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;

public class Main{

	static int count = 0;

	public static void main(String[] args) throws Exception {

		Scanner sc = new Scanner(System.in);
		int n  = sc.nextInt();
		int[] A = new int[n];

		for(int i = 0; i < n; i++) {
			A[i] = sc.nextInt();
		}

		int p = partition (A, 0, n-1);

		StringBuilder sb = new StringBuilder();
        int outLen = A.length;

        if(p != 0){
            sb.append(A[0]);
        }
        else{
            sb.append("[" + A[0] + "]");
        }
        for(int i = 1; i < outLen ; i++){
            if(i == p){
                sb.append(" ["+ A[i] + "]");

            }
            else{
                sb.append(" "+ A[i]);

            }
        }
        System.out.println(sb);
	}

	static int	 partition (int[] A, int p, int r) {
		int x = A[r];
		int i = p - 1;

		for(int j = p; j < r; j++) {
			if(A[j] <= x) {
				i = i + 1;
				swap(A, i, j);
			}
		}

		swap(A, i+1, r);
		return i + 1;
	}

	private static void swap(int[] a, int index1, int index2) {
		int temp = a[index1];
		a[index1] = a[index2];
		a[index2] = temp;
	}


}
