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<bits/stdc++.h>
#define N 200100
using namespace std;
int a[N],id[N];
bool cmp(int i,int j){
	return a[i]<a[j];
}
int main(){
	set<int> del;
	int n;
	long long ans=0;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%d",&a[i]);
		id[i]=i;
	}
	sort(id,id+n,cmp);
	del.insert(-1);
	del.insert(n);
	for(int i=0;i<n;i++){
		int u=id[i],l=*(--del.lower_bound(u)),r=*del.upper_bound(u);
		del.insert(u);
		ans+=1LL*a[u]*(r-u)*(u-l);
	}
	printf("%lld\n",ans);
	return 0;
}