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(target,a,b,shift):
    while(abs(a*b - (a+b)) >= (10**-6) or (a+b)-target >= (10**-6)):
        if (a*b < target):
            a -= shift
            b += shift
        else:
            a += shift
            b -= shift
        shift = shift / 2
    print("Y ",a," ",b)

t = int(input())
for i in range(t):
    target = int(input())
    a = target / 2
    b = a
    if abs(a*b - (a+b)) < (10**-6) and (a+b)-target < (10**-6):
        print("Y ",a," ",b)
    elif (a*b) < target:
        print("N")
    else:
        find(target,target - a/2,a/2,target/8)