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.io.InputStreamReader;
import java.util.Scanner;

public class Main {

	public static int partition(int[] a, int p, int r) {
		int tmp = 0;

		int x = a[r];
		int i = p - 1;

			for(int j = 0; j < r; j++) {
				if (a[j] <= x) {
					i = i + 1;
					tmp =a[i];
					a[i] = a[j];
					a[j] = tmp;
				}
			}

		tmp = a[i + 1];
		a[i + 1] = a[r];
		a[r] = tmp;

		return i + 1;
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(new InputStreamReader(System.in));

		int matrixLength = scan.nextInt();

		int[] a = new int[matrixLength];

		for(int i = 0; i < matrixLength; i++) {
			a[i] = scan.nextInt();
		}

		int targetIndex = partition(a, 0, matrixLength - 1);

		StringBuilder sb = new StringBuilder();

		for(int i = 0; i < a.length; i++) {
			if(i == targetIndex){
				sb.append("[");
				sb.append(a[i]);
				sb.append("]");
			} else {
				sb.append(a[i]);
			}

			if(i == a.length - 1){
				break;
			}
			sb.append(" ");
		}
		System.out.println(sb.toString());
		scan.close();
	}
}