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 <vector>
#include <set>
#include <math.h>
using namespace std;
typedef long long int ll;

int main(){
	int n; cin >> n;
	vector<int> p(n);
	int ra[n+1];
	for(int i=0;i<n;i++){
		cin >> p[i];
		ra[p[i]]=i;
	}
	ll ans=0;
	set<int> S;
	S.insert(-1); S.insert(n);
	for(ll d=1;d<=n;d++){
		int i=ra[d];
		auto it=S.lower_bound(i);
		int r=*it;
		it--;
		int l=*it;
		ans+=d*(i-l)*(r-i);
		S.insert(i);
	}
	cout << ans << endl;
}