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 PYTHON3):

Solution:
def solve():
    results = []
    
    for _ in range(int(input())):
        n = int(input())
        if n < 0:
            results.append("N")
            continue
        
        #equation x*x - n*x + n = 100
        
        x = n**2 - 4*n
        
        if x < 0:
            results.append("N")
            continue
        
        n1 = (n + x**0.5) / 2
        n2 = (n - x**0.5) / 2
        
        if n2 > n1:
            n1, n2 = n2, n1
        
        results.append("Y " + str(n1) + " " + str(n2))
        
    print ('\n'.join(k for k in results))
    
solve()