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;

public class Main {

    static Scanner sc = new Scanner(System.in);
    static int n, x;
    static int[] A;

    public static void main(String[] args) {
        read();
        int i = partition(A, 0, n - 1);
        out(i);
    }

    static void out(int j) {
        for (int i = 0; i < n; i++) {
            if (i == j) {
                System.out.print(String.format("[%d] ", A[i]));
            } else if (i == n - 1) {
                System.out.println(String.format("%d", A[i]));
            } else {
                System.out.print(String.format("%d ", A[i]));
            }
        }
    }

    static int partition(int[] A, int p, int r) {
        x = A[r];
        int i = p - 1;
        for (int j = p; j < r; j++) {
            if (A[j] <= x) {
                i++;
                int tmp = A[j]; A[j] = A[i]; A[i] = tmp;
            }
        }
        int tmp = A[i + 1]; A[i + 1] = A[r]; A[r] = tmp;

        return i + 1;
    }

    static void read() {
        n = sc.nextInt();
        A = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = sc.nextInt();
        }
    }
}