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 <iostream>
#include <algorithm>
#include <set>
using namespace std;
#define int long long

signed main() {
  int n;
  cin >> n;
  int d[n];
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    d[a - 1] = i;
  }
  set<int> s;
  s.insert(-1);
  s.insert(n);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    auto itr = s.lower_bound(d[i]);
    int r = *itr;
    itr--;
    int l = *itr;
    ans += (r - d[i]) * (d[i] - l) * (i + 1);
    s.insert(d[i]);
  }
  cout << ans << endl;
  return 0;
}
