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 9.2.1) (judge verdict: Runtime Error)

#include <cstdio>

const int N = 12 + 3;

char s[N][N];
int n, m;

int cntr[N][30], cntc[N][30];
bool matchr[N], matchc[N];

// inline void debug(int *a, int *b) { for(int *i = a; i != b; i++) std::printf("%d ", *i); }

int main() {
	std::scanf("%d%d", &n, &m);
	for(int i = 1; i <= n; i++)
		std::scanf("%s", s[i] + 1);
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= m; j++)
			cntr[i][s[i][j] - 'a']++, cntc[j][s[i][j] - 'a']++;
	// for(int i = 1; i <= n; i++)
	// 	std::printf("Row %d: {", i), debug(cntr[i], cntr[i] + 26), std::printf("\b}\n");
	// for(int i = 1; i <= m; i++)
	// 	std::printf("Col %d: {", i), debug(cntc[i], cntc[i] + 26), std::printf("\b}\n");
	int totr = n, totc = m;
	for(int i = 1; i <= n; i++) {
		if(matchr[i]) continue;
		for(int j = i + 1; j <= n; j++) {
			if(matchr[j]) continue;
			bool eq = true;
			for(int k = 0; k < 26; k++) eq &= (cntr[i][k] == cntr[j][k]);
			if(eq) { matchr[i] = matchr[j] = true, totr -= 2; break; }
		}
	}
	for(int i = 1; i <= m; i++) {
		if(matchc[i]) continue;
		for(int j = i + 1; j <= m; j++) {
			if(matchc[j]) continue;
			bool eq = true;
			for(int k = 0; k < 26; k++) eq &= (cntc[i][k] == cntc[j][k]);
			if(eq) { matchc[i] = matchc[j] = true, totc -= 2; break; }
		}
	}
	if(totr < 2 && totc < 2) std::puts("YES");
	else std::puts("NO");
	return 0;
}