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.*;


//I have to use hashset
public class Main{
    static int count =0;
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String str;
        
        str = br.readLine();
        int n = Integer.parseInt(str);

        str=br.readLine();
        String[] line = str.split("\\s");

        int[] A = new int[n];
        for(int i=0;i<n;i++){
            A[i] = Integer.parseInt(line[i]);
        }
        String[] B = partition(A,0,n-1);
        for(int i=0;i<n;i++){
            System.out.print(B[i]);
            if(i != B.length-1){
                System.out.print(" ");
            }else{
                System.out.print("\n");
            }
        }
    }
//Errorn case 1 3 2
    public static String[] 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 tmp = A[i];
                A[i] = A[j];
                A[j] = tmp;
            }
        }
        String[] B = new String[A.length];
        for(int j=0;j<B.length;j++){
            B[j] = String.valueOf(A[j]);
        }
        String y = "["; 
        y+=String.valueOf(A[r]);
        y+= "]";
        B[i+1] = y;
        B[r] = String.valueOf(A[i+1]);
        return B;
    }
   
     
}
