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 main(){
	int n;
	long long ans = 0;
	set<int> s;
	int a[200010];
	
	cin >> n;
	for (int i = 0;i < n;i++) {
		int temp;
		cin >> temp;
		a[temp-1] = i;
	}
	
	s.insert(-1),s.insert(n);
	for (long long i = 0;i < n;++i) {
		decltype(s)::iterator it = s.lower_bound(a[i]);
		int r = *it,l = *(--it);
		ans += (i+1)*(a[i]-l)*(r-a[i]);
		s.insert(a[i]);
	}
	cout << ans << endl;
	return 0;
}