#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
using namespace std;
#define pii pair<int, int>
#define MP make_pair
#define fir first
#define sec second
const int N=1e6+5, P=1e9;
typedef long long ll;
inline int read(){char c=getchar();int x=0,f=1;while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;
}int n, m, k, c[N], p, x, y;
struct meow{int r, c;}t;
vector<meow> q[N];
int fa[N];
int find(int x) {return x==fa[x] ? x : fa[x]=find(fa[x]);}
struct UFS{int fa[N], val[N];int find(int x) {if(x == fa[x]) return x;int root = find(fa[x]);val[x] ^= val[fa[x]];return fa[x] = root;}bool Union(int x, int y, int p) {int f1 = find(x), f2 = find(y);if(f1 != f2) {fa[f1] = f2;val[f1] = val[x]^val[y]^p;} else if((val[x]^val[y]) != p) return false;return true;}
}F;
int fix[N], mark[N];
int Pow(ll a, int b) {ll ans=1;for(; b; b>>=1, a=a*a%P) if(b&1) ans=ans*a%P;return ans;
}
int main() {freopen("in","r",stdin);n=read(); m=read(); k=read();for(int i=1; i<=k; i++) {x=read(), t.r=read(), t.c=read(), q[x].push_back(t);mark[x] = 1;if(x == 1) fix[t.r] = 1;}for(int i=1; i<=m; i++) fa[i] = F.fa[i] = i;for(int i=1; i<=n; i++)for(int j=1; j<(int)q[i].size(); j++) {int a = q[i][j-1].c, b = q[i][j].c, x=q[i][j-1].r, y=q[i][j].r;int f1 = find(x), f2 = find(y);fa[f1] = f2;if(fix[f1]) fix[f2] = 1;int p = a^b; if((x&1) != (y&1)) p ^= (i-1)&1;if(!F.Union(x, y, p)) {puts("0"); return 0;}}int ans = 0;for(int i=2; i<=n; i++) ans += !mark[i];for(int i=1; i<=m; i++) if(fa[i]==i && !fix[i]) ans++;printf("%d\n", Pow(2, ans));
}