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;


class Main {
	private static	int array[];
	
	public static void main(String args[]) {
		//実行処理
		run();
	}

	public static void run(){ 
		Scanner scanner = new Scanner(System.in);
		int  num = scanner.nextInt();//要素数
		array = new int[num];
		int cut;
		//配列作成同時にカウント
		for(int i = 0; i < num; i ++ ){
			array[i] = scanner.nextInt();
		}
		//ソート処理
		cut = partition(0, num - 1 );
		//出力呼び
		output(num,cut);
		//後処理
		scanner.close();
	}
	//出力
	public static void output(int num, int cut){
		StringBuilder sb = new StringBuilder("");
		sb.append(array[0]);
		for (int i = 1; i < num; i++) {
				if (i == cut) sb.append(" [" + array[i] + "]");
				else sb.append(" " + array[i]); 
		}
		System.out.println(sb);
	}
	//ソート
	public static int partition(int par,int rim){
		int work = 0;
		int x = array[rim];
		int i = par - 1;
		//ソート処理
		for (int j = par ; j < rim ; j ++ ){
			if ( array[j] <= x ) {
				work = array[++i];
				array[i] = array[j];
				array[j] = work;
			}
		}
		//最後に入れ替え
		work = array[++i];
		array[i] = array[rim];
		array[rim] = work;
		return i;
	}
}
