if (vis[u]) return;

vis[u] = true;

if (color[u] == -1) {

//cerr << u << endl;

ans = (ans*2)%((int)1e9);

color[u] = 0;

}

for (ii v : adj[u]) {

int expected = color[u] ^ v.s ^ topLeftC;

if (color[v.f] == -1) color[v.f] = expected;

if (color[v.f] != expected) {

ans = 0;

}

dfs(v.f);

}

cin.tie(0)->sync_with_stdio(0);

int n, m, k; cin >> n >> m >> k;

int topLeft = -1;

color[n+m] = 0;

color[n+m+1] = 1;

for (int i = 0; i < k; i++) {

int x, y, c; cin >> x >> y >> c;

if (x == y && x == 1) {

topLeft = c;

} else if (x == 1) {

adj[n+y-1].emplace_back(n+m+c, 0);

adj[n+m+c].emplace_back(n+y-1, 0);

} else if (y == 1) {

adj[x-1].emplace_back(n+m+c, 0);

adj[n+m+c].emplace_back(x-1, 0);

} else {

if (x%2==0 && y%2==0) {

c ^= 1;

}

int r = x-1, col = n+y-1;

adj[r].pb(mp(col, c));

adj[col].pb(mp(r, c));

}

}

ll totAns = 0;

for (topLeftC = 0; topLeftC <= 1; topLeftC++) {

if (topLeft != -1 && topLeft != topLeftC) continue;

ans = 1;

for (int i = 0; i < n+m; i++) {

color[i] = -1;

}

for (int i = 0; i < n+m+10; i++) {

vis[i] = false;

}

dfs(n+m);

dfs(n+m+1);

for (int i = 0; i < n+m; i++) {

if (i == 0 || i == n) continue; // these point to the upper left cell that's a special case

dfs(i);

}

totAns = (totAns + ans) % ((int)1e9);

}

cout << totAns << endl;

return 0;