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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

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

/**
 *
 * @author baito
 */
public class Main
{
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static long MOD =1000000007;
    static long[] f;//factorial

    static int N;
    static int[] X,sX;

    public static void main(String[] args)
    {

        N = sc.nextInt();
        X = sc.nextIntArray(N);
        sX = X.clone();
        //longを忘れるなオーバーフローするぞ
        Arrays.sort(sX);
        int l = sX[N/ 2 - 1];
        int r = sX[N/ 2];
        for (int i = 0; i < N; i++)
        {
            if(X[i] <= l){
                System.out.println(r);
            }else{
                System.out.println(l);
            }
        }


    }
    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long comb(int n, int r)
    {
        long result = f[n];
        result = result * modInv(f[n - r]) % MOD;
        result = result * modInv(f[r]) % MOD;
        return result;
    }

    static long modInv(long n)
    {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n)
    {
        f = new long[n + 1];
        f[0] = f[1] = 1;
        for (int i = 2; i <= n; i++)
        {
            f[i] = (f[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n)
    {
        long res = 1L;
        while (n > 0)
        {
            if ((n & 1) == 1)
            {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
    static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }

    static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
    static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }
    public static void reverse(int[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }
    public static void reverse(int[] x,int s, int e)
    {
        int l = s;
        int r = e;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }
    static int length(int a) {int cou = 0; while(a != 0){ a /= 10; cou++; } return cou;}
    static int length(long a) {int cou = 0; while(a != 0){ a /= 10; cou++; } return cou;}
    static int countC2(char[][] a, char c){
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if(a[i][j] == c)
                    co++;
        return co;
    }
    static void fill(int[][] a, int v){
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }
    static class FastScanner {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public int [][] nextIntArray2(int h, int w){
            int[][] a = new int[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < w ; wi++){
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }
        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public char[] nextCharArray(int n){
            char[] a = next().toCharArray();

            return a;
        }
        public char[][] nextCharArray2(int h , int w){
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }
        //スペースが入っている場合
        public char[][] nextCharArray2s(int h , int w){
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = nextLine().replace(" ","").toCharArray();
            }
            return a;
        }
        public char[][] nextWrapCharArray2(int h , int w, char c){
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }
        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h , int w ,char c){
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + nextLine().replace(" ","") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }
        public long [][] nextLongArray2(int h, int w){
            long[][] a = new long[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < h ; wi++){
                    a[h][w] = nextLong();
                }
            }
            return a;
        }
    }
}