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 main():
    EPS = 10 ** -10
    t = int(input())
    nums = list()
    for i in range(t):
        nums.append(int(input()))

    for el in nums:
        if el > 0 and el < 4:
            print('N')
        elif el == 4:
            print('Y 2.000000000 2.000000000')
        else:
            left = 0
            right = el
            while right - left > EPS:
                mid = (left + right) / 2
                mult = mid * (el - mid)
                sum = mid + (el - mid)
                if mult <= el:
                    left = mid
                if mult > el:
                    right = mid
                # print(el - right)
                # print(right)
            print('Y ' + str(format(el - right, '.9f') + ' ' + str(format(right, '.9f'))))


if __name__ == '__main__':
    main()