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 JAVA):

Solution:
import java.util.*;
import java.math.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class a{ 
     static int[] count,count1,count2;
     static Node[] nodes;
     static long[] arr;
     static int[] dp;
     static char[] ch,ch1;
     static long[] darr,farr;
     static char[][] mat,mat1;
     static long x,h;
     static long maxl;
     static double dec;
     static long mx = (long)1e9+7;
     static String s;
     static long minl;
     static int start_row;
     static int start_col;     
     static int end_row;     
     static int end_col;     
     static long mod = 998244353;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y,z;
     static int m;
     static long k;
     static String[] str,str1;
     static Set<Integer> set,set1,set2;
     static SortedSet<Long> ss;
     static List<Integer> list,list1,list2,list3;
     static PriorityQueue<Long> pq,pq1;
     static LinkedList<Integer> ll;
     static Map<Integer,List<Integer>> map,map1;
     static StringBuilder sb,sb1,sb2;
     static int index;
     static int[] dx = {0,-1,0,1,-1,1,-1,1};
     static int[] dy = {-1,0,1,0,-1,-1,1,1};

     // public static void solve(){

     //    FastScanner sc = new FastScanner();
     //    // int t = sc.nextInt();
     //    int t = 1;
     //    for(int tt = 0 ; tt < t ; tt++){
     //        int n = sc.nextInt();
     //        int m = sc.nextInt();
     //        int prev = 0;

     //        for(int i = 0 ; i < n ; i++){
     //           int s = sc.nextInt();
     //           int e = sc.nextInt();
     //           if(s > prev){
     //                System.out.println("NO");
     //                return;
     //           }
     //            prev = Math.max(prev,e);
     //        }
     //        if(prev == m)
     //            System.out.println("YES");
     //        else
     //            System.out.println("NO");

     //        // System.out.println(sb);
     //    }
        
        
     // }

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

     public static void solve(){

        double d = n;
        double dec = Math.sqrt(d*d - 4*d);
        double a1 = (dec + d)/2;
        double a2 = (dec - d)/2;

        double b1 = d - a1;
        double b2 = d - a2;

        if(a2 >= 0 && b2 >= 0){
            System.out.println("Y "+a2 + " "+b2);
        }
        else if(a1 >= 0 && b1 >= 0){
            System.out.println("Y "+a1+" "+b1);
        }
        else
            System.out.println("N");

     }

     public static void main(String[] args) {

            FastScanner sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            int t = sc.nextInt();
            // int t = 1;
            // int l = 1;
            while(t > 0){
                
                // n = sc.nextInt();
                // n = sc.nextLong();
                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();

                // x = sc.nextLong();
                // y = sc.nextLong();
                
                // n = sc.nextLong();
                n = sc.nextInt();
                // n1 = sc.nextInt();

                // m = sc.nextInt();

                // k = sc.nextLong();
                // s = sc.next();

                // ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // arr = new long[n];
                // for(int i = 0 ; i < n ; i++){
                //     arr[i] = sc.nextLong();
                // }
                // ch = sc.next().toCharArray();
                // // m = n;
                // darr = new long[m];
                // for(int i = 0 ; i < m ; i++){
                //     darr[i] = sc.nextLong();
                // }

                // farr = new int[n];
                // for(int i = 0; i < n ; i++){
                //     farr[i] = sc.nextInt();
                // }

                // mat = new int[n][n];
                // for(int i = 0 ; i < n ; i++){
                //     for(int j = 0 ;  j < n ; j++){
                //         mat[i][j] = sc.nextInt();
                //     }
                // }

                // mat = new char[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     String s = sc.next();
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = s.charAt(j);
                //     }
                // }

                // str = new String[n];
                // for(int i = 0 ; i < n ; i++)
                //     str[i] = sc.next();

                // nodes = new Node[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodes[i] = new Node(sc.nextInt(),sc.nextInt());

                // System.out.println(solve()?"YES":"NO");
                 solve();       
                 // System.out.println(solve());
                 t -= 1;
            }

     }

    public static int log(long n){

         if(n == 0 || n == 1)
             return 0;

         if(n == 2)
             return 1;

         double num = Math.log(n);
         double den = Math.log(2);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

    public static boolean isPrime(long n) { 
    // Corner cases 
        if (n <= 1)  
            return false; 

        if (n <= 3)  
            return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0) 
            return false; 
      
        for (int i=5; i*i<=n; i=i+6) 
            if (n%i == 0 || n%(i+2) == 0) 
               return false; 
      
        return true; 
    } 

     public static long gcd(long a,long b){

        if(b%a == 0){
            return a;
        }
        return gcd(b%a,a);

     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        Integer first;
        Integer second;
        Node(Integer f,Integer s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}