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];
    a[i]--;
  }
  vector<int> pos(N);
  for (int i=0;i<N;i++){
    pos[a[i]]=i;
  }
  set<int> s;
  s.insert(-1);
  s.insert(N);
  long long ans=0;
  for (int i=0;i<N;i++){
    int j=pos[i];
    s.insert(j);
    auto itr=s.find(j);
    --itr;
    int l=*itr;
    itr=s.find(j);
    ++itr;
    int r=*itr;
    ans+=(long long)(i+1)*(r-j)*(j-l);
  }
  cout << ans << endl;
}