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:
import java.util.*;
import java.io.*;

public class b
{
    static boolean multiple_testcases = true;
        
    static void solve() {
        int n = in.nextInt();
        double l =0,h=n;
        if(n==0) {
            System.out.println("Y 0.0 0.0");
            return;
        }
        
        while(h-l > 0.0000000001) {
            double mid = l + (h-l)/2;
            double b = n - mid;
            if(mid*b - n < 0.000001 && (mid+b)-(mid*b) < 0.000001) {
                System.out.println("Y "+ mid+" "+b );
                return;
            } else if(mid*b - n < 0) {
                l = mid;
            } else h = mid;
        }
        
        System.out.println("N");
    }

    static int INF = Integer.MAX_VALUE;
    static FastReader in = new FastReader();
    public static void main(String[] args) { 
        if(multiple_testcases) {
            int t = in.nextInt();
            while(t-- >0)  solve();
        } else solve();
    }

    static class FastReader { 
        BufferedReader br; StringTokenizer st; 
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); } 
      
        String next() { while (st == null || !st.hasMoreElements()) { 
            try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e) { e.printStackTrace(); } }
            return st.nextToken(); } 
        int nextInt() { return Integer.parseInt(next()); } 
        long nextLong() { return Long.parseLong(next()); } 
        double nextDouble() { return Double.parseDouble(next()); } 
        char nextChar() { return next().charAt(0); }
        String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
        return str; }
     
        int[] intArray(int n) {
            int[] arr = new int[n];
            for(int i=0;i<n;i++) 
                arr[i] = in.nextInt();
            return arr;    
        } 
        int[] intArray1(int n) {
            int[] arr = new int[n+1];
            for(int i=1;i<=n;i++) 
                arr[i] = in.nextInt();
            return arr;    
        } 
    } 
}