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;

class Main {
	public static void main (String[] args) {
		Scanner scan = new Scanner (System.in);
		final int n = scan.nextInt();
		int[] sequence = new int[n];
		
		for (int i = 0; i < n; i++) {
			sequence[i] = scan.nextInt();
		}
		scan.close();
		
		Partition (sequence, 0, n - 1);
		
		
	}
	
	static void Partition (int[] array, int p, int r) {
		int x = array[r];
		int i = p - 1;
		int temp;
		
		for (int j = p; j < r; j++) {
			if (array[j] <= x) {
				i++;
				temp = array[j];
				array[j] = array[i];
				array[i] = temp;
			}
		}
		
		array[r] = array[i + 1];
		array[i + 1] = x;
		
		printArray (array, i + 1);
		
		
		
	}
	
	static void printArray (int[] data, int x) {
		int n = data.length;
		for (int i = 0; i < n; i++) {
			if ( i != n - 1) {
				if ( i != x) System.out.print(data[i] + " ");
				else System.out.print("[" +data[i] + "] "); 
			}
			else System.out.println(data[i]);
		}
	}

	
}

