// 2024ICPCShenyangE 
#include <iostream>
#include <algorithm>
using namespace std;
#include <math.h>
#include <memory.h>

int m;
char ope[9] = {1, 2, 4, 8, 3, 12, 5, 10, 15 };	// 9种操作 
int a[9];	// 操作的代价 
int grid;
int dp[1<<16];	// dp[i]: 状态i是格子集合的位串表示 

int memoir(int s) {
	// s必不含全1格(1<<15)
	if (dp[s] >= 0)
		return dp[s];
	if (s == 0)
		return dp[s] = 0;
	dp[s] = 2e9;
	for (int i = 0; i < 9; i++) {
		int newst = 0;
		for (int j = 0; j < 16; j++)
			if ((s & (1 << j)) && ((j ^ ope[i]) != 15))
				newst |= (1 << (j ^ ope[i]));
		int suba = memoir(newst);
		dp[s] = min(dp[s], a[i] + suba);
	}
	return dp[s];
}

int main() {
	int t, a0, a1, a2, a3;
	char ch;
	
	ios::sync_with_stdio(false);
	cin >> t >> a0 >> a1 >> a2 >> a3;
	a[0] = a[1] = a[2] = a[3] = a0;
	a[4] = a[5] = a1;
	a[6] = a[7] = a2;
	a[8] = a3;
	for (int i = 0; i < (1 << 16); i++)
		dp[i] = -1;
	while (t--) {
		cin >> m;
		int st = 0;
		for (int i = 0; i < m; i++) {
			grid = 0;
			for (int j = 0; j < 4; j++) {
				cin >> ch;
				if (ch == '1')
					grid |= (1 << j);
			}
			st |= (1 << grid);
		}
		if (st & (1 << 15)) {	// 含全1格 
			int ans = 2e9;
			for (int i = 0; i < 9; i++) {
				int newst = 0;
				for (int j = 0; j < 16; j++)
					if ((st & (1 << j)) && ((j ^ ope[i]) != 15))
						newst |= (1 << (j ^ ope[i]));
				ans = min(ans, a[i] + memoir(newst));
			}
			cout << ans << endl;
		} else
			cout << memoir(st) << endl;
	}
	return 0;
}

/*
4 1000 100 10 1
2
1111
0001
2
1111
1110
*/