#include <bits/stdc++.h>
using namespace std;
const int NMAX = 5e4;
long long primes[NMAX + 1];
int maxPrime[NMAX + 1];
bool isCoprime( int a, int b ) {
// cout << a + 1 << ' ' << b + 1 << endl;
if ( a == 1 || b == 1 ) return true;
if ( a == 0 || b == 0 ) return false;
if ( ( primes[a] & primes[b] ) || ( maxPrime[a] == maxPrime[b] ) ) return false;
return true;
}
int dirl[8] = { -1, -1, 0, 1, 1, 1, 0, -1 };
int dirc[8] = { 0, 1, 1, 1, 0, -1, -1, -1 };
int scad( int x ) {
return x == 0 ? 7 : x - 1;
}
int add( int x ) {
return x == 7 ? 0 : x + 1;
}
int generateFractal( int l, int c, int dir, int siz ) {
if ( siz == 0 ) return 0;
// cout << "The Start is: " << l + 1 << ' ' << c + 1 << endl;
int cnt = 0;
for ( int i = 1; i <= siz; i ++ ) {
cnt += isCoprime( l + i * dirl[dir], c + i * dirc[dir] );
}
int st = scad( dir ), dr = add( dir );
l += siz * dirl[dir];
c += siz * dirc[dir];
for ( int i = 1; i <= siz / 2; i ++ ) {
cnt += isCoprime( l + dirl[st] * i, c + dirc[st] * i );
cnt += isCoprime( l + dirl[dr] * i, c + dirc[dr] * i );
}
cnt += generateFractal( l + dirl[st] * siz / 2, c + dirc[st] * siz / 2, dir, siz / 2 );
cnt += generateFractal( l + dirl[st] * siz / 2, c + dirc[st] * siz / 2, scad( st ), siz / 2 );
cnt += generateFractal( l + dirl[dr] * siz / 2, c + dirc[dr] * siz / 2, dir, siz / 2 );
cnt += generateFractal( l + dirl[dr] * siz / 2, c + dirc[dr] * siz / 2, add( dr ), siz / 2 );
return cnt;
}
//bool brut( int i, int j ) {
// return ( __gcd( i, j ) == 1 );
//}
int main() {
ios_base::sync_with_stdio( false );
cin.tie( NULL );
cout.tie( NULL );
int n, m, f;
cin >> n >> m >> f;
for ( int i = 2; i <= NMAX; i ++ ) {
if ( maxPrime[i] == 0 ) {
for ( int j = i; j <= NMAX; j += i ) {
maxPrime[j] = i;
}
}
}
int cnt = -1;
for ( int i = 2; i * i <= NMAX; i ++ ) {
if ( primes[i] == 0 ) {
cnt ++;
for ( int j = i; j <= NMAX; j += i ) {
primes[j] ^= ( 1LL << cnt );
}
}
}
int answer = 0;
for ( int i = 1, l, c, p; i <= f; i ++ ) {
cin >> l >> c >> p;
// cout << endl;
// cout << generateFractal( l - 1, c - 1, 0, p ) + isCoprime( l - 1, c - 1 ) << endl;
answer += generateFractal( l - 1, c - 1, 0, p ) + isCoprime( l - 1, c - 1 );
}
cout << answer << '\n';
return 0;
}
/**
14 20 1
7 6 2
11 10 4
8 7 2
**/
