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>
#define int long long
using namespace std;

signed main(){
  int N;
  cin>>N;
  std::vector<int> v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  std::vector<int> w(N+1);//w[0]は使わない
  for(int i=0;i<N;i++)w[v[i]]=i;
  set<int> s;
  s.insert(-1);
  s.insert(N);
  int ans=0;
  for(int i=1;i<=N;i++){
    int l=*--s.lower_bound(w[i]);
    int r=*s.lower_bound(w[i]);
    ans+=i*(w[i]-l)*(r-w[i]);
    s.insert(w[i]);
  }
  cout<<ans<<endl;
}
