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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Itwazonce
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scan in = new Scan(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CMemeProblem solver = new CMemeProblem();
        solver.solve(1, in, out);
        out.close();
    }

    static class CMemeProblem {
        public void solve(int testNumber, Scan in, PrintWriter out) {
            int t = in.scanInt();
            while (t-- > 0) {
                double d = in.scanDouble();
                if (d * d < 4 * d) {
                    out.println("N");
                } else {
                    out.print("Y" + " ");
                    double ans = d * d - 4 * d;
                    ans = Math.sqrt(ans);
                    double ans1 = d - ans;
                    double ans2 = d + ans;
                    ans1 /= 2;
                    ans2 /= 2;
                    if (ans1 >= 0 && d - ans1 >= 0) {
                        out.println(ans1 + " " + (d - ans1));
                    } else if (ans2 >= 0 && d - ans2 >= 0) {
                        out.println(ans2 + " " + (d - ans2));
                    }
                }
            }
        }

    }

    static class Scan {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public Scan(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

        public double scanDouble() {
            int c = scan();
            while (isWhiteSpace(c)) c = scan();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = scan();
            }
            double RESULT = 0;
            while (!isWhiteSpace(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return RESULT * Math.pow(10, scanInt());
                }
                RESULT *= 10;
                RESULT += c - '0';
                c = scan();
            }
            if (c == '.') {
                c = scan();
                double m = 1;
                while (!isWhiteSpace(c)) {
                    if (c == 'e' || c == 'E') {
                        return RESULT * Math.pow(10, scanInt());
                    }
                    m /= 10;
                    RESULT += (c - '0') * m;
                    c = scan();
                }
            }
            return RESULT * sgn;
        }

    }
}