Problem: Try guessing the statement from this picture: 

<image>

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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool sq(long double a, long double b, long double c, long double &x1,
        long double &x2) {
  long double D = b * b - 4 * 1 * c;
  if (D < 0)
    return false;
  else {
    x1 = (-b + sqrt(D)) / 2 * a, x2 = (-b - sqrt(D)) / 2;
    return true;
  }
}
signed main() {
  int t;
  cin >> t;
  for (int i = 0; i < t; ++i) {
    long double d, x1, x2;
    cin >> d;
    if (sq(1, -d, d, x1, x2)) {
      cout << "Y " << fixed << setprecision(15) << x1 << " " << x2 << '\n';
    } else {
      cout << "N\n";
    }
  }
  return 0;
}