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:
n = int(input())
eps = float(0.0000001)

for i in range(n):
    x = float(input())

    l = 0.0
    r = x
    f = 0
    it = 0
    a = b = 0.0

    while it < 2000:
        it += 1
        mid = (l + r) / 2
        b = mid
        a = x - b

        if abs((a + b) - a * b) <= eps:
            f = 1
            break

        if a + b <= a * b:
            r = mid
        else:
            l = mid

    if f == 0:
        print('N')
    else:
        print('Y', a, b)