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);
  for (int i = 0; i < N; i++){
    cin >> a[i];
  }
  vector<int> p(N);
  for (int i = 0; i < N; i++){
    p[a[i] - 1] = i;
  }
  set<int> pos;
  pos.insert(-1);
  pos.insert(N);
  long long ans = 0;
  for (int i = 0; i < N; i++){
    long long L = p[i] - *prev(pos.lower_bound(p[i]));
    long long R = *(pos.lower_bound(p[i])) - p[i];
    ans += L * R * a[p[i]];
    pos.insert(p[i]);
  }
  cout << ans << endl;
}