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D. Imbalanced Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array a consisting of n elements. The imbalance value of some subsegment of this array is the difference between the maximum and minimum element from this segment. The imbalance value of the array is the sum of imbalance values of all subsegments of this array.

For example, the imbalance value of array [1, 4, 1] is 9, because there are 6 different subsegments of this array:

  • [1] (from index 1 to index 1), imbalance value is 0;
  • [1, 4] (from index 1 to index 2), imbalance value is 3;
  • [1, 4, 1] (from index 1 to index 3), imbalance value is 3;
  • [4] (from index 2 to index 2), imbalance value is 0;
  • [4, 1] (from index 2 to index 3), imbalance value is 3;
  • [1] (from index 3 to index 3), imbalance value is 0;

You have to determine the imbalance value of the array a.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — size of the array a.

The second line contains n integers a1, a2... an (1 ≤ ai ≤ 106) — elements of the array.

Output

Print one integer — the imbalance value of a.

Example
Input
3
1 4 1
Output
9