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 solve(hi,lo):
    for j in range(1000):
        mid = lo + (hi - lo) / 2
        rest = d - mid
        if abs(mid + rest - mid*rest) <= 10**-8 and abs(mid + rest - d) <= 10**-8:
            return "Y {:.9f} {:.9f}".format(rest, mid)
        if mid*rest > d:
            hi = mid
        else:
            lo = mid
    return "N"

for i in range(int(input())):
    d = int(input())
    print(solve(d,0))