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 <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int n,a[200005],sta[200005],top,l[200005],r[200005];
long long ans=0;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i){
		scanf("%d",a+i);
		r[i]=n+1;
	}
	for(int i=1;i<=n;++i){
		while(top && a[sta[top]]>=a[i]){
			r[sta[top]]=i;
			--top;
		}
		l[i]=sta[top];
		sta[++top]=i;
	}
	for(int i=1;i<=n;++i)
		ans+=(long long)(i-l[i])*(r[i]-i)*a[i];
	printf("%lld\n",ans);
	return 0;
}