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].

Constraints

* 1 ≤ n ≤ 100,000
* 0 ≤ Ai ≤ 100,000

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 [  ].

Example

Input

12
13 19 9 5 12 8 7 4 21 2 6 11


Output

9 5 8 7 4 2 6 [11] 21 13 19 12
#include <iostream>
using namespace std;

int partition(int a[],int p,int r) {
  int x=a[r]; 
  int i=p-1;
  for(int j=p;j<r;j++)
    if(a[j]<=x) i++,swap(a[i],a[j]);
 
  swap(a[i+1],a[r]); 
  return i+1;
}

int main(){
  int n,a[100001];
  cin>>n;
  for(int i=0;i<n;i++) cin>>a[i];

  int idx=partition(a,0,n-1);
  for(int i=0;i<idx;i++)cout <<a[i]<<" ";
  cout <<"["<<a[idx]<<"] ";
  for(int i=idx+1;i<n-1;i++) cout <<a[i]<<" ";
  cout << a[n-1]<<endl;
	
  return 0;
}