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 find_vals(d):
    lo = 0
    high = d
    mid = 0
    iterations = 0
    while lo <= high and iterations < 10000:
        iterations += 1
        mid = (high + lo) / 2
        if mid == 1:
            lo = mid
            continue
        a, b = mid, (mid / (mid - 1))
        # print((a, b))
        if abs(a + b - d) < 0.000001:
            return (True, a, abs(b))
        else:
            if a + b < d:
                lo = mid
            else:
                high = mid
    return (False, 0, 0)


t = int(input())

while t > 0:

    d = int(input())
    y, a, b = find_vals(d)
    if y:
        print("Y %s %s" % (a, b))
    else:
        print("N")
    t -= 1