#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll myRand(ll B) { return (ull)rng() % B; }
inline double time() {
    return static_cast<long double>(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count()) * 1e-9;
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int q;
    cin >> q;
    vector<ll> a(9);
    cin >> a[0];
    a[1] = a[2] = a[3] = a[0];
    cin >> a[4];
    a[5] = a[4];
    cin >> a[6];
    a[7] = a[6];
    cin >> a[8];

    vector<ll> dp(1 << 16, 2e9);
    vector<vector<int>> tr(16, vector<int>(9));
    vector<int> uo = {1, 2, 4, 8, 3, 12, 5, 10, 15};
    for (int i = 0; i < 16; ++i) {
        for (int j = 0; j < 9; ++j) {
            tr[i][j] = i ^ uo[j];
        }
    }
    dp[0] = 0;
    for (int i = 0; i < 1 << 16; ++i) {
        for (int j = 0; j < 9; ++j) {
            int bit = 0;
            for (int k = 0; k < 16; ++k) {
                if (1 << k & i) {
                    bit |= 1 << (k ^ uo[j]);
                }
            }
            dp[bit] = min(dp[bit], dp[i] + a[j]);
            bit |= 1 << (15 ^ uo[j]);
            dp[bit] = min(dp[bit], dp[i] + a[j]);
        }
    }
    //    for (int i = dp.size() - 1; i > 0; --i) {
    //        for (int j = 0; j < 16; ++j) {
    //            if ((1 << j) & i) {
    //                dp[i ^ (1 << j)] = min(dp[i ^ (1 << j)], dp[i]);
    //            }
    //        }
    //    }
    while (q--) {
        int n;
        cin >> n;
        int bit = 0;
        for (int i = 0; i < n; ++i) {
            char c;
            int num = 0;
            for (int j = 0; j < 4; ++j) {
                cin >> c;
                if (c == '1') {
                    num |= 1 << j;
                }
            }
            bit |= (1 << num);
        }
        cout << dp[bit] << '\n';
    }
}