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 coderbd
 */
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 {
    public int n;
    public long[] minL, maxL, minR, maxR;
    public Point[] points;
    public static class Point implements Comparable<Point> {
        public long x, y;
        public Point(long x, long y) {
            this.x = x;
            this.y = y;
        }
        public int compareTo(Point point) {
            if (this.x < point.x)
                return -1;
            if (this.x > point.x)
                return 1;
            if (this.y < point.y)
                return -1;
            if (this.y > point.y)
                return 1;
            return 0;
        }
    }
    public boolean func(long width) {
        for (int i = 0, li = 0; i < n; i++) {
            while (li < n) {
                if (points[li].x > points[i].x + width)
                    break;
                li++;
            }
            long mn = Integer.MAX_VALUE * 2L;
            long mx = Integer.MIN_VALUE * 2L;
            if (i > 0) {
                mn = Math.min(mn, minL[i-1]);
                mx = Math.max(mx, maxL[i-1]);
            }
            if (li < n) {
                mn = Math.min(mn, minR[li]);
                mx = Math.max(mx, maxR[li]);
            }
            if (mx - mn <= width)
                return true;
        }
        return false;
    }
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        n = in.readInt();
        points = new Point[n];
        minL = new long[n];
        maxL = new long[n];
        minR = new long[n];
        maxR = new long[n];
        for (int i = 0; i < n; i++) {
            long x = in.readLong();
            long y = in.readLong();
            points[i] = new Point(x + y, x - y);
        }
        Arrays.sort(points);
        minL[0] = maxL[0] = points[0].y;
        for (int i = 1; i < n; i++) {
            minL[i] = Math.min(minL[i-1], points[i].y);
            maxL[i] = Math.max(maxL[i-1], points[i].y);
        }
        minR[n-1] = maxR[n-1] = points[n-1].y;
        for (int i = n - 2; i >= 0; i--) {
            minR[i] = Math.min(minR[i+1], points[i].y);
            maxR[i] = Math.max(maxR[i+1], points[i].y);
        }
        long low = 0L;
        long up = Integer.MAX_VALUE * 2L;
        long ans = Long.MAX_VALUE;
        while (low <= up) {
            long mid = low + up >> 1;
            if (func(mid)) {
                ans = mid;
                up = mid - 1L;
            }
            else
                low = mid + 1L;
        }
        ans *= 5L;
        out.printLine(ans / 10L + "." + ans % 10L + "00000000000000");
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

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

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            }
            catch (IOException e) {
                throw new InputMismatchException();
            }
            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;
    }

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

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

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

    }