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

// counting sort

import java.util.*;

public class Main {
	public static void main(String[] args)  {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] A = new int[n];
		for (int i = 0; i < n; i++) {
			A[i] = scanner.nextInt();
		}
		int p = partation(A, 0, n - 1);
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
			if (i == p) {
				sb.append("[").append(A[i]).append("]");
			} else {
				sb.append(A[i]);
			}
			sb.append((i != n - 1) ? " " : "\n");
		}
		System.out.print(sb);
	}
	public static int partation(int[] A, int p, int r) {
		int x = A[r];
		int i = p - 1;
		int t;
		for (int j = p; j < r; j++) {
			if (A[j] <= x) {
				i++;
				t = A[i];
				A[i] = A[j];
				A[j] = t;
			}
		}
		t = A[r];
		A[r] = A[i + 1];
		A[i + 1] = t;
		return i + 1;
	}	
}