### Problem Statement

When cat Taro and rabbit Hanako were practicing hard for SRM 484, they noticed an interesting property of 484. They called it Rabbit Number.

Let S(n) be the sum of the digits of n. For example, S(484) = 4+8+4 = 16 and S(22) = 2+2 = 4. A positive integer x is called a Rabbit Number if S(x*x) = S(x)*S(x). For example, 22 is a Rabbit Number because S(484) = S(22)*S(22).

Return the number of Rabbit Numbers between low and high, inclusive.

### Definition

 Class: RabbitNumber Method: theCount Parameters: int, int Returns: int Method signature: int theCount(int low, int high) (be sure your method is public)

### Constraints

-low will be between 1 and 1,000,000,000, inclusive.
-high will be between low and 1,000,000,000, inclusive.

### Examples

0)

 `22` `22`
`Returns: 1`
 22 is a Rabbit Number because S(22*22) = S(484) = 16 S(22) * S(22) = 4 * 4 = 16
1)

 `484` `484`
`Returns: 0`
 484 is not a Rabbit Number because S(484*484) = S(234256) = 22 S(484) * S(484) = 16 * 16 = 256
2)

 `1` `58`
`Returns: 12`
3)

 `58` `484`
`Returns: 24`
4)

 `1000000000` `1000000000`
`Returns: 1`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11131

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14237&pm=11131

rng_58

#### Testers:

PabloGilberto , ivan_metelsky , pieguy

#### Problem categories:

Brute Force, Math