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<stdio.h>
long long int n, a[200100],b[200100][2],sum, k;
long long int s;
int main(){
	int i, j=0;
	scanf("%lld",&n);
	b[0][0]=0;
	for(i=0;i<n;i++){
		scanf("%lld",a+i);
		s=0;
		while(a[i]<=b[j][0]){
			s=s+b[j][1];
			k=k-b[j][0]*b[j][1];
			j--;
		}
		b[++j][0]=a[i];
		b[j][1]=++s;
		k=k+(a[i]*s);
		sum=sum+k;
	}
	printf("%lld",sum);
}