#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif // Tropical matrix // Verify: // A[j][i] = "length of shortest parh i -> j of graph A" // (B * A)[k][i] = min_j (B[k][j] + A[j][i]) template struct tropical_matrix { constexpr static T INF = __int128(1LL << 62); static bool _chmin(T &m, const T q) { if (m > q) { m = q; chmax(m, -INF); return true; } return false; } int H, W; std::vector elem; typename std::vector::iterator operator[](int i) { return elem.begin() + i * W; } inline T &at(int i, int j) { return elem[i * W + j]; } inline T get(int i, int j) const { return elem[i * W + j]; } operator std::vector>() const { std::vector> ret(H); for (int i = 0; i < H; i++) std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i])); return ret; } tropical_matrix(int H = 0, int W = 0) : H(H), W(W), elem(H * W, INF) {} tropical_matrix(const std::vector> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) { for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem)); } static tropical_matrix Identity(int N) { tropical_matrix ret(N, N); for (int i = 0; i < N; i++) ret.at(i, i) = 0; return ret; } tropical_matrix operator+(const tropical_matrix &r) const { tropical_matrix ret(H, W); for (int i = 0; i < H * W; i++) _chmin(ret.elem[i], r.elem[i]); return ret; } tropical_matrix operator*(const tropical_matrix &r) const { tropical_matrix ret(H, r.W); for (int i = 0; i < H; i++) { for (int k = 0; k < W; k++) { for (int j = 0; j < r.W; j++) {_chmin(ret.at(i, j), this->get(i, k) + r.get(k, j)); } } } return ret; } tropical_matrix &operator+=(const tropical_matrix &r) { return *this = *this + r; } tropical_matrix &operator*=(const tropical_matrix &r) { return *this = *this * r; } bool operator==(const tropical_matrix &r) const { return H == r.H and W == r.W and elem == r.elem; } bool operator!=(const tropical_matrix &r) const { return H != r.H or W != r.W or elem != r.elem; } bool operator<(const tropical_matrix &r) const { return elem < r.elem; } tropical_matrix pow(int64_t n) const { tropical_matrix ret = Identity(H); if (n == 0) return ret; for (int i = 63 - __builtin_clzll(n); i >= 0; i--) { ret *= ret; if ((n >> i) & 1) ret *= (*this); } return ret; } }; int main() { constexpr int W = 26; vector C(W), K(W); cin >> C >> K; for (auto &x : C) --x; int N; cin >> N; dbg(C); dbg(K); vector> SABE(N); for (auto &[s, a, b, e] : SABE) cin >> s >> a >> b >> e, a--, b--; dbg(SABE); constexpr int dim = 16; constexpr __int128 INF = 1LL << 60; auto solve = [&](int init, int c, lint k) { vector mat(dim, vector<__int128>(dim, INF)); REP(w, dim) mat[w][w] = 0; for (auto [s, a, b, e] : SABE) { if (count(s.begin(), s.end(), (char)('A' + init))) { chmin<__int128>(mat[a][b], -e); chmin<__int128>(mat[b][a], -e); } } auto Mp = tropical_matrix(mat).pow(k); vector<__int128> ret(dim); REP(w, dim) ret[w] = -Mp[w][c]; return ret; }; vector<__int128> rets(dim); REP(w, W) { auto f = solve(w, C[w], K[w]); // dbg(f); REP(i, f.size()) { rets[i] += f[i]; if (f[i] < -INF) rets[i] = -INF * 2; chmax(rets[i], -INF * 2); } } // dbg(rets); lint ret = *max_element(ALL(rets)); cout << (ret >= -INF / 2 ? to_string(ret) : "Impossible") << '\n'; }