One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

Constraints

* 1 ≦ N ≦ 200,000
* (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85
#include <bits/stdc++.h>

const int N = 200001;

int n, indez[N], value[N];

int main()
{
  while (scanf("%d", &n) == 1) {
    long long result = 0;
    long long sum = 0;
    int t = 1;
    indez[0] = -1;
    value[0] = 0;
    for (int i = 0, a; i < n; ++ i) {
      scanf("%d", &a);
      while (value[t - 1] > a) {
        t --;
        sum -= 1LL * value[t] * (indez[t] - indez[t - 1]);
      }
      indez[t] = i;
      value[t] = a;
      sum += 1LL * a * (i - indez[t - 1]);
      t ++;
      result += sum;
    }
    printf("%lld\n", result);
  }
}
