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 <vector>
#include <set>

using namespace std;

int main () {
	int n;
	cin >> n;
	vector<int> a(n);
	for (int i = 0; i < n; i++) {
		int tmp;
		cin >> tmp;
    a.at(tmp - 1) = i;
	}
	set<int> s;
	s.insert(-1);
	s.insert(n);
	long long int ans = 0;
  for (int i = 0; i < n; i++) {
		auto itr = s.upper_bound(a.at(i));
		long long int l = *itr - a.at(i);
		long long int r = a.at(i) - *(--itr);
		ans += (i + 1) * l * r;
		s.insert(a.at(i));
	}
	cout << ans << endl;
	return 0;
}
