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.*;
import java.util.*;

public class Main{
	public static int max = 0;
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] str = (br.readLine()).split(" ");
		int[] num = new int[n];
		for (int i = 0; i<n ; i++ ) {
			num[i] = Integer.parseInt(str[i]);
		}

		int part = partition(num,0,n-1);

		for (int i = 0; i<n ; i++ ) {
			if (i == n-1) {
				System.out.println(num[i]);
			}else if (i == part){
				System.out.print("[" + num[i] + "] ");
			}else{
				System.out.print(num[i] +" ");
			}
		}

	}

	public 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++;
				int work = a[i];
				a[i] = a[j];
				a[j] = work; 
			}
		}
		int num = a[i+1];
		a[i+1] = a[r];
		a[r] = num;

		return i+1;
	}

	public static void printing(int[] a){
		for (int i = 0; i<a.length ; i++ ) {
			if (i == a.length-1) {
				System.out.println(a[i]);
			}else{
				System.out.print(a[i] + " ");
			}
		}
	}
}