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
import java.util.*;

public class Main {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int n = scanner.nextInt();
        int[] a = new int[n];
        for (int i = 1; i <= n; i++) {
            a[scanner.nextInt() - 1] = i;
        }
        long ans = 0;
        TreeSet<Integer> set = new TreeSet<>(Arrays.asList(0, n + 1));
        for (int i = 0; i < n; i++) {
            set.add(a[i]);
            ans += (long)(i + 1) * (a[i] - set.lower(a[i])) * (set.higher(a[i]) - a[i]);
        }

        System.out.println(ans);
    }
}