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 n;
int A[100000];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)cin>>A[i];
	int x=A[n-1];
	int j=A[0]<x?1:0;
	for(int i=1;i<n-1;i++)
	{
		if (A[i]<=x) 
		{
			int aj=A[j];
			A[j]=A[i];
			A[i]=aj;
			j++;
		}
	}
	A[n-1]=A[j];
	A[j]=x;
	for (int i=0;i<j;i++)
	{
		if (i) cout <<' ';
		cout<<A[i];
	}
	if(j)cout<<' ';
	cout<<'['<<A[j]<<']';
	for(int i=j+1;i<n;i++)//bug here i=j+1
	{
		cout <<' '<<A[i];
	}
	cout<<endl;//bug here
}