Problem: Izua University Elementary School is famous as one of Japan's leading competition programmer training schools. The teachers at this school have a wide range of algorithmic knowledge and utilize it on a daily basis. As a teacher, you will be in charge of drawing and crafting classes this year. In this class, all children are supposed to complete one task in one year. The outline of the class is as follows.

* There are D lessons in a year (no lessons more than once on the same day), all of which are devoted to assignment production.
* There are M types of assignments to create.
* Assign one task from M types to each child.
* There are N children, and each of them is assigned a different task.



Children use several of the K types of parts to complete the task. The outline of the assignment production is as follows.

* The type and number of parts to be used are predetermined for each task.
* The type and number of parts used to complete the task must match the type and number of parts used in the task in just proportion.
* For different tasks, the types and numbers of parts used may all be the same.
* For each task, only two parts of the same type can be used.
* The order in which the parts are used does not affect the completion of the task.
* P bags containing some parts are prepared in advance. However, different bags may contain the same type and number of parts.
* Teachers can only give one bag per child (some children may not give it).
* The same bag cannot be given to two or more children (on the contrary, some bags may not be given to anyone).
* The child who is given the bag must use all the parts contained in the bag for the tasks he / she creates.



Parts used for the assignment other than the parts in the bag must be purchased separately. The conditions for purchasing parts are as follows.

* Parts can only be purchased on class days and can only be used on that day.
* Up to L parts can be purchased in one lesson for each task.
* Prices are set according to the type of parts, and the price fluctuates depending on the date of purchase. However, none of them will be out of stock.



Under these conditions, you want to keep your lesson costs as low as possible. Therefore, I decided to create a program to calculate the minimum total cost of purchasing parts for all children.



input

The input consists of multiple datasets. The end of the input is indicated by three zero lines. Each dataset is given in the following format:


D K L
c1,1 c1,2 ... c1, K
c2,1 c2,2 ... c2, K
::
cD, 1 cD, 2 ... cD, K
M N P
r1,1 r1,2 ... r1, K
r2,1 r2,2 ... r2, K
::
rM, 1 rM, 2 ... rM, K
t1,1 t1,2 ... t1, K
t2,1 t2,2 ... t2, K
::
tP, 1 tP, 2 ... tP, K


The numbers given on each line are separated by a single space.

D (1 ≤ D ≤ 8) indicates the number of lessons, K (1 ≤ K ≤ 8) indicates the number of parts types, and L (1 ≤ L ≤ 8) indicates the number of parts that can be purchased per day. .. cd, k (1 ≤ cd, k ≤ 100) indicates the price of part k on day d.

M (1 ≤ M ≤ 200) indicates the number of task types, N (1 ≤ N ≤ M) indicates the number of students, and P (1 ≤ P ≤ 200) indicates the number of bags.

rm, k (0 ≤ rm, k ≤ 2) indicates the number of parts k required for task m, and tp, k (0 ≤ tp, k ≤ 2) indicates the number of parts k contained in the bag p.

Tasks that do not require any parts or empty bags shall not be given.

The number of datasets does not exceed 20.

output

For each data set, output the minimum value of the total parts purchase cost for all students on one line. If N kinds of works cannot be completed, -1 is output.

Example

Input

2 2 1
5 3
2 2
3 3 1
2 0
1 2
2 2
1 1
2 2 1
5 3
2 2
3 2 1
2 0
1 2
2 2
1 1
2 2 2
5 3
2 2
3 2 1
2 0
1 2
2 2
1 1
4 3 1
2 2 1
3 2 2
2 3 3
1 2 2
5 4 3
1 1 0
1 0 1
1 0 2
1 1 2
2 2 2
1 0 1
2 0 2
1 1 1
0 0 0


Output

-1
9
6
7

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;



#define NUM 450

//辺を表す構造体{行先、容量、コスト、逆辺のインデックス}
struct Edge{
	Edge(int arg_to,int arg_capacity,int arg_cost,int arg_rev_index){
		to = arg_to;
		capacity = arg_capacity;
		cost = arg_cost;
		rev_index = arg_rev_index;
	}

	int to,capacity,cost,rev_index;
};

int V; //頂点数
vector<Edge> G[NUM]; //グラフの隣接リスト表現
int dist[NUM]; //最短距離
int pre_node[NUM],pre_edge[NUM]; //直前の頂点と辺
int num_day,num_item,num_limit;
int num_problem,num_student,num_bag;
int POW[9];
int price[8][8],problem[200][8],bag[200][8];
int dp[9][6561][9];
int min_cost[6561];
int bag_index[200],problem_index[200];



//fromからtoへ向かう容量capacity,コストcostの辺をグラフに追加する
void add_edge(int from,int to,int capacity,int cost){
	G[from].push_back(Edge(to,capacity,cost,G[to].size()));
	G[to].push_back(Edge(from,0,-cost,G[from].size()-1));
}

//sourceからsinkへの、流量flowの最小費用流を求める
//流せない場合は-1を返す
int min_cost_flow(int source,int sink,int flow){
	int ret = 0;
	while(flow > 0){
		//ベルマンフォード方により、source-sink間最短経路を求める
		for(int i = 0; i < V; i++)dist[i] = BIG_NUM;
		dist[source] = 0;
		bool update = true;
		while(update){
			update = false;
			for(int node_id = 0; node_id < V; node_id++){
				if(dist[node_id] == BIG_NUM)continue;
				for(int i = 0; i < G[node_id].size(); i++){
					Edge &e = G[node_id][i];
					if(e.capacity > 0 && dist[e.to] > dist[node_id]+e.cost){
						dist[e.to] = dist[node_id]+e.cost; //node_idを経由した方が早い場合
						pre_node[e.to] = node_id;
						pre_edge[e.to] = i;
						update = true;
					}
				}
			}
		}

		if(dist[sink] == BIG_NUM){
			//これ以上流せない
			return -1;
		}

		//source-sink間最短路に沿って目いっぱい流す
		int tmp_flow = flow;
		for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
			tmp_flow = min(tmp_flow,G[pre_node[node_id]][pre_edge[node_id]].capacity);
		}
		flow -= tmp_flow;
		ret += tmp_flow*dist[sink];
		for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
			Edge &e = G[pre_node[node_id]][pre_edge[node_id]];
			e.capacity -= tmp_flow;
			G[node_id][e.rev_index].capacity += tmp_flow;
		}
	}
	return ret;
}

void func(){

	//商品情報を取得
	for(int i = 0; i < num_day; i++){
		for(int k = 0; k < num_item; k++)scanf("%d",&price[i][k]);
	}

	scanf("%d %d %d",&num_problem,&num_student,&num_bag);

	for(int i = 0; i < num_problem; i++){
		for(int k = 0; k < num_item; k++)scanf("%d",&problem[i][k]);
	}

	for(int i = 0; i < num_bag; i++){
		for(int k = 0; k < num_item; k++)scanf("%d",&bag[i][k]);
	}

	for(int state = 0; state < POW[num_item]; state++)min_cost[state] = BIG_NUM; //部品をstateの組合せで買う時の最小コスト

	for(int day = 0; day <= num_day; day++){
		for(int state = 0; state < POW[num_item]; state++){
			for(int i = 0; i <= num_limit; i++)dp[day][state][i] = BIG_NUM;
		}
	}

	dp[0][0][0] = 0;
	min_cost[0] = 0;

	int next_state,next_cost,tmp;
	int work[num_item];
	stack<int> S;

	//stateの組合せの部品を揃える際の最小コストを求める
	for(int day = 0; day <= num_day-1; day++){
		for(int state = 0; state < POW[num_item]; state++){
			for(int bought_num = 0; bought_num <= num_limit; bought_num++){

				if(dp[day][state][bought_num] == BIG_NUM)continue;

				dp[day+1][state][0] = min(dp[day+1][state][0],dp[day][state][bought_num]);

				if(bought_num == num_limit)continue; //もう買えないので、dp値を伝播させたらSKIP

				//何をいくつ買ったかを計算
				tmp = state;
				for(int i = num_item-1; i >= 0; i--){
					S.push(tmp/POW[i]);
					tmp %= POW[i];
				}

				for(int i = 0; i < num_item; i++){
					work[i] = S.top();
					S.pop();
				}

				for(int i = 0; i < num_item; i++){
					if(work[i] == 2)continue;

					next_state = state+POW[i];
					next_cost = dp[day][state][bought_num]+price[day][i];

					dp[day][next_state][bought_num+1] = min(dp[day][next_state][bought_num+1],next_cost);
					min_cost[next_state] = min(min_cost[next_state],next_cost);
				}
			}
		}
	}

	for(int i = 0; i < NUM; i++)G[i].clear();

	int source = 0, sink = 1, empty_bag = 2, index = 3;

	//袋の採番
	for(int i = 0; i < num_bag; i++)bag_index[i] = index++;
	//課題の採番
	for(int i = 0; i < num_problem; i++)problem_index[i] = index++;

	//sourceから袋への辺張り
	add_edge(source,empty_bag,200,0); //★★空袋はいくつ割り当てても良い★★
	for(int i = 0; i < num_bag; i++){
		add_edge(source,bag_index[i],1,0);
	}

	//課題からsinkへの辺張り
	for(int i = 0; i < num_problem; i++){
		add_edge(problem_index[i],sink,1,0);
	}

	//袋と課題のマッチング
	int tmp_code;

	//空袋と全ての課題を繋ぐ
	for(int i = 0; i < num_problem; i++){
		tmp_code = 0;
		for(int k = 0; k < num_item; k++){
			tmp_code += problem[i][k]*POW[k];
		}
		if(min_cost[tmp_code] != BIG_NUM){
			add_edge(empty_bag,problem_index[i],1,min_cost[tmp_code]);
		}
	}

	//その他の袋と課題を繋ぐ
	bool FLG;

	for(int i = 0; i < num_bag; i++){
		for(int k = 0; k < num_problem; k++){
			FLG = true;
			for(int a = 0; a < num_item; a++){
				if(bag[i][a] > problem[k][a]){ //部品の超過は不可
					FLG = false;
					break;
				}
			}
			if(!FLG)continue;

			tmp_code = 0;
			for(int a = 0; a < num_item; a++){
				tmp_code += (problem[k][a]-bag[i][a])*POW[a];
			}
			if(min_cost[tmp_code] != BIG_NUM){
				add_edge(bag_index[i],problem_index[k],1,min_cost[tmp_code]);
			}
		}
	}

	V = index;

	printf("%d\n",min_cost_flow(source,sink,num_student));
}

int main(){

	for(int i = 0; i < 9; i++)POW[i] = pow(3,i);

	while(true){
		scanf("%d %d %d",&num_day,&num_item,&num_limit);
		if(num_day == 0 && num_item == 0 && num_limit == 0)break;

		func();
	}
	return 0;
}