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(void){
  int n;
  cin>>n;
  int p[n+1];
  for(int i=1;i<=n;++i){
    int v;
    cin>>v;
    p[v]=i;
  }
  set<int>s{0,n+1};
  long long a=0;
  for(int i=1;i<=n;++i){
    auto it=s.lower_bound(p[i]);
    long long l=*it--;
    long long r=*it;
    a+=(r-p[i])*(p[i]-l)*i;
    s.insert(p[i]);
  }
  cout<<a<<'\n';
}