# Make It One CodeChef Solution

### We Are Discuss About CODECHEF SOLUTION

Make It One CodeChef Solution

## Make It One CodeChef Solution

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• ## Problem

Chef is given a positive integer N and we have to convert it to 1 using some operations.\newline

In one operation, Chef can do the following:\newline

• Choose a prime number p such that p | N (p divides N).
• Replace N with \frac{N}{p}.

However, Chef is also given some triggers of the form (a,b) (a is prime). Thus, if we divide by p in some operation, we also have to multiply by x for all triggers of the form (p,x).

For example: Consider N=18, and the triggers (3,4) and (3,2) exist. In one operation, if we choose to divide by 3, we have to multiply the result with 4 and 2. In other words, (18 \mapsto \frac{18}{3} \cdot 4 \cdot 2)=48. Thus, 18 is converted to 48.

Given a number N and M triggers of the form (a,b) (where a is always prime), find the minimum number of operations required to convert N to 1 modulo 998244353. Print -1 if it is not possible to do so.

### Input Format

• The first line of each input contains two integers N and M – the initial integer and the number of triggers given to the Chef.
• The next M lines describe the triggers. The i^{th} of these M lines contains two space-separated integers a and b, denoting that Chef has to multiply by b if he choses to divide by a in some operation.
• It is guaranteed that (a_i, b_i) \ne (a_j, b_j) for i \ne j.

### Output Format

Output on a new line, the minimum number of operations required to convert N to 1, or print -1 if it is not possible to do so. In case it is possible to convert N to 1, the minimum number of operations can be large, so output it modulo 998244353.

### Constraints

• 1 \leq N \leq 10^6
• 0 \leq M \leq 10^5
• 1 \leq a \leq 10^6
• 1 \leq b \leq 10^6
• a is a prime number.

### Sample 1:

Input

Output

6 1
2 3

3


### Explanation:

We can convert 6 to 1 using 3 operations in the following way:

• Divide 6 by 3. Since no trigger of the form (3,x) exists, 6 converts to \frac{6}{3}= 2.
• Divide 2 by 2. Since (2,3) exists, 2 is converted to 2 \mapsto \frac{2}{2} \cdot 3 = 3. – Divide 3 by 3. Since no trigger of the form (3,x) exists, 3 converts to \frac{3}{3}= 1.

It can be proven that we cannot convert 6 to 1 in less than 3 operations.

### Sample 2:

Input

Output

4 3
2 5
2 3
3 7

8


### Sample 3:

Input

Output

2 3
2 3
3 5
5 3

-1


### Explanation:

We can not convert 2 to 1 using any finite number of operations

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