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>
#define maxn 200005
#define LL long long
int n,a[maxn],l[maxn],r[maxn],st[maxn],tp;
LL ans;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n;i++)
	{
		while(tp&&a[st[tp]]>=a[i]) tp--;
		l[i]=st[tp]; st[++tp]=i;
	}
	tp=0; st[0]=n+1;
	for(int i=n;i;i--)
	{
		while(tp&&a[st[tp]]>a[i]) tp--;
		r[i]=st[tp]; st[++tp]=i;
	}
	for(int i=1;i<=n;i++) ans+=1ll*a[i]*(i-l[i])*(r[i]-i);
	printf("%lld\n",ans);
}
