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.*;
import java.io.*;

import static java.lang.System.in;

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