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>
//#include<atcoder/all>
using namespace std;
using ll = long long;

int main()
{
	int n;
	cin >> n;
	vector<int> a(n);
	for(auto &i:a)cin >> i;
	set<int> H,W;
	H.insert(n);
	W.insert(n);
	vector<int> b(n);
	for(int i = 0;i<n;i++)
		b[a[i]-1]=i;
	ll ans = 0;
	for(int i = 0;i<n;i++)
	{
		ll now = 0;
		now = *H.lower_bound(b[i])-b[i];
		now *= *W.lower_bound(n-b[i]-1)-(n-b[i]-1);
		H.insert(b[i]);
		W.insert(n-b[i]-1);
		ans += now*(1+i);

	}
	cout<<ans<<endl;

}
