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.*;
import java.util.*;

public class C {

    static long[] degs;

    public static void main(String[] args) {

        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {

            long t = Long.parseLong(reader.readLine());
            for(int i = 0; i < t; i++) {
                int n = Integer.parseInt(reader.readLine());
                if(n < 4 && n != 0) {
                    println("N");
                } else {
                    double l = 0.0, r = n;
                    while(r - l > .0000000001) {
                        double cur = (r + l) / 2;
                        //println(cur);
                        double dif = n - cur;
                        double mult = n / cur;
                        if(mult - dif <= 0.0) {
                            r = cur;
                        } else {
                            l = cur;
                        }
                    }
                    println("Y " + r + " " + (n - r));
                }
            }

        } catch (IOException e) {
        }
    }

    static String reverse(String s) {
        String ans = "";
        char[] c = s.toCharArray();
        for(int i = s.length() - 1; i >= 0; i--) {
            ans += c[i];
        }
        return ans;
    }

    static long fac(int deg) {
        long ans = 1;
        for(int i = 2; i <= deg; i++) {
            ans *= i;
        }
        return ans;
    }

    static int r(int a, int b) {
        int ans = a / b;
        if(a % b != 0)
            ans++;
        return ans;
    }

    static void print(Object o) {
        System.out.print(o.toString());
    }

    static void println(Object o) {
        System.out.println(o.toString());
    }
}