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>
     
using namespace std;

int a[200000],reva[200001];


int main() {
	int n; cin >> n;
	for(int i=0;i<n;++i) cin>>a[i],reva[a[i]]=i;
	long long ans=0;
	set<int> lst,rst;
	lst.insert(1);
	rst.insert(n);
	for(int i=1;i<=n;++i) {
		auto lit=lst.lower_bound(-reva[i]);
		auto rit=rst.lower_bound(reva[i]);
		ans+=1LL*(reva[i]+*lit)*(*rit-reva[i])*i;
		lst.insert(-reva[i]); rst.insert(reva[i]);
	}
	cout << ans << endl;
	
	return 0;
}
