#include #include #include #include #include #include using namespace std; const __uint128_t D = 1000LL << 49; __uint128_t division(__uint128_t x) { if (x % (D * 1000) == 0) return x / (D * 1000); __uint128_t g = x / (D * 1000); if (g % (D / 1000) == 0) ++g; return g; } int main() { cin.tie(0); ios_base::sync_with_stdio(false); int N; long double sp, sq, sr; string S; cin >> N >> sp >> sq >> sr >> S; __uint128_t P = sp * 1000, Q = sq * 1000, R = sr * 1000; vector node_pos; vector<__uint128_t> dp; for (int i = 0; i < N; ++i) { if (i <= N - 3 && S.substr(i, 3) == "YES") { node_pos.push_back(i); dp.push_back(D); } if (i <= N - 2 && S.substr(i, 2) == "NO") { node_pos.push_back(i); dp.push_back(0); } } vector > merger; int depth = 0; for (int i = 0; i < N; ++i) { if (S[i] == '(') ++depth; if (S[i] == ')') --depth; if (i <= N - 6 && S.substr(i, 6) == "random") { merger.push_back(make_pair(depth * 3 + 2, i)); } if (i <= N - 3 && S.substr(i, 3) == "and" && (i == 0 || i > N - 5 || S.substr(i - 1, 6) != "random")) { merger.push_back(make_pair(depth * 3 + 1, i)); } if (i <= N - 2 && S.substr(i, 2) == "or") { merger.push_back(make_pair(depth * 3, i)); } } sort(merger.begin(), merger.end(), [](pair p1, pair p2) { return p1.first != p2.first ? p1.first > p2.first : p1.second < p2.second; }); set current; for (int i = 0; i < node_pos.size(); ++i) { current.insert(i); } for (pair i : merger) { int ptr = lower_bound(node_pos.begin(), node_pos.end(), i.second) - node_pos.begin(); set::iterator it = current.lower_bound(ptr); if (i.first % 3 == 2) { // RANDOM int lp = *it, rp = *(++it); dp[lp] = division(dp[lp] * dp[rp] * P + (D * D - dp[lp] * dp[rp]) * Q); current.erase(rp); } if (i.first % 3 == 1) { // AND int rp = *it, lp = *(--it); dp[lp] = division(dp[lp] * dp[rp] * (1000 - R) + (D * D - dp[lp] * dp[rp]) * R); current.erase(rp); } if (i.first % 3 == 0) { // OR int rp = *it, lp = *(--it); dp[lp] = division((D - dp[lp]) * (D - dp[rp]) * R + (D * D - (D - dp[lp]) * (D - dp[rp])) * (1000 - R)); current.erase(rp); } } __uint128_t ans = dp[0]; cout << int(ans / (D / 100)) << endl; return 0; }