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 scanner = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		
		int n = Integer.parseInt(scanner.nextLine());
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scanner.nextInt();
		}
		scanner.close();
		
		int q = partition(a, 0, n - 1);
		for (int i = 0; i < q; i++) {
			sb.append(a[i] + " ");
		}
		sb.append("[");
		sb.append(a[q]);
		sb.append("] ");
		for (int i = q + 1; i < n - 1; i++) {
			sb.append(a[i] + " ");
		}
		sb.append(a[n - 1]);
		System.out.println(sb);
	}

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