠁⠀⡜⠀⠀⠀⠀⢸⡇⢸⡆⡇⠈⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠲⠤⢴⠀⠀⠸⡤⠶⡋⠙⡄⠀⠀⠓⢄⠀⠀⠀⠀⣧⣇⠃⠀⠈⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⢣⠀⢧⠀⠹⡀⠀⠀⠈⡆⠀⠀⢀⡟⣟⢸⠸⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠇⠀⠀⠈⡄⢸⠀⠀⡇⠀⠀⠀⢸⡀⠀⢸⣿⣇⢸⠞⠀⠀⣰⣧⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⢳⡞⠀⠀⣿⠀⠀⠀⠀⡇⠀⠘⢉⣿⢸⣦⡀⠀⡏⣿⢷⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡼⠀⠀⠀⠀⠸⡇⠀⠀⡏⠀⠀⠀⠀⢧⠀⠀⠈⣿⣿⣿⣧⠀⠇⢸⡄⠙⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡇⠀⣰⠁⠀⠀⠀⠀⣼⠀⠀⠀⠘⣿⣏⠹⣧⣸⡀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣀⣀⣠⡼⠀⠀⠀⠀⠀⢀⠏⢹⣃⠀⠀⠀⣀⡰⠃⠀⠀⠀⠀⠈⠻⠀⠈⠻⢿⣦⣝⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠤⠒⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣈⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⠿⢻⡹⠀⠤⡜⠓

⠀⠀⣀⠠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢊⠝⡁⠀⠀⠀⠀⠁⡢⠋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢗⠃⠀⠀⡀⢀⠔⠂⠁⢠⢸⢢⠀⣀⡠⠒⡆⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⢀⣠⠊⣷⡷⡄⠲⣄⠂⣬⡦⠊⡐⠀⡼⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠘⠋⠹⡿⠀⢿⢦⣽⠀⠀⡸⢸⠀⣰⠋⡏⢀⡔⠁⢀⣤⠤⠄⡀⠀⠀⠀⠀ ⠀⠀⠨⣀⠄⠈⠛⠁⡠⢔⢁⣿⡹⡘⠰⢉⢅⡠⠄⠊⠀⠙⢢⣌⣱⡀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⡍⢀⣣⣿⢿⠛⠁⠀⡎⡩⠒⠢⡀⠀⠀⠀⢳⢡⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⢸⡟⡟⠸⠀⠐⠊⣹⢸⠀⠀⠘⡀⠀⠀⠘⡏⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢌⠁⠡⡆⠀⠀⡰⠘⡘⠀⠀⠀⡇⠀⠀⠀⡇⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠑⢱⠎⢣⠀⠓⡀⠀⠀⡾⠀⠀⠀⣧⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⡞⠀⡆⠀⢱⠀⠀⠀⡆⣆⠀⣷⠻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠀⠀⣷⠀⡇⠀⠈⠀⠀⠀⠱⡏⢢⣻⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠇⠀⠀⣏⣠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠊⠙⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠤⠤⠄⠃⠐⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠉⠁⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣼⢿⣇⣄⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠘⠸⢿⣿⡗⢲⠄⣀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠙⠛⠛⡳⠧⢤⠀ ⠀⠀⠀⢠⣼⣿⣲⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⡿⢦⡀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠻⣯⠷⢌⡳⡌⣟⣲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠙⡆⠀⠀⠀⠈⠈⠀ ⠀⠀⠀⠀⠀⠈⢳⡄⠉⣽⢢⣉⣳⣬⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⠘⢧⣀⣻⡟⢯⢿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠈⠿⣞⣷⣷⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢠⡇⣀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢹⡌⣿⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⣿⠀⠀⠀⠀ ⢀⣤⣤⠤⠤⠤⠤⢴⠒⠒⣛⡇⠀⠀⠀⠀⢻⡙⣧⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠉⠛⠢⣤⣀⠀⠀⠀⡸⠃⠀⠀⣿⠀⠀⠀⠀ ⢸⣯⣧⡀⠀⠀⠀⠈⠳⣄⠈⢻⡄⠀⠀⠀⠀⡇⣿⣦⠀⠀⠀⣱⠹⣇⠀⠀⠀⠀⣰⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠐⣿⠀⠀⠀⠀ ⢸⠃⠏⣿⣄⠀⠀⠀⠀⠈⢧⠈⢧⠀⠀⠀⢠⢹⢸⣾⢦⠀⠴⠃⠀⢸⢣⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⡋⠀⠀⠀⠀ ⣾⡄⠀⣿⠉⢦⡀⠀⠀⠀⠈⢳⣼⡄⠀⠀⢨⣦⣾⠃⠈⢳⡄⠀⠀⡸⠀⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀ ⢹⡇⠀⢹⢰⡤⢽⡀⠀⠀⠀⠀⢻⡇⠀⠀⠸⣿⠏⠀⠀⠀⠹⣆⠰⠃⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂ ⠈⢷⠀⠀⣧⢧⡀⠹⡄⠀⠀⠀⠈⡇⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⣷⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠹⡌⢷⡀⠹⡆⠀⠀⠀⢳⠀⠀⠈⢸⢘⡶⢦⣀⣰⡗⠛⠁⠀⣄⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣳⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠹⡀⢿⣦⡁⠀⣠⠴⣿⠳⣦⣀⣿⣼⠁⠀⠀⠙⣷⣦⠀⠰⣜⣆⠙⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣶⠒⢲⣖⠀⠀⠀ ⠀⠀⠀⠈⠷⡀⠙⢦⠙⠿⠞⠁⠀⢸⠀⠈⣿⢿⣿⣶⡀⠀⠀⠈⡇⠀⠀⠈⠉⢠⡏⠁⠉⠉⠉⠓⢒⡲⠚⢛⢋⡉⣿⠉⠀⠀⠀⠀⠀⢰⣿⣯⢀⡟⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⠈⠳⣄⠀⠀⠀⢹⠀⠀⣬⣾⠀⠫⣽⣿⣭⣸⣱⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢙⣋⣤⣀⣿⣀⠠⠤⢠⡀⢰⣿⠏⢩⠟⠀⠀⢀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠱⢄⡈⠲⣄⡈⡏⠀⣠⠏⢻⠀⠀⠀⠉⢙⡿⡿⠀⠀⠀⠀⣿⠦⢶⣦⣤⣤⣴⡶⠶⢛⣋⣹⣿⠿⠿⠯⠉⠋⢹⣿⣷⡴⠋⠀⠀⠀⢈⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠼⠿⠚⠉⠀⠈⢷⠀⠀⢀⣨⠿⠃⠀⠀⠀⠀⠈⠀⠉⠍⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⣠⠾⠟⠉⠀⠀⠐⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⡤⣖⣛⣉⣩⣭⣷⣤⣶⣿⣿⡿⠋⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⢤⡿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠀⡼⠋⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⡴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⡿⠁⠛⢀⡞⠀⠀⠀⢠⢀⣠⠤⠤⣀⠀⠀⠀⣠⠏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⣠⠞⠁⠀⢠⠏⠀⠀⢀⡔⠋⠀⠀⠀⠀⣿⠀⠀⣰⠋⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡴⠃⠀⠀⢀⡏⠀⠀⢠⡇⠀⠀⢀⡆⠀⢸⣿⣧⢰⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⣾⠀⠀⠀⣼⠀⠀⠀⠂⣇⠀⣤⠇⢹⠁⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⠀⠀⢸⢻⣷⠂⠀⠀⢸⠀⣿⠀⠀⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⢸⣿⡇⠀⢀⣾⡾⠁⠀⠀⣿⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣦⡈⠈⢷⣷⣶⣭⠞⠁⠀⢀⡼⢹⠘⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠹⣦⡘⠁⠀⠀⢀⣠⠴⠋⢀⡟⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢧⠋⠹⣶⠶⠯⠿⠷⠶⠊⠉⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡠⠤⠄⠀⠤⠴⢊⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠲⠤⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡚⠛⠉⠉⠉⠛⠓⠦⣄⡀⠀⢀⣠⢞⡥⠴⠾⠷⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣤⠽⠛⢉⣀⡤⠤⠶⠶⠶⠶⠤⢤⣀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠞⠉⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠟⠦⣄⡀⠀⠀⠀⣸⢇⡞⢁⢴⣫⠤⠶⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠈⠉⠛⠛⢛⣵⣾⣴⡗⣩⠴⠒⠛⠒⠦⣄⡀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠳⡄⠀⠀⠀⠀⠀⢻⠢⡀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠻⡅⠀⠀⢀⠀⠀⠀⠙⠲⣄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⢦⡀⠀⠀⠀⣸⠀⢱ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⡴⢦⡀⢻⣦⠀⠈⢧⠀⠀⠀⠀⠈⢧⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠙⠲⢶⡶⠁⠀⢈ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠙⡄⢿⣇⠀⠈⣧⠀⠀⠀⠀⠀⢳⡄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⣸ ⠀⠀⢰⡏⠙⣧⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢹⠘⣿⡄⠀⡟⢧⡀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠸⡇⠀⠘⢧⡀⠀⠀⣷⠀⢷⣀⣀⣠⠃⠀⠀⣙⣾⠧⣤⣝⡲⣤⣀⠀⠘⣷⣤⡀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀ ⠀⠀⠀⢻⡄⠀⠈⠳⣄⠀⣻⡄⠀⠀⣌⡙⢷⣤⣾⣯⣤⡀⠀⠈⢳⡄⠉⠙⠓⠛⠦⣽⣷⣤⣄⣀⠀⠀⠀⠉⠉⠛⣛⣩⠽⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⢈⡿⠋⣧⠀⠠⣬⣛⣿⡿⢃⣤⠶⠿⣦⡀⠀⢻⡄⠀⠀⠀⣼⢏⣨⣽⣦⠉⠉⠙⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣦⡟⠀⢠⣏⠃⠀⠈⢙⡟⢠⣿⣧⣀⣀⡿⢧⠀⠈⣷⠀⠀⣼⣳⢻⡅⢀⣿⡇⠀⠀⢸⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⠙⢦⠀⠀⢸⡇⢸⣇⣽⣿⡿⠀⢸⠀⠀⢸⡆⢀⡏⣿⣠⣿⡏⠈⡿⠀⠀⠀⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⢧⡈⠳⣄⠈⠓⢬⡿⢻⡿⠃⠀⡾⠀⢀⣠⣧⡼⢧⣿⣙⡟⠀⣰⠃⠀⢀⣠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠑⢄⠈⠳⣄⠀⠈⠙⠛⠛⠛⠓⠚⢩⡅⠀⠶⠀⠈⠉⠛⠛⠓⠒⠋⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢳⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠂⠀⠀⠀⠀⣰⡛⣆⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⣧⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⣡⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⣄⡀⢀⣀⣤⣏⡀⣸⠉⠉⠙⣿⠓⠒⠶⠶⠶⠶⠶⠶⣖⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡽⣋⡽⣾⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢋⡞⠁⠀⠀⠙⣦⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣣⠞⠀⠀⠀⢠⠀⢸⡏⠀⠀⠀⠀⠀⢠⡆⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠴⢶⣾⣯⡉⠁⠀⠀⠀⣠⠏⢀⡾⠓⠶⢤⣀⠀⠀⠀⡇⠀⠀⢈⣧⣸⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⢋⡥⠞⠋⠉⠉⠉⢙⣓⣲⠖⠋⣿⠶⠋⠀⠀⠀⠀⠈⢷⠀⠀⣷⠀⠀⠀⢻⡏⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢏⡴⠉⠀⠀⢀⣴⡖⣻⠟⠛⠻⣆⣠⡬⠤⠥⣤⡀⠀⠀⢀⡾⠀⣀⣿⠀⠀⠀⠈⢷⡀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣾⠀⠀⠀⠀⠘⠦⣝⡛⠶⢤⣤⣟⣁⠤⠶⠶⢶⣿⢀⣤⠟⠛⣽⠋⢻⡇⣄⠀⣾⠻⣷⢤⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢿⠈⣿⠀⠀⠀⠀⠈⠻⡅⠀⣀⡸⠆⠈⣿⠉⢳⡇⠀⠘⣦⣀⣤⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠿⢤⣤⠴⢊⣩⡙⣿⣄⣻⣄⣀⣀⡿⢤⣤⣄⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣭⣓⡒⢶⣶⣶⡶⠟⠉⠉⠲⣤⣤⠖⠋⠉⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠦⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢶⠒⠚⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠈⠛⠛⠛⠛⣻⢿⣛⠛⠛⠛⠛⠛⠋⠁⢀⣠⡴⠾⣉⠁⠀⠀⠀⠈⢳⠀⢻⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⣠⡿⠁⠀⢻⣆⠀⠀⠀⣀⡴⠚⠉⠀⠉⠒⢌⢳⡀⠀⠀⠀⠀⡇⠘⣇⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢾⠀⠀⠀ ⠀⠀⣴⠟⠀⠀⠀⠀⠹⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢳⣷⠀⠀⠀⠀⣟⣠⠼⣆⠀⠀⠀⢻⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠹⡷⣌⠀⠀⠀ ⠀⢺⠏⠀⠀⠀⠀⢀⡴⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣀⠴⠋⠀⠀⠘⢷⡀⠀⠀⢳⡀⠀⠙⠢⡄⠀⢀⡔⢲⠀⢻⠈⢧⡀⠀ ⡰⠃⠀⠀⠀⠀⡴⢋⣉⡬⠭⠭⣗⣦⣄⠀⠀⠀⠀⠀⠀⢸⣇⡴⠁⢀⣀⠄⠀⠀⠀⠙⢦⡀⠀⠙⠦⢀⣤⠾⠦⡼⠀⢸⠀⠘⡇⠀⠹⡄ ⠓⠒⠒⠒⢠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⢸⠏⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠲⣤⠀⡴⣟⣢⠀⡇⠀⡄⠘ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡈⠢⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⠁⠀⠀⠀⡇⠀⠸⡀ ⠀⠀⢠⠇⠀⠀⠀⠀⣀⣴⠶⠛⣉⠽⢩⠏⠀⠉⠳⢴⣼⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣷⣶⣤⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢳ ⠀⠀⡎⠀⠀⢀⣠⡾⠋⠀⣠⡾⠁⢀⡏⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣾⣿⠿⢿⣿⣿⣦⠈⠙⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠂⢸ ⠀⢸⠁⠀⡰⣿⠏⠀⢀⣼⠟⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⡇⠀⠀⣽⣿⣿⣤⡀⠀⠈⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻ ⠀⠘⠀⡜⣱⠃⠀⢀⣾⠏⠀⠀⢸⣿⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⠀⣰⣿⣿⢿⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘ ⠀⣦⡜⢠⠃⠀⠀⡞⡼⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠾⣿⡏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀ ⠀⣿⠀⡞⠀⠀⣼⢱⠃⠀⠀⠀⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⢀⣀⡾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠁ ⠀⣧⠀⡇⠀⠀⣯⣼⠀⠀⠀⠀⣿⣧⠈⢇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀ ⠀⠸⡆⣇⠀⠀⣿⢿⠀⠀⠀⠀⢹⣿⠀⠘⣿⣶⣶⣶⠾⠛⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀ ⠀⠀⠹⣿⡀⠀⢹⣸⡀⠀⠀⠀⠀⢻⣇⠀⡇⠘⠙⢧⠀⠀⠀⠐⠃⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⢸⠓⠒⠤⢤⣀⡀⠀⠀⠀⣰⠏⣠⡆⠀ ⠀⠀⠀⠘⢷⡀⠀⢻⣧⠀⠀⠀⠀⠀⠙⣼⠁⠀⠀⠈⠳⣄⡀⠀⠀⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀⢸⠀⢰⠢⠤⢄⣉⠓⠢⣤⠋⣰⣟⡔⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠙⢧⣀⣀⣠⠤⠶⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠛⠁⠈⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢉⡷⢁⣼⣿⠟⠀⠀ ⠀⠠⣶⠖⠒⠒⠒⠛⠉⢉⣉⣀⡤⠤⠖⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⡰⠋⡴⢋⡾⠋⠀⠀⠀ ⠀⠀⠈⠛⢦⣀⠀⠛⢧⡈⠻⠂⠐⠂⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⢰⠇⠀⡇⠀⣠⠞⠡⠊⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⠤⠽⠷⠶⠶⠿⠶⠶⠤⣀⡀⠐⠷⠀⠀⢠⣭⡓⠲⠦⢤⣀⣀⡀⠀⠀⣀⣠⠴⠚⢹⠀⢰⡷⠚⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⣠ ⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡀⠀⠀⠀⠉⠀⠀⠀⠃⣠⣿⣿⡿⠟⠉⠀⠀⢀⣾⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡈⠁⠀⠀⠛⠀⠀⠰⠀⣴⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣄⣀⣀⣀⣀⣠⡞⠉⠀⠀⠀⠀⣠⠶⢋⣠⠔⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⣻⡿⣿⣗⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠀⠀⣰⣻⡲⢾⣷⣷⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⠀⠀⠀⠙⣯⣷⣾⣷⠿⠷⠿⣄⠀⠀⠻⣷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⣟⠁⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⣀⣀⣬⠷⣤⣀⣈⡇⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⢳⡀⠀⠀⣠⣾⡿⠋⢀⣠⢴⡒⠛⠿⢤⣀⠀⠀⠀⠀⠉⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⢳⢀⣴⡿⠃⡠⠞⠻⢤⣀⠳⣤⣄⣀⡀⠉⠉⠛⣒⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠳⠄⠀⢨⡿⢋⡴⠋⠀⠀⠀⠀⠈⠓⠿⣆⠀⢹⡿⢿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠳⡄⠀⣰⡿⣡⠞⠐⣦⠖⠚⣿⡶⣶⣄⠀⠀⠀⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠈⣿⣿⡞⠁⠈⣿⠃⠀⢸⣿⠀⣿⣿⣧⠀⠀⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⡿⠿⡇⠀⠈⡇⠀⠀⠀⢻⡻⣿⣿⣿⠀⠀⠈⠺⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠉⣉⣑⡒⠦⣄⣀⠀⢀⣄⠀⢰⠖⢦⡷⠄⡇⠀⠀⠹⣄⠀⠀⠀⠳⢽⣻⡏⠀⠀⡀⠒⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠚⠉⠁⠀⠀⠈⢻⡀⠉⢻⡈⠳⢼⡆⠀⠱⣄⡇⠀⠀⠀⠈⠳⠤⠤⠤⠖⠋⠀⠀⠀⢈⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢠⠎⠀⠀⡠⠚⠉⠉⠉⠒⠳⡄⣀⣷⡄⠀⣿⠒⢦⣻⣇⠀⠀⠀⠀⠀⠒⢶⣤⢤⣤⣖⣒⣏⣁⣀⣀⣀⣀⡤⠤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡏⠀⠀⡼⠁⠀⣤⠤⠖⠒⠒⣿⠁⣤⠟⢲⣳⡀⢀⣿⣯⣗⢦⣀⠀⠀⠀⠀⣿⡛⠻⢭⣉⡉⠉⣖⡋⠩⢉⣽⣿⡷⣖⡪⢭⡓⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣸⠀⠀⢰⠃⠀⠀⠈⣳⡀⣠⠞⢻⡟⠙⠦⢿⡟⣻⣉⢸⠀⠈⠓⠮⣓⢦⣄⣠⣾⣧⣀⠀⠀⠉⠓⠢⢭⣙⠛⠛⣯⣿⡷⡧⠴⠃⠀⠀⠉⠓⠢⣄⣀⠀ ⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⢿⠀⠀⣸⠀⠀⠀⢠⡇⠉⠁⠀⣾⣿⣿⡆⢠⣷⣿⣿⣿⡀⠀⠀⠀⠈⠙⣾⣿⣟⢧⣈⠙⠒⢤⣄⡀⠀⠀⢹⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡷ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⣤⡀⢳⡀⠀⢰⡿⣿⡟⠁⢀⡟⣿⣿⣏⡇⠀⠀⠀⠀⢰⠋⣿⡜⣆⠈⠓⠖⠋⠀⠈⠛⠢⢤⣇⣀⣀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠧ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⣿⠙⠒⠽⠄⢸⡆⠉⠀⠀⢯⣇⢿⣿⣿⣧⠀⠀⠀⢤⣯⣰⡿⣷⣸⠆⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠀⣰⡇⠀⢸⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⢀⣻⡄⠀⢠⣏⣿⠿⠿⣯⣼⠀⠀⠀⣼⠁⠈⠁⠘⠉⠙⠒⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠾⠉⢀⡴⣿⠁⠀⢸⠀⠀⡇⠀⠀⣿⠀⠀⠀⢰⠏⠉⠁⠀⣾⡏⠀⠀⠀⡏⠸⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣄⠉⠉⠉⣠⠃⠀⠀⡞⠀⢸⠁⠀⢠⡇⠀⠀⠀⡞⠀⠀⠀⢸⢻⡇⠀⠀⠀⡇⢸⠇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠈⠓⠒⠚⠁⠀⠀⡰⠁⢀⡞⠀⢀⡟⠀⠀⠀⢠⠇⠀⠀⠀⢸⠘⡇⠀⠀⠀⢹⣸⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⡀⠀⠀⢀⣠⠞⠁⣠⠞⠀⣠⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡆⣇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠲⠾⣍⣠⣴⡾⠥⠖⠋⠀⠀⠀⠀⠀⠀⢿⣀⣀⡀⣀⣀⣧⠈⠓⠒⠒⠒⢻⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠒⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⠤⣀⠀⠀⠈⡕⢤⡒⠂⠉⠀⠀⠀⠀⠈⠉⠥⠒⠒⠒⠒⠂⠄⡀⠀⠀ ⢀⠁⠀⠀⠑⡤⠊⢹⠁⡹⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠣⡀ ⢸⠀⠀⠀⡐⠁⠀⠀⢇⠀⢀⠗⡄⠀⠀⠀⠀⡀⡄⣀⡀⠀⠀⠀⠀⢀⣀⠅ ⢸⠀⢠⢠⢁⠀⠀⠀⠈⠆⠁⡠⠁⠀⠀⠰⢠⠟⠀⣀⠀⠸⠈⠉⠁⠀⠈⠂ ⢸⡀⠈⣸⡌⠀⠀⠀⠀⠘⠈⠀⠀⠀⢀⡷⠉⡲⠚⠒⠲⣶⢷⠀⠀⠀⠀⠀ ⠀⢧⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠀⠀⠀⡇⡆⢺⠀⠀⠀⠀ ⠀⠈⠳⣀⢠⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠁⠒⠎⠊⠀⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⢂⠀⠀⠀⢐⣉⡾⠊⠉⠀⡀⠔⠂⠩⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠢⠀⠀⠈⠹⠀⠀⠀⠀⠀⠁⠀⠀⡠⡇⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢑⠤⣀⣀⠀⠀⠀⣈⠇⠠⠐⡾⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠸⡀⠀⠀⠀⠏⠀⠀⠈⠒⠊⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠑⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠈⠦⣀⠃⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠚⠓⠂⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀

⣿⡏⠎⣴⣿⣿⢟⠏⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⢁⠀ ⣿⢻⠮⠾⠟⠛⡎⠀⠀⠀⠀⢈⠝⠐⣲⠤⠤⠤⠤⠤⠤⢤⢶⢀⠋⢁⠞⡴⠃⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡰⠁⣠⣾⣥⣤⢤⣀⣀⢀⣀⠎⠀⡟⣐⣡⠞⠀⠤⢤ ⠀⠀⠀⠀⠀⡇⠀⠀⢀⠞⣢⣾⠃⠀⣿⣿⠇⠹⣆⢁⠎⢀⣠⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⢎⡜⢛⣷⣦⣼⣿⣿⡎⠀⡱⣫⠔⠋⠁⠁⠀⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⣎⠎⠀⢹⢟⣏⠙⠃⡼⠁⠚⠉⠀⠀⠀⠀⠀⠘⠉⢹⣿⣧⠀ ⠀⠀⠀⠀⠀⡇⢰⡏⠀⠀⡞⢀⠈⠉⠉⠀⠀⢀⠃⠀⠀⠀⠀⠀⣄⣠⣾⣿⡟⠀ ⠀⠀⠀⠀⠀⢹⢸⠀⠀⢰⠃⠈⣄⠀⠀⠀⢀⢌⣀⣀⣀⠀⠠⠀⡿⠻⠿⣿⡇⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠴⠭⠓⠒⠒⠚⡇⠀⠀⠄⠀⠀⠀⠑⠲⠤⠮⠄⠀ ⢭⡭⠒⠒⠤⢄⣀⡠⢶⡹⡄⠀⠀⠀⠀⠀⠀⠁⣀⡀⠤⠒⠢⡀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⢀⡴⠊⡁⠀⠀⢳⠙⢦⡀⠀⠀⠀⠀⠀⡇⠀⡠⠐⠒⢱⡀⠀⠀⠀⠀⠀ ⠀⢀⠔⠁⠀⡜⠁⠀⠀⠈⡇⠀⠈⠲⢄⡀⠀⠀⢇⡘⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐ ⡠⠃⠀⠀⡼⠀⠀⠀⠀⠀⣧⠰⠀⠀⠈⢏⠒⢦⢄⣀⣁⣒⣂⣉⣠⡤⠖⠂⡠⠀ ⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⢼⡀⢷⡀⠀⠘⣄⠀⢆⢸⣿⣿⠿⠋⠁⠀⣠⣞⡡⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢳⣄⠀⢀⣀⣠⠤⠴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠦⣤⣀⣀⣠⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠓⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⢿⡊⠉⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠙⠳⢦⡀⠀⢀⡴⠟⣿⠴⠞⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢑⡶⠋⠀⠀⢹⡆⠀⢀⣠⠿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀ ⢸⠁⠀⠀⣴⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢻⡚⠉⠁⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⢸⠀⠀⠀⣿⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢠⡏⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠼⠇ ⣿⠀⠀⠀⣿⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⡤⠴⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡞⣰⠟⠀⠀⠉⠉⠉⠛⠳⡖⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⢧⠀⠀ ⣿⠀⠀⠀⢹⡀⠀⣾⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢀⡏⢀⣾⡿⠋⠀⠀⠀⠀⣀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀ ⢹⡇⠀⠀⠀⡇⠀⡏⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⢠⡾⢯⣀⣀⣠⢴⣚⣉⣀⣤⣤⣄⣘⣇⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⢸⣷⠀⠀⠀⢹⡀⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠏⠁⠀⣨⡽⠗⠛⠉⠉⠉⠉⢿⣻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡆⠀⠀⠈⢧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⢰⢻⡆⠀⠀⠀⠀⠀⠀⠀⣧⢻⡄⠘⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⡀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢸⡌⢧⠀⠀⠀⠀⠀⠀⢠⡿⢸⡇⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⣄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠳⠈⠳⣄⠀⠀⢀⣠⡿⢁⡼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠿⣦⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠥⠴⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠶⣤⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠒⣶⢟⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠳⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣼⡿⠛⠉⠀⠀⠉⠀⠀⠀⣠⠴⠚⠉⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠻⣄⠀⠀⠀⠀⠀⠤⠬⣟⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⣄⠀⠀⠀⠀⠋⠀⠀⠀⡜⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡅⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠞⡋⠈⢧⠀⢀⣼⠃⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢷⡀⠈⣿⣹⣧⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠉⠙⠲⠶⠶⠦⠤⠤⣤⢤⡤⠤⠶⠒⠋⢧⡀⠀⠁⠀⣼⠟⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣷⡀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⣦⡀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣶⣄⠀⠀⠀⠀⠈⢿⣦⡀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣄⣀⠀⠀⠙⠿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⡤⠬⢽⣳⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⠋⠀⠀⢀⣀⣠⣤⡤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣰⠃⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⢀⣼⠁⣰⠏⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡾⢃⡴⠋⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠇⠀⠀⣀⣠⡤⠶⠛⠒⠛⠓⠛⠒⠒⠒⠶⠤⣤⣀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠶⠒⠒⣲⠖⠒⠲⠤⣤⡀⠀⠀⠀⠀⢸⠀⢀⡟⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢀⡞⠁⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⢸⠀⣼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀ ⠀⠀⠀⡿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀ ⠀⠀⢀⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⣸⢡⡏⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀ ⠀⢀⡏⢸⠀⠠⠤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⢀⠞⠀⢸⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⢸⠀⢲⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠘⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣼⡟⠁⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢻⡇⠉⠛⠲⠤⣤⣀⣀⣀⡀⠀⠀ ⡀⠀⠀⢸⣴⡿⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠘⢿⣿⣏⢣⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡀⠀⠀⠉⢻⡅⠀⠀ ⣧⠀⠀⣸⠉⠃⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⠧⠄⠀⠀⠀⠈⡿⠀⠀⢸⡇⠀⠀⠀⠀⢻⡀⠀ ⠙⣧⣴⠿⠶⠛⠛⠓⠂⠀⠀⣴⠛⠛⠓⠶⠄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠓⢲⡄⠀⠀⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠈⠧⠀ ⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠶⠾⠄⠀⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⣉⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣀⣙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣺⣻⣶⣄⣀⠀⠀⠀⠀⠀⢻⣰⠛⠉⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣠⡾⠃⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠛⠉⠉⠀⠀⠉⠛⣦⡀⠀⠀⠘⡇⠀⠀⠀⠀⠘⡇⠀⢀⡴⠞⠛⠉⠉⠉⠉⠛⠻⠿⣥⣀⠀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢳⠶⢤⣄⣀⡀⠀⠀⠘⢃⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣉⠀⠀⠀⠀⠀⠀⠀⣠⢦⢆⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣇⠀⠀⠀⠉⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⢠⠾⠟⣡⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣏⣀⣰⣿⣀⣀⣀⣠⣿⣿⣻⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⢶⣶⣖⣚⣋⣁⣀⣀⣀

⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠫⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢏⢢⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣨⠒⡊⠁⠀⠀⠀⠀⠀⠉⠂⡴⠁⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠛⢤⠁⠱⢄⣀⠠⠄⠀⠀⡜⠀⠀⡀⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠄⠀⠳⡡⠊⡀⠠⢤⡶⢊⡃⠀⠐⢁⠷⠐⣄⠀⠀⢀⠤⠂⠀⠀ ⠀⠀⡎⠀⡜⠀⠀⠈⡰⠉⢁⠉⣡⣴⣿⡿⠀⠀⢹⠁⠃⢸⣤⠊⠀⢀⠤⠂⠀ ⠀⠀⢇⠀⡇⠀⠀⠀⡇⠀⢨⡾⣋⣿⡿⠀⠀⡠⠃⠀⡄⠸⠇⠀⡰⠁⠀⠀⠀ ⠀⠀⠈⢆⠘⠀⠀⠢⡰⡀⠈⢃⢀⠽⠋⡀⡨⠂⠀⡐⠀⢰⠇⢠⠁⠔⠁⠀⠀ ⠀⠀⠀⠀⠁⢢⠀⡠⠋⠘⠂⠀⠉⠀⣼⠊⠀⠀⠔⠀⠀⡞⠀⠆⡌⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⡇⠢⡀⠀⠀⡀⠴⣾⠇⠀⢀⠊⠀⠀⠜⠀⠔⠸⠀⠀⡔⠁⠀ ⠀⠀⠀⣀⢀⡜⠀⠀⠈⠉⠉⠀⢰⢸⠀⠠⠁⠀⢠⠊⠠⠊⢀⠃⣀⠔⠁⠀⠀ ⠀⠀⠀⢣⠉⠀⠀⣰⠀⠀⠀⣰⣧⡺⡀⡆⠀⢠⢟⠜⠀⡠⠁⡄⠂⠀⢠⢄⡀ ⠀⠀⠀⠀⠈⠒⠾⠥⠀⠒⠁⡞⢾⡧⡷⡇⠐⡈⡄⠰⣂⣠⣤⣀⡸⠒⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢿⣄⠀⡷⠋⠀⠀⠙⢄⠀⠙⠒⣀⠾⠀⡑⠄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡄⠂⠁⠀⣸⠄⠀⠀⠀⠀⠉⣉⡉⠰⣄⠎⠀⠀⠀⠱⠀⠀ ⠀⢀⠤⠐⠒⠒⠂⠬⢀⡀⠀⠇⡄⠀⠀⣇⡠⠊⢹⠂⢊⣼⠀⠀⠀⠀⠐⡆⠀ ⠄⠁⠀⢀⠠⠤⠠⠄⣀⠈⠙⠠⡀⠀⠀⢹⠁⠀⠀⠀⣰⠇⠀⠀⠀⢀⠌⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡈⠑⠂⠸⠤⠄⠐⠋⠂⠀⠀⠀⠄⠂⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⡀⠀⠤⠒⠁⢀⢴⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⠀⣀⠀⠀⠀⢀⣀⡠⢔⡡⠂⠀⠀⠀

⡻⠿⣟⣿⣽⣿⠟⠉⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣠⡤⠶⠚⠛⠓⠒⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣷ ⡄⡀⠉⠛⢻⠏⠀⠀⢀⣼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣋⣤⠾⠋⣁⣤⠴⠒⠚⣋⠙⠒⢦⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯ ⠾⣥⡐⣴⣿⣄⠀⣠⠟⠁⠈⠉⠙⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⣰⣿⣿⣿⣿⠶⠋⠁⢰⠀⢀⡾⢿⠀⠀⠀⢱⡀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿ ⣶⡾⠛⠉⠀⠀⢠⡟⠀⠀⠀⢦⡀⠀⠀⠈⠙⢶⣄⢰⡆⠀⣠⣶⣻⣶⠀⢻⣦⣴⣿⡿⠛⠁⠀⣀⣀⣰⡋⣠⠞⠀⠋⠀⠀⡀⢸⡇⠻⠋⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⠟⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠱⡄⠀⠐⣆⠀⠙⣿⣷⣤⣿⣿⠿⠿⠟⢉⡀⠙⠋⠀⠠⠴⣾⠋⠀⠀⠉⠳⢦⣀⣀⣀⡴⠃⢠⣧⠖⢫⠋⣼⠃⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⡱⠄⠀⢹⠀⠀⠻⡀⠀⠘⢟⣿⡾⠟⠛⠛⠷⣿⣤⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠻⡌⠡⡀⠀⠈⠁⢀⡞⢀⣿⡀⠀⠀⠀⣠⣶⠟⠙⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⡿⡄⠀⢧⠀⠀⠈⣷⡀⠀⠳⣤⣴⡟⠁⠀⠀⠀⠀⠀⠁⠹⣧⠀⠀⠀⠀⣇⢠⣾⣿⣛⣦⡀⠀⠹⣤⢵⡄⠀⠀⢸⡃⢸⡹⣧⠀⠀⢸⣟⠁⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢻⣧⠙⠲⡘⢧⡀⠀⠿⠳⢤⣤⣾⠋⠀⠀⣀⣤⡤⢤⡀⠀⠀⠈⢷⠀⠀⠀⣻⡼⠓⠻⢿⠟⠛⠒⠒⢛⡙⠳⢄⡀⠘⣇⠈⣧⠘⢧⡀⠀⠙⠳⢤⣤⡼⠟⣹⣏⢙ ⠀⠀⠀⠀⠀⠀⠀⢿⣳⣄⣙⢦⡉⠀⠀⠀⠀⣸⡏⠀⢀⣾⠛⣻⣧⣤⡿⡆⠀⣀⣨⢇⡤⠚⠁⠀⠀⠀⠈⠷⠀⠀⠈⣿⠉⠀⠀⢹⡀⠈⠳⢽⣧⡈⠛⠦⠤⠤⠤⠞⣃⡴⠏⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡉⣁⣭⡧⠤⢤⣄⣿⠁⠀⢸⣿⠀⢿⣿⡯⠟⠛⠉⠁⠀⠈⠀⠀⠤⠄⠀⠀⣠⡤⠒⠒⠚⡏⠀⠀⠀⠀⢻⡅⠀⠀⠀⠉⠓⠒⠒⠒⠒⠚⠉⠀⠁⠀⠀ ⠀⠀⠀⠉⠉⠻⣦⠀⠀⣠⡿⠋⠁⠀⠀⠀⠻⣿⣇⠀⣠⠿⠛⠉⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⢁⣠⡀⣾⠀⣷⠀⠀⠀⠀⢸⣿⣻⣭⣭⡉⠙⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢀⣠⠏⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠁⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣀⣤⠖⠋⣀⣴⣾⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⢸⢺⠁⠹⢦⣉⡉⠻⢯⡀⠀⠀⠀⠀⠀⠀⠀ ⠉⡛⠖⠚⠋⠁⢀⣼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⢻⢹⠀⠀⠀⠀⠀⠀⠙⠳⢶⡒⠋⠁⠀⣇⣴⣿⣿⣿⣿⠿⠿⢭⣉⠈⡆⠀⠀⠀⣾⣿⠀⠀⠀⠀⠙⠳⣄⠙⢆⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣼⠟⣭⣿⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⣿⣿⡟⠛⠛⠦⣤⠀⢻⣿⢸⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠘⣷⣜⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡏⠀⠿⠋⠀⠀⣺⡿⠖⢛⡿⠒⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠛⢧⡀⣀⣀⡀⣠⡿⢡⡟⠀⠀⣰⣧⠟⠀⠀⠀⢀⣀⡀⠀⠀⢸⡿⣿⠀⠀⠀⠐⣘ ⠀⠀⠀⠀⣀⣀⡁⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⣴⡟⠀⣴⣫⡤⠴⠶⠤⣤⣀⠀⠀⠀⠈⠛⢽⣀⡈⠛⠏⠛⠛⢉⡠⠏⠀⢀⣴⠋⠁⠀⠀⠀⣸⠟⠉⣻⡇⠀⢸⡇⣿⡇⠀⠀⠀⠠ ⡀⠀⠀⠀⠁⣨⡇⠀⠀⠀⠀⠀⠀⠙⠛⠲⠞⠋⠀⡼⠋⠀⠀⠀⠀⠀⠀⠉⣷⡄⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠉⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⣿⡴⠀⠙⠃⢠⣞⣰⣿⠇⠀⠀⠀⠀ ⠷⠦⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣵⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⣤⡀⠐⢻⡆⠀⢀⠀⠀⠀⣼⠟⣻⢦⣤⣦⠿⠿⠿⠟⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⣲⣶⡶⠛⠉⠀⠒⠲⣦⡀⢹⡆⠀⠙⢻⢿⠷⣶⡞⠡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣰⠟⠋⠀⠀⠀⠀⠀⢀⣀⣿⣤⣿⣀⣠⠞⣾⠚⠉⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠙⣷⣼⠏⠀⣰⡆⠃⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⣦⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠀⠀⠀⠞⠁⢀⡼⢹⣇⠤⠖⠛⠋⣉⠭⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠁⠘⣆⠀⠀⠀⠴⠋⠀⠘⠀⠀⠀⠀⠈⠛⠛⠛⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠃⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣵⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠿⣦⣀⠀⠀⠀⢀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⢹⡀⠀⢀⣠⠤⠴⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⣛⣛⢯⣙⣿⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣷⣿⣤⣤⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⣳⠔⠉⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣿⠙⠉⠿⢦⡄⠀⠀⠹⣿⣶⣦⣶⣶⣾⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠈⠱⠀⠀⠀⠉⣿⢶⣶⣾⡿⠛⠛⢻⡛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠀⢠⠀⠀⠀⢠⣤⣶⣿⠁⡀⠀⠀⠀⠁⢘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⡀⡀⢀⢆⠀⠀⠀⣸⣿⣿⠿⣿⣭⣴⠄⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣠⠀⣀⣱⣮⣻⣿⣟⣷⣦⣴⣿⣯⣿⣿⣽⣿⣿⡖⠀⠀⠈⠛⢻⡀⠀⠀⠀⢀⡞⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡘ ⠀⠀⢀⠈⠀⠁⠙⠁⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢻⣿⢃⣀⠀⢪⣷⣄⠀⢀⡾⠀⠀⠀⠀⠰⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⡇⠀ ⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⠤⢤⠐⡇⠠⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⡇⠀ ⠈⠉⣩⠏⢯⠉⠉⠉⡠⠔⠮⡑⡀⠀⠀⢡⢰⠀⠱⡀⠀⠀⠀⠀⠀⠑⡄⢀⡇⠀ ⠀⡴⠃⠀⠈⢃⠔⠉⠀⠀⠀⠈⢺⡀⠀⢸⠠⢧⡀⠈⠗⠢⣀⠀⠀⠀⠘⡦⡁⠀ ⡰⠁⠀⢀⢔⣑⣂⣤⣀⠀⠀⠀⠈⣇⠔⢁⣀⠀⠑⢄⠈⠢⢀⡱⢄⠊⡇⢳⠘⢄ ⠓⠒⢢⠋⠁⠀⠀⠀⠈⠑⢄⠀⢀⠋⠀⠁⠀⠀⠀⠀⠁⠀⠀⠑⡆⡔⠵⢸⠐⡈ ⠀⢠⠁⠀⢀⣠⠔⣒⢟⠃⠒⢥⡌⠀⠀⢀⣤⣴⣾⣤⣀⡠⠀⠀⠉⠀⠀⢸⡀⢱ ⠀⡇⠀⣴⠋⢀⡞⠁⡌⠀⠀⠀⠁⠀⣀⣿⠋⢻⣿⡂⠙⢶⡄⠀⠀⠀⠀⠘⡈⢨ ⠀⢠⢪⠃⢠⡟⠀⣸⡇⠀⠀⠀⠀⠀⠈⠹⣀⣾⡿⣿⡀⢸⠇⠀⠀⠀⠀⠀⠃⠘ ⢸⠆⠇⢀⢷⠁⠀⣿⢣⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠸⡀⠀⢸⡌⠀⠀⢿⡆⢆⡀⢀⣠⡄⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁ ⠀⠣⡆⠘⣡⠀⠀⠘⣇⢸⠙⢫⠁⠀⠔⠀⣰⡀⠀⠀⠀⠐⠠⢄⡀⠀⠀⡰⢡⠀ ⠀⠀⠙⢄⠹⢆⠀⠀⢈⡆⠀⠀⠑⠤⣤⣴⡿⠟⡀⠀⠀⡇⠘⠒⠂⠭⡒⣱⡯⠁ ⠀⢤⠐⠒⢓⣒⣉⠭⠔⠣⡀⠀⠀⠀⠈⠿⠀⢀⠇⠀⠀⡇⡄⠀⢀⢎⢌⠞⠁⠀ ⠀⠀⣑⣦⣈⣢⣍⣈⠀⢠⠈⢒⡤⢀⣀⠀⠀⠁⠀⡀⢤⠁⣇⠔⠁⡡⠃⠀⠀⢀ ⠂⠁⠀⠀⠀⠀⠀⠀⢡⢠⠀⢀⠁⠀⠀⣼⡿⠛⠉⠀⡸⠚⠁⠀⠀⠀⠀⠀⡠⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⣀⢀⢀⣈⠞⠉⠀⢀⠤⣊⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡀⡤⠑⠲⠦⠤⠤⣤⣀⡠⠒⠠⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠈⠁⠢⡀⠀⠀⢊⠇⠀⣤⠘⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡚⠅⠒⠈⠉⠉⠉⠉⠐⠢⢀⠀⠈⠄⠀⢸⡀⠀⠀⣶⠞⡄⠀⠀⠀⠀ ⠀⠀⡴⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠔⠊⠁⠁⠀⠀⠀⣔⠋⠆⠀⠀⠀ ⠀⡼⢡⡞⠀⠀⠀⠀⡠⠒⣩⠕⠋⠑⠒⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀ ⠀⡠⡛⠁⠀⠀⠠⠊⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⡂⢸⡄⠀⠀⠀ ⠀⠁⠃⠀⠀⠀⠀⠀⢠⣃⣀⣀⣀⣤⠖⠀⠀⠓⢲⣯⠽⠛⢿⣄⡁⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢸⡿⠛⠛⠻⢻⠀⠀⠀⠀⢸⠀⠀⠀⢧⣿⣲⣤⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢰⣿⠀⠀⠀⠀⠀⢂⠀⠀⣨⠿⠓⠘⡜⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⡦⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⢉⡤⡆⠀⠇⡗⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⢀⠀⠀⢹⣿⣦⣀⢀⣀⠰⠊⠉⢑⣠⠴⠋⢀⠁⢰⢀⡷⠤⠤⠄ ⠀⠀⠘⣇⠀⠀⢸⠀⠀⠀⡿⣿⣿⣿⠑⢌⠡⠤⢼⠀⠀⠀⡘⠀⡄⢸⡷⢄⠀⢀ ⠉⠐⠒⢿⡄⠀⠈⠀⠀⠀⢉⢋⡝⣰⡷⢤⣑⠠⡇⠀⠀⠀⠇⢀⠁⡇⠑⣼⠑⠒ ⠀⠀⠀⠀⢳⡀⠀⡆⠀⠀⠘⠸⡄⡇⢹⡀⠀⡱⡇⠀⠀⢰⠀⠸⢠⡇⠀⣼⠀⠀

⠀⠀⠀⡠⠤⢄⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠉⡇⠠⡡⠂⠉⣎⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⡧⢀⢡⡞⢀⢤⣂⠙⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠎⣾⣭⡟⡷⢸⠷⣦⡈⠗⢄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀ ⢸⠸⡷⣦⡔⠃⠀⠹⠿⠋⠸⣦⠇⠀⢔⠅⠒⠪⠀⡀⠀⡀ ⠘⡇⡇⠛⡏⠀⢀⣦⠀⠀⣰⠇⠀⢰⠈⡔⢈⢐⣄⡙⣀⢿ ⠀⢀⠒⡤⢀⠙⠿⠌⠀⢎⢌⠇⠀⠬⠻⢔⠀⠀⠈⠁⠀⠁ ⠀⠸⠀⠃⠀⠈⠋⠁⠀⠈⢥⣴⠤⠒⢺⡾⢃⠀⠀⠀⠀⠀ ⠀⠀⠑⠬⢾⢄⣀⠀⠀⢀⢔⢯⢢⠀⠈⡆⠸⠲⠀⠀⠀⠀ ⠀⠀⠀⢀⠨⠭⠿⠩⠍⠐⠁⠀⣆⡶⣜⠁⡰⠀⢃⠀⠀⠀ ⠀⠀⠀⠆⠀⣄⣤⡃⠄⡜⠀⡤⡞⠊⢀⠉⣠⠀⢀⡆⠀⠀ ⠀⠀⢸⠀⠀⠙⡯⠝⡝⠀⠰⠀⡸⠀⡄⠀⠳⡔⡪⠃⠀⠀ ⠀⠀⢸⢄⡂⡔⠇⠰⠀⠀⡇⡐⠁⠀⠇⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠒⠣⠜⠀⡆⠀⠀⢗⢄⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠖⠐⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠰⠃⠀⠈⢷⠀ ⢀⣞⡠⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀ ⠘⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠇⠀ ⠀⠀⠀⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠴⣲⡿⢫⢻⠀ ⠀⠀⠀⠀⠹⣣⡀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣠⣤⡴⠾⢍⠃⣸⣼⠀ ⠀⠀⠀⠀⠀⠘⠍⠐⠒⠤⢄⡀⠀⠘⡆⠀⠀⢠⠋⢻⣕⢄⠑⠞⠅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠳⣤⡇⠀⠀⢸⠀⢸⣿⣧⢃⠈⡞⡄ ⠀⠀⠀⠀⡀⠱⡴⠋⡴⠋⠙⣿⣶⣜⠁⠀⠀⠘⣤⣾⣧⣿⠆⠀⢻⡇ ⠀⠀⠀⠀⠈⢲⠁⢸⡇⠀⠀⣿⠿⣿⣦⠀⠀⠀⠹⢿⣿⡿⠘⠒⠚⡇ ⠀⠀⡘⡀⠐⢚⠀⠘⡐⣄⣴⣿⣿⣿⡿⡆⠀⠀⡀⠼⠁⠀⠀⠀⠸⡇ ⠀⠢⣜⠕⡀⠀⢃⠀⠐⢌⠻⣿⠿⠛⠛⠃⠀⠀⠀⠀⢈⠄⠀⢠⣿⠇ ⠐⢷⣿⡓⢈⢄⠀⠑⢄⡠⠛⠁⠀⠈⠀⠀⠸⣆⣀⣤⡾⠀⢠⠟⠛⠀ ⠀⠀⢹⠿⣯⣓⢕⡠⣈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠕⡺⢀⡴⠻⠀⠀⡘ ⠀⠀⠀⠀⠘⠛⠛⠾⢴⡁⠲⠤⠤⠀⠀⠀⢀⣤⠝⠊⠋⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠐⠢⠆⠊⡇⠀⠀⠀⠀⠀⠀⠗⠹⢀⣐⣀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⡠⠄⠒⠈⢁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⣤⣀⠀⠀⠀ ⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⡈⠙⢺⣆⡀ ⠀⠈⢿⠙⢵⢦⣄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢂⠈⠉⠁ ⠀⠀⠀⠱⡉⠫⢿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡘⡆⠀⠀ ⢀⣀⣀⡀⠱⡀⠀⢻⠆⠙⢦⡀⠀⠀⠀⡀⠀⠀⠀⠠⠄⣀⠀⢀⠁⠑⠀⠀ ⡿⢂⠀⠈⢂⢁⠀⠈⣼⡄⠘⢱⡀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡙⠀⠀ ⡇⢰⡕⡀⠀⢹⠀⢸⡏⠈⢢⠘⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀ ⠈⡈⠷⡘⡀⠀⡀⠘⣧⠤⣸⠋⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀ ⠀⠘⢌⢜⠖⠁⡇⢻⣿⣄⢘⡇⠉⢸⠁⠐⠒⢒⡒⢒⠀⠀⢠⡿⡝⠘⡄⠀ ⠀⠀⠀⠀⢕⢄⡁⠞⡅⠉⢹⠇⠀⠘⠰⠤⠴⠲⠽⠛⠛⢛⡿⠊⠀⠸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⡠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⢱⣷⣺⠟⠁⡠⠂⠀⢀⡔⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡴⠃⠔⠁⣀⠀⢀⠀⡠⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⠔⠀⡌⠀⠌⢀⠀⣾⡰⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢠⡀⠘⡆⠀⣆⠃⢃⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⠳⠾⠃⡠⠛⢾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠱⡒⠚⠂⠁⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠀⠢⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠸⣆⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠟⠛⠉⠉⠉⠙⣿⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠓⠶⠤⠀⠀⠀⣿⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣀⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠳⣦⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⡿⣹⣿⣿⡒⠶⣤⡈⠙⣷⡄⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠘⠁⡟⠀⠘⣿⣷⣮⡹⣦⡈⢿⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠈⢧⠀⠀⠀⠀⠀⠀⠰⣶⣿⡿⠟⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⣿⣄⣼⣟⢉⣿⣷⡞⣷⠈⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⢷⣄⠀⠀⠀⠀⣴⡿⢁⣠⣶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠸⣯⢻⣿⣿⣿⣿⣿⢸⣇⡿⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⠻⣷⣄⠀⢸⣿⢠⡾⠉⠹⣿⣦⡙⢧⠀⠀⠀⠀⠀⠀⣀⡈⠳⣭⣛⣛⣛⣩⣾⠟⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢸⡇⢸⡅⢀⣸⡿⢿⣿⣸⣆⠀⠀⣠⠞⠋⢁⡤⠀⠀⠀⣀⣼⠿⠗⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢸⣧⢸⡟⣿⣿⣷⣾⣿⣇⡿⠀⠈⠳⠤⠤⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣾⣿⡈⢷⡸⣿⣿⣿⡿⣼⠃⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⣻⣮⣍⣩⡾⠋⠀⠀⢸⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠶⣦⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠉⠙⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠙⢷⡄⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣆⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠳⣶⣄⣀⣀⣀⣀⣀⣤⡴⠖⠋⠁⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⣠⠶⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼ ⠀⠀⣠⠟⠁⠀⠀⡼⠀⠀⠈⠻⣦⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀ ⠀⣼⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠻⣦⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠙⠲⢤⣄⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣦⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣠⣤⣄⣐⣒⠒⠒⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⣶⣶⣤⣄⣀⡴⠋⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣱⠶⠖⠛⠉⠁⠀⠀⠈⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠛⢿⡇⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠘⣇⠘⣿⠀⠀⢠⣤⣄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⣀⣤⡤⠤⠤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠘⠛⠋⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣡⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⢰⣿⣿⣧⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢠⣾⡵⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠸⡄⠀⣀⣤⣯⣶⣇⠀⠀⠀⠀⠈⠻⠟⠃⠀⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⣷⠞⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡃⣠⠴⠟⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠛⠉⣉⡥⠞⠛⠛⠳⢶⣤⣀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⣼⢳⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⡞⠃⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠃⠠⡏⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠼⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⣆⠀⠀⣀⣠⣴⡶⢿⣿⣿⣿⣾⣷⠀⠀⢷⠀⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠹⠛⢹⣿⣿⣇⣴⣾⠿⠿⠿⢿⣿⡆⠀⢸⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣛⣋⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠋⠁⠀⠀⠀⠀⡿⠉⣿⣿⣋⠀⣀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢹⣿⣾⠿⠋⠉⠉⠉⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣧⣼⣻⡟⠿⢯⣉⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⣼⡿⠁⠀⠀⠀⠀⢰⡇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⡽⣿⣿⡿⠿⠿⢰⠛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠿⠆⠀⣾⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣷⡂⠀⠀⠀⠀⠀⠀⢻⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣀⣴⠿⠛⡙⠃⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣿⣿⣶⣄⡀⠀⠀⠀⠈⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⢀⠖⣼⠃⠀⠀⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⡛⠿⠷⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⡏⠀⠀⠀⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⠿⠭⠤⢦⣄⡀⠀⠀⢀⣤⣿⠟⠁⢠⠇⠀⠀⢠⡇⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣶⣄⡀⠠⢀⡀⠀⠀⠼⠋⠀⠀⠀⠀⠀⢀⣀⣤⣾⡽⠟⠁⠀⠀⢸⠀⠀⠀⣼⠀⠀⣏⡟⠛⠿⠿⠶⠶⠤⣤ ⡀⠀⠀⠀⠂⢻⣵⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⡬⠍⠛⠶⠶⠶⠂⠀⠀⠈⣥⠞⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡏⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣻⣿⠿⣿⣿⣿⣿⣿⡁⠛⠳⣄⣀⣀⡤⠤⢤⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠁⠀⣾⣿⠹⢷⣄⠀⠀⠀⠀⠀ ⣥⣀⣀⠀⠀⠀⢹⣟⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡧⣹⣿⣿⣿⣿⡿⠛⣧⡀⠀⠈⢩⡁⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⢠⡟⣿⡀⠀⢹⣧⡀⠀⠐⣋ ⠀⠉⠉⠛⠿⠶⢮⣿⣷⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢹⡘⢻⡏⢉⡿⠃⣰⣿⣷⣤⣀⠀⠑⣄⠀⢀⢾⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⣼⠀⠈⠿⣄⢠⡏⢀⠶⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡇⢈⣷⡟⠀⢰⡿⢽⣷⠈⠙⠻⠶⢾⠉⠉⢿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠌⣷⡇⠘⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢷⢸⣹⡇⠀⣿⠇⠀⣿⡆⠀⠀⠀⠈⢱⣤⣸⡇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡞⠀⢠⢿⡆⠀⠀⡀⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠦⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠓⣷⢸⣿⡂⠀⢹⣿⣄⠀⠀⢀⡾⠘⣿⡇⠀⠀⠀⠀⠀⠠⡇⠀⠀⢰⡇⠀⢸⣾⡇⠀⠀⢠⡏⠿⠀⠀⢄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠴⠒⠶⠶⠦⠤⠤⠤⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⣦⣄⣠⡤⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣳⡶⠴⠒⠒⠒⠒⠒⠒⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⢘⣿⠀⠈⢹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣄⠀⠀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⢀⡴⠋⢹⡶⠞⠋⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⠏⠀⠀⠀⢿⡄⠀⢀⣠⠾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠘⣿⠚⠋⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⢸⠁⠀⠀⢠⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣼⠁⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈ ⢸⠀⠀⠀⠸⡄⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣠⠞⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡜⢀⡞⠀⠉⠉⠓⠒⠒⠲⢶⡦⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠋⢅⠀ ⢸⡄⠀⠀⢰⣇⠀⠀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⣣⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⢸⡇⠀⠀⠈⣿⠀⠀⡇⠠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣼⠟⠃⠀⠀⢀⣠⠴⠒⠒⠂⢀⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢸⣇⠀⠀⠀⠘⡇⠀⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⡾⠁⠀⠠⣤⣶⣭⡶⠶⠖⠒⣷⡷⣶⣶⢿⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠀⠀⠀⢳⡀⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠈⢳⠹⣯⠉⢿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣧⠀⠀⠀⠈⢧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢹⡄⠈⢧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣆⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠹⡄⢷⡀⠀⠀⠀⠀⠀⠀⣸⠇⢸⡇⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠈⠳⣤⣀⠀⠀⣀⣴⠟⢀⡾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣷⣄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠭⠤⠖⠋⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢶⣄⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡶⠛⣓⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⢀⣾⣵⠞⠋⠉⠉⠛⠃⠀⠀⠀⢀⡤⠖⠊⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠻⡄⠀⠀⠀⠀⠀⠀⢀⣐⣶⡶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡁⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⡇⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠘⠛⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⠀⠀⠀⢰⡟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠏⠁⢱⠀⠀⢧⣀⢴⡟⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠘⢆⡀⠈⣇⣾⠟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⢲⡒⠒⠒⠒⠋⠉⠀⠹⣄⠀⠀⢀⣠⠿⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢻⣦⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⢷⣆⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣦⣀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠛⠷⣤⣀⠀⠀⠀⠈⠻⣶⣄⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣄⣀⡈⠛⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡟⠙⠓⠚⠛⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⠀⠀⠀⠀⠀⣴⣶⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠙⠻⣿⣗⣶⣤⠀⠀ ⠀⠀⠀⢀⣤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣄⡀⠀⠉⣽⣽⣵⡄ ⠀⠀⠀⠛⣿⡯⣻⢟⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⣄⠀⠛⠙⠙⠁ ⠀⠀⠀⠀⠈⠳⡌⢩⣶⣭⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣆⠈⠓⠎⢯⣻⣿⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡾⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⢻⣻⡇⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠇⠚⡧⠀⠀⠀ ⠀⣤⡴⠶⠶⠶⢖⠒⢚⣆⠀⠀⠀⢯⢳⡀⠀⠉⢿⣄⠀⠀⠀⠀⠀⣀⠔⠒⠁⠀⠀⠉⠉⠉⠙⠲⢤⣄⡀⠀⠞⠀⠀⣇⠀⠀⠀ ⢰⣿⡷⡄⠀⠀⠀⠱⡄⢹⡀⠀⠀⠸⣽⣷⡀⠀⡼⠙⣦⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⡈⡟⠀⠀⠀ ⢸⣇⠀⣟⢦⡀⠀⠀⠘⢆⣇⠀⠀⣳⣿⠏⠹⣌⠀⠀⡏⢧⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀ ⠈⣿⠀⢿⣦⠵⡀⠀⠀⠘⣿⠀⠀⢻⡟⠀⠀⠘⢦⡘⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠸⡄⠸⡾⣄⠹⡄⠀⠀⢸⠀⠀⢾⣇⣀⠀⠀⣾⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⠆⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠹⡜⣦⡹⠀⢀⣼⡧⣄⣠⣷⡏⠙⠛⣿⣀⠀⣼⡝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣤⠤⣤⠄⠀⠀ ⠀⠀⠀⠙⢄⠙⢌⠻⠖⠁⢸⡇⠘⣿⣿⣷⣀⣀⠘⡇⠀⠈⠉⣼⠉⠉⠛⠓⢒⠲⣛⣛⡛⣟⠀⠀⠀⠀⢠⣿⣏⡼⠀⢘⡇⠀⠀ ⠀⠀⠀⠀⠈⠳⡈⠳⣄⠀⢸⠇⢀⣾⡇⠑⠿⢷⣾⣷⠀⠀⠀⣿⢀⡀⠀⠀⣀⣀⣭⣴⣶⣿⣶⣶⣶⣤⣿⢉⠞⠁⠀⢼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢬⣓⣾⠤⠚⠀⢧⠀⠀⠐⣮⠇⠀⠀⠀⠋⠙⠿⠿⠟⠛⠁⠒⠚⠋⠉⠉⠀⣠⡿⠟⠁⠀⠄⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⣠⣤⢤⡀⢀⣀⣀⣤⠖⠋⠁⠀⡠⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠙⠓⢚⣿⣿⣟⣿⠟⠁⠀⢀⠴⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⢉⠟⠁⠀⠀⠐⠁⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠏⠈⣠⠋⠀⠀⡤⠤⠒⠒⣤⠀⢀⡜⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⡴⠁⠀⣰⠃⠀⣠⠋⠀⢠⠀⢰⣿⢀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⡠⠊⠀⠀⢰⡇⠀⢀⡇⠀⠠⢻⡀⣼⠟⡏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⣿⡆⠀⢸⣇⡟⠀⢹⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠇⢻⣧⣠⣾⠟⠀⢀⣾⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢲⣔⠋⠉⠁⣀⠴⠋⡼⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠈⢷⡛⠛⠓⠒⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⡀⢀⣀⡠⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠫⠭⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣷⣿⠟⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣶⣤⡀⠀⠂⠠⣾⠟⠉⠉⠀⠀⠙⣿⣇⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠛⠋⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀ ⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀ ⠀⢠⣿⠟⣀⣤⡶⠶⠿⠿⠿⠷⠶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀ ⠀⣻⣿⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀ ⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣤⣾⡿⣵⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠶⢶⣤⣤⣄⣀⣀⣀⣤⣤⣴⣶⣾⢿⣿⣷⠟⢸⡿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⣠⣶⣿⠟⠁⠀⣾⠁⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡜⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡟⠋⢸⠃⠀⠀⢼⡂⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢷⣶⣶⣦⣤⣶⣶⣶⣶⣾⣿⣟⡛⠉⠙⠛⢶⣾⠀⠀⢶⣾⣷⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⣧⡀⠀⠀⠉⠉⠈⠀⢀⡿⠻⣿⣏⠙⠶⣄⠀⠉⢳⣄⣸⣿⠻⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⣿⣿⣦⡈⠳⡄⠀⠙⣇⠀⢲⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣿⣿⣿⣆⠙⡄⠀⠈⢇⣌⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠙⢿⣷⣤⣼⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣇⠸⡄⠀⠸⡿⡈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢀⣤⣶⠿⠛⣻⣿⣿⣿⣿⣶⣤⣄⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠸⢷⠀⠀⢀⣿⣿⠛⢿⣿⣿⡀⢇⠀⠀⢿⡇⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⠏⠁⢠⣾⠟⠁⠀⠈⢿⣿⣿⣿⣷⣄⠈⠋⠀⠀⠀⠀⠀⠀⠘⠺⣄⣠⣾⣿⣿⣄⣸⣿⣿⠇⢸⠀⠀⠸⣿⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡿⠁⠀⢀⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⣿⣷⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠃⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⠰⠧⠒⠲⠒⢻⡏⡇⠀ ⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⢻⡆⠀⠀⠀⠀⢀⣿⣿⡀⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⠻⣟⠿⠃⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⣤⣤⣴⠿⠀⠀⠀⠸⡆⠳⣄⠀⠀⢀⣾⠿⣿⣿⣾⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡇⠀ ⠠⠀⠀⠀⠸⣆⢳⡄⠀⠀⠀⠀⢼⡀⠀⠀⠀⢳⡀⠙⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠀⠀ ⠀⠈⢦⡀⠀⠹⡄⢻⡀⠀⠀⠀⠀⢷⠀⠀⠀⠈⢳⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⣿⠇⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠿⠀⡀⠀⠀⠀⠀⢀⣿⣻⣿⠀⠀ ⠀⠀⠀⠙⢲⣄⠹⠄⢳⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠹⣄⠀⠙⠿⣿⡿⠟⠿⠉⠀⠀⣠⠁⠀⠀⢠⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣾⣿⡛⠻⠄⠀ ⠀⢠⣤⣉⣻⣿⣷⣤⡀⠙⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⢢⣶⠞⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⣾⣷⣟⣻⡆⠀⠀ ⠀⠈⠻⣿⣿⣿⡛⠛⠛⠳⠘⢳⡄⠀⠀⠀⠈⢦⣀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⢀⢀⣠⣶⣿⣿⠁⠀⠀⢀⣾⡟⠉⠉⠉⠛⠀⠀ ⠀⠀⠀⠈⠻⣿⡟⣿⡷⣤⣽⣦⠙⢦⣄⠀⠀⠀⠨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢛⡋⣱⣿⠁⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠈⡿⢿⣿⣦⣍⠛⠻⢦⣍⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣤⠾⠿⣿⠉⠀⣀⣴⠟⠿⣷⠀⢸⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠓⠀⠙⠻⢿⣷⣶⣤⡙⠳⣬⣙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣤⠔⢋⣠⣾⣿⠍⠇⠀⠸⠀⢸⡇⠀⣼⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠯⠟⠿⢿⣷⣶⣧⣴⡆⠉⠻⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠞⢋⡿⠋⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⡾⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠒⡉⠿⣻⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⣅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠶⠒⠲⠾⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣻⠷⠀⠀⠒⠲⠶⠒⠀⠀⠴⠃⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠓⠶⢶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⢀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⢠⠗⠠⠄⠀⡆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠉⠉⠂⢄⡔⠁⠀⠀⠀⠀⢀⣴⣒⡒⢤⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⡀⠀⠀⢁⣀⣠⣞⠀⠀⠘⣞⢹⢮⡳⡱⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⠘⣄⠀⣰⡫⢶⡢⡁⠀⠀⠘⢽⡾⢿⣷⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⡀⠁⣇⡧⣼⣻⣶⠠⢂⠉⢀⡩⠛⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢿⣵⣟⣻⠏⢠⡤⠚⠁⠀⠀⠀⣠⢇⡀⠀⠀⢀⠤⠒⠐⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⣁⡀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⢦⡴⠁⠀⠀⠀⠀⢡ ⠀⢀⠤⠤⢄⡀⠀⠀⠔⠁⠀⠈⠓⠒⠒⠂⠉⠀⠈⢆⠀⠀⠀⠑⠀⠀⠀⠀⢀⡠ ⠠⠁⢠⠃⠀⠈⢢⡌⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡠⠊⠁⠀ ⡇⡠⠁⠀⠀⠀⠀⠧⠀⠀⠀⡠⠺⡀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠤⠔⠋⠀⠀⠀⠀ ⠈⠒⢄⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠒⢄⡀⠀⡠⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⣿⣿⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣦⣿⣿⡟⢿⠛⢏⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢻⡏⢻⢯⢳⣾⠷⡀⠱⡀⠀⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⠀⣸⣿⠘⠈⡆⢻⡆⠱⠀⢱⠀⠘⡧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣷⣇⣰⣀⣇⣸⣿⣄⣧⣼⣶⣾⠃⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡅⠀⠉⠉⠓⠒⠒⣶⣿⣿⣭⣭⣉⠉⠙⣦⣿⣿⠁⣶⣿⡇⠀⠀⣸⠷⣌⢻⣿⠃⣠⠴⠒⠒⠲⣦⣤⣤⣀⣀⣀⣀⣠⣤⠤⠤⣄ ⠈⠻⣦⣀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠈⠙⢦⣏⣹⣿⣶⣿⣿⠇⠀⠀⣿⣾⣿⣿⣯⡞⠁⣠⡴⠚⠛⠉⠉⠛⢳⡌⠉⠁⠀⠀⠀⢀⡿ ⠀⣶⠛⠉⠁⠀⠀⠀⠀⠀⠉⣹⠖⠂⠀⠀⢻⡿⣿⡿⠿⠿⢈⠉⣁⣿⡿⢿⣿⣿⢁⡾⠁⠀⠀⣤⡤⠶⠚⠋⠀⠀⠀⢀⣤⣖⠋⠀ ⠀⠙⠷⣄⣀⡀⠀⠀⠀⠀⢸⣁⣀⣀⣀⡄⠀⠱⢻⡓⢦⣀⣻⣧⣟⣠⣤⣾⣿⡇⠎⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢉⣷⠀ ⠀⠀⠀⠀⢈⡽⠛⠁⠀⠀⣀⠈⠉⠁⢿⣀⣤⡆⠈⣷⣾⠋⠉⠉⠉⠀⣿⣿⡿⣆⣄⣸⢸⡟⠒⠒⠛⠁⠀⠀⢠⣤⡤⠴⠚⠋⠁⠀ ⠀⠀⠀⠀⠘⠳⠖⠒⠚⣿⣁⣀⣠⡴⠈⠀⠀⣙⠛⢻⠻⡄⠀⠀⠀⠀⡿⢻⠳⡈⠛⣿⡏⢄⡀⠀⠘⣶⣤⣀⡀⢉⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠓⠒⢺⡟⣁⣠⣾⠐⣿⣄⠀⢀⣼⡅⣸⡄⠈⠛⢹⡧⣬⠟⠓⠲⠞⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⣥⠤⣿⢷⣮⣿⠶⣿⢿⣷⣿⣼⣦⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⠖⣻⡀⠈⠙⣶⠛⠉⢸⣿⣟⠯⣄⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠴⣶⣊⣹⠟⠯⣽⣩⣇⡴⢿⣟⣌⠓⠦⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⣿⡿⡿⣆⣀⣻⣿⣟⡁⣸⠿⡿⣿⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⣻⡟⠁⣇⠀⢀⣏⣉⣉⣿⡄⠹⣾⡿⢤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡟⠛⣾⠀⠀⠀⡇⠀⠀⢽⢿⡶⠛⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠘⢊⣠⠞⡿⠀⠀⠀⡇⠀⠀⢸⣆⠙⣆⡘⠖⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⣠⡖⠋⡀⣠⡇⣠⢦⢀⡇⣠⣄⠀⣯⢧⣿⠙⠦⣀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⠉⠉⠉⠉⠉⣿⡟⣰⡟⣿⣿⢳⡦⢻⣿⣈⡿⠓⠒⠛⠛⠶⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣈⣇⣹⣏⣈⢉⣀⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡟⢰⠃⢀⣴⣫⣾⣿⣿⢿⡏⠉⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠁⠀⠀ ⣿⣿⣇⡏⣠⢯⣾⣿⣿⣿⢃⡟⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢡⠏⢀⣴⠃⠀ ⣿⣿⢈⡶⣷⡿⠿⠿⠛⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠙⠓⣢⡤⠤⠤⢤⢤⡤⠤⠤⠤⠤⠤⣴⢶⡄⢸⠏⠀⠀⡴⠋⣠⠟⠁⠀⠀ ⠛⠋⠘⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢷⡾⠀⣠⠞⣡⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣴⡿⠿⣿⣿⣿⣿⠳⣶⣤⣤⣄⣀⣤⢴⠏⠀⠀⢸⢃⣜⣥⡾⠛⠉⠉⠉⠙⠻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⠏⢤⣴⣿⠟⠀⠀⢹⣿⣿⣿⡆⠘⣿⣦⠀⠉⣰⠏⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⣃⣠⣾⣿⡟⠀⠀⢀⣿⣿⣿⣏⣡⠀⠘⢿⢆⣴⠋⠀⣠⣾⠟⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡾⢁⡼⠋⢻⣹⣿⣷⣤⣾⣿⣿⢿⣿⡇⠀⠀⣠⠟⣡⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⢁⡞⠁⠐⢾⣿⣿⣿⠛⢿⡿⠏⢸⡿⠀⢠⡾⠗⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣧⡟⠀⠀⠀⢸⠙⠇⢻⣄⡀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣽⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⡟⠀⠀⠀⠀⣿⠠⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣴⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠀⠀⠀⢰⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⠀⠀⠀⣿⠁⠀⢠⣧⡀⠀⠀⠀⠀⠀⢀⡴⢁⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡟⢿⠻⢿⠿⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⢸⡇⠀⢀⣐⠚⢳⣦⣄⣀⣠⡤⠼⣿⠉⠉⠀⠀⠈⡉⠁⠀⠀⠀⠀⠻⣤⣀⡀⢀⣸⠟⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠃⠀⠀ ⣄⣉⣩⠿⠿⠶⠤⢤⣄⣀⠀⠀⣀⣴⣞⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⣀⡤⠶⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠛⠁⠀⠀⠀⠀⠀⢀⣩⠷⠛⠉⠁⠙⣧⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢀⣠⠾⠋⠀⣠⠀⠀⠀⠀⠸⣧⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡴⠊⠉⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠘⠲⠤⣀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢧⡀⠀⠀⠀⠘⣦⠉⠛⠶⣤⣄⣀⡀⠀⠉⠓⠚⠋⠁⢀⣀⣀⣤⠶⠒⠋⠀⢠⠆⠀ ⠟⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⣷⠀⠀⠀⠀⠘⣇⠀⠀⠹⡄⠉⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⢸⣷⡄⠀⠀⠀⢹⣤⠀⠀⢻⡄⢸⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣀⡴⣋⡠⣶⠂⠀

⣿⣿⣿⡟⢰⡟⠀⠀⣤⢞⣵⣾⣿⣿⡿⣽⠏⠉⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠋⠀⠀⠁ ⣿⣿⣿⠃⡿⠀⣠⡞⣥⣿⣿⣿⣿⡿⢰⡏⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢫⡟⠀⢀⣴⠀⠀ ⣿⣿⣿⢸⠃⣴⢫⣾⣿⣿⣿⣿⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣶⠞⠛⠉⠀⣠⠏⠀⣰⡿⠁⠀⠀ ⣿⣿⡇⢨⡟⣵⡿⠿⠿⠛⠛⠛⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⣉⣾⠿⠟⠷⠦⠤⠤⠤⠤⠤⠤⠶⠿⠟⠛⣿⠿⣷⠀⣸⡇⠀⠀⢀⡾⠃⣠⣾⠟⠀⠀⠀⠀ ⠛⠛⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠸⡆⣿⠀⢀⣴⠟⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢀⣴⣿⣿⣿⣿⣷⣶⣦⢤⣤⣀⣀⠀⠀⠀⠀⢀⡀⣼⡏⠀⠀⠀⣿⠃⢠⡞⣁⣶⡿⠟⠛⠛⠻⠿⢶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢀⣴⣿⡟⠉⠙⣿⣿⣿⣿⣿⡄⠘⣿⣿⡙⠛⠷⠶⠛⣹⠏⠀⠀⠀⠀⣯⡴⣣⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢠⡟⠁⢳⣶⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠘⣿⣷⡀⠀⢀⣼⠏⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣟⠀⣠⣾⣹⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⡍⢉⡀⠀⠈⢿⠧⢀⣾⠋⠀⢀⣤⣾⡿⠋⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⣼⠏⢉⣽⠋⢿⠛⣿⣽⣦⣀⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢈⣴⠟⢁⣠⣶⠿⠋⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣰⠏⢠⡾⠁⠀⣸⣴⣿⣿⣿⣿⣿⣷⣿⣿⠏⣿⣿⡏⠀⠀⣠⣞⣥⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢰⡟⣠⡟⠁⠀⠉⢹⡏⣿⡹⣿⠃⠈⠛⠛⠃⠀⣹⡟⠀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠈⢻⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡿⣠⡟⠀⠀⠀⠀⢸⡇⠹⠇⠻⣧⡀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⢷⡿⠀⠀⠀⠀⠀⣼⠇⣂⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣸⣿⠁⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣄⣠⣾⣿⣿⣿⣿⣿⣏⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⠀⠀⠀⣼⡏⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠤⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢣⠀⢸⣯⠻⢯⠻⠿⠿⢟⣵⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡰⠾⠛⣷⣄⣀⣀⣀⣀⣀⡨⣿⡟⠋⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠟⠳⠤⠴⠋⠀⠉⠉⠉⠉⠁⠀⢹⡇⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠿⠥⠤⠤⠄⠀⠀ ⠲⠶⠦⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣀⣤⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣄⣠⡴⠟⠛⠛⠛⠛⠿⢦⣤⣀⡀⠀⣀⣤⣾⣯⡁⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠶⠟⠋⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⠟⠋⠁⠀⠘⢿⣦⣈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⣯⠉⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡴⠾⠋⠉⠻⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣤⡀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⢰⠟⠁⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⣇⠀⠀⠀⠀⠀⠈⢷⡉⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠙⠓⠲⠒⠚⠋⠁⠀⠀⠀⢀⣠⣤⣶⠖⠒⠀⠀⣠⠃⠀ ⣴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣆⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠙⢯⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠟⠋⠉⠀⠀⠀⢀⣼⠏⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣇⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠸⣿⣷⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⢸⣇⠀⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣴⢋⣁⡤⢶⠟⠀⠀

⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠓⠢⣀⣀⣀⣀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠞⢻⠁⠀⠀⢠⠞⠁⢀⡤⠟⠛⢢⣴⢁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠁⠀⢸⠀⠀⢠⡏⣠⠞⠉⠀⠀⠀⢰⡇⡾⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠛⢿⡇⠀⠀⠘⡆⠀⣸⡴⠃⠀⠀⠀⣀⣀⠾⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢮⠳⣄⠀⠀⢱⡀⣿⠃⠀⢀⡴⢾⢍⠀⠀⠀⠗⠀⣼⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠘⣦⣈⣙⣲⠶⠒⣿⣤⣾⠃⠰⣿⣟⠟⠓⠀⠀⠘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡼⠁⣰⣿⣿⣄⣴⡏⢹⣏⡇⠀⢬⣽⣾⡲⣶⣄⠀⠘⣌⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⢠⣿⡋⠿⠞⠁⢧⡸⡏⠁⠀⠏⢠⣇⢸⡿⣿⡷⡄⢹⣆⠀⢱⣄⠀⠀⠀⠀⠀⣠⠴⠒⠋⠓⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⡾⣼⣾⣿⣷⣤⡈⠓⠓⠀⠀⠀⠈⣯⣿⣿⡿⠃⠁⠀⢻⢧⣀⣿⠀⠀⠀⢠⡜⢁⡤⠞⠛⠛⠓⢄⡈⢣⡀⠀⠀⠀⠀⠀⠀ ⠘⣿⢰⡇⣿⡇⣽⣽⣿⣿⣀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⢸⣼⠟⠁⠀⠀⠀⡼⢠⠏⠀⠀⢀⣀⠀⠀⠙⢦⡱⣄⠀⠀⢰⣦⡀ ⠀⠹⣼⡁⢻⠧⣘⡿⣿⣏⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⢸⠃⡞⠀⡠⠞⠉⠈⠙⠲⣄⡀⠈⠚⠦⢤⠼⣿⡇ ⠀⠀⠙⠇⠸⡇⠀⠀⠀⠻⣅⣀⣤⣀⣾⡿⣿⠀⠀⠀⠀⢀⠾⡇⢸⠀⠀⠀⠀⢸⡀⡇⣰⠁⢀⡤⠖⠒⠒⢮⣝⡢⠤⠤⠼⠚⣽⠇ ⠀⠀⠀⠀⢰⠿⣆⡀⠀⠀⠀⠙⢿⣿⣿⢈⡿⠀⠀⢠⣾⠉⣸⠁⡾⠀⠀⠀⢀⣀⣷⣷⣿⠰⠋⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀ ⠀⠀⠀⢀⡇⠀⢨⡟⠓⠤⣤⣀⣀⣈⣛⣋⡀⠀⠀⠀⢿⡴⣣⠞⠁⠀⣠⠖⠋⠁⠀⢀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠁⠀⠸⡇⠀⢸⠇⠀⠉⢹⠉⠉⠀⠀⠀⠀⠈⢿⠁⠀⣠⣾⣁⣀⣠⠤⢤⡏⣴⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⢧⠀⢸⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠳⠿⣓⣲⠞⠋⠀⠀⠀⢻⡻⠟⠓⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠈⢧⡘⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⢦⠀⠀⠀⠀⠀⢷⠀⠀⠀⣧⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠶⢽⡾⠦⠤⣴⣇⠀⠀⠀⠀⠀⣀⡴⢛⡵⠋⢳⠐⢷⠀⠀⠀⠀⣈⣇⠀⠀⠃⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢛⡟⢹⣏⠙⠒⠒⠒⠛⢉⡴⠋⠀⠀⠘⡇⠈⡇⢀⣤⢞⡽⠋⠀⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠦⠯⠴⡯⢿⡉⠒⠒⠒⠋⠁⡀⠀⠀⠀⠀⣧⣀⣇⡿⣾⡏⠀⠀⠀⣠⠏⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸⢫⣧⡴⡏⠙⠓⠒⠚⢹⠂⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣷⣤⠤⣖⠋⠙⠢⣤⣀⡼⠁⠀⠀⣶⣴⡿⠛⠁⠀⣧⣄⠀⠀⠀⣼⣴⠀⠀⢀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢿⣻⣿⠯⠿⠦⣤⣄⡾⠀⠀⠀⢸⠁⠀⠹⣆⡀⠀⠀⢸⠀⠀⠀⣿⢱⠀⢡⡀⣷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⣯⣷⣦⠖⢋⡞⠀⠀⠀⢠⡏⠀⠀⢀⡞⠀⠀⠀⡏⠀⠀⠀⠻⣯⠤⠟⠚⣡⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡞⠀⠀⠀⠀⡾⠀⠀⢀⡞⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⠶⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⢀⠘⠓⠀⣤⠚⡇⠀⠀⣸⠁⠀⠀⠀⢰⡇⠀⢀⡞⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠈⣿⠂⢀⡟⢰⠇⠀⠀⡏⠀⠀⠀⠀⠈⡇⢀⡞⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠾⢭⣁⣀⠎⠀⠀⢸⠃⠀⠀⠀⠀⠀⣧⢞⡄⢀⠀⡀⢰⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢻⡖⠃⢮⣷⣿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⢷⠤⠤⠬⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⢀⠀⠀⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠄⢠⣀⣠⠖⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠒⠠⠤⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠂⢉⣩⠭⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠒⠉⠈⠉⠐⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠱⡀⠀⢀⠴⣊⠤⠐⠒⠉⠉⠑⠒⠢⠄⡀⠀⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⢀⠎⠀⠀⡆⠘⡴⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⡞⠀⠀⠀⡽⠀⢸⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⢠⠇⠀⠀⠀⣧⠀⠀⡦⣶⣂⣤⡀⠀⠀⠀⠹⡙⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⢳⠀ ⢸⡄⠀⠀⢰⠁⠃⠸⠁⡠⠄⠀⠉⠙⠲⢤⡀⢱⠀⢀⣼⣀⡈⢟⠢⣄⠀⠀⢸⠀ ⣸⢳⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠢⡇⣾⠃⠙⣷⡸⡄⠀⠑⢄⢈⠀ ⡇⠀⢣⡀⠀⠀⠀⠀⠈⢲⣾⠟⠻⣦⣄⠀⠀⠀⠁⣿⠀⠀⠘⠿⢇⣀⡀⠈⢾⠀ ⢣⠀⠀⣇⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠙⠂⠀⠀⠑⠚⠛⡄⠐⠊⠲⣎⠁⠀⠀⠀ ⢸⡀⠀⢸⡄⠀⠀⠀⠈⠻⢃⣀⣀⠀⠀⠀⢠⣇⠀⠃⢀⠇⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⢧⠀⠈⢟⢄⠀⠀⢠⣊⠡⠔⠋⠀⡠⣺⠉⠙⠷⣶⠋⠀⠆⠀⢀⡼⠁⠀⠀⠀ ⠀⠈⢧⠀⠈⠢⣙⠢⢄⣀⣀⣀⣀⡠⢀⡇⠀⠀⠀⠙⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠉⠀⣀⣤⠊⠀⠈⠧⣄⡀⠀⢀⡤⠒⢫⡀⠀⣀⣀⠀⣀⠀ ⠀⠀⠀⠀⣙⣦⣀⣈⡉⠉⠀⠀⢧⠀⠀⢀⣀⡤⠤⠾⠭⢽⡶⠻⣿⣭⣿⠴⠷⠊ ⡠⠖⠛⠉⠁⠀⠀⠀⢹⠀⠀⠢⣘⡤⠚⠉⠀⠀⠀⠀⠀⢈⠏⣉⣉⣡⠤⠤⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⠠⠤⠤⠒⠉⡀

⠀⣀⠀⠀⠀⠀⠈⣗⣄⣀⠠⠄⠒⠀⠀⠀⠀⠒⠒⠂⣤⠀⠤⠤⠄⢀⡀⠀⠀⠀ ⢀⠁⠈⠑⠢⡀⡠⢺⠤⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠑⢤⠀ ⠈⠀⠀⠀⢀⠎⠀⠀⢣⠒⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠡ ⡇⠀⡇⠀⠎⠀⠀⠀⠈⢆⠠⠜⢀⠇⠀⠀⠀⡄⡘⡘⠐⠒⠀⠤⠤⠤⠤⠀⠒⠀ ⣧⠀⢡⢸⢠⠂⠀⠀⠀⠈⣄⠄⠂⠀⠀⠀⠰⡰⠋⢀⢤⣒⣀⣈⣄⠀⠀⠀⠀⠈ ⢸⡀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣴⠋⠁⠀⠘⣽⠹⣀⠀⠀⠀⠀ ⠈⢧⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠣⢂⡀⠀⡠⢣⠂⢹⠀⠀⠀⠀ ⠀⠀⠓⢤⣸⡀⠀⠀⠀⠀⠀⡀⣀⢜⣁⠀⠀⠀⠀⢀⣈⠙⠂⠁⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠡⡀⠀⠀⢀⣥⣴⠛⠁⠀⠁⠠⡂⠉⠀⠆⠀⡀⠀⢰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⡀⢀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠤⣀⣀⡀⠀⠀⢀⡠⡀⠆⢱⡿⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢡⠀⠀⠀⠀⢰⠀⠀⠀⠁⠒⠈⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣀⠀⠙⢦⡀⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢢⠭⠦⠤⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣿⢿⣫⣧⡑⡌⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣇⣿⢈⠁⢳⠱⠘⣀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠑⠒⠂⢠⠶⠶⣖⡒⣮⣿⢩⣽⠉⢉⢯⣹⡝⡠⠄⠀⣤⣤⣀⣀⣀⠤⠤⡀ ⡨⠶⠀⠀⠘⠒⢤⠄⠈⢷⢿⣿⣿⠀⢸⣿⣿⡟⡠⠊⢁⣀⠨⠕⠀⠀⣀⠔⠁ ⠙⠢⠤⣀⠀⠀⠥⠤⡄⠀⠺⣑⡤⠷⠧⣴⡿⠓⢁⣄⣈⣱⠀⠀⠀⠀⣈⠅⠀ ⠀⠀⠸⠤⠔⣖⣁⣠⠉⢉⠒⡛⠇⠀⠀⡝⡗⡙⣿⢃⡀⠰⡄⣈⣙⡍⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣒⣧⣻⣄⣴⣧⣧⡈⡸⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣒⢧⡈⡳⢋⣸⡿⡫⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡿⣯⣘⣿⣟⣹⢶⣾⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠿⡘⠐⠘⠀⢿⣌⢿⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⡊⠔⡇⠀⠀⠀⢸⣜⣌⡊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠞⠒⠛⠒⢺⢴⡿⣶⢾⢺⡏⡧⠩⠦⠵⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠃⠬⠔⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⢏⡟⠁⣾⢧⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⡆⣰⣿⢣⡏⠀⠀⣇⠀⡟⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣿⢹⢳⠃⡼⠀⠀⠀⢻⣸⡇⠀⠹⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠈⢏⢇⠀⠀⠻⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⢳⣸⠀⡇⠀⠀⠀⠀⢸⠘⡄⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣠⠿⠚⢯⣇⢳⠀⠀⠀⠀⡼⠁⢻⡀⠀⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢾⣁⡀⢀⡀⠻⣞⣇⠀⢀⣴⣁⣀⣾⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣷⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠼⠟⠻⢷⣭⡤⠈⠛⠒⠋⠁⠀⠀⠈⠙⠛⠉⣉⡨⠭⠽⣗⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢆⠙⢎⠳⣤⡀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣤⡈⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣦⠈⣧⣳⡙⣦⡀⠀⠀⠀⣼⠃⢹⣿⣿⡟⣦⡄⠀⠀⠠⣄⣀⣀⠀⠀⠀⠀⠐⡆⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠿⠹⣧⣘⡽⣦⡀⢠⡇⠀⠀⠉⠛⠛⠟⠁⠀⠀⠀⣽⣿⣟⣛⠷⣄⡀⣸⠛⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀ ⠀⠀⠀⠀⢹⡳⡟⢾⡿⡇⠻⢱⣌⣧⠀⠀⠀⣄⠈⠉⠉⠒⢆⣸⣿⣿⣴⣟⣿⠟⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠁⠀⠀ ⠀⠀⠀⠀⠈⢿⠃⠘⡇⠹⠟⣿⠛⣮⢧⡀⠀⢸⣷⣦⣤⣀⠐⣀⡀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢁⡼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⢻⠒⢶⡏⢢⣉⣯⡳⣤⡀⠛⠦⣭⣿⠟⠋⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠖⣉⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣌⠧⠀⠓⠀⠃⢻⡽⣄⣹⠦⢤⣀⣀⣀⣀⣀⣠⠤⠞⠁⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠡⠒⠛⢹⠆⠔⠚⠉⣻⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠲⣟⠛⢮⣿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⡡⠐⠒⠒⣶⣀⣤⣞⢑⣶⡤⠔⣻⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠲⢤⡀⡾⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⢀⡴⣞⠁⠖⠋⢉⣹⣆⣀⡀⠀⢀⣠⠜⠭⠤⠴⣶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠙⣤⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠖⠛⠋⠩⠗⠢⢤⠀⠀⠀⣠⠝⠚⢙⡿⠀⢤⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⣆⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⠶⠋⠀⢈⡿⠀⣀⡾⣭⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡿⠁⠀⢧⠀⠀⠀⠀⢰⠇⠀⢸⠀⠀⠈⠙⠻⠥⠤⣤⣹⣡⣶⣒⡒⠚⠯⣄⠙⢦⡀⠀⠀⠀⠀⢀⣀⡸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠹⣦⠀⣨⣧⡀⠀⢠⠏⠀⠀⡜⠀⠀⠀⡄⠀⠀⠀⠈⣹⡏⢙⣿⣍⠲⡄⠈⢦⡀⠉⠒⠒⢒⣶⠿⠛⣱⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠘⠏⢿⠁⠀⠙⢦⠏⠀⠀⢸⠇⠀⠀⠀⠙⢦⡀⠀⠀⠉⠀⠈⣏⢻⣧⠈⢦⡀⠙⠢⣄⣀⣀⣀⡴⢚⣟⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡚⠀⡆⠘⢾⡖⠠⣼⠃⠀⢠⠏⠀⠀⠀⡟⠒⠒⠲⣖⠒⠋⠛⢦⡀⠀⠀⠀⢹⡄⢻⣣⡀⠳⣄⠀⠀⠉⠉⠁⠀⣿⣽⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢡⣄⠐⣶⡶⠃⠀⠀⡏⠀⠀⠀⠸⣇⣀⠀⠀⠈⠓⢦⣤⠀⢹⠶⣄⡀⠀⠹⢦⠙⢷⣄⡈⠓⠶⠤⠤⢴⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠭⠽⠛⠁⠀⠀⢠⡇⠀⠀⠀⠀⠙⡎⢳⣄⠀⠀⡸⠀⠀⠘⡇⠀⢹⠀⠀⠈⣇⠀⠙⠛⠒⠦⠒⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢳⠀⠏⣇⢰⡇⠀⠀⠀⣿⣢⡘⡆⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⡤⠀⢹⣾⠀⠀⠀⠀⡁⠘⡗⡇⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣤⠀⡀⠀⠀⢰⡿⣿⣤⠀⢀⣰⠁⢠⡿⡇⠀⠀⠀⠠⠼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⢹⠯⢥⢾⡿⠁⠹⣿⡀⢈⣛⣠⠟⠀⣇⡀⠀⠀⠸⠗⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠀⠀⠀⠈⠻⢿⠟⠁⠀⠀⣇⣹⠀⣖⡂⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣀⡀⣼⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⣠⡿⡿⠁⢸⠉⠻⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⣽⢻⢡⠃⠀⠘⣆⡇⠈⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣿⠇⢸⠀⠀⠀⠸⣧⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣸⠿⣾⡸⡀⠀⠀⢠⠂⢇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣮⣁⢀⣈⠳⣧⠀⣠⣊⣠⣏⣴⣿⣁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡶⣦⢄⠀⠀⠀⠀⠀⠀⢠⣟⠛⠉⡿⡾⠀⠈⠉⠁⠀⠀⠀⠉⢀⠤⠘⠛⠿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡈⢮⢻⢦⡀⠀⠀⢀⡿⢻⣿⣶⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⡸⠹⣇⣻⣦⡀⢸⠀⠈⠙⠛⢿⠀⠀⠀⣹⣿⣓⡶⣀⣠⠗⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀ ⠀⠀⠀⢿⡏⢻⠿⣙⣳⣼⡄⠀⠰⣄⠀⠉⠒⠼⠿⠷⠾⠿⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡿⠀⠀⠀ ⠀⠀⠀⠘⣇⠈⣦⣁⡯⡙⢿⣦⡀⠻⣟⣳⣦⠴⠂⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⢞⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⡱⠈⠃⠹⠹⣿⣙⡦⢄⣉⣁⣀⣀⣠⠴⠊⠀⠀⠀⠀⢀⣠⠤⠖⠊⠕⠒⡦⠠⠖⢛⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣾⠋⠻⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⣠⠔⢊⣁⡐⠂⠹⠆⠤⢌⡱⠤⠒⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠉⠑⢴⠃⠀⠀⠀⠀⠈⠣⣄⣴⠾⣤⣈⡀⠐⠓⠂⡄⠤⣶⠉⢒⣸⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣇⣀⢾⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⢠⡤⠛⠀⣲⠋⢠⣶⣡⡴⠋⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⠁⠘⡄⠀⠀⢀⡆⠀⡐⠀⠈⠙⠛⠶⢤⣭⣴⣖⡓⠻⢄⠑⢄⠀⠀⠀⢀⣀⢾⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣷⣤⠟⢆⣀⡞⠀⢠⠃⠀⠀⢄⠀⠀⠀⠟⠠⣿⣯⠢⡀⠣⣀⠉⠉⠻⠛⣡⡟⠀ ⠀⠀⠀⠀⠀⠀⣷⠄⠀⠠⣤⢀⡳⠀⢀⡟⠀⠀⡾⠤⠤⡤⠤⠳⢄⠀⠀⠀⢣⠹⣧⠈⢆⠀⠉⠒⠂⠈⣻⡿⠁ ⠀⠀⠀⠀⠀⠀⠙⣦⣠⣀⣲⡴⠃⠀⡞⠀⠀⠰⣧⣀⠀⠈⠲⡤⠀⢹⠦⣀⠈⠳⡜⢷⣄⠑⠢⠤⢤⡶⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⣇⠀⠀⠀⠘⡈⢦⡀⢠⠃⠀⠸⣄⢸⡀⠀⠹⡀⠈⠉⠑⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢁⠈⢳⡜⠀⠀⠀⠋⣷⡇⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⣀⡀⠈⢠⣾⣧⠄⢀⣴⠀⣼⡇⠀⠀⠠⠼⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⡟⢶⡟⠁⠹⣇⣠⣥⠜⠁⡧⡀⠀⠘⠃⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⢳⡃⠘⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠶⠶⣶⣶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠈⠙⠲⣤⠀⠈⢿⣦⠀⠀⡎⡝⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠲⣄⠹⣧⠀⢻⣇⠀⠀⠙⣦⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠛⠉⠉⠙⣯⠈⣿⢶⡦⢤⣄⠀⠀⠈⠳⣜⢧⡘⣿⠀⠀⣰⠋⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠒⠋⣩⣭⠤⠬⠷⡃⢰⠏⠳⣄⡉⣳⡤⠴⠚⠛⠛⠛⠒⡶⠃⠀⠀⢀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢁⡴⠛⡇⠹⡄⠀⠀⠹⣏⠀⢀⡏⢻⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣾⠀⠀⢹⡀⠹⣄⠀⠀⣼⢷⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠙⠲⣄⠹⣄⠈⠳⣶⠧⡀⠁⠀⠀⠀⢀⡠⠶⠒⠒⠦⢄⠀⠀⢀⡼⠁⠀⣼⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠈⠳⣌⠓⢤⡿⠀⢰⡀⠀⠀⢰⠏⠀⠀⣠⠀⡄⠀⢱⣦⡾⠁⠀⣰⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣄⡀⠘⢇⢠⣷⣤⣄⡇⠀⠀⡇⠀⠀⢀⣿⣤⣧⣴⣯⣽⣧⡼⠃⡿⢹⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡤⠾⠛⢦⡘⡇⣿⣿⢿⡇⠀⠀⣇⣠⣶⣿⣿⣿⣄⠀⣗⠟⠛⠀⢸⢿⠀⢧⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠉⢹⣷⣶⣴⣷⣥⠟⣿⣿⠁⠀⠀⢹⠈⣿⣿⣿⣬⡿⢭⠟⠓⠒⢀⣿⠘⡄⠘⣿⢸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠙⠻⢽⡒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⢤⣈⣹⠾⠟⠁⡴⠟⠁⠀⠀⠀⠸⠧⣘⣛⣛⡿⠖⠃⠀⠀⠀⢸⠟⠀⡇⣰⠇⢸⠀⠀⠀⠀⢀⡴⠚⠁⣀⡠⠴⠒⠦⢤⡀⠀⠀⠘⢦⡀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡏⠀⣇⡿⠃⠀⣾⠀⠀⢀⡴⠋⢀⡴⠚⠁⢀⣀⣀⣀⡀⠈⠳⣄⠀⠀⢷⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣤⣤⣀⣀⣤⣤⠤⠒⠛⠉⠀⠀⣸⣧⣴⣿⠴⠛⢉⡟⠀⢠⠟⠀⡴⢋⣠⠖⠋⠁⠀⠀⠀⠙⠳⣄⠈⠳⣄⠈⣧⠀⠀⠀⢸⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣋⣀⡀⠀⡼⠀⣰⠇⢀⣞⡵⠋⠀⣠⠴⠖⠋⠉⠙⠲⢤⡈⢣⡀⠙⣆⢸⠀⠀⠀⢸⢾⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠙⠦⣄⠀⢸⠃⠀⠀⠀⠀⠀⠀⣴⢻⠟⣵⣮⣭⠀⣿⣶⠃⢀⡇⢠⣯⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠱⡀⠘⣿⠀⠀⠀⡼⢸⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⠙⡏⠀⠀⠀⠀⠀⠀⣼⢡⠏⠀⣧⠽⢻⡼⢻⣧⣄⣼⢀⡞⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣴⠇⠀⠀⣰⠃⢸⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢦⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢿⣮⣀⣀⡼⠶⠋⣠⠞⣇⠀⠉⠻⢧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠁⠀⠀⣰⠃⢀⡏⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣟⠳⣤⣹⡀⠀⠀⠀⠀⠀⠈⣧⣤⣤⣤⠴⠚⠁⣴⣿⡀⣶⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠚⠉⠀⠀⣠⠞⠁⠀⡜⠀⢠⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢣⠀⠸⡇⠀⠀⢰⡀⠀⠀⢻⠀⠀⠀⢀⡠⠞⠁⣼⠠⠇⢠⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣀⡴⠚⠁⠀⢀⡜⠁⢀⣾⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⡇⠀⢧⠀⠀⠀⠱⣄⠀⢸⣷⣒⡊⣉⣀⠴⣺⠿⠇⠀⡆⢸⡄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡁⠀⠀⠀⣠⠏⠀⢀⣾⣿⡟⢻⡄ ⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢰⠇⠀⢸⠀⠀⠀⠀⢻⡶⣜⠧⠤⠤⠴⠚⢫⠀⠀⠀⠀⠙⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡤⠚⠁⢀⣴⣿⡿⠋⣠⡏⣿ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢠⡞⠀⠀⢸⡇⠀⠀⠀⠀⣧⠈⠳⠦⣄⡀⠀⠀⠱⣄⠒⠀⠀⠀⠀⣼⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠀⢀⣴⣿⡿⠋⢀⡴⡟⢱⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠞⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⡄⠀⠀⠈⠉⠑⢲⡖⠚⠳⣄⠀⠀⠀⠀⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⡿⠟⠁⠀⣠⠞⡼⢁⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢿⣟⠋⠁⠀⣀⡴⠊⢁⡞⢠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢹⠈⢳⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠳⡖⠋⠉⢀⡴⠏⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡇⠀⠹⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠘⣶⠒⢋⣤⣾⡏⢰⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠙⡄⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠸⢷⠋⡏⢸⣅⡟⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢀⡟⣇⢧⡈⠻⢶⡿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⣧⡈⠳⠽⢶⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣼⣷⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣸⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⡠⠴⣖⠒⠒⠲⣶⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠊⠁⠀⠀⠀⠉⠒⢄⡘⢷⡀⢰⡆⠙⠢⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠒⠒⣾⠓⡦⣤⣄⣀⠀⠙⠪⣷⡈⡇⠀⢀⠞⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣉⡬⡶⠒⠻⣁⡜⠑⣤⣉⠶⠒⠛⠋⠙⠒⠎⠀⠀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡔⠉⢇⠹⡄⠀⠙⣦⣰⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡓⠦⡈⢦⠈⠢⣼⡉⠃⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⡼⠀⢸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠈⠢⡑⢴⡇⠈⡄⠀⢀⠎⠀⢀⡀⡀⢈⣶⡞⢀⣀⣏⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣲⣄⠱⡼⣿⣶⡆⠀⠈⠀⣀⣼⣷⡓⢺⣿⡿⠋⣸⠘⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢻⣦⣤⣷⣧⢿⣿⠇⠀⠘⡟⣿⣿⣟⣷⣺⠿⠀⢀⡟⡂⠰⡼⡇⠀⠀⠀⠀⠀⣀⡤⠔⠒⠛⠛⢶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⠭⠿⠟⠁⡴⠋⠀⠀⠀⠧⠜⠛⠻⠗⠁⠀⠀⡸⠃⢣⡴⠃⡇⠀⠀⢀⡴⠊⢁⡠⠐⠒⠤⣄⠀⠈⢢⡈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢤⣠⠂⠀⠀⠀⠀⠀⣀⠤⠀⢀⡇⣸⣟⣁⢰⠃⠀⡴⠋⡠⠊⣁⠠⠤⠲⠤⣀⠑⢄⠀⢳⡀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠖⠉⠉⠁⠀⠀⢀⣾⣿⣛⠉⠀⡞⢀⡞⢀⣾⠕⠋⣀⠤⠤⠤⠤⣌⠳⡀⠱⡀⡇⠀⠀⢸⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠉⠲⢄⡀⡞⠀⠀⠀⠀⢀⡴⡿⣿⣯⡍⣹⡾⠁⡼⢠⡟⠁⡴⠊⠀⠀⠀⠀⠀⠀⠑⡝⡄⢹⡇⠀⠀⡟⡿⣧⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣾⡘⠀⢳⣋⡿⢫⡗⠰⣧⡎⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⠟⠀⠀⡜⢀⠇⣿⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢷⢤⣀⡇⠀⠀⠀⠀⠘⣏⣉⣉⡡⠔⢁⣷⢡⠀⠙⣅⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠜⠁⠀⣠⠞⠀⡜⠀⣟⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⠈⢻⠀⠀⢄⠀⠀⣯⠀⠀⢀⠔⠋⣽⠿⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡤⠚⠁⢀⡜⠀⣸⣿⡆⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠘⡄⠀⠈⢣⡀⢸⡖⣉⣠⣶⠿⠛⠀⢰⣼⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡠⠊⢀⣴⣿⠏⣷⡀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⡸⠁⠀⡇⠀⠀⠈⡏⠲⢍⡉⠁⠀⢢⡀⠄⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠁⢀⣴⣿⠟⢁⡾⢹⠁ ⠀⠀⠀⠀⠀⠀⠙⠤⠴⠁⠀⠀⠃⠀⠀⠀⢹⠀⠀⠈⠙⠒⡶⠿⢦⡀⠀⠀⠉⠉⠑⢄⠀⠀⠀⠀⠀⣼⣿⣿⣶⠿⠋⠁⡰⣻⢁⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠈⠑⡦⢄⠀⠀⠈⠳⡄⠀⠀⠀⠘⠿⣉⣀⣠⠔⠋⡴⣡⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠈⢣⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⢣⣀⠴⢋⣴⠃⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⢳⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢳⡞⡟⢹⡸⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀⢣⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠳⡱⣈⣹⠟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠃⠀⠀⠀⠀⠀⣷⣤⣤⣴⠁⠀⠀⠀⠀⣸⣤⣄⣀⣈⡇⠀⠀⠀⠀⠹⡄⠀⠀⠘⠢⠬⠽⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣷⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠓⠀⠁⠗⠚⠀⠀⠐⠀⠀⠀⠀⣰⢋⣀⣀⣀⠀⠀⣀⢠⡎⠉⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠉⠑⠪⡟⢀⠄⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡄⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⣀⣀⡤⠶⠛⣁⡤⠤⠖⠒⣲⠂⠀⠀⢀⣠⢼⡀⠀⣧⠀⠀⠀⢹⠀ ⢹⠋⠉⠉⠁⢀⡠⠖⣋⣁⣀⠄⠀⡼⠁⢀⡠⢞⡉⠀⠀⢳⠀⡇⢳⡄⠀⢸⡇ ⡎⠀⠀⣠⠖⡏⣲⠞⢋⣿⡆⠀⢰⢃⡴⠋⠀⣠⠽⢶⡤⠄⠃⠈⠀⠁⠀⢼⠁ ⠃⢀⡞⠁⠰⡷⠁⣾⢿⣿⡇⠀⣿⠞⠀⠀⠞⠁⠀⠀⠹⣦⡄⠀⠀⠀⢀⡏⠀ ⣠⠋⠀⠀⠀⡇⠀⠻⣂⡨⠃⠀⠋⠀⠀⠈⠘⣿⡄⠀⠀⢷⠤⠀⠀⠀⡎⡇⠀ ⠁⠀⠀⠀⢠⠷⡄⠀⠀⣀⠤⣄⣀⠀⠀⢸⣾⣿⡇⠀⠀⠾⠂⠀⠀⢀⡇⡇⠀ ⠀⠀⠀⠀⡾⠐⠈⠙⠉⠁⠸⠄⠠⠉⠀⢸⣻⡩⠃⠀⡀⠂⠀⠀⠀⢸⢹⠁⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠈⠉⠉⠩⠤⠦⠀⠀⣠⢇⡏⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡿⠛⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠘⠧⢄⠀⠼⠂⠀⠀⠀⠀⢀⡰⠋⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠙⢳⡦⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡀⠳⣄⡀⠀⠀⠀⠀⠀⣇⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣯⡛⠓⠛⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠤⠤⣀⣀⡴⠋⠀⣰⠀⣸⠃⠙⠦⣄⡀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡚⠉⠉⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠑⠇⠀⠀⣇⠔⠉⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡲⠖⢀⢀⠛⠂⢄⡐⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⢰⡾⢒⡄⠀⠁⢀⡀⢀⡅⡰⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⣂⡇⣴⡷⠀⢰⣉⢽⡆⠛⣡⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡞⣛⠁⠂⠘⠿⠿⠤⢤⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠊⠐⡢⠄⡀⠀⠀⠀⠡⣹⢃⠄⢀⠝⠁⡠⠊⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⡅⠀⠀⠁⠂⠄⡀⢈⠗⠒⠒⠲⡉⠀⠠⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠒⠚⠀⠤⠤⠀⢀⣀⣠⠁⠀⠀⣔⠉⡠⠀⢪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⢹⡑⣒⢿⠊⠁⠉⠐⢄⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠤⡇⠀⠀⠀⠀⠈⡶⠒⠼⣀⠐⠀⠀⠂⠉⠀⠀⡱⡤⡰⠄ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⡆⠀⠀⡇⠀⠀⠀⢣⠀⡖⢂⠈⡄⠘⠤⠁⠐⢀ ⠀⠀⠀⠀⣀⠠⠌⠂⠤⠀⢣⣀⠃⠀⠀⡧⢀⡀⠔⡃⠀⠡⡜⠀⠈⠀⠈⡺⠈⠁ ⠀⠀⢰⠭⡀⠀⠀⣀⠤⠐⠒⡝⠀⠀⠀⠧⢀⠀⠀⠈⠑⢎⠈⠒⠀⠀⠊⠀⠀⠀ ⠀⠀⠀⠈⠐⠒⠈⠀⠀⠀⠘⠤⠤⠤⠜⠀⠀⠑⢄⣐⣈⠔⠀⠀⠀⠀⠀⠀⠀⠀

⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⣽⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣏⡟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⢸⠳⣄⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢯⠀⢸⠗⢴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⠊⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣻⣞⠀⢨⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠏⠉⠈⠣⡞⠀⠀⡗⢦⡀⣀⡠⠴⠒⠒⠒⠒⠒⣺⠁⠀⠀⠀⣸⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣦⡜⢁⡶⠋⠁⠀⠀⠀⣀⣀⠴⢚⡇⠀⠀⠀⢠⠇⢀⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⠀⠀⡜⠀⠀⠀⠈⡳⠋⢀⡠⠖⠚⣉⣉⠥⠞⢀⣼⣦⡀⠀⠀⠀⢀⡾⡃⢣⠈⢿⣄⠀⠀⢀⡤⠖⠉⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⣾⠀⠀⠀⠀⠈⠁⡾⠁⠈⠉⡉⠁⢀⣠⣴⣿⣿⣯⡟⠀⠀⠀⠉⡗⠀⠘⡄⠈⣾⣀⡴⠋⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⢀⣴⡿⠻⣿⣿⣿⠉⠀⠀⠀⠀⡼⠃⠀⠀⡇⠀⣿⣿⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠈⣼⠀⠀⠀⠀⠀⢹⡀⠀⠀⢘⣾⠛⢧⡠⢿⢿⡏⣀⠀⠀⡠⠞⠁⠀⠀⣸⠀⠀⡟⣿⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣄⠀⢡⠂⠀⠀⠀⢦⡀⢣⠀⠀⠐⢻⡀⠀⠈⣩⡿⠋⠁⡠⢊⠔⠀⠀⠀⢠⠇⠀⠀⣇⡟⠀⢠⠃⠀⣠⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⢳⣌⠳⣀⠀⠀⠑⢤⠞⠁⠀⢠⢊⡴⠁⠀⠀⠀⣠⠋⠀⠀⢠⡻⠀⠀⡎⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⣀⡠⠟⠀⠉⠉⠉⠀⠀⠀⠀⠀⢰⣳⠟⠀⠀⠀⠀⡴⠁⠀⠀⠀⣸⠃⠀⢰⠁⡞⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⠃⠀⠀⠀⢠⠎⠀⠀⠀⠀⡴⠁⠀⢠⠇⢸⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠙⠦⣄⣀⠀⣀⠤⠒⠉⢹⢀⡟⠀⠀⠀⣰⠋⠀⠀⠀⢀⡜⠁⠀⣠⠋⠀⡏⠀⠠⠤⢺⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡾⢸⡇⠀⠀⡴⠁⠀⠀⠀⣠⠋⠀⢀⠜⠁⠀⡼⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠲⡶⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡾⠁⢸⡇⠀⣰⠁⠀⠀⠀⣼⣇⢀⠔⠁⠀⢀⠜⠁⠀⣪⠏⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢠⣴⠇⠀⠀⠀⠀⣠⣾⣷⣖⠹⣇⠀⡇⠀⠀⠀⢸⠟⣹⠋⠀⠀⡰⠋⠀⢰⠖⠁⠀⠀⠀⢰⡤⣀⣀⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣴⢞⣁⣀⣠⠤⠔⠋⢡⡯⣏⣷⣇⣼⡔⡇⠀⢱⡀⢹⡀⠏⢀⣤⠄⠀⣉⠉⠁⠀⠈⡖⠤⠤⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣰⠀⠀⠀⣾⠀⢙⡿⠟⠙⠫⣿⡀⠀⠙⢤⡱⣄⠀⠛⠒⢒⣿⠻⣕⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⡦⠀⠀⣿⡴⠏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠛⠛⠒⢒⡿⠇⠀⠀⢑⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠉⢠⡕⠛⠃⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠴⠒⠚⣉⡀⠀⣠⠚⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡦⠔⢉⡀⠀⠀⢠⡿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠀⢸⢹⢼⠁⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢄⣉⡁⠀⠁⠀⠀⣼⠀⡇⠀⠀⠀⢈⣿⠀⢀⡴⠋⢹⡗⠤⠤⠞⣸⡎⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠏⠀⡇⠀⠀⠀⠀⢹⣧⠏⠀⠀⠈⠓⠒⠔⠒⣽⠃⠀⠀⠀⠀⠀⠀⠀⡰⢸⠀⠀⠀⠀ ⠎⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠈⠓⢤⡇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⢞⠏⠀⠀⠀⠀⠀⠀⠀⡰⠃⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠀⠈⠓⠦⢄⣀⡀⡇⠀⠀⠀⣠⡤⠞⠡⠎⠀⠀⠀⠀⠀⠀⣠⠞⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣠⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⡴⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⢀⡴⢋⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠉⠉⠁⠒⠀⠀⠄⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠴⢚⣁⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⡶⠋⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⢀⠞⠁⠀⠙⢿⡇⠀⠀⣀⡔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⠻⠀⠀⠀⠀⢸⡀⡰⠋⠀⠀⣼⠤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⡁⠀⠀⠀⣠⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⣯⡤⠚⠉⠑⡄⢠⠏⠀⠉⠙⢦⣠⠏⠀⠀⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣽⣏⠤⣄⠀⠀⠘⠃⠀⠀⠀⠀⠀⢉⠀⠀⡄⢸⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡿⠁⠐⣿⡄⠀⠀⠀⢀⣴⣚⡑⠲⣞⣠⡴⠁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⡄⠇⢠⣠⣿⡷⠀⠀⢀⡏⢀⣼⣿⠀⠙⠓⢁⡜⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣺⣾⣿⡿⠃⢀⠀⢸⣿⣿⣾⡏⠀⠀⠘⡟⠉⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢡⣬⠀⠀⠀⠀⠀⠛⣛⠛⠓⠒⠛⣶⠃⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢻⣯⡓⠒⠒⠒⢚⡽⠃⠀⠀⣰⠃⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠁⠀⠀⠀⢣⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠈⠲⣝⠢⠤⠤⠤⠛⠁⢀⡤⠞⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⡼⠉⠒⠒⠒⠒⢿⠁⠀⠀⠀⣤⠀⢲⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠧⣀⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠞⠁⠀⠀⠀⢀⡤⠒⠛⢲⠂⣶⡧⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠒⠒⠂⠤⠤⠤⢀⣀⣀⠏⠀⠀⠀⠀⠀⣯⡀⢀⣠⠎⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠃⠀⠉⡿⠋⠤⠴⢾⣷⠖⠊⠉⠉⠑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⢻⡦⠤⠒⠁⡏⠀⠀⠀⠀⢀⠀⠀⠙⢆⣀⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣷⠀⠀⠀⠀⢸⠀⠀⠀⠸⡷⡶⠶⠦⢼⣄⠀⡰⠊⠁⠉⠉⠒⢌⠁⠀⠀⠀⠈⣳⡤⣀⠙⡦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠳⡇⠀⠀⢀⣀⠀⠀⢱⡀⠀⠀⡎⢀⡇⠀⢡⡇⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⣇⠀⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣹⠀⠀⡏⠀⢳⠀⠀⢇⢀⣀⡓⠊⠀⢠⠀⠀⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣤⡀⠀⠀⠘⢦⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠰⡀⢸⠀⠀⠘⠁⠀⠀⠑⢦⡏⠉⠈⠁ ⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠈⠉⠂⠀⠠⣿⢺⠁⠀⠀⠀⠀⡟⠁⠤⠔⠊⠙⠒⠤⣀⠀⠀⡹⢧⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⢼⠥⣀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠋⢁⡏⠀⠀⠀⠀⠀⡷⢄⡀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠉⠒⠢⠤⠒⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠤⣑⡄⢀⡠⠖⠉⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣸⠀⠀⠉⠢⣄⠀⠀⢀⡠⠄⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠈⢧⣈⣁⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀