// 2024ICPCShenyangE 
#include <iostream>
#include <algorithm>
using namespace std;
#include <math.h>
#include <memory.h>
#define int long long
int m;
int a1, a2, a3, a4, a[9];
char ope[9] = {1, 2, 4, 8, 3, 12, 5, 10, 15 };
int grid;
int dp[1<<17];

int memoir(int s) {
    // s does not include (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 newset = 0;
        for (int j = 0; j < 16; j++)
            if ((s & (1 << j)) && ((j ^ ope[i]) != 15))
                newset |= (1 << (j ^ ope[i]));
        int suba = memoir(newset);
        dp[s] = min(dp[s], a[i] + suba);
    }
    return dp[s];
}

signed main() {
    int t;
    char ch;
    
    ios::sync_with_stdio(false);
    cin >> t >> a1 >> a2 >> a3 >> a4;
    a[0] = a[1] = a[2] = a[3] =  a1;
    a[4] = a[5] = a2;
    a[6] = a[7] = a3;
    a[8] = a4;
    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)) {
            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
*/