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 <algorithm>
#include <vector>
#include <set>
using namespace std;
#define int long long
int t[234567];
set<int>s;
signed main() {
	int n; cin >> n;
	for (int i = 1; i <= n; i++) {
		int a; cin >> a;
		t[a] = i;
	}
	int ans = 0;
	s.insert(0);
	s.insert(n + 1);
	for (int i = 1; i <= n; i++) {
		auto itr = s.upper_bound(t[i]);
		ans += i * (*itr - t[i])*(t[i] - *(--itr));
		s.insert(t[i]);
	}
	cout << ans << endl;
}