One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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>

using namespace std;

typedef long long ll;

int n;
ll d[202020];
vector<pair<int,int>> v;
ll s;

int main() {
	cin >> n;
	for (int i = 1; i <= n; i++) {
		int x;
		cin >> x;
		while (v.size() && v.back().first > x) v.pop_back();
		if (v.size()) {
			d[i] += (ll)x*(i-v.back().second);
			d[i] += d[v.back().second];
		} else {
			d[i] += (ll)x*i;
		}
		s += d[i];
		v.push_back({x,i});
	}
	cout << s << "\n";
}
