Problem:
Score : 1200 points

Problem Statement

Snuke loves flags.

Snuke is placing N flags on a line.

The i-th flag can be placed at either coordinate x_i or coordinate y_i.

Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.

Constraints

2 ≤ N ≤ 10^{4}

1 ≤ x_i, y_i ≤ 10^{9}

x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 3
2 5
1 9

Sample Output 1

4

The optimal solution is to place the first flag at coordinate 1, the second flag at coordinate 5 and the third flag at coordinate 9. The smallest distance between two of the flags is 4 in this case.

Sample Input 2

5
2 2
2 2
2 2
2 2
2 2

Sample Output 2

0

There can be more than one flag at the same position.

Sample Input 3

22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269

Sample Output 3

17

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.util.TreeSet;


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    int[] x = new int[N];
    int[] y = new int[N];
    for (int i = 0; i < N; i ++) {
      x[i] = sc.nextInt();
      y[i] = sc.nextInt();
    }
    
    int left = 0;
    int right = Integer.MAX_VALUE;
    
    while (left <= right) {
      int k = (left + right) / 2;
      
      TreeSet<Integer> set = new TreeSet<>();
      boolean ret = dfs(set, N, 0, k, x, y);
      if (ret) {
        left = k + 1;
      } else {
        right = k - 1;
      }
    }
    System.out.println(right);
   }

  private static boolean dfs(TreeSet<Integer> set, int n, int now, int min, int[] x, int[] y) {
    if (now == n) {
      return true;
    }

    int p = x[now];
    int q = y[now];
    
    Integer a = set.ceiling(p);
    Integer b = set.floor(p);
    Integer c = set.ceiling(q);
    Integer d = set.floor(q);
    
    if (a == null) {
      a = Integer.MAX_VALUE / 2;
    }
    if (b == null) {
      b = Integer.MAX_VALUE / 2;
    }
    if (c == null) {
      c = Integer.MAX_VALUE / 2;
    }
    if (d == null) {
      d = Integer.MAX_VALUE / 2;
    }
    
    if (Math.abs(p - a) >= min && Math.abs(p - b) >= min) {
      set.add(p);
      boolean ret = dfs(set, n, now + 1, min, x, y);
      if (ret) {
        return true;
      }
      set.remove(p);
    }

    if (Math.abs(q - c) >= min && Math.abs(q - d) >= min) {
      set.add(q);
      boolean ret = dfs(set, n, now + 1, min, x, y);
      if (ret) {
        return true;
      }
      set.remove(q);
    }
    
    return false;
  }
}


class FastScanner {
	public static String debug = null;

	private final InputStream in = System.in;
	private int ptr = 0;
	private int buflen = 0;
	private byte[] buffer = new byte[1024];
	private boolean eos = false;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				if (debug != null) {
					buflen = debug.length();
					buffer = debug.getBytes();
					debug = "";
					eos = true;
				} else {
					buflen = in.read(buffer);
				}
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen < 0) {
				eos = true;
				return false;
			} else if (buflen == 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean isEOS() {
		return this.eos;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		return (int) nextLong();
	}

	public long[] nextLongList(int n) {
		return nextLongTable(1, n)[0];
	}

	public int[] nextIntList(int n) {
		return nextIntTable(1, n)[0];
	}

	public long[][] nextLongTable(int n, int m) {
		long[][] ret = new long[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextLong();
			}
		}
		return ret;
	}

	public int[][] nextIntTable(int n, int m) {
		int[][] ret = new int[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextInt();
			}
		}
		return ret;
	}
}