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 PYTHON3):

Solution:
def bin(n):
    n*=1000000000
    left=0
    right=n//2
    a=n//2
    n*=1000000000
    while right-left>1:
        middle=(right+left)//2
        if (a-middle)*(a+middle)>=n:
            left=middle
        else:
            right=middle
    return [(a-left)/1000000000,(a+left)/1000000000]
t=int(input())
for i in range(t):
    n=int(input())
    if n==1 or n==2 or n==3:
        print('N')
    else:
        print('Y',*bin(n))