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
from array import array  # noqa: F401
import typing as Tp  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def main():
    for _ in range(int(input())):
        n = float(input())
        ok1, ng1 = 0.0, n
        ans2 = 0.0

        for _ in range(50):
            mid1 = (ok1 + ng1) / 2
            ok2, ng2 = 0.0, 1e9

            for _ in range(100):
                mid2 = (ok2 + ng2) / 2
                if mid1 * mid2 <= mid1 + mid2:
                    ok2 = mid2
                else:
                    ng2 = mid2

            if mid1 + ok2 <= n:
                ok1 = mid1
                ans2 = ok2
            else:
                ng1 = mid1

        if abs(n - (ok1 + ans2)) <= 1e-7:
            print(f'Y {ok1} {ans2}')
        else:
            print('N')


if __name__ == '__main__':
    main()