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
import java.util.*;
import java.io.*;

public class Main {
    
    public static void main(String[] args) {
        Main main = new Main();
        main.solv();
    }
    
    private void solv() {
        Scanner input = new Scanner(System.in);
        
        int n = input.nextInt();
        int[]A = new int[n];
        for(int i = 0; i < n; i++) {
            A[i] = input.nextInt();
        }
        int k = partition(A, 0, A.length - 1);
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < k; i++) {
            sb.append(A[i]).append(' ');
        }
        sb.append('[').append(A[k]).append(']');
        for (int i = k + 1; i < A.length; i++) {
            sb.append(' ').append(A[i]);
        }
        System.out.println(sb.toString());
    }
    
    private int partition(int[] A, int p, int r) {
        int x = A[r];
        int i = p - 1;
        int temp;
        for (int j = p; j < r; j++) {
            if (A[j] <= x) {
                i = i + 1;
                temp = A[i];
                A[i] = A[j];
                A[j] = temp;
            }
        }
        temp = A[i+1];
        A[i+1] = A[r];
        A[r] = temp;
        return i+1;
    }
    
    private void print(Object[] xs) {
        StringBuilder sb = new StringBuilder();
        for (Object x : xs) sb.append(x.toString()).append(' ');
        System.out.println(sb.toString().trim());
    }
    
    private void print(int[] xs) {
        StringBuilder sb = new StringBuilder();
        for (int x : xs) sb.append(x).append(' ');
        System.out.println(sb.toString().trim());
    }
    
    private static class Scanner {
        BufferedReader r;
        StreamTokenizer st;
        
        public Scanner(InputStream in) {
            r = new BufferedReader(new InputStreamReader(in));
            st = new StreamTokenizer(r);
        }
        
        public String next() {
            nextToken();
            return st.sval;
        }
        
        public Integer nextInt() {
            nextToken();
            return (int)st.nval;
        }
        
        private int nextToken() {
            int token = st.TT_EOF;
            try {
                token = st.nextToken();
            } catch (IOException e) {
            }
            return token;
        }
    }
}