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 PYTHON):

Solution:
for test in range(input()):
    n = input()
    if n==0:
        print 'Y',0,0
        continue
    if n==1:
        print 'N'
        continue
    if n==4:
        print 'Y',2,2
        continue
    a = 1
    b = n-1
    p = -1
    #print a,b
    i = 0
    f = 0
    while abs((a+b)-(a*b))>(10**(-8)):
        i+=1
        #print a,b,
        if (a*b)<n:
            if p==-1:
                p = float(n-(a*b))/2
            p = p/2
            a+= p
            b-=p
            #print p,a,b
        else:
            if p==-1:
                p = float((a*b)-n)/2
            p = p/2
            a-=p
            b+=p
            #print p,a,b
        if i==500:
            f = 1
            print 'N'
            break
    if f==0:
        print 'Y',a,b