#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{int x=0,f=1;char c=getchar();while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();return x*f;
}
#define P 1000000000
#define N 100010
int n,m,k,fa[N<<2],color[N<<2];
struct data{int x,y,c;
}a[N];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int solve(int c)
{memset(color,0,sizeof(color));for (int i=1;i<=(n+m-2<<1);i++) fa[i]=i;for (int i=1;i<=k;i++)if (a[i].x!=1&&a[i].y!=1)if ((a[i].c==c)^(((a[i].x-1)&1)*(a[i].y-1)&1)) fa[find((a[i].x-1<<1)-1)]=find((n+a[i].y-2<<1)-1),fa[find(a[i].x-1<<1)]=find(n+a[i].y-2<<1);else fa[find((a[i].x-1<<1)-1)]=find(n+a[i].y-2<<1),fa[find(a[i].x-1<<1)]=find((n+a[i].y-2<<1)-1);int cnt=0;for (int i=1;i<=n+m-2;i++) if (find((i<<1)-1)==find(i<<1)) return 0;for (int i=1;i<=k;i++){if (a[i].x==1&&a[i].y==1){if (a[i].c!=c) return 0;}else{if (a[i].y==1){if (color[find((a[i].x-1<<1)-a[i].c)]!=-1) color[find((a[i].x-1<<1)-a[i].c)]=1;else return 0;if (color[find((a[i].x-1<<1)-(a[i].c^1))]!=1) color[find((a[i].x-1<<1)-(a[i].c^1))]=-1;else return 0;}if (a[i].x==1){if (color[find((n+a[i].y-2<<1)-a[i].c)]!=-1) color[find((n+a[i].y-2<<1)-a[i].c)]=1;else return 0;if (color[find((n+a[i].y-2<<1)-(a[i].c^1))]!=1) color[find((n+a[i].y-2<<1)-(a[i].c^1))]=-1;else return 0;}}}for (int i=1;i<=(n+m-2<<1);i++)if (find(i)==i&&!color[i]) cnt++;cnt>>=1;int ans=1;while (cnt--) ans=(ans<<1)%P;return ans;
}
int main()
{
#ifndef ONLINE_JUDGEfreopen("bzoj2303.in","r",stdin);freopen("bzoj2303.out","w",stdout);const char LL[]="%I64d\n";
#elseconst char LL[]="%lld\n";
#endifn=read(),m=read(),k=read();for (int i=1;i<=k;i++) a[i].x=read(),a[i].y=read(),a[i].c=read();cout<<(solve(0)+solve(1))%P;return 0;
}