One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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<iostream>
#include<algorithm>
#include<set>
using namespace std;
set<int> s;
int n,a[200010],p[200010],b,c;
int main(){
	cin>>n;s.insert(-1),s.insert(n);
	for(int i=0;i<n;i++){cin>>a[i];p[a[i]-1]=i;}
	long long r=0,h,w;
	for(int i=0;i<n;i++){
		s.insert(p[i]);
		set<int>::iterator t=s.find(p[i]);
		t++;b=*t;t--;t--;c=*t;
		h=b-p[i],w=p[i]-c;r+=h*w*(i+1);
	}cout<<r<<endl;
	return 0;
}
