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 <set>
#include <algorithm>
using namespace std;

int main(){
	int n;
	cin >> n;
	long long ans = 0, a[n];
	for(int i = 0; i < n; i++) cin >> a[i];
	pair<long long, long long> ord[n];
	for(int i = 0; i < n; i++) ord[i] = make_pair(a[i], i);
	sort(ord, ord + n);
	set<long long> s;
	s.insert(-1);
	s.insert(n);
	for(int i = 0; i < n; i++){
		auto it = s.lower_bound(ord[i].second);
		auto up = *it;
		auto lo = *--it;
		auto m = ord[i].second;
		ans += ord[i].first * (m - lo) * (up - m);
		s.insert(ord[i].second);
	}
	cout << ans << endl;
}