Task

Given two child nodes of a binary split (each described by the count of positive examples and the total count), compute the weighted Gini impurity and weighted entropy for the split, then report their difference. Gini impurity for a node: 2p(1-p). Binary entropy for a node: -plog2(p) - (1-p)log2(1-p). The weighted value for the split is w1impurity(node1) + w2impurity(node2) where wi = Ni / (N1 + N2).

Input

• Line 1: n1 N1 n2 N2 — positive count and total count for the left node, positive count and total count for the right node

Output

Print three values each on its own line: weightedgini, weightedentropy, giniminusentropy — each with up to 10 significant digits.

Example

Input:

3 5 2 5

Output:

0.48
0.9709505945
-0.4909505945

Scaffolding

Submit a Python file defining:

def gini_entropy_split(n1: int, N1: int, n2: int, N2: int) -> tuple[float, float, float]:
    ...

Receives positive counts and totals for two child nodes; returns a tuple (weighted_gini, weighted_entropy, gini_minus_entropy).