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;
#define INFTY (int)(1e9)


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[100002], p;

	cin>>n;
	
	for(int i = 0; i < n; i++){
		cin>>A[i];
	}
	
	p = partition(A,0,n-1);
	
	for(int i = 0; i < n; i++){
		if(i)cout<<" ";
		if(i == p) cout<<"["<<A[i]<<"]";
		else cout<<A[i];
	}cout<<endl;
	return 0;
}
