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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
class Main {
    public static void main (String[] args) throws Exception {
        Scanner sch = new Scanner(System.in);
        int q = sch.nextInt();
           int[] A = new int[q];
        int f = 0;
        for (int c = f; c < q; c++) {
            A[c] = sch.nextInt();
           
        }
         int k = 0;
         k = pa(A,q-1);
       StringBuilder dd = new StringBuilder();
        for(int i = 0; i < q; i++) {
            if(i != 0){
                dd.append(" ");
            }
            if(i == k){
                dd.append('[');
                dd.append(A[i]);
                dd.append(']');
            }else{
                dd.append(A[i]);
            }
        }
        System.out.println(dd);
    }

    public static int pa(int[] A,int r) {
         
       int f = 0;
        int sort = 0;
        int x = A[r];
        int i = f - 1;
        for (int j = 0; j < r; ++j){
            if (A[j] <= x){
                ++i;
                sort = A[i];
                A[i] = A[j];
                A[j] = sort;
            }
        }
        sort = A[i + 1];
        A[i + 1] = A[r];
        A[r] = sort;
        return i + 1;
    }

}
