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 sqrt(n):
    low = 0
    high = 1000
    mid = 0
    for i in range(50):
        mid = (low+high)/2
        sqr = mid*mid
        if sqr > n:
            high = mid
        elif sqr < n:
            low = mid
        else:
            return mid
    return mid

t = int(input())

for i in range(t):
    d = int(input())
    if 0<d<4:
        ans = "N"
    else:
        c = d/2
        s = sqrt(c*c-d)
        a = c + s
        b = c - s
        ans = f"Y {a} {b}"
    print(ans)