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<algorithm>
#include<cstring>
using namespace std;
#define MAXN 200002
int n,a[MAXN],pos[MAXN],pre[MAXN],nex[MAXN];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		pos[a[i]]=i;
	}
	for(int i=0;i<=n+1;i++)
		pre[i]=i-1,nex[i]=i+1;
	long long ans=0;
	for(int i=n;i>0;i--)
	{
		int j=pos[i];
		ans+=i*1LL*(j-pre[j])*(nex[j]-j);
		pre[nex[j]]=pre[j];
		nex[pre[j]]=nex[j];
	}
	printf("%lld",ans);
}