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<set>
#include<vector>

using namespace std;

int main()
{
	int n;
	cin >> n;
	vector<int> a(n),pos(n);
	for(int i=0;i<n;i++)
		cin >> a[i];
	for(int i=0;i<n;i++)
		pos[a[i]-1]=i;
	set<int> st;

	st.insert(-1);
	st.insert(n);

	long long ans=0;
	for(int i=0;i<n;i++)
	{
		auto itr=st.lower_bound(pos[i]);
		long long right=*itr-pos[i];
		itr--;
		long long left=pos[i]-*itr;	
		ans+=(i+1)*right*left;
		st.insert(pos[i]);		
	}

	cout << ans << endl;

}
