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;
void run() {
  double d;
  cin >> d;
  if (d * d / 4 + 1e-10 < d) {
    cout << "N" << endl;
    return;
  }
  double t;
  double a = 0, r = d;
  while (true) {
    t = (a + r) / 2;
    if (t * (d - t) - d < 1e-10 && d - t * (d - t) < 1e-10) break;
    if (t * (d - t) - d > 1e-10)
      a = t;
    else
      r = t;
  }
  printf("Y %.9f %.9f\n", t, d - t);
  return;
}
int main() {
  int T;
  cin >> T;
  while (T--) run();
  return 0;
}