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;
#define all(a) (a).begin(),(a).end()
#define ll long long

set<int> c;
int main(){
  int N; cin>>N;
  c.insert(-1);
  c.insert(N);
  int a[N],b[N];
  ll cnt=0,cp;
  for(int i=0;i<N;i++){
    cin>>a[i];
    b[a[i]-1]=i;
  }
  for(int i=0;i<N;i++){
    auto s=c.upper_bound(b[i]);
    cp=(*s-b[i]); s--;
    cp*=(b[i]-*s);
    cnt+=(i+1)*cp;
    c.insert(b[i]);
  }
  cout<<cnt<<endl;
}
