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);
  vector<int> ra(n);
  for(int i=0;i<n;i++){
    cin>>a[i];
    ra[a[i]]=i;
  }
  long long int ans=0;
  set<int> s;
  s.insert(-1);
  s.insert(n);
  for(long long int i=1;i<=n;i++){
    int x=ra[i];
    auto y=s.lower_bound(x);
    int r=*y;
    y--;
    int l=*y;
    ans+=i*(x-l)*(r-x);
    s.insert(x);
  }
  cout<<ans<<endl;
}
