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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>

// バブルソート（昇順）
void bubbleSort(int* numbers, int array_size){
  int i, j, temp;

  for (i = 0; i < (array_size - 1); i++) {
    for (j = (array_size - 1); j > i; j--) {
      if (numbers[j-1] > numbers[j]) {
        temp = numbers[j-1];
        numbers[j-1] = numbers[j];
        numbers[j] = temp;
      }
    }
  }
}

int main(void) {
    int N;
    scanf("%d", &N);

    int X[N], i;
    for(i=0;i<N;i++){
        scanf("%d", &X[i]);
    }

    // 省いた配列作成
    int A[N][N-1], j, count;
    for(i=0;i<N;i++){     // 縦
        count = 0;
        for(j=0;j<N;j++){ // 横
            if(i == j) continue;
            
            A[i][count] = X[j];
            count++;
        }
    }

    // 並び替え（昇順）
    for(i=0;i<N;i++){
        bubbleSort(A[i], N-1);
    }
    
    // 各中央値計算    
    int B[N];
    for(i=0;i<N;i++){
        int center_index = ( (N-1) + 1 ) / 2 - 1;
        B[i] = A[i][center_index];
    }

    // 各中央値表示
    for(i=0;i<N;i++){
        printf("%d\n", B[i]);
    }

    return 0;
}