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 p[200001];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	for(int i=1,x;i<=n;i++){
		cin>>x;
		p[x]=i;
	}
	long long int ans=0;
	set<int> s;
	s.insert(0);
	s.insert(n+1);
	for(int i=1;i<=n;i++){
		int x=p[i];
		auto it=s.insert(x).first;
		ans+=1LL*i*(x-(*prev(it)))*(*next(it)-x);
	}
	cout<<ans<<endl;
}

