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<algorithm>
#include<set>
using namespace std;
set<int>s;
long ans,n,a[1<<18],p[1<<18];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		p[a[i]-1]=i;
	}
	s.insert(-1);s.insert(n);
	for(int i=0;i<n;i++)
	{
		set<int>::iterator it=s.lower_bound(p[i]);
		long r=(*it)-p[i];
		it--;
		long l=p[i]-(*it);
		ans+=(i+1)*r*l;
		s.insert(p[i]);
	}
	cout<<ans<<endl;
}