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.*;

public class Main{
    public static void main (String args[]){

        //初期処理
        Scanner sc=new Scanner(System.in);
        int n=Integer.parseInt(sc.nextLine());
        String[] sElementArray=sc.nextLine().split(" ");
        int[] array=Arrays.stream(sElementArray).mapToInt(Integer::parseInt).toArray();
        sc.close();

   
            int q=partition(array,0,n-1);
            String[] ss=Arrays.stream(array).mapToObj(Integer::toString).toArray(s->new String[s]);
            for(int i=0;i<n;i++){
                if(q==i){
                    System.out.print("["+ss[i]+"]"+" ");
                }else if (i!=n-1){
                    System.out.print(ss[i]+" ");
                }else{
                    System.out.println(ss[i]);
                }
            }
        
            
        }
public static int partition(int[] array,int startIndex,int endIndex){
        // int n=array.length;
        int i=startIndex-1;
        for(int j=startIndex;j<endIndex;j++){
            if(array[j]<=array[endIndex]){
                i++;
                swap(array,i,j);
            }
        }
        i++;
        swap(array,i,endIndex);
        return i;
    }

    public static void swap(int[] array,int i, int j){
                int tmp=array[i];
                array[i]=array[j];
                array[j]=tmp;
    }
    }
    
