CF235E.Number Challenge

普及/提高-

通过率：0%

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题目描述

Let's denote $d(n)$ as the number of divisors of a positive integer $n$ . You are given three integers $a$ , $b$ and $c$ . Your task is to calculate the following sum:

Find the sum modulo $1073741824$ $(2^{30})$ .

输入格式

The first line contains three space-separated integers $a$ , $b$ and $c$ ( $1<=a,b,c<=2000$ ).

输出格式

Print a single integer — the required sum modulo $1073741824$ $(2^{30})$ .

输入输出样例

输入#1
```
2 2 2
```
输出#1
```
20
```
输入#2
```
4 4 4
```
输出#2
```
328
```
输入#3
```
10 10 10
```
输出#3
```
11536
```

说明/提示

For the first example.

$d(1·1·1)=d(1)=1$ ;
$d(1·1·2)=d(2)=2$ ;
$d(1·2·1)=d(2)=2$ ;
$d(1·2·2)=d(4)=3$ ;
$d(2·1·1)=d(2)=2$ ;
$d(2·1·2)=d(4)=3$ ;
$d(2·2·1)=d(4)=3$ ;
$d(2·2·2)=d(8)=4$ .

So the result is $1+2+2+3+2+3+3+4=20$ .

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