跳到主要内容
图灵 OJTURING / ONLINE JUDGE

#F2661. Number Challenge

    ID: 2667 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 9 上传者: 标签>组合数学动态规划模拟数学数论编程与模拟挑战难度共享题库Codeforces英文题面题目来源题面语言

Number Challenge

题目描述

E. Number Challenge
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 (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).

Examples
Input
2 2 2
Output
20
Input
4 4 4
Output
328
Input
10 10 10
Output
11536
Note

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.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 2322 题。保留原作者与原赛事署名。