There are $N$ integers $a_1,\ldots,a_N$ written on a whiteboard.  
Here, $a_i$ can be represented as $a_i = p_{i,1}^{e_{i,1}} \times \ldots \times p_{i,m_i}^{e_{i,m_i}}$ using $m_i$ prime numbers $p_{i,1} \lt \ldots \lt p_{i,m_i}$ and positive integers $e_{i,1},\ldots,e_{i,m_i}$.  
You will choose one of the $N$ integers to replace it with $1$.  
Find the number of values that can be the least common multiple of the $N$ integers after the replacement.

Input is given from Standard Input in the following format:

```
$N$
$m_1$
$p_{1,1}$ $e_{1,1}$
$\vdots$
$p_{1,m_1}$ $e_{1,m_1}$
$m_2$
$p_{2,1}$ $e_{2,1}$
$\vdots$
$p_{2,m_2}$ $e_{2,m_2}$
$\vdots$
$m_N$
$p_{N,1}$ $e_{N,1}$
$\vdots$
$p_{N,m_N}$ $e_{N,m_N}$
```

Print the answer.

-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq m_i$
-   $\sum{m_i} \leq 2 \times 10^5$
-   $2 \leq p_{i,1} \lt \ldots \lt p_{i,m_i} \leq 10^9$
-   $p_{i,j}$ is prime.
-   $1 \leq e_{i,j} \leq 10^9$
-   All values in input are integers.

3

The integers on the whiteboard are $a_1=7^2=49,\ a_2=2^2×5^1=20,\ a_3=5^1=5,\ a_4=2^1×7^1=14$.
If you replace $a_1$ with 1, the integers on the whiteboard become 1,20,5,14, whose least common multiple is 140.
If you replace $a_2$ with 1, the integers on the whiteboard become 49,1,5,14, whose least common multiple is 490.
If you replace $a_3$ with 1, the integers on the whiteboard become 49,20,1,14, whose least common multiple is 980.
If you replace $a_4$ with 1, the integers on the whiteboard become 49,20,5,1, whose least common multiple is 980.
Therefore, the least common multiple of the N integers after the replacement can be 140, 490, or 980, so the answer is 3.

1

There may be enormous integers on the whiteboard.