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(){
	int n; cin >> n;
	vector<int> a(n + 1);
	for(int i = 0; i < n; i++) cin >> a[i + 1];
	long long sum = 0, res = 0;
	vector<int> stk;
	stk.push_back(0);
	for(int i = 1; i <= n; i++){
		while(a[stk.back()] > a[i]){
			int lst = stk.back(); stk.pop_back();
			sum -= 1ll * (lst - stk.back()) * a[lst];
		}
		sum += 1ll * (i - stk.back()) * a[i];
		stk.push_back(i);
		res += sum;
	}
	cout << res << endl;
	return 0;
}
