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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分