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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int A[] = new int[n];
		String[] tmps = br.readLine().split(" ");
		for(int i = 0 ; i < n ; i++){
			A[i] = Integer.parseInt(tmps[i]);
		}
		int q = partition(A,0,n - 1);
		disp(A,n,q);
	}

	public static void disp(int[] A,int n,int q){
		StringBuffer sb = new StringBuffer();
		for(int i = 0 ; i < n ; i++ ){
			if(i == q){
				sb.append("[");
				sb.append(A[i]);
				sb.append("]");
				sb.append(" ");
			}else{
				sb.append(A[i]);
				sb.append(" ");
			}
		}
		System.out.println(sb.toString().trim());
	}

	public static int partition(int[] A,int p,int r){
		int x = A[r];
		int mI = -1;
		int tmp;
		for(int i = 0 ; i < r ; i++){
			if(A[i] <= x){
				tmp = A[i];
				A[i] = A[++mI];
				A[mI] = tmp;
			}
		}
		tmp = x;
		A[r] = A[++mI];
		A[mI] = tmp;
		return mI;
	}
}