#include <bits/stdc++.h>
using namespace std;
int dx[] = {-1,0,1,0};
int dy[] = {0,1,0,-1};
int m,n,f;
int rez = 0;
bool coprime(int x, int y)
{
return (__gcd(x,y) == 1);
}
void solve(int x, int y, int s, int dir)
{
for(int i=1;i<=s;i++)
{
int xx = x + i * dx[dir];
int yy = y + i * dy[dir];
rez += coprime(xx - 1,yy - 1);
}
x = x + s * dx[dir];
y = y + s * dy[dir];
if(s==1)
{
return;
}
for(int i=1;i<=s/2;i++)
{
int xs = x + i * dx[dir] + i * dx[(dir + 3) % 4];
int ys = y + i * dy[dir] + i * dy[(dir + 3) % 4];
rez += coprime(xs - 1,ys - 1);
}
solve(x + (s / 2) * dx[dir] + (s / 2) * dx[(dir + 3) % 4], y + (s / 2) * dy[dir] + (s / 2) * dy[(dir + 3) % 4], s / 2, dir);
solve(x + (s / 2) * dx[dir] + (s / 2) * dx[(dir + 3) % 4], y + (s / 2) * dy[dir] + (s / 2) * dy[(dir + 3) % 4], s / 2, (dir + 3) % 4);
for(int i=1;i<=s/2;i++)
{
int xd = x + i * dx[dir] + i * dx[(dir + 1) % 4];
int yd = y + i * dy[dir] + i * dy[(dir + 1) % 4];
rez += coprime(xd - 1,yd - 1);
}
solve(x + (s / 2) * dx[dir] + (s / 2) * dx[(dir + 1) % 4], y + (s / 2) * dy[dir] + (s / 2) * dy[(dir + 1) % 4], s / 2, dir);
solve(x + (s / 2) * dx[dir] + (s / 2) * dx[(dir + 1) % 4], y + (s / 2) * dy[dir] + (s / 2) * dy[(dir + 1) % 4], s / 2, (dir + 1) % 4);
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
#ifdef home
freopen("nr.in","r",stdin);
freopen("nr.out","w",stdout);
#endif // home
cin>>m>>n>>f;
for(int i=1;i<=f;i++)
{
int x,y,s;
cin>>x>>y>>s;
rez += coprime(x,y);
solve(x,y,s,0);
}
cout<<rez<<'\n';
return 0;
}
