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<long> A(N), Idx(N+1);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    Idx[A[i]] = i;
  }

  long ans = 0, r, l;
  set<int> S;
  S.insert(-1);
  S.insert(N);
  for (int i = 1; i <= N; i++) {
    auto it = S.lower_bound(Idx[i]);
    r = (*it) - Idx[i];
    it--;
    l = Idx[i] - (*it);
    ans += i * l * r;
    S.insert(Idx[i]);
  }
  cout << ans << endl;
}