Problem: Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet.

The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area.

Input

The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105).

Output

Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. 

Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range.

Examples

Input

5 3 3 1 1


Output

3.7677669529663684 3.7677669529663684 3.914213562373095


Input

10 5 5 5 15


Output

5.0 5.0 10.0

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.*;
import java.util.*;

public class Codeforces
{
	static FastReader fr = new FastReader();
	static OutputWriter out = new OutputWriter(System.out);
	
	static int MOD = 1000000007, prime[];
	static long gcd, x, y;
	static boolean isPrime[];
	static long nCr[][] = new long[1004][1004];
	
	public static void main(String[] args) throws IOException
	{
		double R = fr.nextDouble(), x1 = fr.nextDouble(), y1 = fr.nextDouble(), x2 = fr.nextDouble(), y2 = fr.nextDouble();
		if(Math.pow(x1-x2, 2) + Math.pow(y1-y2, 2) >= Math.pow(R, 2))
			out.printLine(x1+" "+y1+" "+R);
		else {
			if(x1 == x2 && y1 == y2) {
				double x = (x1 + x1 + R)/2.0;
				out.printLine(x+" "+y1+" "+(R/2.0));
			}
			else {
				double r = (R + Math.sqrt(Math.pow(x1-x2, 2) + Math.pow(y1-y2, 2)))/2.0;
				if((x1 - x2) == 0) {
					double y;
					if(y1 < y2)
						y = y2 - r;
					else
						y = y2 + r;
					out.printLine(x1+" "+y+" "+r);
				}
				else {
					double m = (y1 - y2)/(x1 - x2);
					double c = y2 - (m * x2);
					double A = 1 + Math.pow(m, 2);
					double B = (2 * m * (c - y1)) - (2 * x1);
					double C = (Math.pow(x1, 2) + Math.pow(c-y1, 2)) - Math.pow(R, 2);
					double D = Math.sqrt(Math.pow(B, 2) - (4 * A * C));
					double x;
					if(x1 < x2)
						x = ((((-1) * B) - D)/(2 * A) + x2)/2.0;
					else
						x = ((((-1) * B) + D)/(2 * A) + x2)/2.0;
					double y = (m * x) + c;
					out.printLine(x+" "+y+" "+r);
				}
			}
		}
		out.flush();
		out.close();
	}
	
	static long min_3(long a, long b, long c)
	{
		if(a < b && a < c)
			return a;
		if(b < c)
			return b;
		return c;
	}
	
	static long max_3(long x, long y, long z)
	{
		if(x >= y && x >= z)
			return x;
		if(y >= x && y >= z)
			return y;
		return z;
	}
	
	static long power(long x, long y, long m)
	{
	    if (y == 0)
	        return 1;
	    long p = power(x, y/2, m) % m;
	    p = (p * p) % m;
	    return (y%2 == 0) ? p : (x * p) % m;
	}
	
	static void prime_sieve(int N)
	{
        isPrime = new boolean[N+1];
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for(int i = 2; i*i <= N; i++)
        {
            if(isPrime[i]==true)
            {
            	for(int j = 2*i; j <= N; j += i)
            	{
            		isPrime[j] = false;
            		prime[j] = i;
				}
            }
        }
    }
	
	static void Calc_nCr()
	{
		for(int i = 0; i <= 1000; i++)
			nCr[i][0] = 1;
		for(int i = 1; i <= 1000; i++)
			for(int j = 1; j <= 1000; j++)
				nCr[i][j] = (nCr[i-1][j-1] + nCr[i-1][j]) % MOD;
	}
	
	static long factorial(long num)
	{
		long result = 1;
		for(int i = 1; i <= num; i++)
			result = result * (long)i;
		return result;
	}
	
	static void ExtendedEuclidian(long a, long b)
	{
		if(b == 0)
		{
	        gcd = a;
	        x = 1;
	        y = 0;
	    }
	    else
	    {
	        ExtendedEuclidian(b, a%b);
	        int temp = (int) x;
	        x = y;
	        y = temp - (a/b)*y;
	    }
	}
	
	static long GCD(long n, long m)
	{
		if(m != 0)
			return GCD(m, n % m);
		else
			return n;
	}
	
	static class CustomComp implements Comparator<Object>
	{
		@Override
        public int compare(Object o1, Object o2)
		{
			return 1;
        }
	}
	
	static class Graph
	{
		
	    private int V;
	    private LinkedList<Integer> adj[];
	    boolean visited[];
	    
	    Graph(int v)
	    {
	        V = v + 1;
	        visited = new boolean[V];
	        adj = new LinkedList[V];
	        for(int i = 0; i < V; ++i)
	            adj[i] = new LinkedList<Integer>();
	    }
	 
	    void addEdge(int v, int w)
	    {
	        adj[v].add(w);
	        adj[w].add(v);
	    }
	    
	    // prints BFS traversal from a given source s
	    void BFS(int s)
	    {
	        LinkedList<Integer> queue = new LinkedList<Integer>();
	        visited[s] = true;
	        queue.add(s);
	        while (queue.size() != 0)
	        {
	            s = queue.poll();
	            System.out.print(s+" ");
	            Iterator<Integer> i = adj[s].listIterator();
	            while (i.hasNext())
	            {
	                int n = i.next();
	                if (!visited[n])
	                {
	                    visited[n] = true;
	                    queue.add(n);
	                }
	            }
	        }
	    }
	    
	    void DFS(int v, boolean visited[])
	    {
	        visited[v] = true;
	        System.out.print(v+" ");
	        Iterator<Integer> i = adj[v].listIterator();
	        while (i.hasNext())
	        {
	            int n = i.next();
	            if (!visited[n])
	                DFS(n, visited);
	        }
	    }
	    
	    boolean isCyclicUndirectedUtil(int v, boolean visited[], int parent)
	    {
	        // Mark the current node as visited
	        visited[v] = true;
	        Integer i;
	 
	        // Recur for all the vertices adjacent to this vertex
	        Iterator<Integer> it = adj[v].iterator();
	        while (it.hasNext())
	        {
	            i = it.next();
	 
	            // If an adjacent is not visited, then recur for that
	            // adjacent
	            if (!visited[i])
	            {
	                if (isCyclicUndirectedUtil(i, visited, v))
	                    return true;
	            }
	 
	            // If an adjacent is visited and not parent of current
	            // vertex, then there is a cycle.
	            else if (i != parent)
	                return true;
	        }
	        return false;
	    }
	 
	    // Returns true if the graph contains a cycle, else false.
	    boolean isCyclicUndirected()
	    {
	        // Mark all the vertices as not visited and not part of
	        // recursion stack
	        boolean visited[] = new boolean[V];
	 
	        // Call the recursive helper function to detect cycle in
	        // different DFS trees
	        for (int u = 1; u <= V; u++)
	            if (!visited[u]) // Don't recur for u if already visited
	                if (isCyclicUndirectedUtil(u, visited, -1))
	                    return true;
	 
	        return false;
	    }
	    
	    boolean isCyclicDirectedUtil(int v, boolean visited[], boolean recStack[])
	    {
	    	if(visited[v] == false)
	    	{
	            // Mark the current node as visited and part of recursion stack
	            visited[v] = true;
	            recStack[v] = true;
	     
	            // Recur for all the vertices adjacent to this vertex
	            Iterator<Integer> i = adj[v].listIterator();
	            while(i.hasNext())
	            {
	            	int n = i.next();
	                if (!visited[n] && isCyclicDirectedUtil(n, visited, recStack))
	                    return true;
	                else if (recStack[n])
	                    return true;
	            }
	        }
	        recStack[v] = false;  // remove the vertex from recursion stack
	        return false;
	    }
	    
	    boolean isCyclicDirected()
	    {
	    	boolean visited[] = new boolean[V];
	    	boolean recStack[] = new boolean[V];
	    	for(int i = 1; i <= V; i++)
	            if (isCyclicDirectedUtil(i, visited, recStack))
	                return true;
	    	return false;
	    }
	    
	    void topologicalSortUtil(int v, boolean visited[], Stack stack)
	    {
			// Mark the current node as visited.
			visited[v] = true;
			
			// Recur for all the vertices adjacent to this vertex
			Iterator<Integer> it = adj[v].iterator();
			while (it.hasNext()) {
				int i = it.next();
				if (!visited[i])
					topologicalSortUtil(i, visited, stack);
			}
			
			// Push current vertex to stack which stores result
			stack.push(new Integer(v));
		}
			
		// The function to do Topological Sort. It uses recursive topologicalSortUtil()
		void topologicalSort()
		{
			Stack stack = new Stack();
			
			// Mark all the vertices as not visited
			boolean visited[] = new boolean[V];
			
			// Call the recursive helper function to store Topological Sort starting from all
			// vertices one by one
			for (int i = 1; i <= V; i++)
			if (visited[i] == false)
				topologicalSortUtil(i, visited, stack);
			
			// Print contents of stack
			while (stack.empty()==false)
				System.out.print(stack.pop() + " ");
		}
	}
}

class FastReader
{
	
    BufferedReader br;
    StringTokenizer st;
 
    public FastReader()
    {
        br = new BufferedReader(new
                 InputStreamReader(System.in));
    }
 
    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try
            {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException  e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt()
    {
        return Integer.parseInt(next());
    }
 
    long nextLong()
    {
        return Long.parseLong(next());
    }
 
    double nextDouble()
    {
        return Double.parseDouble(next());
    }
 
    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}
 
class OutputWriter {
	
	private final PrintWriter writer;
 
	public OutputWriter(OutputStream outputStream)
	{
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
 
	public OutputWriter(Writer writer)
	{
		this.writer = new PrintWriter(writer);
	}
 
	public void print(Object...objects)
	{
		for (int i = 0; i < objects.length; i++)
		{
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
 
	public void printLine(Object...objects)
	{
		print(objects);
		writer.println();
	}
 
	public void close()
	{
		writer.close();
	}
 
	public void flush()
	{
		writer.flush();
	}
}