This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
import java.io.*; import java.util.*;
public class plusminus{
static class FastReader
{
BufferedReader br;
StringTokenizer st;
public FastReader()
{
br = new BufferedReader(new
InputStreamReader(System.in));
}
String next()
{
while (st == null || !st.hasMoreElements())
{
try
{
st = new StringTokenizer(br.readLine());
}
catch (IOException e)
{
e.printStackTrace();
}
}
return st.nextToken();
}
int nextInt()
{
return Integer.parseInt(next());
}
}
static int MOD=1000000007;
static int[] rk, p,siz;
static HashMap<Integer, Integer> labelB, labelC;
public static void main(String[] args){
FastReader br=new FastReader();
int N=br.nextInt(); int M=br.nextInt(); int K=br.nextInt();
int[][] cond=new int[K][3];
for (int i = 0; i < K; i++) {
if(br.next().charAt(0)=='+'){
cond[i][2]++;
}else{
cond[i][2]--;
}
cond[i][0]=br.nextInt()-1; cond[i][1]=br.nextInt()-1;
}
//a_ij=(-1)^i b_i + (-1)^j c_j - cond[i][2]
//Case 1: a00=-1
long cur1; long cur2; long ans=0;
int i,j,k;
boolean checkerboard;
for (int X = -1; X <=1; X+=2) {//X=a00
cur1=1; cur2=1; checkerboard=true;
labelB=new HashMap<>(); labelC=new HashMap<>();
//b is ai0, c is a0i
labelB.put(0,X); labelC.put(0,X);
for (int n = 0; n < K; n++) {//Case 1: c_j=X(-1)^j
i=cond[n][0]; j=cond[n][1]; k=cond[n][2];
if((i+j)%2==0 ^ k==X)checkerboard=false;
if(j%2==0){
if(labelB.containsKey(i)){
if(labelB.get(i)!=k){
cur1=0; break;
}
}else{
labelB.put(i,k);
}
}else{
if(labelB.containsKey(i)){
if(labelB.get(i)==k){
cur1=0; break;
}
}else{
labelB.put(i, -k);
}
}
}
if(cur1==1){
cur1=pow(N-labelB.size());
}
for (int n = 0; n < K; n++) {//Case 2
i=cond[n][0]; j=cond[n][1]; k=cond[n][2];
if(i%2==0){
if(labelC.containsKey(j)){
if(labelC.get(j)!=k){
cur2=0; break;
}
}else{
labelC.put(j,k);
}
}else{
if(labelC.containsKey(j)){
if(labelC.get(j)==k){
cur2=0; break;
}
}else{
labelC.put(j, -k);
}
}
}
if(cur2==1){
cur2=pow(M-labelC.size());
}
ans+=cur1; ans%=MOD; ans+=cur2; ans%=MOD;
//System.out.println(cur1+" "+cur2+" "+checkerboard);
if(cur1>0 && cur2>0 && checkerboard){//-1 only if checkerboard
ans+=(MOD-1); ans%=MOD;
}
//System.out.println(X);
//System.out.println(cur1+" "+cur2);
//System.out.println(labelB);
//System.out.println(labelC);
}
System.out.println((ans+MOD)%MOD);
}
public static long pow(int x){
if(x==0)return 1; if(x==1)return 2;
long y=pow(x/2);
y*=y; y%=MOD; y*=pow(x&1); return y%MOD;
}
}
//Debugging:
//Are you sure your algorithm is correct?
//Bounds: long
//Special cases: n=0,1?
//Make sure you remove your debugging code before you submit!
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