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 OCaml (judge verdict: Accepted)

let partition (a : int array) p r =
  let x = a.(r) in
  let swap i j = let t = a.(i) in a.(i) <- a.(j); a.(j) <- t
  in
  let rec doit i j =
    if j >= r then i
    else begin
      if a.(j) <= x then (swap (i + 1) j; doit (i + 1) (j + 1))
      else doit i (j + 1)
    end
  in
  let i = doit (p - 1) p in
  swap (i + 1) r;
  i + 1

let () =
  let n = read_int () in
  let a = Array.init n (fun _ -> Scanf.scanf "%d " (fun i -> i)) in
  let k = partition a 0 (n - 1) in
  Array.iteri (fun i e ->
    Printf.printf (if i = 0 then "%d" else if i = k then " [%d]" else " %d") e) a;
  print_newline ()