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.*;
import java.awt.geom.Point2D.Double;

public class Main {
    private static int MAX = 100000;

    public static void main(String[] args) throws Exception {
            // 入力
            int[]   A = new int[MAX];
            int     n;
            Scanner sc = new Scanner(System.in);
            n = Integer.parseInt(sc.nextLine());
            for (int i = 0; i < n; i++) {
                A[i] = Integer.parseInt(sc.next());
            }
            sc.close();

            // パーティション
            int     q = partition(A, 0, n - 1);

            // 出力
            for (int i = 0; i < n; i++) {
                if (i > 0) System.out.print(" ");
                if (i == q) System.out.print("[");
                System.out.print(A[i]);
                if (i == q) System.out.print("]");
            }
            System.out.println();
    }

    static int partition(int[] A, int p, int r) {
        int         x = A[r];       // 配列の末尾。判定の基準になる
        int         i = p - 1;      // A[r]以下を差す
        int         temp = 0;
        for (int j = p; j < r; j++) {
            if (A[j] <= x) {
                i = i + 1;
                temp = A[i];
                A[i] = A[j];
                A[j] = temp;
            }
        }
        temp = A[i + 1];
        A[i + 1] = A[r];
        A[r] = temp;
        return i + 1;
    }
}

