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 PYTHON3):

Solution:
import sys

input = sys.stdin.readline

t = int(input())
for zzz in range(t):
    d = int(input())
    l = 0
    r = d
    ans = (0, 0)
    found = False
    while (l < r):
        a = (l + r)/2
        val = pow(a, 2) - a*d + d
        if abs(val) <= 0.000001:
            ans = (a, d - a)
            if (ans[0] > 0 and ans[1] > 0):
                found = True
                break
        if (val < 0):
            l = a
        else:
            r = a
    if found or d == 0:
        print("Y " + str(ans[0]) + " " + str(ans[1]))
    else:
        print("N")