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>
using namespace std;
const int N=2e5+1;
int n,a[N],q[N],t,L[N],R[N];
long long A;
void D(int k,int l,int r)
{
	A+=(long long)a[k]*(k-l+1)*(r-k+1);
	if(L[k])
		D(L[k],l,k-1);
	if(R[k])
		D(R[k],k+1,r);
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	for(int i=1;i<=n;i++)
	{
		while(t&&a[q[t]]>a[i])
			L[i]=q[t--];
		R[q[t]]=i,q[++t]=i;
	}
	D(q[1],1,n);
	cout<<A;
	return 0;
}