You have $N$ numbers, $X_{1}, X_{2}, X_{3}, ... , X_{N}$. How many ways you can choose 4 numbers such that their product is a perfect cube. Formally, how many ways you can choose 4 integeres $a, b, c, d$ and $1 <= a < b < c < d <= N$ such that product of $X_{a} , X_{b}, X_{c}, X_{d}$ is a perfect cube.

A number $Z$ is said to be a perfect cube if there exists an integer $Y$ such that $Z = Y^3$.

Since the numbers can be quite large, so instead of giving a number directly, you will be given $K_{i}$  integers, $P_{1}, P_{2}, P_{3}, ... , P_{K}$. Formally, each number $X_{i}$  is a product of $P_{1}, P_{2}, P_{3}, ... , P_{K}$_.

Input Format

First line will contain $N$. 
Each of next $N$ lines will start with $K_{i}$. Next $K_{i}$ integers $P_{1}, P_{2}, P_{3}, ... , P_{K}$  will be sperated by a space.

$4 <= N <= 1000$

$1 <= K_{i} <= 100$

$1 <= P_{j} <= 500$

Ouput Format

Print only one integer, which is many ways you can choose 4 numbers such that their product is a perfect cube.

Addition Information

For 20 points: $4 <= N <= 50$, $1 <= K_{i} <= 25$, $1 <= P_{j} <= 20$

For 100 Points: Original constraints.