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 f(x, d):
    return x**2-d*x+d 

def findroot(d):
    def bsearch(left, right):
        mid = (left + right)*0.5
        if d < 4 and d != 0:
            return 'N'
        elif f(mid, d) > 10**(-6):
            return bsearch(mid, right)
        elif f(mid, d) < -10**(-6):
            return bsearch(left, mid)
        else:
            return ['Y', mid, mid if (d == 0) else d/mid]
    return bsearch(0, d)

T = int(input())
seq = []
for i in range(T):
    seq.append(int(input()))

for i in range(T):
    root = findroot(seq[i])
    if root == 'N':
        print('N')
    else:
        print('{} {} {}'.format(root[0], root[1], root[2]))