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;


const int MAXN = 200 * 1000 + 123;






long long n, a[MAXN], b[MAXN];
set<long long> s;
long long ans;

int main() {
	cin >> n;
	s.insert(n + 1);
	s.insert(0);
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		b[a[i]] = i;
	}
	for (int i = 1; i <= n; i++) {
		auto x = s.upper_bound(b[i]);
		ans += (*x - b[i]) * (b[i] - *(--x)) * i;
		s.insert(b[i]);
	}
	cout << ans;
	return 0;
}	