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

Find the following:

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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 <iostream>

const int N = 1234567;

int a[N], pos[N], pr[N], ne[N];

int main () {
  int n;
  std::cin >> n;
  for (int i = 0; i <= n; ++i) {
    std::cin >> a[i];
    pos[a[i]] = i;
    pr[i] = i - 1;
    ne[i] = i + 1;
  }
  long long ans = 0;
  for (int i = n; i>= 1; --i) {
    int j = pos[i];
    ans += i * 1LL * (j - pr[j]) * (ne[j] - j);
    pr[ne[j]] = pr[j];
    ne[pr[j]] = ne[j];
  }
  std::cout << ans << std::endl;
}
