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.*;

class Main{
  public static void main(String args[]) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int a[] = new int[n+1];
    long sum = 0;
    TreeSet<Integer> ts = new TreeSet<>();
    ts.add(0);
    ts.add(n+1);
    for (int i = 1; i <= n; i++) {
      a[sc.nextInt()] = i;
    }
    for (int i = 1; i <= n; i++) {
      ts.add(a[i]);
      sum += (long)i * (a[i] - ts.lower(a[i])) * (ts.higher(a[i]) - a[i]);
    }
    System.out.println(sum);
  }
}
