Distinct Numbers

Interview

Time limit2sMemory limit512 MB

Summary

Given integers a and b, count how many distinct values appear among the ten expressions a+b, a-b, a*b, a/b, a^b and their swapped forms, skipping invalid ones.

Level: Medium4 of 10
Topics: Implementation, Math, Hash map, Brute force
Solved: No attempts yet

Problem

The other day Alice was cleaning her room and found a diary she kept in elementary school. In it she was surprised to find an entry about how amazed she was that $2 + 2 = 2 \cdot 2$ . Unbelievable, multiplication and addition give the same result!

That entry led Alice to the following problem. Given integers $a$ and $b$ , how many distinct values are there in the set of numbers

$a + b$ , $a - b$ , $a \cdot b$ , $a / b$ , $a^b$ ,

$b + a$ , $b - a$ , $b \cdot a$ , $b / a$ , $b^a$ .

Division is performed without rounding, and the result of a division need not be an integer. If any expression in this set is invalid, Alice does not consider it. Division by zero and raising zero to a non-positive power count as invalid.

Input

The first line of the input file contains integers $a$ and $b$ separated by a space ( $|a|, |b| \le 10^9$ ).

Output

Print the number of distinct numbers in the given set.

Examples2

Example 1
Input
```
2 5
```
Expected output
```
8
```
Example 2
Input
```
0 1
```
Expected output
```
3
```