Problem: Gena doesn't like geometry, so he asks you to solve this problem for him.

A rectangle with sides parallel to coordinate axes contains n dots. Let's consider some point of the plane. Let's count the distances from this point to the given n points. Let's sort these numbers in the non-decreasing order. We'll call the beauty of the point the second element of this array. If there are two mimimum elements in this array, the beaty will be equal to this minimum.

Find the maximum beauty of a point inside the given rectangle.

Input

The first line contains three integers w, h, n (1 ≤ w, h ≤ 106, 2 ≤ n ≤ 1000) — the lengths of the rectangle sides and the number of points. Next n lines contain two integers xi, yi (0 ≤ xi ≤ w, 0 ≤ yi ≤ h) each — the coordinates of a point. It is possible that it will be coincident points.

Output

Print a single number — the maximum beauty of a point with the absolute or relative error of at most 10 - 9.

Examples

Input

5 5 4
0 0
5 0
0 5
5 5


Output

4.99999999941792340


Input

5 5 3
4 0
2 5
4 1


Output

5.65685424744772010

Note

The point which beauty we need to find must have coordinates (x, y), where 0 ≤ x ≤ w, 0 ≤ y ≤ h. Some of the n points can coincide.

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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class Div1_253E {

	static final double EPS = 1e-11;

	long W;
	long H;
	int N;

	long[] x;
	long[] y;

	public static void main(String[] args) throws IOException {
		new Div1_253E().main();
	}

	double ans = 0;

	double[][] angles;
	double[][] dist;

	void main() throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		StringTokenizer inputData = new StringTokenizer(reader.readLine());
		W = Integer.parseInt(inputData.nextToken());
		H = Integer.parseInt(inputData.nextToken());
		N = Integer.parseInt(inputData.nextToken());
		x = new long[N];
		y = new long[N];

		for (int i = 0; i < N; i++) {
			inputData = new StringTokenizer(reader.readLine());
			x[i] = Integer.parseInt(inputData.nextToken());
			y[i] = Integer.parseInt(inputData.nextToken());
		}

		angles = new double[N][N];
		dist = new double[N][N];

		for (int i = 0; i < N; i++) {
			for (int j = 0; j < N; j++) {
				dist[i][j] = Math.hypot(x[i] - x[j], y[i] - y[j]);
				angles[i][j] = Math.atan2(y[j] - y[i], x[j] - x[i]);
			}
		}

		ArrayList<Integer> order = new ArrayList<>();
		for (int i = 0; i < N; i++) {
			order.add(i);
		}
		Collections.shuffle(order);

		for (int i : order) {
			binSearch(i);
		}
		printer.println(ans);
		printer.close();
	}

	void binSearch(int pv) {
		fInts(pv, ans + 2e-9);

		if (!gap()) {
			return;
		}

		double low = ans + 2e-9;
		double high = 1_414_214;

		int i = 50;

		while (i-- > 0) {
			double mid = (low + high) / 2;
			fInts(pv, mid);
			if (gap()) {
				low = mid;
			} else {
				high = mid;
			}
		}

		ans = Math.max(ans, low);
	}

	Int[] ints = new Int[2010];
	int iS = 0;

	void fInts(int pv, double r) {
		iS = 0;

		double r2 = 2 * r;
		double inv2r = 1 / (2 * r);
		double[] cDist = dist[pv];
		double[] cAng = angles[pv];
		for (int i = 0; i < N; i++) {
			double d = cDist[i];

			if (d < EPS) {
				continue;
			}

			// no contact
			if (d > r2) {
				continue;
			}

			double angle = cAng[i];

			double theta = Math.acos(d * inv2r);
			double st = angle - theta;
			double end = angle + theta;

			if (st < -Math.PI) {
				ints[iS++] = new Int(st + PI2, Math.PI);
				ints[iS++] = new Int(-Math.PI, end);
			} else if (end > Math.PI) {
				ints[iS++] = new Int(st, Math.PI);
				ints[iS++] = new Int(-Math.PI, end - PI2);
			} else {
				ints[iS++] = new Int(st, end);
			}
		}

		// down
		double d = y[pv];
		if (d < 2 * r) {
			double theta = Math.acos(d / r);
			addInts(-HALF_PI - theta, -HALF_PI + theta);// twice because they're not ignorable
			addInts(-HALF_PI - theta, -HALF_PI + theta);
		}

		// right
		d = W - x[pv];
		if (d < 2 * r) {
			double theta = Math.acos(d / r);
			addInts(-theta, theta);
			addInts(-theta, theta);
		}

		// up
		d = H - y[pv];
		if (d < 2 * r) {
			double theta = Math.acos(d / r);
			addInts(HALF_PI - theta, HALF_PI + theta);
			addInts(HALF_PI - theta, HALF_PI + theta);
		}

		// left
		d = x[pv];
		if (d < 2 * r) {
			double theta = Math.acos(d / r);
			addInts(Math.PI - theta, Math.PI + theta);
			addInts(Math.PI - theta, Math.PI + theta);
		}
	}

	static final double PI2 = 2 * Math.PI;
	static final double HALF_PI = Math.PI / 2;

	// assuming end-st < 2pi
	void addInts(double st, double end) {
		if (st < -Math.PI) {
			ints[iS++] = new Int(st + PI2, Math.PI);
			ints[iS++] = new Int(-Math.PI, end);
		} else if (end > Math.PI) {
			ints[iS++] = new Int(st, Math.PI);
			ints[iS++] = new Int(-Math.PI, end - PI2);
		} else {
			ints[iS++] = new Int(st, end);
		}
	}

	// an Int can span anywhere from -pi to pi
	// error on the side of returning true
	boolean gap() {
		Arrays.sort(ints, 0, iS);

		if (iS < 2 || EPS < ints[1].st) {
			return true;
		}

		double f1 = Double.NEGATIVE_INFINITY;
		double f2 = Double.NEGATIVE_INFINITY;

		for (int i = 0; i < iS; i++) {
			if (i != 0) {
				if (f2 + EPS < ints[i].st) {
					return true;
				}
			}

			if (ints[i].end > f1) {
				f2 = f1;
				f1 = ints[i].end;
			} else if (ints[i].end > f2) {
				f2 = ints[i].end;
			}

			while (i + 1 < iS && ints[i + 1].st < ints[i].st + EPS) {
				i++;
				if (ints[i].end > f1) {
					f2 = f1;
					f1 = ints[i].end;
				} else if (ints[i].end > f2) {
					f2 = ints[i].end;
				}
			}
		}

		if (f2 + EPS < Math.PI) {
			return true;
		}
		return false;
	}

	class Int implements Comparable<Int> {
		double st;
		double end;

		Int(double st, double end) {
			this.st = st;
			this.end = end;
		}

		public int compareTo(Int o) {
			double d2 = o.st;
			if (st < d2)
				return -1;
			if (st > d2)
				return 1;

			// Cannot use doubleToRawLongBits because of possibility of NaNs.
			long thisBits = Double.doubleToLongBits(st);
			long anotherBits = Double.doubleToLongBits(d2);

			return (thisBits == anotherBits ? 0 : // Values are equal
					(thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
							1)); // (0.0, -0.0) or (NaN, !NaN)
		}
	}
}