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:
import sys
import math

n = int(sys.stdin.readline())
for i in range(0, n):
    val = float(sys.stdin.readline())
    a = val - 2.0
    b  = 2.0
    kmax = 1.0000000
    kmin = 0.0000000
    found  = True
    if abs(val) < 0.0000001:
        print("Y 0.000000000 0.000000000")
        continue
    while True:
        m = kmin + (kmax-kmin)/2.0
        valp = (a+m)*(b-m)
        if abs(valp - val) < 0.000000001:
            break
        if valp > val:
            kmin = m
        else:
            kmax = m
        if abs(m - 1.0000) < 0.00000001 or abs(m) < 0.000000001:
            found = False
            break
        #print("m is ", m)
    if found:
        #m = kmin + (kmax-kmin)/2.0
        print("Y " + str(a+m) + " " + str(b-m))
    else:
        print("N")