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 lint=int64_t;
using namespace std;

int main()
{
	int N;
	int index[200010]={};
	set<int> s;

	cin >> N;
	for(int i=1;i<=N;i++)
	{
		int a;
		cin >> a;
		index[a]=i;
	}

	s.insert(0);
	s.insert(N+1);
	lint ans=0;
	for(int i=1;i<=N;i++)
	{
		int mid=index[i];
		auto itr=s.lower_bound(mid);
		lint l,r;
		r=*itr;
		--itr;
		l=*itr;

		ans+=i*((mid-l)*(r-mid));
		s.insert(index[i]);
	}

	cout << ans << endl;

	

	return 0;
}
