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:
//package All_in_all;

import java.io.*;

/**
 * Created by nikitos on 25.08.17.
 */


public class simvoli {

    public StreamTokenizer t;

    private class Pair implements Comparable<Pair> {
        int from;
        int to;

        private Pair(int from, int to) {
            this.from = from;
            this.to = to;
        }

        @Override
        public int compareTo(Pair o) {
            if (this.from == o.from && this.to == o.to)
                return 0;

            if (this.from > o.from || this.from == o.from && this.to > o.to)
                return 1;

            return -1;
        }
    }

    public int nextInt() throws IOException {
        t.nextToken();
        return (int) t.nval;
    }

    public long nextLong() throws IOException {
        t.nextToken();
        return (long) t.nval;
    }

    public String nextString() throws IOException {
        t.nextToken();
        return t.sval;
    }

    public void start() throws IOException {
        t = new StreamTokenizer( new BufferedReader(new InputStreamReader(System.in)));

        int n = nextInt();

        for (int i = 0; i < n; i++) {
            int d = nextInt();

            if (d * d - 4 * d < 0)
                System.out.println("N");
            else {
                double a = (d * 1.0 + Math.sqrt(d * d - 4 * d)) / 2;
                double b = d - a;
                System.out.println("Y " + a + " " + b);
            }
        }
    }

    public static void main(String[] args) throws IOException {
        new simvoli().start();
    }

}