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 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		sc.useDelimiter(System.getProperty("line.separator"));
		int n = sc.nextInt();
        String aStr = sc.next();
        int[] A = toIntAry(aStr, n);

        int q = partition(A,0,n-1);

        for (int i = 0; i < A.length; i++) {
        	if(i!=A.length-1){
        		if(i==q){
    				System.out.print("["+A[i]+"] ");
    			}else{
    				System.out.print(A[i]+ " ");
    			}
        	}else{
        		System.out.println(A[i]);
        	}
		}

	}


	private static int partition(int[] a, int p, int r) {
		//??????????±??????????????????????????´???????????????????
		int x = a[r];
		//????????????????°????????????°???????????????????????????????????????????´?
		int i = p-1;

		//?????????2?????????????´????????????????????´?????????????????????§????????????
		for(int j=p; j<r; j++){
			//????????????????°?????????£??????????°?????????°?????????????§????
			if(a[j]<=x){
				i++;
				int tmp = a[i];
				a[i] = a[j];
				a[j] = tmp;
			}
		}
		//????????????????°?????????°?????????????????????????¬?????????¨?????????????????????
		int tmp = a[i+1];
		a[i+1] = a[r];
		a[r] = tmp;

		return i+1;

	}


	private static int[] toIntAry(String str, int n) {
        String[] tmp = str.split(" ");
        int[] A = new int[n];
        for (int i = 0; i < n; i++) {
			A[i] = Integer.parseInt(tmp[i]);
		}
        return A;
	}


}