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;
template <class C>
void min_self(C &a, C b) {
  a = min(a, b);
}
template <class C>
void max_self(C &a, C b) {
  a = max(a, b);
}
const long long MOD = 1000000007;
template <class T1, class T2>
void add(T1 &x, T2 y, long long m = MOD) {
  x += y;
  if (x >= m) x -= m;
}
template <class T1, class T2>
void sub(T1 &x, T2 y, long long m = MOD) {
  x -= y;
  if (x < 0) x += m;
}
long long mod(long long n, long long m = MOD) {
  n %= m;
  if (n < 0) n += m;
  return n;
}
const int MAXN = 1e5 + 5;
const int LOGN = 21;
const long long INF = 1e16;
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
void solve() {
  int d;
  cin >> d;
  if (d == 0 || d == 4) {
    cout << "Y " << d / 2 << " " << d / 2, cout << "\n";
    return;
  }
  if (d <= 3) {
    cout << "N\n";
    return;
  }
  long double a = d + -sqrtl(1.0 * d * d - 4.0 * d);
  a /= 2;
  long double b = d - a;
  cout << fixed << setprecision(10) << "Y " << a << " " << b, cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  for (int test = 1; test <= t; test++) {
    solve();
  }
  cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
  return 0;
}