// OB���h2009 Day2 H : Galaxy Wide Web Service

#include <iostream>
#include <vector>
#include <cstring>

using namespace std;

int gcd(int a, int b) { return b==0?a:gcd(b,a%b); }
int lcm(int a, int b) { return a*b/gcd(a,b); }

int main(){
	int n;
	while(cin >> n, n){
		int size[100];
		vector<int> vol[100];
		for(int i=0;i<n;i++){
			int offset;
			cin >> size[i] >> offset;
			vol[i].resize(size[i]);
			for(int j=0;j<size[i];j++) cin >> vol[i][(j+size[i]-offset)%size[i]];
		}
		int left = n;
		bool used[100];
		memset(used, false, sizeof(used));
		while(true){
			int prevsize = left;
			for(int i=0;i<n;i++){
				if(used[i]) continue;
				for(int j=0;j<n;j++){
					if(i==j||used[j]) continue;
					int gd = lcm(size[i], size[j]);
					if(gd==size[i]*size[j]) continue;
					vector<int> vi;
					for(int k=0;k<gd;k++)
						vi.push_back(vol[i][k%size[i]]+vol[j][k%size[j]]);
					size[i] = gd;
					vol[i] = vi;
					used[j] = true;
					left--;
				}
			}
			if(prevsize == left) break;
		}
		int ans = 0;
		for(int i=0;i<n;i++){
			if(used[i]) continue;
			int tmp = 0;
			for(int j=0;j<size[i];j++) tmp = max(tmp, vol[i][j]);
			ans += tmp;
		}
		cout << ans << endl;
	}
}