Problem:
Score : 300 points

Problem Statement

When l is an odd number, the median of l numbers a_1, a_2, ..., a_l is the (\frac{l+1}{2})-th largest value among a_1, a_2, ..., a_l.

You are given N numbers X_1, X_2, ..., X_N, where N is an even number.
For each i = 1, 2, ..., N, let the median of X_1, X_2, ..., X_N excluding X_i, that is, the median of X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N be B_i.

Find B_i for each i = 1, 2, ..., N.

Constraints

2 \leq N \leq 200000

N is even.

1 \leq X_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample Output 1

4
3
3
4

Since the median of X_2, X_3, X_4 is 4, B_1 = 4.

Since the median of X_1, X_3, X_4 is 3, B_2 = 3.

Since the median of X_1, X_2, X_4 is 3, B_3 = 3.

Since the median of X_1, X_2, X_3 is 4, B_4 = 4.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;

namespace _094C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] x = new int[n];

            string[] str = Console.ReadLine().Split(' ');
            for (int i = 0; i < str.Length; i++)
            {
                x[i] = int.Parse(str[i]);
            }

            for (int i = 0;i < n; i++)
            {
                int v2len = n - i - 1;
                int[] vv = new int[n - 1];
                if (i == 0)
                {
                    // first
                    Array.Copy(x, i + 1, vv, 0, vv.Length);
                } else if (i == (n - 1))
                {
                    // last
                    Array.Copy(x, 0, vv, 0, vv.Length);
                } else
                {
                    Array.Copy(x, 0, vv, 0, i);
                    Array.Copy(x, i + 1, vv, i, v2len);
                }

                Array.Sort(vv);
                int mindex = (vv.Length + 1) / 2;
                int med = vv[mindex - 1];
                System.Console.WriteLine(med);
            }
        }
    }
}