Problem Statement

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.

Constraints

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

Input

Input is given from Standard Input in the following format:

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

Output

Print the answer.

Sample Input 1

4
1
7 2
2
2 2
5 1
1
5 1
2
2 1
7 1

Sample Output 1

3

The integers on the whiteboard are $a_1 =7^2=49, a_2=2^2 \\times 5^1 = 20, a_3 = 5^1 = 5, a_4=2^1 \\times 7^1 = 14$.
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 $3$.

Sample Input 2

1
1
998244353 1000000000

Sample Output 2

1

There may be enormous integers on the whiteboard.