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>
using namespace std;
int n, a[200009], s[200009];
int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	cin >> n;
	int c = 1;
	long long cur = 0, sum = 0;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		while (a[i] <= a[s[c - 1]]) {
			c--;
			cur -= 1LL * a[s[c]] * (s[c] - s[c - 1]);
		}
		cur += 1LL * a[i] * (i - s[c - 1]);
		s[c++] = i;
		sum += cur;
	}
	cout << sum << "\n";
	return 0;
}