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.*;
import java.util.*;
import java.util.List;


/**
 * Created by Katushka on 11.03.2020.
 */
public class Main {

    static void sortArray(int[] a) {
        Random random = new Random();

        for (int i = 0; i < a.length; i++) {
            int randomPos = random.nextInt(a.length);
            int t = a[i];
            a[i] = a[randomPos];
            a[randomPos] = t;
        }
        Arrays.sort(a);
    }

    static int[] readArray(int size, InputReader in, boolean subOne) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt() + (subOne ? -1 : 0);
        }
        return a;
    }

    static long[] readLongArray(int size, InputReader in) {
        long[] a = new long[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    private static final boolean DEBUG = false;
    private static final long MOD = 1000000007;


    private static int[] getBinary(long a, int size) {
        int[] result = new int[size];
        for (int i = 0; i < size; i++) {
            result[i] = (int) ((a >> i) & 1);
        }
        return result;
    }

    private static long fastPow(long x, long y, long mod) {
        if (x == 1) {
            return 1;
        }
        if (y == 0) {
            return 1;
        }
        long p = fastPow(x, y / 2, mod) % mod;
        p = p * p % mod;
        if (y % 2 == 1) {
            p = p * x % mod;
        }
        return p;
    }

    private static long inv(long x, long mod) {
        return fastPow(x, mod - 2, mod);

    }

    private static long addMod(long x, long y, long mod) {
        long res = x + y;
        if (res >= mod) {
            return res - mod;
        }
        return res;
    }

    private static long multMod(long x, long y, long mod) {
        long res = x * y;
        if (res >= mod) {
            return res % mod;
        }
        return res;
    }

    private static long subMod(long x, long y, long mod) {
        long res = x - y;
        if (res < 0) {
            return res + mod;
        }
        return res;
    }

    public static final Comparator<long[]> PAIR_COMPARATOR = (o1, o2) -> {
        if (o1[0] == o2[0]) {
            return Long.compare(o1[1], o2[1]);
        }
        return Long.compare(o1[0], o2[0]);
    };

    public static void main(String[] args) throws FileNotFoundException {
//        InputReader in = new InputReader(new FileInputStream("input.txt"));
//        PrintWriter out = new PrintWriter(new BufferedOutputStream(new FileOutputStream("seating.out")));

        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int n = in.nextInt();
        long[][] points = new long[n][];
        for (int i = 0; i < n; i++) {
            long x = in.nextLong();
            long y = in.nextLong();
            points[i] = new long[]{x + y, y - x};
        }

        Arrays.sort(points, PAIR_COMPARATOR);
        long[] sufMin = new long[n];
        long[] prefMin = new long[n + 1];
        prefMin[0] = Long.MAX_VALUE;
        long[] sufMax = new long[n];
        long[] prefMax = new long[n + 1];
        prefMax[0] = Long.MIN_VALUE;

        for (int i = 0; i < n; i++) {
            prefMin[i + 1] = Math.min(prefMin[i], points[i][1]);
            prefMax[i + 1] = Math.max(prefMax[i], points[i][1]);
        }

        sufMax[n - 1] = points[n - 1][1];
        sufMin[n - 1] = points[n - 1][1];

        for (int i = n - 2; i >= 0; i--) {
            sufMax[i] = Math.max(points[i][1], sufMax[i + 1]);
            sufMin[i] = Math.min(points[i][1], sufMin[i + 1]);
        }

        long l = -1;
        long r = 2000000002;
        while (r - l > 1) {
            long m = (r + l) / 2;
            if (check(m, points, n, prefMin, prefMax, sufMin, sufMax)) {
                r = m;
            } else {
                l = m;
            }
        }
        out.println(r * 1.0 / 2);

        out.close();
    }

    private static boolean check(long m, long[][] points, int n, long[] prefMin, long[] prefMax, long[] sufMin, long[] sufMax) {
        for (int i = 0; i < n; i++) {
            long x0 = points[i][0];
            long x1 = points[i][0] + m;
            int ind1 = binSearchRight(points, x1);
            int ind0 = binSearchLeft(points, x0);
            long max = Long.MIN_VALUE;
            long min = Long.MAX_VALUE;
            if (ind1 + 1 < n) {
                max = Math.max(max, sufMax[ind1 + 1]);
                min = Math.min(min, sufMin[ind1 + 1]);
            }
            if (ind0 - 1 >= 0) {
                max = Math.max(max, prefMax[ind0]);
                min = Math.min(min, prefMin[ind0]);
            }
            if (max == Long.MIN_VALUE) {
                return true;
            }
            if (max - min <= m) {
                return true;
            }
        }

        return false;
    }

    static int binSearchRight(long[][] list, long key) {
        int l = -1;
        int r = list.length;
        while (l < r - 1) {
            int m = (l + r) / 2;
            if (list[m][0] <= key) {
                l = m;
            } else {
                r = m;
            }
        }
        return l;
    }

    static int binSearchLeft(long[][] list, long key) {
        int l = -1;
        int r = list.length;
        while (l < r - 1) {
            int m = (l + r) / 2;
            if (list[m][0] < key) {
                l = m;
            } else {
                r = m;
            }
        }
        return r;
    }


    private static void outputArray(long[] ans, PrintWriter out, boolean addOne) {
        StringBuilder str = new StringBuilder();
        for (int i = 0; i < ans.length; i++) {
            long an = ans[i] + (addOne ? 1 : 0);
            str.append(an).append('\t');
        }
        out.println(str);
        out.flush();
    }

    private static void outputArray(List<Long> ans, PrintWriter out) {
        StringBuilder str = new StringBuilder();
        for (long an : ans) {
            str.append(an).append(' ');
        }
        out.println(str);
        out.flush();
    }


    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public String nextWord() {
            return next();
        }

        private List<Integer>[] readTree(int n) {
            List<Integer>[] result = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                result[i] = new ArrayList<>();
            }
            for (int i = 0; i < n - 1; i++) {
                int u = nextInt() - 1;
                int v = nextInt() - 1;
                result[u].add(v);
                result[v].add(u);
            }
            return result;
        }

    }
}