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:
t = int(input())
itog = []
for _ in range(t):
    n = int(input())
    if n == 0:
        itog.append(['Y', 0.000000, 0.000000])
    else:
        l = -1
        r = n + 1
        while l + 1 != r:
            mid = (l + r)//2
            if mid * (n - mid) >= n:
                r = mid
            else:
                l = mid

        for i in range(100):
            mid = (l + r)/2
            if mid * (n - mid) > n:
                r = mid
            else:
                l = mid
        if round(l * (n - l)) == n and round(l + (n - l)) == n:
            itog.append(['Y', n - l, l])
        else:
            itog.append(['N'])
for i in itog:
    print(*i)