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:
n = int(input())
for i in range(n):
    v = int(input())
    if v == 1:
        print("N")
    elif v == 0:
        print("Y", 0.000000000, 0.000000000)
    else:
        left = 0
        right = v

        while True:
            mid = (left + right) / 2
            left_a = (mid + left) / 2
            right_a = (mid + right) / 2
            left_b1 = v / left_a
            left_b2 = v - left_a
            right_b1 = v / right_a
            right_b2 = v - right_a

            if abs(left_b1 - left_b2) < abs(right_b1 - right_b2):
                if right == mid:
                    a = mid
                    b = v / mid
                    if abs(a + b - a * b) <= 0.000001:
                        print('Y', mid, v / mid)
                    else:
                        print('N')
                    break
                right = mid
            else:
                if left == mid:
                    a = mid
                    b = v / mid
                    if abs(a + b - a * b) <= 0.000001:
                        print('Y', mid, v / mid)
                    else:
                        print('N')
                    break
                left = mid