#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define THIRD "1/3 "
#define HALF "1/2 "

int main ()
{
	int i,j,k,NoAcc[3], SumNoAcc;
	FILE *f;

	f=fopen("file.txt","w");

	fprintf(f,"U = \n");

	for (i=1;i<=3;i++)
	{
		for (j=1;j<=3;j++)
		{
			for (k=1;k<=3;k++)
			{
				if (i+j+k!=3)
					fprintf(f,"+ ");

				SumNoAcc=0;
				if (i==1)
				{
					fprintf(f,"n");
					NoAcc[0]=1;
					SumNoAcc++;
				}
				else
				{
					fprintf(f,"a1f");
					NoAcc[0]=0;
				}
				fprintf(f,"%d * ",i);

				if (j==2)
				{
					fprintf(f,"n");
					NoAcc[1]=1;
					SumNoAcc++;
				}
				else
				{
					fprintf(f,"a2f");
					NoAcc[1]=0;
				}
				fprintf(f,"%d * ",j);

				if (k==3)
				{
					fprintf(f,"n");
					NoAcc[2]=1;
					SumNoAcc++;
				}
				else
				{
					fprintf(f,"a3f");
					NoAcc[2]=0;
				}
				fprintf(f,"%d * ",k);


				// probability of event printed, now need payoff
				if (SumNoAcc==0)
					// everyone accepted someone
					fprintf(f,"(%sUB%dR1 + %sUB%dR2 + %sUB%dR3)\n",THIRD,i,THIRD,j,THIRD,k);


				else if (SumNoAcc==1)
					// two accepted, other didn't
				{
					if (NoAcc[0]==1)
						// P1 didn't accept, others did
						fprintf(f,"(%sUB%dR2 + %sUB%dR3)\n",HALF,j,HALF,k);
					else if (NoAcc[1]==1)
						fprintf(f,"(%sUB%dR1 + %sUB%dR3)\n",HALF,i,HALF,k);
					else					
						fprintf(f,"(%sUB%dR1 + %sUB%dR2)\n",HALF,i,HALF,j);
				}
				else if (SumNoAcc==2)
					// only one accepted
				{
					if (i!=1)
						// P1 accepted
						fprintf(f,"UB%dR1\n",i);
					else if (j!=2)
						// P2 accepted
						fprintf(f,"UB%dR2\n",j);
					else
						fprintf(f,"UB%dR3\n",k);
				}
				else
					// all three did not accept
					fprintf(f,"((1-e4)*U + e4*0)\n");
			}
		}
	}
	return 0;
}