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 find_pair(d):
    left = 0
    right = d
    a = 1
    b = 0
    eps = 1 / 1e7
    while abs(d / a - (d-a)) >= eps:
        a = (left + right) / 2
        if a == 0:
            break
        b = d / a
        if a + b + eps < d:
            left = a
        else:
            right = a

    if abs(a + b - a * b) <= eps and abs(a + b - d) <= eps:
        return a, b
    else:
        return -1, -1

test_count = int(input())
for _ in range(test_count):
    d = float(input())
    ans = find_pair(d)
    if ans[0] != -1:
        print("Y", ans[0], ans[1])
    else:
        print("N")