#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair <int, int> pa;
int cost[5];
ll a[20];
ll f[20][20];
int p1[5] = {0, 1, 2, 4, 8};
int p2[3] = {0, 3, 12};
int p3[3] = {0, 5, 10};
int p4[2] = {0, 15};
struct node{
    int x, y, z;
}b[1001];
int fa[20];

inline void read(int &x)
{
    x = 0;
    int w = 1; char c = getchar();
    while (!isdigit(c)) {if (c == '-') w = -1; c = getchar();} 
    while (isdigit(c)) {x = x * 10 + (c ^ 48); c = getchar();}
    x = x * w;
}

bool cmp(node f1, node f2)
{
    return f1.z < f2.z;
}

int find(int x)
{
    if (x == fa[x]) return x;
    return fa[x] = find(fa[x]);
}

int main()
{
    memset(f, 0x3f3f3f, sizeof(f));
    int T;
    read(T); 
    int h = 1e7 + 10;
    for (int i = 1; i <= 4; i++) 
    {
        read(cost[i]);
        h = min(h, cost[i]);
    } 

    for (int i = 0; i <= 15; i++)
    {
        f[i][i] = 0;
        for (int j = 1; j <= 4; j++)
        {
            int x = i ^ p1[j];
            f[i][x] = cost[1];
        }
        for (int j = 1; j <= 2; j++)
        {
            int x = i ^ p2[j];
            f[i][x] = cost[2];
        }
        for (int j = 1; j <= 2; j++)
        {
            int x = i ^ p3[j];
            f[i][x] = cost[3];
        }
        int x = i ^ 15;
        f[i][x] = cost[4];
    }   
    for (int k = 0; k <= 15; k++)
    {
        for (int i = 0; i <= 15; i++)
        {
            for (int j = 0; j <= 15; j++)
            {
                f[i][j] = min(f[i][k] + f[k][j], f[i][j]);
            }
        }
    }
    f[15][15] = 2 * h;
    // cout << T << "    " << f[15][15] << endl;
    while (T > 0)
    {
        T--;
        int m;
        int tot = 0;
        read(m);
        int p = 0;
        // cout << m << endl;
        for (int k = 1; k <= m; k++)
        {
            ll t = 1;
            a[k] = 0;
            for (int i = 1; i <= 2; i++)
            {
                for (int j = 1; j <= 2; j++)
                {
                    char ch;
                    cin >> ch;
                    if (ch == '1') a[k] += t;
                    t = t * 2;
                }
            }        
            if (a[k] == 15) p = 1;
        }
        fa[15] = 15;
        for (int i = 1; i <= m; i++)
        {
            fa[a[i]] = a[i];
            for (int j = 1; j <= m; j++)
            {
                if (i == j) continue;
                tot++; b[tot].x = a[i]; b[tot].y = a[j]; b[tot].z = f[a[i]][a[j]];
                // cout << tot << " " << a[i] << " " << a[j] <<"   "  << f[a[i]][a[j]]<< endl;
            }
            if (p == 0)
            {
                tot++;
                b[tot].x = a[i];
                b[tot].y = 15;
                b[tot].z = f[a[i]][15];
                // cout << "    " << a[i] << " " << 15 << " " << f[a[i]][15] << endl;
            }
        }
        if (p == 0)
        {
            m++;
        }
        sort(b + 1, b + tot + 1, cmp);
        ll sum = 0;
        for (int i = 1; i <= tot; i++)
        {
            int fx = find(b[i].x);
            int fy = find(b[i].y);
            // cout << b[i].x << " " << b[i].y << " " << fx << " " << fy << " " << b[i].z << endl;
            if (fx == fy) continue;
            sum += b[i].z;
            fa[fx] = fy;
        }
        if (m == 1) sum = f[a[1]][15];
        cout << sum << endl;
    }
    return 0;
}