Problem: Sereja placed n points on a plane. Now Sereja wants to place on the plane two straight lines, intersecting at a right angle, so that one of the straight lines intersect the Ox axis at an angle of 45 degrees and the maximum distance from the points to the straight lines were minimum. 

In this problem we consider the distance between points (x1, y1) and (x2, y2) equal |x1 - x2| + |y1 - y2|. The distance between the point and the straight lines is the minimum distance from the point to some point belonging to one of the lines.

Help Sereja, find the maximum distance from the points to the optimally located straight lines.

Input

The first line contains integer n (1 ≤ n ≤ 105). Next n lines contain the coordinates of the lines. The i-th line contains two integers xi, yi (|xi|, |yi| ≤ 109).

Output

In a single line print a real number — the answer to the problem. Your answer will be considered correct iff its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

4
0 0
2 0
0 2
2 2


Output

0.000000000000000


Input

4
1 0
0 1
2 1
1 2


Output

1.000000000000000

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Zhipeng Jia
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
	private Pair<Integer, Integer>[] points;
	private int[] rMax;
	private int[] rMin;

	private boolean check(double limit) {
		int n = points.length;
		int j = 0;
		int lMax = Integer.MIN_VALUE;
		int lMin = Integer.MAX_VALUE;
		for (int i = 0; i < n; i ++) {
			while (j < n && points[j].first - points[i].first <= limit) j ++;
			int max = Math.max(lMax, rMax[j]);
			int min = Math.min(lMin, rMin[j]);
			if (max == Integer.MIN_VALUE && min == Integer.MAX_VALUE || max - min <= limit) return true;
			lMax = Math.max(lMax, points[i].second);
			lMin = Math.min(lMin, points[i].second);
		}
		return false;
	}

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int n = in.readInt();
		points = new Pair[n];
		for (int i = 0; i < n; i ++) {
			int t1 = in.readInt();
			int t2 = in.readInt();
			points[i] = new Pair<Integer, Integer>(t1 + t2, t1 - t2);
		}
		Arrays.sort(points);
		rMax = new int[n + 1];
		rMax[n] = Integer.MIN_VALUE;
		rMin = new int[n + 1];
		rMin[n] = Integer.MAX_VALUE;
		for (int i = n - 1; i >= 0; i --) {
			rMax[i] = Math.max(rMax[i + 1], points[i].second);
			rMin[i] = Math.min(rMin[i + 1], points[i].second);
		}
		double head = 0;
		double tail = 1e9;
		for (int i = 0; i < 70; i ++) {
			double mid = (head + tail) / 2;
			if (check(mid * 2)) tail = mid; else head = mid;
		}
		out.printLineDouble(tail, 12);
	}
}

class Pair<T1 extends Comparable<T1>, T2 extends Comparable<T2>> implements Comparable<Pair<T1, T2>> {
	public T1 first;
	public T2 second;

	public boolean equals(Object o) {
		if (this == o) return true;
		if (o == null || getClass() != o.getClass()) return false;

		Pair pair = (Pair) o;

		if (!first.equals(pair.first)) return false;
		if (!second.equals(pair.second)) return false;

		return true;
	}

	public int hashCode() {
		int result = first.hashCode();
		result = 31 * result + second.hashCode();
		return result;
	}

	public Pair(T1 first, T2 second) {
		this.first = first;
		this.second = second;
	}

	public int compareTo(Pair<T1, T2> o) {
		if (first.compareTo(o.first) != 0) return first.compareTo(o.first);
		return second.compareTo(o.second);
	}
}

class InputReader {
	private InputStream stream;
	private byte[] buf = new byte[1000];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	private int read() {
		if (numChars == -1)
			throw new UnknownError();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new UnknownError();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9') throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printDouble(double x, int precision) {
		writer.printf("%." + precision + "f", x);
	}

	public void printLineDouble(double x, int precision) {
		printDouble(x, precision);
		printLine();
	}

	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}

	public void close() {
		writer.close();
	}
}