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<iostream>
#include<algorithm>
#include<set>
#define LL long long
LL N;
LL A[200010], map[200010];
std::set<LL> memo;
LL ans;
int main() {
	std::cin >> N;
	for (int i = 1; i <= N; i++) {
		std::cin >> A[i];
		map[A[i]] = i;
	}
	memo.insert(0);
	memo.insert(N + 1);
	for (int i = 1; i <= N; i++) {
		memo.insert(map[i]);
		auto it = memo.find(map[i]);
		LL l = *(--it);
		it++;
		LL r = *(++it);
		ans += (map[i] - l)*(r - map[i])*i;
	}
	std::cout << ans << std::endl;
	return 0;
}