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>
#include <algorithm>
#include <vector>
#include <set>
using namespace std;

int n, a;

int main()
{
  cin >> n;
  vector<pair<long, int>> p;
  for (int i = 0; i < n; ++i)
  {
    cin >> a;
    p.emplace_back(a, i);
  }
  sort(p.begin(), p.end());
  set<int> unko = {-1, n};

  long ans = 0;
  for (int i = 0; i < n; ++i)
  {
    auto [un, ko] = p[i];
    unko.insert(ko);
    auto ima = unko.find(ko);
    ans += un * (*++ima - ko) * (ko - *----ima);
  }
  cout << ans << endl;
  return 0;
}
