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 {
	public static int[] num = new int[100000];
	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt(); // 要素の個数
		//int[] num = new int[n]; // 個数のリスト

		for (int i = 0; i < n; i++) {
			num[i] = scan.nextInt();
		}
		int partition_num = Partition(0,n-1);
		for (int i = 0; i < partition_num; i++) {
			System.out.print(num[i] + " ");
		}
		System.out.print("["+num[partition_num]+"]");
		for (int i = partition_num+1; i < n ; i++) {
			System.out.print(" " + num[i]);
		}
		System.out.println();
	}

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

}

