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.awt.geom.AffineTransform;
import java.awt.geom.Point2D;
import java.awt.geom.Point2D.Double;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class F {
	static double[] minXFromBottom;
	static double[] maxXFromBottom;
	static double[] minXToTop;
	static double[] maxXToTop;
	static Point2D.Double[] points;
	static double[] yVals;
	static int n;
	
	public static void main(String[] args) throws Exception{
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		n = in.nextInt();
		points = new Point2D.Double[n];
		for(int i = 0; i < n; i++){
			int x = in.nextInt();
			int y = in.nextInt();
			points[i] = (Double) AffineTransform.getRotateInstance(Math.toRadians(-45)).transform(new Point2D.Double(x,y), null);
		}
		
		Arrays.sort(points, new Comparator<Point2D.Double>(){
			@Override
			public int compare(Double o1, Double o2) {
				return java.lang.Double.compare(o1.y, o2.y);
			}
		});
		
		//for points[0->i], what's min X?
		minXFromBottom = new double[n];
		maxXFromBottom = new double[n];
		
		//for points[i->n-1], what's min X?
		minXToTop = new double[n];
		maxXToTop = new double[n];
		
		double curMinX = Integer.MAX_VALUE;
		double curMaxX = Integer.MIN_VALUE;
		
		for(int i = 0; i < n; i++){
			curMinX = Math.min(curMinX, points[i].x);
			curMaxX = Math.max(curMaxX, points[i].x);
			minXFromBottom[i] = curMinX;
			maxXFromBottom[i] = curMaxX;
		}
		
		curMinX = Integer.MAX_VALUE;
		curMaxX = Integer.MIN_VALUE;
		for(int i = n-1; i >= 0; i--){
			curMinX = Math.min(curMinX, points[i].x);
			curMaxX = Math.max(curMaxX, points[i].x);
			minXToTop[i] = curMinX;
			maxXToTop[i] = curMaxX;
		}
		
		yVals = new double[n];
		for(int i = 0; i < n; i++){
			yVals[i] = points[i].y;
		}
		
		double left = 0;
		double right = Integer.MAX_VALUE;
		while(right - left > 0.001){
			double mid = (left+right)/2.0;
			if(good(mid)){
				right = mid;
			}else{
				left = mid;
			}
		}
		Integer trunc = (int)left; 
		if(left-trunc > 0.75 || left-trunc < 0.25){
			out.println(Math.round(left));
		}else{
			out.println(Math.floor(left) + 0.5);
		}
		out.close();
	}
	
	static boolean good(double w){
		w = w * Math.sin(Math.PI/4.0) * 2.0;
		for(int i = 0; i < n; i++){
			int top = Arrays.binarySearch(yVals, yVals[i] + w);
			if(top < 0){
				top = -1-top;
				top--;
			}
			
			int bottom = Arrays.binarySearch(yVals, yVals[i] - 0.00001);
			if(bottom < 0){
				bottom = -1-bottom;
			}
			double bottomMinX = Integer.MAX_VALUE;
			double bottomMaxX = Integer.MIN_VALUE;
			double topMinX = Integer.MAX_VALUE;
			double topMaxX = Integer.MIN_VALUE;
			
			if(bottom != 0){
				bottomMinX = minXFromBottom[bottom-1];
				bottomMaxX = maxXFromBottom[bottom-1];
			}
			
			if(top != n-1){
				topMinX = minXToTop[top+1];
				topMaxX = maxXToTop[top+1];
			}
			
			if(Math.max(topMaxX, bottomMaxX) - Math.min(bottomMinX, topMinX) < w){
				return true;
			}
		}
		
		return false;
	}
	
	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		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 nextInt() {
			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 nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long 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 String nextToken() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}

		public static boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}