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:
if __name__ == '__main__':
    q = int(input())

    def f(d, a):
        return 1 / a + 1 / (d - a)

    for i in range(q):
        d = int(input())

        if d == 0.0:
            print('Y 0.000000000 0.000000000')
            continue
        if 0 < d < 4:
            print('N')
            continue

        r = d
        l = d / 2
        m = (l + r) / 2
        res = f(d, m)

        while abs(d - (d - m) * m) >= 1e-11:
            if abs(1 - res) < 1e-11:
                break
            elif res < 1.0:
                l = m
            elif res > 1.0:
                r = m
            m = (l + r) / 2
            res = f(d, m)

        if l > r:
            print('N')
        else:
            print('Y', m, d - m)