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;
typedef long long ll;

int main(){
 int n,b[200010];
 set<int> p;
 cin>>n;
 for(int i=1;i<=n;i++){
  int a;
  cin>>a;
  b[a]=i;
 }
 p.insert(0);
 p.insert(n+1);
 ll ans=0;
 for(int i=1;i<=n;i++){
  int l=*(--p.lower_bound(b[i])),r=*p.upper_bound(b[i]);
  ans+=(ll)i*(b[i]-l)*(r-b[i]);  
  p.insert(b[i]);
 }
 cout<<ans<<endl;
 return 0;
}