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 JavaScript (judge verdict: Accepted)

(function main(){
  const lines = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
  const n = Number(lines.shift());
  const arr = lines.shift().split(' ').map(Number);
  let base_idx = partition(arr, 0, n - 1);
  arr[base_idx] = `[${arr[base_idx]}]`;
  console.log(arr.join(` `));
})();

function partition(arr, p, r) {
   let x  = arr[r];
   let i = p - 1;
   for (let j = p; j < r; j++) {
     if (arr[j] <= x) {
       [arr[i], arr[j]] = [arr[j], arr[++i]];
     }
   }
   [arr[i + 1], arr[r]] = [arr[r], arr[i + 1]];
   return i + 1;
}