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 JAVA):

Solution:
function solve(n) {
    var a = 0;
    var b = n;

    var min = 1;
    var max = 2;
    var average = 0;

    if (n === 0) {
        print('Y 0 0');
        return;
    }

    while (max - min > 10e-13) {
        average = (min + max) / 2;
        a = n - average;
        b = average;

        if (a * b > n) {
            max = average;
        } else {
            min = average;
        }
    }

    if (Math.abs(a + b - a * b) < 10e-6 && Math.abs(a + b - n) < 10e-6) {
        print('Y ' + a + ' ' + b);
    } else {
        print('N');
    }
}

var lines = +readline();
for(var i = 0; i<lines; i++) {
    solve(+readline())
}