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;
long N,b[200001],a,x,i;
int main(){
	cin>>N;
	for(i=1L;i<=N;++i){
		scanf("%d",&a);
		b[a]=i;
	}
	set<long>s;
	s.insert(0L);
	s.insert(N+1);
	for(i=1L;i<=N;++i){
		auto it=s.upper_bound(b[i]);
		x+=i*(*it-b[i])*(b[i]-*--it);
		s.insert(b[i]);
	}
	cout<<x<<endl;
}
