One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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() {
	long long N, A, ans = 0;
	static long long X[200010];
	set<long long> S;
	cin >> N;
	for (int i = 1; i <= N; i++) {
		cin >> A;
		X[A] = i;
	}
	S.insert(0);
	S.insert(N + 1);
	for (long long i = 1; i <= N; i++) {
		auto it = S.upper_bound(X[i]);
		ans += i * (*it - X[i]) * (X[i] - *--it);
		S.insert(X[i]);
	}
	cout << ans;
}