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
#include <bits/stdc++.h>
using namespace std;
int main() {
  double i, b, c, n;
  while (scanf("%lf", &n) != EOF) {
    for (i = 0; i < n; i++) {
      scanf("%lf", &c);
      if (c * c - 4 * c < 0)
        printf("N\n");
      else {
        b = ((-c + sqrt(c * c - 4 * c)) / (-2));
        printf("Y %.9f %.9f\n", c - b, b);
      }
    }
  }
  return 0;
}
