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.File;
import java.io.IOException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {

		Scanner scan = new Scanner(System.in);
		// Scanner scan = new Scanner(new
		// File("D:\\UserArea\\J0124567\\Downloads\\ALDS1_6_A-in9.txt"));

		int n = scan.nextInt();
		int[] a = new int[n];

		for (int i = 0; i < n; i++)
			a[i] = scan.nextInt();

		int v = Q2sort(a, 0, n - 1);

		StringBuilder s = new StringBuilder(String.valueOf(a[0]));
		for (int i = 1; i < a.length; i++)
			if (i == v)
				s.append(" [" + a[i] + "]");
			else
				s.append(" " + a[i]);
		System.out.println(s);

		scan.close();
		System.exit(0);
	}

	private static int Q2sort(int[] a, int st, int ed) {
		int x = a[ed];
		int i = st - 1;
		for (int j = st; j < ed; j++)
			if (a[j] <= x) {
				i++;
				int tmp = a[j];
				a[j] = a[i];
				a[i] = tmp;
			}
		int tmp = a[i + 1];
		a[i + 1] = a[ed];
		a[ed] = tmp;
		return i + 1;
	}

	private static void Qsort(int[] a, int st, int ed) {
		if (st >= ed)
			return;
		int x = a[ed];
		int l = st, r = ed - 1;
		while (true) {
			for (; l < ed && a[l] <= x; l++)
				;
			for (; r >= st && a[r] > x; r--)
				;
			if (l < r) {
				int tmp = a[l];
				a[l] = a[r];
				a[r] = tmp;
			} else
				break;
		}
		int tmp = a[l];
		a[l] = a[ed];
		a[ed] = tmp;
		Qsort(a, st, l - 1);
		Qsort(a, l + 1, ed);
	}

	private static void Csort(int[] a, int[] b, int k) {
		int[] c = new int[k + 1];
		for (int i = 0; i < a.length; i++)
			c[a[i]]++;
		for (int i = 1; i < c.length; i++)
			c[i] += c[i - 1];

		for (int i = a.length - 1; i >= 0; i--) {
			c[a[i]]--;
			b[c[a[i]]] = a[i];
		}
	}
}