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1. Alternating sum of minimum values ●●●○○ 50 ptsFor a positive integer $n$, define $f_n(x)=\left(\sum_{i=1}^{n}|x-i|\right)^2-\sum_{i=1}^{n}(x-i)^2$ on the interval $[0,n+1]$. Let $a_n$ be the minimum value of $f_n(x)$. Find $\sum_{n=1}^{11}(-1)^{n+1}a_n$.