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>
#include<algorithm>
using namespace std;
#define MAXN 200000
#define LL long long
int stk[MAXN+5];
int n,top;
LL a[MAXN+5],d[MAXN+5],ans;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",&a[i]);
		while(a[stk[top]]>=a[i])top--;
		d[i]=stk[top];stk[++top]=i;
	}
	top=0,stk[0]=n+1;
	for(int i=n;i>=1;i--)
	{
		while(a[stk[top]]>=a[i])top--;
		ans+=a[i]*(i-d[i])*(stk[top]-i);stk[++top]=i;
	}
	printf("%lld",ans);
}