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:
from decimal import *
getcontext().prec = 20
t = int(input())


def p(a,d):
    if a >= d:
        return False
    b = d-a
    return d/a <= b


for _ in range(t):
    d = int(input())

    low = Decimal(0)
    high = Decimal(d)
    while True:
        if high-low <= 0.00000000001:
            break
        mid = low + (high-low)/2
        # print(low, mid, high)
        if p(mid, d):
            low = mid
        else:
            high = mid
    if low == 0 and d-low != 0:
        print('N')
    else:
        print('Y {:.12} {:.12}'.format(low, d-low))