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Contest: Task: Related: TaskF TaskH

Score : $600$ points

Problem Statement

There are integers with $N$ different values written on a blackboard. The $i$-th value is $A_i$ and is written $B_i$ times.

You may repeat the following operation as many times as possible:

  • Choose two integers $x$ and $y$ written on the blackboard such that $x+y$ is prime. Erase these two integers.

Find the maximum number of times the operation can be performed.

Constraints

  • $1 \leq N \leq 100$
  • $1 \leq A_i \leq 10^7$
  • $1 \leq B_i \leq 10^9$
  • All $A_i$ are distinct.
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ 
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_N$ $B_N$

Output

Print the answer.

Sample Input 1

3
3 3
2 4
6 2

Sample Output 1

3

We have $2 + 3 = 5$, and $5$ is prime, so you can choose $2$ and $3$ to erase them, but nothing else. Since there are four $2$s and three $3$s, you can do the operation three times.

Sample Input 2

1
1 4

Sample Output 2

2

We have $1 + 1 = 2$, and $2$ is prime, so you can choose $1$ and $1$ to erase them. Since there are four $1$s, you can do the operation twice.