Problem: Try guessing the statement from this picture: 

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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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public final class MemeProblem {

    static class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        MyScanner() {
            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;
        }

    }

    static void solve(int d) {
        int delta = d * d - 4 * d;
        if (d == 0) {
            System.out.println(String.format("Y %.9f %.9f", 0.0, 0.0));
        } else if (d >= 4) {
            double a = (d + Math.sqrt(delta)) / 2.0;
            double b = (d - Math.sqrt(delta)) / 2.0;
            System.out.println(String.format("Y %.9f %.9f", a, b));
        } else {
            System.out.println("N");
        }
    }


    public static void main(String[] args) {
        MyScanner sc = new MyScanner();

        int t = sc.nextInt();
        for (int i=0; i<t; ++i) {
            int d = sc.nextInt();
            solve(d);
        }
    }
}