AT_abc456_b.456

There are three dice, each with six faces.
The $j$-th face of the $i$-th die has $A_{i,j}$ written on it.
For each die, each face comes up with probability $\frac{1}{6}$.

When these dice are rolled simultaneously, find the probability that the values $4,5,6$ each appear exactly once.

有三个骰子，每个骰子有六个面。
第 $i$ 个骰子的第 $j$ 个面上写有数字 $A_{i,j}$。
对于每个骰子，每个面朝上的概率均为 $\frac{1}{6}$。

当这三个骰子同时掷出时，求数字 $4,5,6$ 各恰好出现一次的概率。

The input is given from Standard Input in the following format:

$A_{1,1}$ $A_{1,2}$ $A_{1,3}$ $A_{1,4}$ $A_{1,5}$ $A_{1,6}$
$A_{2,1}$ $A_{2,2}$ $A_{2,3}$ $A_{2,4}$ $A_{2,5}$ $A_{2,6}$
$A_{3,1}$ $A_{3,2}$ $A_{3,3}$ $A_{3,4}$ $A_{3,5}$ $A_{3,6}$

输入从标准输入中按以下格式给出：

$A_{1,1}$ $A_{1,2}$ $A_{1,3}$ $A_{1,4}$ $A_{1,5}$ $A_{1,6}$
$A_{2,1}$ $A_{2,2}$ $A_{2,3}$ $A_{2,4}$ $A_{2,5}$ $A_{2,6}$
$A_{3,1}$ $A_{3,2}$ $A_{3,3}$ $A_{3,4}$ $A_{3,5}$ $A_{3,6}$

Output the answer. The answer is considered correct if the absolute or relative error from the true answer is at most $10^{-6}$.

输出答案。若答案与真实答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

Sample 1 Explanation:
The desired probability is $\frac{1}{36}$. An output such as 0.027778 is also accepted.

Sample 2 Explanation:
The desired probability is $\frac{2}{9}$.

Constraints

• $A_{i,j}$ is an integer between $1$ and $6$, inclusive.

样例 1 解释：
所求概率为 $\frac{1}{36}$。输出如 0.027778 也是可接受的。

样例 2 解释：
所求概率为 $\frac{2}{9}$。

限制条件

• $A_{i,j}$ 是介于 $1$ 和 $6$（含）之间的整数。