#include<iostream> #include<string>#include<cstdio>#include<cmath>#include<cstring>#include<algorithm>#include<queue>#include<stack>#include<vector>#include<climits>using namespace std; #define rep(i,n) for(int i=0; i<(n); i++)#define repf(i,n,m) for(int i=(n); i<=(m); i++)//正循环的#define repd(i,n,m) for(int i=(n); i>=(m); i--) //负循环的 #define max(a,b) (a)>(b)?(a):(b)#define min(a,b) (a)<(b)?(a):(b)#define ll __int64#define arc(a) ((a)*(a))#define inf 10000000 //最大值的#define exp 0.0000001 //浮点型的#define N 10005 //记录开的数组double a[104][N];int n;int test=0;struct node{ int st,p; node() {}; node(int st,int p):st(st),p(p){};};vector<node>q[N];void dfs(int i,int l,double r){ rep(j,q[l].size()) { if(q[l][j].st==2) dfs(i,q[l][j].p,r/q[l].size()); if(q[l][j].st==1) a[i][q[l][j].p]-=r/q[l].size(); if(q[l][j].st==0) a[i][n+1]+=q[l][j].p*r/q[l].size(); }}void fun(){ memset(a,0,sizeof(a)); char s[N]; int len; repf(i,1,n) { rep(j,N) q[j].clear(); gets(s); len=strlen(s); stack<int>r; int now=0,t=0,m=0; int sign=0; r.push(0); int l; a[i][i]=1; rep(j,len) if(s[j]=='(') {l=j+1; break;} repf(j,l,len-1) { if(isdigit(s[j])) { m=m*10+s[j]-'0';if(sign==0) sign=1;} else { if(sign!=0) {q[now].push_back(node(0,m*sign)); m=sign=0;} if(isalpha(s[j])) q[now].push_back(node(1,s[j]-'a'+1)); if(s[j]=='(') {r.push(now); q[now].push_back(node(2,++t)); now=t;} if(s[j]==')') { now=r.top();r.pop();} if(s[j]=='-') sign=-1; } } dfs(i,0,1); }}double fab(double x){ if(fabs(x-0)<exp) return true; return false;}void guess(){ repf(i,1,n) { int k=n+1; repf(j,i,n) if(!fab(a[j][i])) {k=j; break;} if(k>n) continue; repf(j,1,n+1) swap(a[i][j],a[k][j]); repf(j,1,n) { if(j!=i) { double x=a[j][i]/a[i][i]; repf(k,i,n+1) a[j][k]-=a[i][k]*x;} } } repf(i,1,n) if(fab(a[i][i])) repf(j,1,n) if(!fab(a[j][i])) a[j][j]=0; printf("Game %dn",++test); repf(i,1,n) if(fab(a[i][i])) printf("Expected score for %c undefinedn",i+'a'-1); else printf("Expected score for %c = %0.3lfn",i+'a'-1,a[i][n+1]/a[i][i]); printf("n");}int main(){ while(scanf("%d",&n)) { if(n==0) break; getchar(); fun(); guess(); } return 0;}
