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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class D314 {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    static class Sort implements Comparable<Sort> {
        int x, y;
        public int compareTo(Sort arg0) {
            if (this.x > arg0.x)
                return 1;
            if (this.x < arg0.x)
                return -1;
            return 0;
        };
    }
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int[]x = new int[n+1], y = new int[n+1];
        Sort[]a = new Sort[n+1];
        for (int i = 1; i <= n; i++) {
            x[i] = nextInt();
            y[i] = nextInt();
            int t = x[i];
            x[i] = x[i]+y[i];
            y[i] = t-y[i];
            a[i] = new Sort();
            a[i].x = x[i];
            a[i].y = y[i];
        }
        Arrays.sort(a, 1, n+1);
        for (int i = 1; i <= n; i++) {
            x[i] = a[i].x;
            y[i] = a[i].y;
        }
        long[]maxBegin = new long[n+2], maxEnd = new long[n+2], minBegin = new long[n+2], minEnd = new long[n+2];
        maxBegin[1] = minBegin[1] = y[1];
        for (int i = 2; i <= n; i++) {
            maxBegin[i] = Math.max(maxBegin[i-1], y[i]);
            minBegin[i] = Math.min(minBegin[i-1], y[i]);
        }
        maxEnd[n] = minEnd[n] = y[n];
        for (int i = n-1; i >= 1; i--) {
            maxEnd[i] = Math.max(maxEnd[i+1], y[i]);
            minEnd[i] = Math.min(minEnd[i+1], y[i]);
        }
        double left = 0, right = 2e9;
        for (int it = 1; it <= 60; it++) {
            double middle = (left+right) / 2;
            boolean found = false;
            int j = 1;
            for (int i = 1; i <= n; i++) {
                while (x[i]-x[j] > middle)
                    j++;
                if (maxBegin[j-1]-minBegin[j-1] > middle)
                    break;
                long max = Math.max(maxBegin[j-1], maxEnd[i+1]);
                if (j==1)
                    max = maxEnd[i+1];
                if (i==n)
                    max = maxBegin[j-1];
                long min = Math.min(minBegin[j-1], minEnd[i+1]);
                if (j==1)
                    min = minEnd[i+1];
                if (i==n)
                    min = minBegin[j-1];
                if (max-min <= middle) {
                    found = true;
                    break;
                }
            }
            if (found)
                right = middle;
            else
                left = middle;
        }
        System.out.println(left/2);
        pw.close();
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

}