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 n;
int a[200010];
set<int> s;
long long ans;

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	cin >> n;
	for(int i=0; i<n; ++i){
		int t;
		cin >> t;
		a[t] = i+1;
	}
//	for(int i=1; i<=n; ++i)
//		cout << a[i] << "\n";
	s.insert(0);
	s.insert(n+1);
	for(int i=1; i<=n; ++i){
		auto ite = s.lower_bound(a[i]);
		ans += (long long)i * (*ite - a[i]) * (a[i] - *prev(ite));
		s.insert(a[i]);
	}
	cout << ans << "\n";
}