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 check(mid,n):
    l=n/mid
    if abs((mid+l)-n)<=10**(-6):
        return True
    return False


def f(n):
    hi=n+1
    lo=1
    cnt=0
    res=None
    if n==0:
        return ("Y",0,0)

    while lo<=hi and cnt<1000:
        mid=(lo+hi)/2
        # print(mid,n/mid,n-mid)
        if check(mid,n):
            res=mid
            # hi=mid
        if (mid+n/mid>n):
            hi=mid
        else:
            lo=mid
        cnt+=1
    if res==None:
        return ("N",'','')
    return "Y",res,n/res
for _ in range(int(input())):
    print(*f(int(input())))