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:
$$\sum_{i=1}^{a}\sum_{j=1}^{b}\sum_{k=1}^{c}d(i \cdot j \cdot k)$$
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 2000).
Output
Print a single integer — the required sum modulo 1073741824 (230).
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分
样例输入
2 2 2
样例输出
20
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.