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 PHP (judge verdict: Accepted)

<?php

function input() {
    return trim(fgets(STDIN));
}
function input_array() {
    return explode(' ', input());
}

function partition(&$A, $p, $r) {
    $x = $A[$r];
    $i = $p - 1;
    for ($j = $p; $j < $r; $j++) {
        if ($A[$j] <= $x) {
            $i++;
            $t = $A[$i]; $A[$i] = $A[$j]; $A[$j] = $t;
        }
    }
    $t = $A[$i + 1]; $A[$i + 1] = $A[$r]; $A[$r] = $t;
    return $i + 1;
}

$n = (int)input();
$A = array_map(function($numeric_string) {
    return (int)$numeric_string;
}, input_array());
$q = partition($A, 0, $n - 1);

echo implode(' ', array_slice($A, 0, $q)) . ' [' . $A[$q] . '] ' . implode(' ', array_slice($A, $q + 1)) . "\n";