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[] a = new int[n];
        int[] pos = new int[n];
        for(int i=0; i<n; i++){
            int tmp = sc.nextInt();
            a[i] = tmp;
            pos[tmp-1] = i;
        }

        TreeSet<Integer> ts = new TreeSet<Integer>();
        long ans = 0;

        for(int i=0; i<n; i++){
            int h, l;
            if(ts.higher(pos[i]) == null){
                h = n;
            }else{
                h = ts.higher(pos[i]);
            }
            if(ts.lower(pos[i]) == null){
                l = -1;
            }else{
                l = ts.lower(pos[i]);
            }

            ans += (long)(pos[i] - l) * (long)(h - pos[i]) * (long)(i+1);

            ts.add(pos[i]);
        }

        System.out.println(ans);
    }

}
