#pragma GCC target ("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #define _USE_MATH_DEFINES #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 ll = long long; using ld = long double; #define all(a) (a).begin(),(a).end() #define fs first #define sc second #define xx first #define yy second.first #define zz second.second #define H pair #define P pair> #define Q(i,j,k) mkp(i,mkp(j,k)) #define rng(i,s,n) for(ll i = (s) ; i < (n) ; i++) #define rep(i,n) rng(i, 0, (n)) #define mkp make_pair #define vec vector #define vi vec #define pb emplace_back #define siz(a) (int)(a).size() #define crdcomp(b) sort(all((b)));(b).erase(unique(all((b))),(b).end()) #define getidx(b,i) (lower_bound(all(b),(i))-(b).begin()) #define ssp(i,n) (i==(ll)(n)-1?"\n":" ") #define ctoi(c) (int)(c-'0') #define itoc(c) (char)(c+'0') #define cyes printf("Yes\n") #define cno printf("No\n") #define cdf(n) for(int quetimes_=(n);quetimes_>0;quetimes_--) #define gcj printf("Case #%lld: ",qq123_+1) #define readv(a,n) a.resize(n,0);rep(i,(n)) a[i]=read() #define found(a,x) (a.find(x)!=a.end()) constexpr ll mod = (ll)1e9 + 7; constexpr ll Mod = 998244353; constexpr ld EPS = 1e-10; constexpr ll inf = (ll)3 * 1e18; constexpr int Inf = (ll)15 * 1e8; constexpr int dx[] = { -1,1,0,0 }, dy[] = { 0,0,-1,1 }; templatebool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } templatebool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } ll read() { ll u, k = scanf("%lld", &u); return u; } string reads() { string s; cin >> s; return s; } H readh(short g = 0) { H u; int k = scanf("%lld %lld", &u.fs, &u.sc); if (g == 1) u.fs--, u.sc--; if (g == 2) u.fs--; return u; } bool ina(H t, int h, int w) { return 0 <= t.fs && t.fs < h && 0 <= t.sc && t.sc < w; } bool ina(int t, int l, int r) { return l <= t && t < r; } ll gcd(ll i, ll j) { return j ? gcd(j, i % j) : i; } ll popcount(ll x) { int sum = 0; for (int i = 0; i < 60; i++)if ((1ll << i) & x) sum++; return sum; } template class csum { vec v; public: csum(vec& a) :v(a) { build(); } csum() {} void init(vec& a) { v = a; build(); } void build() { for (int i = 1; i < v.size(); i++) v[i] += v[i - 1]; } T a(int l, int r) { if (r < l) return 0; return v[r] - (l == 0 ? 0 : v[l - 1]); }//[l,r] T b(int l, int r) { return a(l, r - 1); }//[l,r) T a(pairt) { return a(t.first, t.second); } T b(pairt) { return b(t.first, t.second); } }; class mint { public:ll v; mint(ll v = 0) { s(v % mod + mod); } constexpr static int mod = (ll)1e9 + 7; constexpr static int fn_ = (ll)2e6 + 5; static mint fact[fn_], comp[fn_]; mint pow(int x) const { mint b(v), c(1); while (x) { if (x & 1) c *= b; b *= b; x >>= 1; } return c; } inline mint& s(int vv) { v = vv < mod ? vv : vv - mod; return *this; } inline mint inv()const { return pow(mod - 2); } inline mint operator-()const { return mint() - *this; } inline mint& operator+=(const mint b) { return s(v + b.v); } inline mint& operator-=(const mint b) { return s(v + mod - b.v); } inline mint& operator*=(const mint b) { v = v * b.v % mod; return *this; } inline mint& operator/=(const mint b) { v = v * b.inv().v % mod; return *this; } inline mint operator+(const mint b) const { return mint(v) += b; } inline mint operator-(const mint b) const { return mint(v) -= b; } inline mint operator*(const mint b) const { return mint(v) *= b; } inline mint operator/(const mint b) const { return mint(v) /= b; } friend ostream& operator<<(ostream& os, const mint& m) { return os << m.v; } friend istream& operator>>(istream& is, mint& m) { int x; is >> x; m = mint(x); return is; } bool operator<(const mint& r)const { return v < r.v; } bool operator>(const mint& r)const { return v > r.v; } bool operator<=(const mint& r)const { return v <= r.v; } bool operator>=(const mint& r)const { return v >= r.v; } bool operator==(const mint& r)const { return v == r.v; } bool operator!=(const mint& r)const { return v != r.v; } explicit operator bool()const { return v; } explicit operator int()const { return v; } mint comb(mint k) { if (k > * this) return mint(); if (!fact[0]) combinit(); if (v >= fn_) { if (k > * this - k) k = *this - k; mint tmp(1); for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i); return tmp * comp[k.v]; } return fact[v] * comp[k.v] * comp[v - k.v]; }//nCk mint perm(mint k) { if (k > * this) return mint(); if (!fact[0]) combinit(); if (v >= fn_) { mint tmp(1); for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i); return tmp; } return fact[v] * comp[v - k.v]; }//nPk static void combinit() { fact[0] = 1; for (int i = 1; i < fn_; i++) fact[i] = fact[i - 1] * mint(i); comp[fn_ - 1] = fact[fn_ - 1].inv(); for (int i = fn_ - 2; i >= 0; i--) comp[i] = comp[i + 1] * mint(i + 1); } }; mint mint::fact[fn_], mint::comp[fn_]; //-------------------------------------------------------------- //--------------------------------------------------------------------- int n; ld p, q, r; string s; vectokens = { "(",")","YES","NO","or","and" }; vi pri = { 0,0,0,0,2,3,1 }; vi a; using T = pair; T solve() { stackope; vecres; for (auto g : a) { if (g == 0) { ope.push(0); } else if (g == 1) { while (ope.top() != 0) { res.pb(ope.top()); ope.pop(); } ope.pop(); } else if (g == 2 || g == 3) { res.pb(g); } else { while (!ope.empty() && pri[ope.top()] >= pri[g]) { res.pb(ope.top()); ope.pop(); } ope.push(g); } } while (!ope.empty()) { res.pb(ope.top()); assert(ope.top()!=0); ope.pop(); } stacknum; for (auto g : res) { if (g == 2) num.push(T{ 1,0 }); else if (g == 3) num.push(T{ 0,1 }); else { T a, b; b = num.top(); num.pop(); a = num.top(); num.pop(); if (4 <= g && g <= 5) { T t; if (g == 4) { t = T{ 1 - a.sc * b.sc,a.sc * b.sc }; } else if (g == 5) { t = T{ a.fs * b.fs,1 - a.fs * b.fs }; } num.push(T{ t.fs * (1 - r) + t.sc * r,t.sc * (1 - r) + t.fs * r }); } else { ld k = a.fs * b.fs * p + (1 - a.fs * b.fs) * q; num.push(T{ k,1 - k }); } } } return num.top(); } signed main() { cin >> n >> p >> q >> r; getchar(); getline(cin, s); assert(2<=n&&n<=1e6); assert(0<=p&&p<=1); assert(0<=q&&q<=1); assert(0<=r&&r<=1); assert(n==siz(s)); string tt = "", tr = " "; int sum=0,tmp=0; rep(i, siz(s)) { if (s[i] == ' ') assert(0); if(s[i]=='(') tmp++; if(s[i]==')'){ tmp--; if(tmp<0) assert(0); } if (i + 6 <= siz(s) && s.substr(i, 6) == "random") { assert(s[i+6]=='('); sum++; i += 5; goto loop; } tt += s[i]; loop:; } s = tt; assert(tmp==0); for (int i = 0; i < siz(s);) { rep(j, 6) { if (i + siz(tokens[j]) <= siz(s) && s.substr(i, siz(tokens[j])) == tokens[j]) { if (siz(a) > 0 && a.back() != 0 && j != 1 && a.back() <= 3 && j <= 3) { a.pb(6); sum--; } a.pb(j); i += siz(tokens[j]); } } } assert(sum==0); printf("%d\n", (int)floor((solve().fs-0.0001) * 100)); }