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.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

public class Main{

    public static void main(String[] args) throws IOException{
        //input                                                                   
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        String[] temp_A = br.readLine().split(" ");
        int[] A = new int[n];
        for(int i = 0; i < n; i++){
            A[i] = Integer.parseInt(temp_A[i]);
        }
        //solve                                                                   
        int pivot = partition(A, 0, n-1);
        //output                                                                  
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < n; i++){
            if(i != 0){
                sb.append(" ");
            }
            if(i == pivot){
                sb.append('[');
                sb.append(A[pivot]);
                sb.append(']');
            }else{
                sb.append(A[i]);
            }
        }
        System.out.println(sb);

    }
    public static int partition(int[] A, int p, int r){
        int x = A[r];
        int i = p-1;
        int temp = 0;
        for(int j = p; j < r; j++){
            if(A[j] <= x){
                i++;
                //A[j]??¨A[i]?????????                                                
                temp = A[j];
                A[j] = A[i];
                A[i] = temp;
            }
        }
        temp = A[i+1];
        A[i+1] = A[r];
        A[r] = temp;

        return i+1;
    }

}