Vasiliy lives at point (a, b) of the coordinate plane. He is hurrying up to work so he wants to get out of his house as soon as possible. New app suggested n available Beru-taxi nearby. The i-th taxi is located at point (xi, yi) and moves with a speed vi. 

Consider that each of n drivers will move directly to Vasiliy and with a maximum possible speed. Compute the minimum time when Vasiliy will get in any of Beru-taxi cars.

Input

The first line of the input contains two integers a and b ( - 100 ≤ a, b ≤ 100) — coordinates of Vasiliy's home.

The second line contains a single integer n (1 ≤ n ≤ 1000) — the number of available Beru-taxi cars nearby. 

The i-th of the following n lines contains three integers xi, yi and vi ( - 100 ≤ xi, yi ≤ 100, 1 ≤ vi ≤ 100) — the coordinates of the i-th car and its speed.

It's allowed that several cars are located at the same point. Also, cars may be located at exactly the same point where Vasiliy lives.

Output

Print a single real value — the minimum time Vasiliy needs to get in any of the Beru-taxi cars. You answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

0 0
2
2 0 1
0 2 2


Output

1.00000000000000000000

Input

1 3
3
3 3 2
-2 3 6
-2 7 10


Output

0.50000000000000000000

Note

In the first sample, first taxi will get to Vasiliy in time 2, and second will do this in time 1, therefore 1 is the answer.

In the second sample, cars 2 and 3 will arrive simultaneously.
import java.io.*;
import java.util.*;

/**
 * @author Ivan Pryvalov (ivan.pryvalov@gmail.com)
 */
public class CF367_Div2_A implements Runnable {

    static EventType eventType = EventType.DEFAULT;
//    static EventType eventType = EventType.GOOGLE_CODE_JAM;

    // Set T=0 if T should be read from input.
    // Set T=1 if there is only one testcase.
    static int T = 1;

    // Set it to `null' when the input is std in.
//    static String inputFilename = null;
//    static String inputFilename = "A-sample.in";
//    static String inputFilename = "A-small-attempt0.in";
    static String inputFilename = null;


    // Set to true if you have prepared a large test with fake data.
    static boolean largeFakeTest = false;
    //Number of tests in the large fake test.
    static int largeFakeTest_T = 1;


    //--------------------------------------------------------------------

    public static class Solver extends  SolverAbstract{

        String res;


        @Override
        public void readInput() throws IOException {
            int a = scanner.nextInt();
            int b = scanner.nextInt();
            int n = scanner.nextInt();
            double tBest = 0;
            for (int i = 0; i < n; i++) {
                int x = scanner.nextInt();
                int y = scanner.nextInt();
                int v = scanner.nextInt();
                double dist = Math.sqrt((x-a)*(x-a) + (y-b)*(y-b));
                double t = dist / v;
                if (i==0 || t < tBest){
                    tBest = t;
                }
            }
            res = ""+tBest;
        }

        @Override
        protected String solve() throws IOException {
            return res;
        }
    }

    // ------------- Some stardard tools that are currently not tested.

    static class Graph{
        int[][] G;
        int N;

        int[][] A;
        int[][] F;

        int[] path;
        int pathLen;
        boolean[] visited;
        int target;
        boolean flowFound;

        public Graph(int[][] g) {
            G = g;
            N = G.length;
        }

        public int[][] maxflow(int iSource, int iSink) {
            path = new int[N];
            visited = new boolean[N];

            A = new int[N][];
            for (int i = 0; i < N; i++) {
                A[i] = G[i].clone();
            }
            F = new int[N][N];

            target = iSink;
            //dfs from source to sink
            //increase path
            while(true){
                flowFound = false;
                visited[iSource] = true;
                pathLen = 0;
                path[pathLen++] = iSource;
                dfs(iSource);
                if (!flowFound)
                    break;
            }
            return F;
        }

        private void dfs(int u) {
            if (u==target){
                flowFound = true;
                for (int i = 0; i < pathLen-1; i++) {
                    int from = path[i];
                    int to  = path[i+1];
                    F[from][to]++;
                    F[to][from]--;
                }
            }else {
                for (int i = 0; i < N && !flowFound; i++) {
                    if (!visited[i] && A[u][i] > F[u][i]) {
                        visited[i] = true;
                        path[pathLen] = i;
                        pathLen++;
                        dfs(i);
                        visited[i] = false;
                        pathLen--;
                    }
                }
            }
        }
    }

    //--------------------------------------------------------------------

    private void solveAll() throws IOException, InterruptedException {
        long timeStart = System.currentTimeMillis();

        if (T==0) {
            if (largeFakeTest) {
                T = largeFakeTest_T;
            } else {
                T = scanner.nextInt();
            }
        }
        final String[] results = new String[T+1];
        for (int test = 0; test < T; test++) {
            Solver solver = new Solver(){
                @Override
                public void callback() {
                    results[testNo] = answer;
                }
            };
            solver.testNo = test+1;
            if (largeFakeTest) {
                solver.readFakeInput();
            }else{
                solver.readInput();
            }
            solver.solveWrapped();
        }

        long timeEnd = System.currentTimeMillis();
        if (isInputFromFile())
            System.out.println("All tasks are solved! Elapsed time "+(timeEnd-timeStart)/1000.0+" sec.");

        // write all responses in the proper order
        for (int i = 1; i <= T; i++) {
            if (eventType == EventType.GOOGLE_CODE_JAM){
                out.printf("Case #%d: %s", i, results[i]);
            }else {
                out.println(results[i]);
            }
        }
    }

    enum EventType{
        DEFAULT,
        GOOGLE_CODE_JAM
    }

    static boolean isInputFromFile() {
        return inputFilename != null;
    }

    public static abstract class SolverAbstract {
        int testNo;
        String answer = null;

        public void callback(){};

        public abstract void readInput() throws IOException;

        //generate a randomized test with the maximal input values
        public void readFakeInput() throws  IOException{
            throw new RuntimeException("not implemented");
        }

        protected abstract String solve() throws IOException;

        protected void solveWrapped() throws IOException {

            if (isInputFromFile())
                System.out.println("SOLVER: solving task #"+testNo+" out of "+ T+"...");

            answer = solve();
/*
            StringBuilder sbAnswer = new StringBuilder();
            sbAnswer.append(String.format("Case #%d:\n", testNo));
            good.forEach( (k,v) -> {
                sbAnswer.append(k).append(" ");
                for(int x:v){
                    sbAnswer.append(x).append(" ");
                }
                sbAnswer.append("\n");
            });


            answer = sbAnswer.toString();
*/

            if (isInputFromFile()) {
                System.out.println("\t"+answer);
            }
            callback();
        }

    }

    ////////////////////////////////////////////////////////

    /**
     * Source: http://stackoverflow.com/questions/4521983/java-executorservice-that-blocks-on-submission-after-a-certain-queue-size
     *
     * @param <E>
     */
//    public class LimitedQueue<E> extends LinkedBlockingQueue<E>{
//
//        public LimitedQueue(int maxSize) {
//            super(maxSize);
//        }
//
//        @Override
//        public boolean offer(E e){
//            // turn offer() and add() into a blocking calls (unless interrupted)
//            try {
//                put(e);
//                return true;
//            } catch(InterruptedException ie) {
//                Thread.currentThread().interrupt();
//            }
//            return false;
//        }
//    }

    /**
     * Move to Utilities
     *
     * //List<Integer> primesLimited = getPrimes(1_000_000).subList(0, 100);
     *
     * @param limit
     * @return
     */
    public static List<Integer> getPrimes(int limit) {
        boolean[] primes = new boolean[limit+1];
        Arrays.fill(primes, true);

        primes[1] = false;
        for(int i=2; i<=limit; i++){
            if (primes[i]){
                for(int j=i+i; j<=limit; j+=i){
                    primes[j] = false;
                }
            }
        }
        List<Integer> listPrimes = new ArrayList<>();
        for(int i=2; i<=limit; i++){
            if (primes[i]){
                listPrimes.add(i);
            }
        }
        return listPrimes;
    }


    public static class Modulo{
        long mod = (long)1e9+7;

        public Modulo(long mod) {
            super();
            this.mod = mod;
        }

        public long inv(long a) {
            long res =  pow(a, mod-2);
            return res;
        }

        public long pow(long a, long x) {
            if (x==0)
                return 1;
            long part = 1;
            if ((x&1)!=0)
                part = a;
            return (part * pow((a*a)%mod, x>>1)) % mod;
        }

        public long c(long n, long m){
            long res = 1;
            for(int i=1; i<=m; i++){
                res = (res * (n-m+i)) % mod;
                res = (res * inv(i)) % mod;
            }
            return res;
        }
    }

    /**
     * Added 26.04.2013.
     * See KROK 2013, Round 1, Problem D.
     */
    static class DisjointUnionSet implements Cloneable{
        int[] rank;
        int[] parent;

        protected DisjointUnionSet clone(){
            DisjointUnionSet cloned = new DisjointUnionSet(parent.length);
            for(int i=0; i<parent.length; i++){
                cloned.parent[i] = parent[i];
                cloned.rank[i] = rank[i];
            }
            return cloned;
        }

        public DisjointUnionSet(int n) {
            rank = new int[n];
            parent = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        @Override
        public String toString() {
            return "disj [parents=" + Arrays.toString(parent) + "]";
        }

        /**
         * Problem specific or general?
         * O(N * alpha)
         */
        public void union(DisjointUnionSet set2){
            for(int i=0; i<parent.length; i++){
                parent[find(i)] = parent[find(set2.find(i))];
            }
        }

        /**
         * @param index1 range 0..n-1
         * @param index2
         */
        public void union(int index1, int index2){
            int p1 = find(index1);
            int p2 = find(index2);
            if (rank[p1] > rank[p2]){
                parent[p2] = p1;
            }else if (rank[p2] > rank[p1]){
                parent[p1] = p2;
            }else{
                parent[p2] = p1;
                rank[p1]++;
            }
        }

        // O(alpha(n))
        private int find(int index) {
            if (parent[index] != index)
                parent[index] =  find(parent[index]);
            return parent[index];
        }

        // O(N alpha(N)) ==> see find()
        public int getCountDisjointSets(){
            int[] used = new int[parent.length];
            for(int i=0; i<parent.length; i++){
                used[find(i)] = 1;
            }
            int res = 0;
            for(int i=0; i<parent.length; i++){
                res += used[i];
            }
            return res;
        }
    }

    private static Random rnd = new Random();
    public static class ArrayUtils{
        public static void shuffle(int[] a){
            for(int j=a.length-1; j>=1; j--){
                int i = rnd.nextInt(j+1);
                swap(a, i, j);
            }
        }

        public static void swap(int[] a, int i, int j){
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
    }

    ////////////////////////////////////////////////////////
    /// Typically, you don't want to edit anything below
    ///////////////////////////////////////////////////////
    final int BUF_SIZE = 1024 * 1024 * 8;//important to read long-string tokens properly
    final int INPUT_BUFFER_SIZE = 1024 * 1024 * 8 ;
    final int BUF_SIZE_INPUT = 1024;

    final int BUF_SIZE_OUT = 1024;

    boolean useClassResourceTopDir = true;
    String outSuffix = ".out";

    //InputStream bis;
    //OutputStream bos;
    static PrintStream out;
    static ByteScanner scanner;
    static ByteWriter writer;

    public void run() {
        try{
            InputStream bis = null;
            OutputStream bos = null;
            if (inputFilename !=null){

                File inputFile = null;
                File outputFile = null;
                if (useClassResourceTopDir) {
                    File baseFile = new File(getClass().getResource("/").getFile());
                    inputFile = new File(baseFile, inputFilename);
                    outputFile = new File(baseFile, inputFilename +outSuffix);
                }else{
                    inputFile = new File(inputFilename);
                    outputFile = new File(inputFilename +outSuffix);
                }
                System.out.println("Input file canonical path: "+inputFile.getCanonicalPath());
                bis = new BufferedInputStream(
                        new FileInputStream(inputFile),
                        INPUT_BUFFER_SIZE);
                bos = new BufferedOutputStream(new FileOutputStream(outputFile));
                out = new PrintStream(bos);
            }else{
                bis = new BufferedInputStream(System.in, INPUT_BUFFER_SIZE);
                bos = new BufferedOutputStream(System.out);
                out = new PrintStream(bos);
            }
            scanner = new ByteScanner(bis, BUF_SIZE_INPUT, BUF_SIZE);
            writer = new ByteWriter(bos, BUF_SIZE_OUT);

            solveAll();
            out.flush();
        }catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public interface Constants{
        byte ZERO = '0';//48 or 0x30
        byte NINE = '9';
        byte SPACEBAR = ' '; //32 or 0x20
        byte MINUS = '-'; //45 or 0x2d

        char FLOAT_POINT = '.';
    }

    public static class EofException extends IOException{
    }

    public static class ByteWriter implements Constants {

        int bufSize = 1024;
        byte[] byteBuf = new byte[bufSize];
        OutputStream os;

        public ByteWriter(OutputStream os, int bufSize){
            this.os = os;
            this.bufSize = bufSize;
        }

        public void writeInt(int num) throws IOException{
            int byteWriteOffset = byteBuf.length;
            if (num==0){
                byteBuf[--byteWriteOffset] = ZERO;
            }else{
                int numAbs = Math.abs(num);
                while (numAbs>0){
                    byteBuf[--byteWriteOffset] = (byte)((numAbs % 10) + ZERO);
                    numAbs /= 10;
                }
                if (num<0)
                    byteBuf[--byteWriteOffset] = MINUS;
            }
            os.write(byteBuf, byteWriteOffset, byteBuf.length - byteWriteOffset);
        }

        /**
         * Please ensure ar.length <= byteBuf.length!
         *
         * @param ar
         * @throws IOException
         */
        public void writeByteAr(byte[] ar) throws IOException{
            for (int i = 0; i < ar.length; i++) {
                byteBuf[i] = ar[i];
            }
            os.write(byteBuf,0,ar.length);
        }

        public void writeSpaceBar() throws IOException{
            byteBuf[0] = SPACEBAR;
            os.write(byteBuf,0,1);
        }

    }

    public static class ByteScanner implements Constants{

        InputStream is;

        public ByteScanner(InputStream is, int bufSizeInput, int bufSize){
            this.is = is;
            this.bufSizeInput = bufSizeInput;
            this.bufSize = bufSize;

            byteBufInput = new byte[this.bufSizeInput];
            byteBuf = new byte[this.bufSize];
        }

        public ByteScanner(byte[] data){
            byteBufInput = data;
            bufSizeInput = data.length;
            bufSize = data.length;
            byteBuf = new byte[bufSize];
            byteRead = data.length;
            bytePos = 0;
        }

        private int bufSizeInput;
        private int bufSize;

        byte[] byteBufInput;
        byte by=-1;
        int byteRead=-1;
        int bytePos=-1;

        byte[] byteBuf;
        int totalBytes;

        boolean eofMet = false;

        private byte nextByte() throws IOException{

            if (bytePos<0 || bytePos>=byteRead){
                byteRead = is==null? -1: is.read(byteBufInput);
                bytePos=0;
                if (byteRead<0){
                    byteBufInput[bytePos]=-1;//!!!
                    if (eofMet)
                        throw new EofException();
                    eofMet = true;
                }
            }
            return byteBufInput[bytePos++];
        }

        /**
         * Returns the next meaningful character as byte.<br>
         *
         * @return
         * @throws IOException
         */
        public byte nextChar() throws IOException{
            while ((by=nextByte())<=0x20);
            return by;
        }

        /**
         * Returns the next meaningful character OR space as byte.<br>
         *
         * @return
         * @throws IOException
         */
        public byte nextCharOrSpacebar() throws IOException{
            while ((by=nextByte())<0x20);
            return by;
        }

        /**
         * Reads line.
         *
         * @return
         * @throws IOException
         */
        public String nextLine() throws IOException {
            readToken((byte)0x20);
            return new String(byteBuf,0,totalBytes);
        }

        public byte[] nextLineAsArray() throws IOException {
            readToken((byte)0x20);
            byte[] out = new byte[totalBytes];
            System.arraycopy(byteBuf, 0, out, 0, totalBytes);
            return out;
        }

        /**
         * Reads token. Spacebar is separator char.
         *
         * @return
         * @throws IOException
         */
        public String nextToken() throws IOException {
            readToken((byte)0x21);
            return new String(byteBuf,0,totalBytes);
        }

        /**
         * Spacebar is included as separator char
         *
         * @throws IOException
         */
        private void readToken() throws IOException {
            readToken((byte)0x21);
        }

        private void readToken(byte acceptFrom) throws IOException {
            totalBytes = 0;
            while ((by=nextByte())<acceptFrom);
            byteBuf[totalBytes++] = by;
            while ((by=nextByte())>=acceptFrom){
                byteBuf[totalBytes++] = by;
            }
        }

        public int nextInt() throws IOException{
            readToken();
            int num=0, i=0;
            boolean sign=false;
            if (byteBuf[i]==MINUS){
                sign = true;
                i++;
            }
            for (; i<totalBytes; i++){
                num*=10;
                num+=byteBuf[i]-ZERO;
            }
            return sign?-num:num;
        }

        public long nextLong() throws IOException{
            readToken();
            long num=0;
            int i=0;
            boolean sign=false;
            if (byteBuf[i]==MINUS){
                sign = true;
                i++;
            }
            for (; i<totalBytes; i++){
                num*=10;
                num+=byteBuf[i]-ZERO;
            }
            return sign?-num:num;
        }

		/*
		//TODO test Unix/Windows formats
		public void toNextLine() throws IOException{
			while ((ch=nextChar())!='\n');
		}
		*/

        public double nextDouble() throws IOException{
            readToken();
            char[] token = new char[totalBytes];
            for (int i = 0; i < totalBytes; i++) {
                token[i] = (char)byteBuf[i];
            }
            return Double.parseDouble(new String(token));
        }

        public int[] loadIntArray(int size) throws IOException{
            int[] a = new int[size];
            for (int i = 0; i < a.length; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public long[] loadLongArray(int size) throws IOException{
            long[] a = new long[size];
            for (int i = 0; i < a.length; i++) {
                a[i] = nextLong();
            }
            return a;
        }
    }

    public static void main(String[] args) {
        new CF367_Div2_A().run();
    }
}