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 {
    static long count = 0;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); //数列の長さ
        int[] a = new int[n]; //数列A
        for(int i=0; i<n; i++) {
            a[i] = sc.nextInt();
        }
        int x = partition(a, 0, a.length-1);
        StringBuilder sb = new StringBuilder();
        for(int i=0; i<n; i++) {
            if(i>0) sb.append(" ");
            if(i==x) sb.append("[" + a[i] + "]");
            else sb.append(a[i]);
        }
        System.out.println(sb); //出力
    }
    /**
     * Partition
     */
    static int 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 g = a[j];
                a[j] = a[i];
                a[i] = g;
            }
        }
        int g = a[i+1];
        a[i+1] = a[r];
        a[r] = g;
        return i+1;
    }
}
