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,a[200001],b[200001];
  long long ans=0;
  set<int> s;
  cin>>n;
  for(int i=1;i<=n;i++)cin>>a[i],b[a[i]]=i;
  s.insert(0);
  s.insert(n+1);
  for(int i=1;i<=n;i++){
    set<int>::iterator it=s.lower_bound(b[i]);
    long long right = (*it) -b[i];
    it--;
    long long left = b[i] - (*it);
    ans+=right*left*i;
    s.insert(b[i]);
  }
  cout<<ans<<endl;
  return 0;
}
