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The numbers $1, 2, 3, \dots , 13$ are written on a board. Every minute you choose four numbers $a, b, c, d$ from the board, erase them and write onto the board the square-root of $(a×a + b×b + c×c + d×d)$. If you keep doing this, eventually you won’t have four numbers on the board to choose. When that happens, what is the square of the largest number that can remain on the board?

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