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() {
  cin.tie(0); ios::sync_with_stdio(false);
  int n; cin >> n;
  int dmy[n + 2];
  int *a; a = dmy + 1;
  a[-1] = 0;
  a[0] = n + 1;
  for (int i = 1; i <= n; i++) {
    int j; cin >> j;
    a[j] = i;
  }
  set<int> s{0, n + 1};
  long long res = 0;
  for (int i = 1; i <= n; i++) {
    auto lb = s.insert(a[i]).first;
    auto ub = lb;
    lb--; ub++;
    res += (long long) i * (a[i] - *lb) * (*ub - a[i]);
  }
  cout << res << "\n";
  return 0;
}