Problem: Try guessing the statement from this picture: 

<image>

You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.

Input

The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.

Each test case contains one integer d (0 ≤ d ≤ 10^3).

Output

For each test print one line.

If there is an answer for the i-th test, print "Y", and then the numbers a and b.

If there is no answer for the i-th test, print "N".

Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.

Example

Input


7
69
0
1
4
5
999
1000


Output


Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.*;
import java.util.*;
import java.util.LinkedList;
import java.math.*;
import java.lang.*;
import java.util.PriorityQueue;
import static java.lang.Math.*;
@SuppressWarnings("unchecked")
public class Solution implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            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 c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static long min(long a,long b)
    {
        if(a>b)
        {
            return b;
        }
        return a;
    }
    public static int min(int a,int b)
    {
        if(a>b)
        {
            return b;
        }
        return a;
    }
    public static long max(long a,long b)
    {
        if(a>b)
        {
            return a;
        }
        return b;
    }
    public static int max(int a,int b)
    {
        if(a>b)
        {
            return a;
        }
        return b;
    }
    static class pair implements Comparable<pair>
    {
      int x;
      int y;
      pair(int x,int y)
      {
        this.x = x;
        this.y = y;
      }
      public int compareTo(pair b)
      {
        if(this.x>b.x)
        {
          return 1;
        }
        else if(this.x<b.x)
        {
          return -1;
        }
        else
        {
          return this.y-b.y;
        }
      }
    }
    public static int gcd(int a,int b)
    {
        if(a==0)
        return b;
        if(b==0)
        return a;
        while((a%=b)!=0&&(b%=a)!=0);
        return a^b;
    }
    public static int mod(int a)
    {
      if(a>0)
        return a;
      return -a;
    }
    static int mod = (int)1e9+7;;
    public static long expo(long exp,long pow)
    {
      long ans = 1;
      while(pow!=0)
      {
        if((pow&1)==1)
        {
          ans = ans*exp;
        }
        exp = exp*exp;
        pow = pow>>1;
      }
      return ans;
    }
    static int max = (int)1e6;
    public static long fact(int num)
    {
        if(num==0)
        {
          return 1;
        }
        return (fact(num-1)*num)%mod;
    }
    static int[] sieve;
    public static void sieve()
    {
      sieve = new int[max+1];
      for(int i=1;i<=max;i++)
      {
        sieve[i] = i;
      }
      for(int i=2;i<max;i++)
      {
        if(sieve[i]==i)
        {
          for(int j=i*2;j<=max;j+=i)
          {
            if(sieve[j]==j)
            {
              sieve[j] = i;
            }
          }
        }
      }
    }
    public static int random(int min,int max)
    {
      return min+(int)((max-min)*Math.random());
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Solution(),"Main",1<<26).start();
    }
    static long[][] c;
    public static void combi()
    {
      c = new long[2001][2001];
      for(int i=0;i<=2000;i++)
      {
        c[i][0] = 1;
      }
      for(int i=1;i<=2000;i++)
      {
        for(int j=1;j<=i;j++)
        {
          c[i][j] = (c[i-1][j]+c[i-1][j-1])%mod;
        }
      }
    }
    public void run() {
      InputReader sc  = new InputReader(System.in);
      PrintWriter out = new PrintWriter(System.out);
      int t1 = sc.nextInt();
      while(t1-->0)
      {
        int d = sc.nextInt();
        if(d*d-4*d<0)
        {
          out.println("N");
          continue;
        }
        double b = (d-Math.sqrt(d*d-4*d))/2;
        double a = d-b;
        out.println("Y "+a+" "+b);
      }
      out.close();
  }
}