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 Python (3.4.3) (judge verdict: Runtime Error)

from collections import defaultdict


def main():
    h, w = map(int, input().split())
    s = []
    for _ in range(h):
        col = []
        s.append(col)
        for c in input().strip():
            col.append(ord(c))
    c_row = defaultdict(int)
    for col in s:
        c_row[tuple(sorted(col))] += 1
    if sum(c % 2 for c in c_row.values()) > h % 2:
        print('NO')
        return
    for row, c in c_row.items():
        if c % 2:
            count = defaultdict(int)
            for ch in row:
                count[ch] += 1
            if sum(cc % 2 for cc in count.values()) > w % 2:
                print('NO')
                return

    c_col = defaultdict(int)
    for col in zip(*s):
        c_col[tuple(sorted(col))] += 1
    if sum(c % 2 for c in c_col.values()) > w % 2:
        print('NO')
        return

    for col, c in c_col.items():
        if c % 2:
            count = defaultdict(int)
            for ch in col:
                count[ch] += 1
            if sum(cc % 2 for cc in count.values()) > h % 2:
                print('NO')
                return

    if s[0][0] == ord('b'):
        print('NO')
    else:
        print('YES')


main()