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:
t = int(input())
for i in range(t):
    d = int(input())
    l = d - 2
    r = d + 2
    while True:
        b = (l + r) / 2
        if b == 0:
            a = d
        else:
            a = d / b
        if abs(a + b - d) <= 0.000001 and (a * b - d) <= 0.000001:
            print('Y', a, b)
            break
        else:
            if b == 1:
                print('N')
                break
            d_b = b ** 2 / (b - 1)
            if d_b > d:
                r = b
            else:
                l = b