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+1];
      for(int i = 1; i <= n; i++)
        arr[sc.nextInt()] = i;
      TreeSet<Integer> idxTree = new TreeSet<>();
      long sum = 0L;
      for(int i = 1; i <= n; i++) { // value
        int idx = arr[i];
        Integer left = idxTree.lower(idx);
        Integer right = idxTree.higher(idx);
        if(left == null)
          left = 0;
        if(right == null)
          right = n + 1;
        idxTree.add(idx);
        sum += (long)(idx - left) * (long)(right - idx) * i;
      }
      System.out.println(sum);
  }
}