Problem: Try guessing the statement from this picture: 

<image>

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:
from bisect import bisect_right as br
from bisect import bisect_left as bl
from collections import defaultdict
import sys
MAX = sys.maxsize
MAXN = 10**6+10
def isprime(n):
    n = abs(int(n))
    if n < 2:
        return False
    if n == 2: 
        return True    
    if not n & 1: 
        return False
    for x in range(3, int(n**0.5) + 1, 2):
        if n % x == 0:
            return False
    return True

def mhd(a,b,x,y):
    return abs(a-x)+abs(b-y)

def numIN():
    return(map(int,sys.stdin.readline().strip().split()))

def charIN():
    return(sys.stdin.readline().strip().split())

def chk(n):
	return (n*n-4*n)>=0

def ans(n):
	x = (n*n-4*n)**0.5
	x+=n
	x = x/2
	return x

for _ in range(int(input())):
	d = int(input())
	if d==0:
		print('Y',0,0)
		continue
	if chk(d):
		z = ans(d)
		print('Y',z,d/z)
	else:
		print('N')