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;
import java.util.Arrays;
class Main{
    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
	//数列Aの長さ決定
	int N = sc.nextInt();
	int[] A = new int[N];
	for(int i = 0;i < N;i++){
	    A[i] = sc.nextInt();
	}
	int q = partition(A,0,N-1);
	System.out.print(A[0]+" ");
	for(int j = 1;j < N-1;j++){
	    if(j == q) {
		System.out.print("[");
		System.out.print(A[q]);
		System.out.print("] ");
	    }else{
		System.out.print(A[j]);
		System.out.print(" ");
	    }
	}
	System.out.println(A[N-1]);
	
    }
    public static int partition(int[] A,int p,int r){
	int temp1,temp2;
	int x = A[r];
	int i = p-1;
	for(int j = p;j <= r-1;j++){
	    if(A[j] <= x){
		//A[r]の値より小さかったらA[i]とA[j]を交換
		i = i+1;
		temp1 = A[i];
		A[i] = A[j];
		A[j] = temp1;
	    }
	    
	}
	temp2 = A[i+1];
	A[i+1] = A[r];
	A[r] = temp2;
	
	return i+1;

    }
    
}

