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 bin_search(first,last,y):
    if first>last:
        print('N')
        return
    i = (first+last)//2
    b=(y-i)/10**12
    a=i/10**12
    #print('wyl WAR: ',abs(a*b*10**6-y))
    if abs(a*b*10**12-y) <=100000:
        print ('Y',round(b,15),round(a,15))
        return
    if a*b>y/10**12:
        bin_search(first,i-1,y)
    else:
        bin_search(i+1,last,y)

n = int(input())
for x in range(n):
    d = int(input())
    d = d*10**12
    if d == 0:
        print('Y 0 0')
    else:
        bin_search(1,d,d)