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<long long> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}

	long long ans = 0;
	long long sum = 0;

	stack<int> stk;
	stk.push(-1);

	for (int i = 0; i < n; i++) {
		while (stk.size() >= 2 && a[stk.top()] >= a[i]) {
			int j = stk.top();
			stk.pop();
			sum -= (j - stk.top()) * a[j];
		}
		sum += a[i] * (i - stk.top());
		stk.push(i);
		ans += sum;
	}

	cout << ans << endl;
}