Minimum Sum Value

Algebra Level 2

Let y1,y2,y3,,y8 y_1, y_2, y_3, \ldots, y_{8} be a permutation of the numbers 1,2,3,,8 1, 2, 3, \ldots, 8 . What is the minimum value of i=18(yi+i)2 \displaystyle \sum_{i=1}^8 (y_i + i )^2 ?

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