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
import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];
		int[] indexes = new int[n + 1];
		TreeSet<Integer> set = new TreeSet<>();
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
			indexes[arr[i]] = i;
			set.add(i);
		}
		set.add(n);
		set.add(-1);
		long ans = 0;
		for (int i = n; i >= 1; i--) {
			int idx = indexes[i];
			long left = set.lower(idx) + 1;
			long right = set.higher(idx) - 1;
			ans += (idx - left + 1) * (right - idx + 1) * i;
			set.remove(idx);
		}
		System.out.println(ans);
	}
}
