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.Scanner;

/**
 * Created by zhangrunfeng on 2/17/20
 */
public class Main {
    private int N;
    private int[] arr;

    public Main(Scanner sc) {
        N = sc.nextInt();
        arr = new int[N];
        for (int i = 0; i < N; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public int partition(int p, int r) {
        int pivot = arr[r];
        int i = p - 1;
        for (int j = p; j < r; j++) {
            if (arr[j] <= pivot) {
                i++;
                int tmp = arr[i];
                arr[i] = arr[j];
                arr[j] = tmp;
            }
        }
        arr[r] = arr[i + 1];
        arr[i + 1] = pivot;
        return i + 1;
    }

    public void printResult(int startIx, int endIx, int partitionIx) {
        for (int ix = startIx; ix < endIx-1; ix++) {
            if (ix == partitionIx) {
                System.out.print("[");
            }
            System.out.print(arr[ix]);
            if (ix == partitionIx) {
                System.out.print("]");
            }
            System.out.print(" ");
        }
        if (endIx-1 == partitionIx) {
            System.out.print("[");
        }
        System.out.println(arr[endIx-1]);
        if (endIx-1 == partitionIx) {
            System.out.print("]");
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        Main m = new Main(sc);
        int partitionIx = m.partition(0, m.N - 1);
        m.printResult(0, m.N, partitionIx);
    }
}

