#include <stdio.h>
#define N 50000
int di[] = { -1, -1, 0, 1, 1, 1, 0, -1 };
int dj[] = { 0, 1, 1, 1, 0, -1, -1, -1 };
long long bb[N + 1]; int pp[N + 1];
void init() {
int i, j, k;
for (i = 1; i <= N; i++)
bb[i] = 0, pp[i] = i;
k = 0;
for (i = 2; i * i <= N; i++) {
if (pp[i] != i)
continue;
for (j = i; j <= N; j += i) {
bb[j] |= 1LL << k;
while (pp[j] % i == 0)
pp[j] /= i;
}
k++;
}
}
int visible(int i, int j) {
if (i == 0)
return j == 1;
if (j == 0)
return i == 1;
return (bb[i] & bb[j]) == 0 && (pp[i] == 1 || pp[i] != pp[j]);
}
int cnt;
void count(int i, int j, int l, int d) {
int k;
for (k = 1; k <= l; k++)
if (visible(i + di[d] * k, j + dj[d] * k))
cnt++;
if (l == 1)
return;
for (k = 1; k <= l / 2; k++) {
if (visible(i + di[d] * l + di[(d + 7) % 8] * k, j + dj[d] * l + dj[(d + 7) % 8] * k))
cnt++;
if (visible(i + di[d] * l + di[(d + 1) % 8] * k, j + dj[d] * l + dj[(d + 1) % 8] * k))
cnt++;
}
count(i + di[d] * l + di[(d + 7) % 8] * l / 2, j + dj[d] * l + dj[(d + 7) % 8] * l / 2, l / 2, d);
count(i + di[d] * l + di[(d + 7) % 8] * l / 2, j + dj[d] * l + dj[(d + 7) % 8] * l / 2, l / 2, (d + 6) % 8);
count(i + di[d] * l + di[(d + 1) % 8] * l / 2, j + dj[d] * l + dj[(d + 1) % 8] * l / 2, l / 2, d);
count(i + di[d] * l + di[(d + 1) % 8] * l / 2, j + dj[d] * l + dj[(d + 1) % 8] * l / 2, l / 2, (d + 2) % 8);
}
int main() {
int q;
init();
scanf("%*d%*d%d", &q);
while (q--) {
int i, j, l;
scanf("%d%d%d", &i, &j, &l), i--, j--;
if (visible(i, j))
cnt++;
count(i, j, l, 0);
}
printf("%d\n", cnt);
return 0;
}
