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)

// Partition
#include <stdio.h>
#include <stdlib.h>

int Partition(int*, int, int);

int main(){
  int i, n, *A, std;

  // 配列Aの入力
  scanf("%d", &n);

  A = malloc(sizeof(int) * n + 1);
  
  for(i=0; i < n; i++){
    scanf("%d", &A[i]);
  }

  std = Partition(A, 0, n-1); // パーティションを実施

  // 結果を出力
  for(i=0; i < n; i++){
    if(i != 0)printf(" ");
    if(i == std)printf("[%d]", A[i]);
    else printf("%d", A[i]);
  }
  printf("\n");
  
  return 0;
}

int Partition(int *A, int p, int r){
  int i, j, swap;

  // 配列の要素0からiまでは基準A[r]より小さい値、
  // 要素i+1からr-1までは基準A[r]より大きい値を格納していく
  i = p-1;
  for(j=p; j < r; j++){
    if(A[j] <= A[r]){
      i++;
      swap=A[i];  A[i]=A[j];  A[j]=swap; // A[i]とA[j]を交換
    }
  }
  swap=A[i+1];  A[i+1]=A[r];  A[r]=swap; // 最後にA[i+1]A[r]を交換
  return i+1; // パーティションの基準となる要素を返す
}