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:
mod = 0.000000001
def ab(b):
    return b*b / (b - 1)
def binsearch(number):
    last = number
    first = 2
    mid = (last + first) / 2
    while(last >= first):
    
        if(ab(mid) < number + mod and ab(mid) > number - mod):
            return mid
        elif(ab(mid) > number):
            last = mid - mod
        else:
            first = mid + mod
        mid = (last + first) / 2
    return -1

t = int(input())
while t > 0:
    d = int(input())
    if d < 4:
        if d != 0:
            print("N")
        elif d == 0:
            print("Y 0.000000000 0.000000000")
    else:
        b = binsearch(d)
        if b == -1:
            print("N")
        else:
            a = d - b 
            print("Y",a,b)
    t -= 1