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][2],sum,s,t;
int main(){
	int i,j=0;
	scanf("%lld",&n);
	for(i=1;i<=n;i++){
		scanf("%lld",&a[i][0]);
		t=0;
		while(a[i][0]<a[j][0]){
			t=t+a[j][1];			
			s=s-(a[j][0]*a[j][1]);	
			j--;		
		}
		a[++j][1]=t+1;
		a[j][0]=a[i][0];
		s=s+a[i][0]*(t+1);
		sum=sum+s;
	}
	printf("%lld",sum);
}