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<bits/stdc++.h>
using namespace std;
const int g=200005;
int n,a[g],b[g],m;
long long s;

int main()
{
	//freopen("in","r",stdin);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		for(;a[i]<a[b[m]];m--)
			s+=(long long)a[b[m]]*(b[m]-b[m-1])*(i-b[m]);
		b[++m]=i;
	}
	for(;m;m--)
		s+=(long long)a[b[m]]*(b[m]-b[m-1])*(n-b[m]+1);
	printf("%lld",s);
	return 0;
}
