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 <bits/stdc++.h>
using namespace std;

int main() {
  int n;
  cin >> n;

  vector<int> a(n + 1), idx(n + 1);
  // for (auto &i : a) cin >> i;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    idx[a[i]] = i;
  }

  vector<int> l(n + 2), r(n + 2);
  for (int i = 0; i <= n + 1; ++i) {
    l[i] = i - 1;
    r[i] = i + 1;
  }

  long long ans = 0;
  for (long long i = n; i > 0; --i) {
    long long j = idx[i];
    ans += i * (j - l[j]) * (r[j] - j);
    l[r[j]] = l[j];
    r[l[j]] = r[j];
  }

  cout << ans << endl;
}
