CZ-SK-MO 1991 Problem 3

For any permutation $p$ of the set $\{1,2,...,n\}$ , let us denote $d(p) = |p(1)-1|+|p(2)-2|+...+|p(n)-n|$ . Let $i(p)$ be the number of inversions of $p$ , i.e. the number of pairs $1 \le i < j \le n$ with $p(i) > p(j)$ . Prove that $d(p)\le 2i(p)$ $.