Meme Problem

Try guessing the statement from this picture:

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

inputFormat

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).

outputFormat

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

样例

7
69
0
1
4
5
999
1000

Y 67.9850713005 1.01492869949
Y 0.0 0.0
N
Y 2.0 2.0
Y 3.61803398875 1.38196601125
Y 997.998996998 1.00100301004
Y 998.998998021 1.00100200501

</p>