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) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		for(int i = 0;i < n;i++ ) {
			a[i] = sc.nextInt();
		}
		sc.close();
		int q =partition1(a, 0, n-1);
		for(int i = 0 ;i < a.length ; 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();
	}
	public static int partition(int[] arr,int p,int r ) {
		int x = arr[r];
		int i = p-1;
		for(int j = p;j < r;j++) {
			if(arr[j] <= x) {
				i++;
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}	
		}
		arr[i+1] = arr[i+1] ^ arr[r];
		arr[r] = arr[i+1] ^ arr[r];
		arr[i+1] = arr[i+1] ^ arr[r];
		return i+1;
	}
	public static int partition1(int[] arr,int p,int r ) {
		int x = arr[r];
		int i = p-1;
		int t;
		for(int j = p;j < r;j++) {
			if(arr[j] <= x) {
				i++;
				t = arr[i];
				arr[i] = arr[j];
				arr[j] = t;
			}	
		}
		t = arr[i+1];
		arr[i+1] = arr[r];
		arr[r] = t;
		return i+1;
	}
	
}

