Problem Easy Number Challenge

Link: http://codeforces.com/problemset/problem/236/B

B. Easy Number Challenge

time limit per test

2 seconds

memory limit per test

256 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, band 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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (2³⁰).

Sample test(s)

input

2 2 2

output

20

input

5 6 7

output

1520

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.

code:

#include<cstdio>
#include<iostream>

using namespace std;

int a,b,c;
int d[1000001];
int res = 0;

int main()
{
/*
    freopen("TEST.INP","r",stdin);
    freopen("TEST.OUT","w",stdout);
  */  
    for(int i=1;i<1000001;i++)
    for(int j=i;j<1000001;j+=i)
        d[j]++;
    
    cin >> a >> b >> c;
    for(int i=1;i<=a;i++)
    for(int j=1;j<=b;j++)
    for(int k=1;k<=c;k++)
        res += d[i*j*k];
    cout << res << endl;
}