Problem:
Partition

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].

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 [  ].

Constraints

1 ≤ n ≤ 100,000

0 ≤ Ai ≤ 100,000

Sample Input 1

12
13 19 9 5 12 8 7 4 21 2 6 11

Sample Output 1

9 5 8 7 4 2 6 [11] 21 13 19 12

Solution in C (judge verdict: Accepted)

/*
 * Problem
 * http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_6_B&lang=jp
 *
 * Author
 * Leonardone @ NEETSDKASU
 */
#include <stdio.h>

void exchange(int A[], int i, int j) {
	int tmp = A[i];
	A[i] = A[j];
	A[j] = tmp;
}

int Partition(int A[], int p, int r) {
	int x = A[r];
	int i = p - 1;
	int j;
	
	for (j = p; j < r; ++j) {
		if (A[j] <= x) {
			++i;
			exchange(A, i, j);
		}
	}
	exchange(A, i + 1, r);
	return i + 1;
}

int main(void) {
	int A[100001];
	int n, i, q;
	
	scanf("%d", &n);
	for (i = 1; i <= n; ++i) {
		scanf("%d", &A[i]);
	}
	
	q = Partition(A, 1, n);
	
	for (i = 1; i <=n ; ++i) {
		if (i > 1) {
			putchar(' ');
		}
		if (i == q) {
			printf("[%d]", A[i]);
		} else {
			printf("%d", A[i]);
		}
	}
	putchar('\n');
	
	return 0;
}