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 = Integer.parseInt(sc.next());
        int[] rev = new int[n+1];
        for(int i=0; i<n; i++){
            int idx = Integer.parseInt(sc.next());
            rev[idx] = i;
        }
        
        TreeSet<Integer> ts = new TreeSet<>();
        ts.add(-1);
        ts.add(n);
        
        long ans = 0L;
        for(int i=1; i<=n; i++){
            int ridx = rev[i];
            ts.add(ridx);
            int l = ridx - ts.lower(ridx);
            int r = ts.higher(ridx) - ridx;
            ans += (long)l*r*i;
        }
        
        System.out.println(ans);
    }
}

