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.util.*;
import java.util.regex.Pattern;
public class MemeProblem {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int n = in.nextInt(); // 

int d[] = new int[n];
for (int i=0; i<n; i++) {
    d[i] = in.nextInt();
} // end for i

double a = 0;
double b = 0;
double diff = 0;

for (int i=0; i<n; i++) {
    if (d[i]>0 && d[i]<4) {
        System.out.println ("N");
    } else if (d[i] == 0) {
        System.out.println ("Y 0.0 0.0");
    } else if (d[i] == 4) {
        System.out.println ("Y 2.0 2.0");
    } else {
        a = 1; 
        diff = 0.5;
        double dd = d[i];
        while (diff > 0.00000000001) {
           
           b = dd - a - diff;
           if (((a+diff)*b) <= dd) a += diff;
           diff *= 0.5;
        }
        System.out.println( "Y " + b + " " + a);
        
    }
        
} // end for i

} // end main
}