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 Ruby (judge verdict: Wrong Answer)

num = gets.chop
line = gets
num_array = line.split(" ")

class Test 
    def partition(a, pp,r)
        x = a[r].to_i
        i = pp - 1
        j = pp
        while true do
            if j == r then
                break
            end
            if a[j].to_i <= x then
                i += 1
                buf = a[i]
                a[i] = a[j]
                a[j] = buf
            end
            j += 1
        end
        buf2 = a[i + 1]
        a[i + 1] = a[r]
        a[r] = buf2
        # result = ""
        for a_val in a do
            if a_val == a[i + 1] then
                if a_val == a[a.length - 1] then
                    print "["
                    print a_val.to_i 
                    p "]"
                else
                    print "["
                    print a_val.to_i 
                    print "] "
                end
            else
                if a_val == a[a.length - 1] then
                    p a_val.to_i
                else
                    print a_val.to_i
                    print " "
                end
            end
        end
        return i + 1
    end
end
test = Test.new
test.partition(num_array,0,num_array.length - 1)