Minimum Sum Value

Algebra Level 2

Let \( y_1, y_2, y_3, \ldots, y_{8} \) be a permutation of the numbers \( 1, 2, 3, \ldots, 8 \). What is the minimum value of \( \displaystyle \sum_{i=1}^8 (y_i + i )^2 \)?

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