3452: Number Challenge
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
time limit per test
3 secondsmemory limit per test
512 megabytesinput
standard inputoutput
standard outputLet'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.