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>

const int N = 200010;

int a[N], left[N], right[N];

int main(){
	int n;
	scanf("%d", &n);
	for (int i = 1; i <= n; ++ i){
		scanf("%d", &a[i]);
	}
	std::stack <int> s;
	for (int i = 0; i <= n + 1; ++ i){
		while (!s.empty() && a[s.top()] > a[i]){
			right[s.top()] = i;
			s.pop();
		}
		if (!s.empty()) left[i] = s.top();
		s.push(i);
	}
	long long ans = 0;
	for (int i = 1; i <= n; ++ i){
		ans += 1ll * a[i] * (right[i] - i) * (i - left[i]);
	}
	printf("%lld\n", ans);
	return 0;
}