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 _ in range(T):
    d = int(input())
    if d==0:
        print("Y 0.000000000 0.000000000")
        continue
    l = 0.0
    h = d
    EPS = 0.000000000001
    b = True
    while h-l>EPS and b:
        m = (l+h)/2
        if abs(d-(m+(d/m)))<EPS and abs((m*(d/m))-(m+(d/m)))<EPS:
            print('Y {0} {1}'.format(m,(d-m)))
            b = not b
        elif (m+(d/m))<d:
            l = m
        else:
            h = m
    if b:
        print("N")