A broken line

is drawn in a

square, so that the distance from any point of the square to the broken line is less than

. Prove that its total length is greater than
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A broken line $A_1A_2 \ldots A_n$ is drawn in a $50 \times 50$ square, so that the distance from any point of the square to the broken line is less than $1$. Prove that its total length is greater than $1248.$