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;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);  
	int n; cin >> n;
	vector<int> p(n + 1);
	for(int i = 1; i <= n; i++) {
		int x; cin >> x;
		p[x] = i;
	}
	set<int> s;
	s.insert(0);
	s.insert(n + 1);
	long long ans = 0;
	for(int i = 1; i <= n; i++) {
		int pos = p[i];
		auto j = s.upper_bound(pos);
		int r = *j;
		j--;
		int l = *j;
		ans += i * 1LL * (pos - l) * 1LL * (r - pos);
		s.insert(pos);
	}
	cout << ans << endl;
	return 0;	
}
