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 <set>
#include <vector>
#include <iostream>
using namespace std;

int main() {
	int n;
	cin >> n;
	vector<int> a(n);
	vector<int> pos(n);
	set<int> s;
	
	for(int i = 0; i < n; i++){
		cin >> a[i];
		pos[a[i]-1] = i;
	}
	
	s.insert(-1);
	s.insert(n);
	
	unsigned long long ans = 0;
	
	for(int i = 0; i < n; i++){
		auto ite = s.lower_bound(pos[i]);
		int r = *ite - pos[i];
		int l = pos[i] - *(--ite);
		ans += (long long)r * l * (i+1);
		s.insert(pos[i]);
	}
	
	cout << ans << endl;
	
	return 0;
}