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<iostream>
#include<cstdio>
#define M 200010
using namespace std;
int n,top;
int L[M],R[M],a[M],st[M];
long long ans;
int main() {
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	top=0;st[0]=0;
	for(int i=1;i<=n;i++) {
		while(top&&a[st[top]]>a[i]) top--;
		L[i]=st[top]+1;st[++top]=i;
	}
	top=0;st[0]=n+1;
	for(int i=n;i>=1;i--) {
		while(top&&a[st[top]]>a[i]) top--;
		R[i]=st[top]-1;st[++top]=i;
	}
	for(int i=1;i<=n;i++) 
		ans+=1ll*(R[i]-i+1)*(i-L[i]+1)*a[i];
	printf("%lld\n",ans);
	return 0;
}