#include <bits/stdc++.h>
#define pii pair<int, int>

using namespace std;

const int INF = 1e9 + 7, M = 16, COMPLETE = 1 << 15;

vector<pii> edge;
vector<pii> adj[1 << M];

int d[1 << M];
signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int t, a1, a2, a3, a4; cin >> t >> a1 >> a2 >> a3 >> a4;


    for(int i = 0; i < 4; i++) edge.push_back({a1, (1 << i)});
    for(int i = 0; i < 4; i += 2) edge.push_back({a2, (1 << i) | (1 << (i + 1))});
    for(int i = 0; i < 2; i += 1) edge.push_back({a3, (1 << i) | (1 << (i + 2))});
    edge.push_back({a4, (1 << 4) - 1});

    vector<int> x;
    for(int mask = 0; mask < (1 << M); mask++){
        for(int i = 0; i < M; i++){
            if(mask & (1 << i)) x.push_back(i);
        }
        for(pii e : edge){
            int nmask = 0;
            for(int y : x){
                if((y ^ e.second) != 15) nmask |= (1 << (y ^ e.second));
            }
            adj[nmask].push_back({mask, e.first});
            adj[mask].push_back({nmask, e.first});
        }
        x.clear();
    }

    for(int i = 0; i < 1 << M; i++) d[i] = INF;
    d[COMPLETE] = 0; priority_queue<pii> pq;
    pq.push({-d[COMPLETE], COMPLETE});
    while(!pq.empty()){
        pii cur = pq.top(); pq.pop();
        if(-cur.first != d[cur.second]) continue;
        int mask = cur.second;
        for(pii e : adj[mask]){
            if(d[e.first] > d[mask] + e.second){
                d[e.first] = d[mask] + e.second;
                pq.push({-d[e.first], e.first});
            }
        }
    }
    for(int i = 1; i <= t; i++){
        int m; cin >> m;
        int mask = 0;
        while(m--){
            int bit = 0;
            for(int r = 0; r < 2; r++){
                for(int c = 0; c < 2; c++){
                    char ch; cin >> ch;
                    bit |= ((ch - '0') << (r * 2 + c));
                }
            }
            mask |= (1 << bit);
        }
        cout << d[mask] + ((mask & COMPLETE) ? 2 * d[1] : 0) << '\n';
    }
    return 0;
}

/*
2 1000 100 10 1
4
10
00

01
00

00
10

00
01

1
11
11
*/