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{
    public static void main(String args[]){
	int A[] = new int[100000];
	int i,j,n,l,count=0;
	Scanner scan = new Scanner(System.in);
	
	n = scan.nextInt();
	
	for(i=0;i<n;i++){
	    A[i] = scan.nextInt();
	}
	
	l = partition(A,0,n-1);
	for(i=0;i<n;i++){
	    if(A[l]==A[i]){
		count++;
	    }
	}
	
	for(i=0;i<n;i++){
	    if(A[l]==A[i]){
		if(count>1){
		    System.out.print(A[i]+" ");
		    count--;
		    continue;
		}
		if(count==1){
		System.out.print("["+A[i]+"] ");
		continue;
		}
	    }
	    if(i==n-1){
		System.out.println(A[i]);
		break;
	    }
	    System.out.print(A[i]+" ");
	}
    }
    
    public static int partition(int A[],int p,int r){
	int i,j,x,temp=0;
	
	x = A[r];
	i = p-1;
	for(j=p;j<r;j++){
	    if(A[j]<=x){
		i++;
		temp = A[i];
		A[i] = A[j];
		A[j] = temp;
	    }
	}
	temp = A[i+1];
	A[i+1] = A[r];
	A[r] = temp;
	return i+1;
    }
}

