Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:


Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4     do if A[j] <= x
5        then i = i+1
6            exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1


Note that, in this algorithm, Partition always selects an element A[r] as a pivot element around which to partition the array A[p..r].

Constraints

* 1 ≤ n ≤ 100,000
* 0 ≤ Ai ≤ 100,000

Input

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, Ai (i = 1,2,...,n), elements of the sequence are given separated by space characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].

Example

Input

12
13 19 9 5 12 8 7 4 21 2 6 11


Output

9 5 8 7 4 2 6 [11] 21 13 19 12
import java.util.NoSuchElementException;
import java.util.Scanner;
import java.util.StringJoiner;
import java.util.stream.Stream;

public class Main {
    public static void main(String[]args) {
        Scanner sc = new Scanner(System.in);
        try {
            int n = Integer.parseInt(sc.nextLine());
            int[] a = Stream.of(sc.nextLine().split(" "))
                    .mapToInt(Integer::parseInt)
                    .toArray();
            int c = partition(a, 0, a.length - 1);
            StringJoiner sj = new StringJoiner(" ");
            for (int i = 0; i < a.length; i++) {
                if (i == c) {
                    sj.add("[" + a[i] + "]");
                    continue;
                }
                sj.add(Integer.toString(a[i]));
            }
            System.out.println(sj.toString());
        } catch (NoSuchElementException | NumberFormatException e) {
            System.out.println(e);
        }
    }

    private static int partition(int[] a, int p, int r) {
        int x = a[r];
        int i = p - 1;
        for (int j = p; j < r + 1; j++) {
            if (a[j] <= x) {
                i = i + 1;
                int tmp = a[i];
                a[i] = a[j];
                a[j] = tmp;
            }
        }
        return i;
    }
}

