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:

PRECISION = 0.00000001

def solve(n):
    left, right, off = n / 2, n / 2, n / 2
    pd = left * right

    while pd != n:
        off /= 2
        diff = abs(pd - n)

        if diff < PRECISION:
            if left < right:
                left, right = right, left
            return left, right

        if off <= PRECISION * 0.0001:
            return -1, -1

        if pd > n:
            left -= off
            right += off
        elif pd < n:
            left += off
            right -= off
        pd = left * right
    if left < right:
        left, right = right, left
    return left, right

def driver():
    tc = int(input())

    for _ in range(tc):
        l, r = solve(int(input()))
        if l != -1:
            print("Y", l, r)
        else:
            print("N")

driver()