#ifndef LOCAL #define FAST_IO #endif // ============ #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i) #define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i) #define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__) #define ALL(x) begin(x), end(x) #define LEN(x) (i32)(x.size()) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; using pi = pair; using pl = pair; template using V = vector; template using VV = V>; template using VVV = V>>; template using VVVV = V>>>; template using PQR = priority_queue, greater>; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } template i32 lob(const V &arr, const T &v) { return (i32)(lower_bound(ALL(arr), v) - arr.begin()); } template i32 upb(const V &arr, const T &v) { return (i32)(upper_bound(ALL(arr), v) - arr.begin()); } template V argsort(const V &arr) { V ret; iota(ALL(ret), 0); sort(ALL(ret), [&](i32 i, i32 j) -> bool { if (arr[i] == arr[j]) { return i < j; } else { return arr[i] < arr[j]; } }); return ret; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; void scan(char &x) { cin >> x; } void scan(u32 &x) { cin >> x; } void scan(u64 &x) { cin >> x; } void scan(i32 &x) { cin >> x; } void scan(i64 &x) { cin >> x; } void scan(string &x) { cin >> x; } template void scan(V &x) { for (T &ele : x) { scan(ele); } } void read() {} template void read(Head &head, Tail &...tail) { scan(head); read(tail...); } #define CHAR(...) string __VA_ARGS__; read(__VA_ARGS__); #define U32(...) u32 __VA_ARGS__; read(__VA_ARGS__); #define U64(...) u64 __VA_ARGS__; read(__VA_ARGS__); #define I32(...) i32 __VA_ARGS__; read(__VA_ARGS__); #define I64(...) i64 __VA_ARGS__; read(__VA_ARGS__); #define STR(...) string __VA_ARGS__; read(__VA_ARGS__); #define VEC(type, name, size) V name(size); read(name); #define VVEC(type, name, size1, size2) VV name(size1, V(size2)); read(name); // ============ #ifdef DEBUGF #else #define DBG(x) (void) 0 #endif // ============ #include #include #include #include class HeavyLightDecomposition { std::vector siz; std::vector par; std::vector hea; std::vector in; std::vector out; std::vector dep; std::vector rev; template void dfs1(G &g, int v) { if (!g[v].empty() && (int) g[v][0] == par[v]) { std::swap(g[v][0], g[v].back()); } for (auto &e : g[v]) { int u = (int)e; if (u != par[v]) { par[u] = v; dfs1(g, u); siz[v] += siz[u]; if (siz[u] > siz[(int) g[v][0]]) { std::swap(g[v][0], e); } } } } template void dfs2(const G &g, int v, int &time) { in[v] = time; rev[time++] = v; for (auto &e : g[v]) { int u = (int)e; if (u == par[v]) { continue; } if (u == (int) g[v][0]) { hea[u] = hea[v]; } else { hea[u] = u; } dep[u] = dep[v] + 1; dfs2(g, u, time); } out[v] = time; } public: template HeavyLightDecomposition(G &g, int root = 0) : siz(g.size(), 1), par(g.size(), root), hea(g.size(), root), in(g.size(), 0), out(g.size(), 0), dep(g.size(), 0), rev(g.size(), 0) { assert(root >= 0 && root < (int) g.size()); dfs1(g, root); int time = 0; dfs2(g, root, time); } int subtree_size(int v) const { assert(v >= 0 && v < (int) siz.size()); return siz[v]; } int parent(int v) const { assert(v >= 0 && v < (int) par.size()); return par[v]; } int in_time(int v) const { assert(v >= 0 && v < (int) in.size()); return in[v]; } int out_time(int v) const { assert(v >= 0 && v < (int) out.size()); return out[v]; } int depth(int v) const { assert(v >= 0 && v < (int) dep.size()); return dep[v]; } int time_to_vertex(int t) const { assert(t >= 0 && t < (int) rev.size()); return rev[t]; } int head(int v) const { assert(v >= 0 && v < (int) out.size()); return hea[v]; } int la(int v, int k) const { assert(v >= 0 && v < (int) dep.size()); assert(k >= 0); if (k > dep[v]) { return -1; } while (true) { int u = hea[v]; if (in[u] + k <= in[v]) { return rev[in[v] - k]; } k -= in[v] - in[u] + 1; v = par[u]; } return 0; } int forward(int v, int dst) const { assert(v >= 0 && v < (int) dep.size()); assert(dst >= 0 && dst < (int) dep.size()); assert(v != dst); int l = lca(v, dst); if (l == v) { return la(dst, dep[dst] - dep[v] - 1); } else { return par[v]; } } int lca(int u, int v) const { assert(u >= 0 && u < (int) dep.size()); assert(v >= 0 && v < (int) dep.size()); while (u != v) { if (in[u] > in[v]) { std::swap(u, v); } if (hea[u] == hea[v]) { v = u; } else { v = par[hea[v]]; } } return u; } int dist(int u, int v) const { assert(u >= 0 && u < (int) dep.size()); assert(v >= 0 && v < (int) dep.size()); return dep[u] + dep[v] - 2 * dep[lca(u, v)]; } std::vector> path(int u, int v, bool edge) const { assert(u >= 0 && u < (int) dep.size()); assert(v >= 0 && v < (int) dep.size()); std::vector> fromu, fromv; bool rev = false; while (true) { if (u == v && edge) { break; } if (in[u] > in[v]) { std::swap(u, v); std::swap(fromu, fromv); rev ^= true; } if (hea[u] == hea[v]) { fromv.emplace_back(in[v], in[u] + (int)edge); v = u; break; } else { fromv.emplace_back(in[v], in[hea[v]]); v = par[hea[v]]; } } if (rev) { std::swap(fromu, fromv); } std::reverse(fromv.begin(), fromv.end()); fromu.reserve(fromv.size()); for (auto [x, y] : fromv) { fromu.emplace_back(y, x); } return fromu; } int jump(int u, int v, int k) const { assert(u >= 0 && u < (int) dep.size()); assert(v >= 0 && v < (int) dep.size()); assert(k >= 0); int l = lca(u, v); int dis = dep[u] + dep[v] - 2 * dep[l]; if (k > dis) { return -1; } if (k <= dep[u] - dep[l]) { return la(u, k); } else { return la(v, dis - k); } } int meet(int u, int v, int w) const { return lca(u, v) ^ lca(v, w) ^ lca(w, u); } }; // ============ // ============ #include #include #include #include class BigInt { static constexpr long long B = 1000000; static constexpr int L = 6; // a >= 0 static void normalize(std::vector &a) { if (a.empty()) { return; } for (int i = 0; i < (int)a.size() - 1; ++i) { if (a[i] < 0) { long long v = (-a[i] + B - 1) / B; a[i] += v * B; a[i + 1] -= v; } if (a[i] >= B) { long long v = a[i] / B; a[i] -= v * B; a[i + 1] += v; } } while (a.back() >= B) { long long v = a.back() / B; a.back() -= v * B; a.push_back(v); } while (!a.empty() && a.back() == 0) { a.pop_back(); } } static std::vector nn_add(const std::vector &lhs, const std::vector rhs) { std::vector ret(std::max(lhs.size(), rhs.size()), 0); for (int i = 0; i < (int)lhs.size(); ++i) { ret[i] += lhs[i]; } for (int i = 0; i < (int)rhs.size(); ++i) { ret[i] += rhs[i]; } normalize(ret); return ret; } // lhs >= rhs static std::vector nn_sub(const std::vector &lhs, const std::vector rhs) { std::vector ret(lhs.size(), 0); for (int i = 0; i < (int)lhs.size(); ++i) { ret[i] += lhs[i]; } for (int i = 0; i < (int)rhs.size(); ++i) { ret[i] -= rhs[i]; } normalize(ret); return ret; } static std::vector nn_mul(const std::vector &lhs, const std::vector rhs) { std::vector ret = atcoder::convolution_ll(lhs, rhs); normalize(ret); return ret; } static std::strong_ordering cmp(const std::vector &lhs, const std::vector &rhs) { if (lhs.size() != rhs.size()) { return lhs.size() <=> rhs.size(); } else { for (int i = (int)lhs.size() - 1; i >= 0; --i) { if (lhs[i] != rhs[i]) { return lhs[i] <=> rhs[i]; } } return std::strong_ordering::equivalent; } } std::vector expr; bool pos; BigInt(std::vector expr, bool pos) : expr(expr), pos(pos) {} public: BigInt() : expr(), pos(true) {} BigInt(long long x) : expr(), pos(true) { if (x < 0) { pos = false; x = -x; } while (x > 0) { expr.push_back(x % B); x /= B; } } // [0-9]* BigInt(const std::string &s) : expr(), pos(true) { int cur = (int)s.size(); while (cur > 0) { int nx = std::max(0, cur - 6); long long val = 0; long long p = 1; for (int i = cur - 1; i >= nx; --i) { val += p * (s[i] - '0'); p *= 10; } expr.push_back(val); cur = nx; } } int size() const { return (int)expr.size(); } const BigInt operator-() const { return BigInt(expr, !pos); } BigInt &operator+=(const BigInt &rhs) { if (pos == rhs.pos) { expr = nn_add(expr, rhs.expr); } else { auto c = cmp(expr, rhs.expr); if (c > 0) { expr = nn_sub(expr, rhs.expr); } else if (c < 0) { expr = nn_sub(rhs.expr, expr); pos = !pos; } else { expr.clear(); } } return *this; } BigInt &operator-=(const BigInt &rhs) { if (pos != rhs.pos) { expr = nn_add(expr, rhs.expr); } else { auto c = cmp(expr, rhs.expr); if (c > 0) { expr = nn_sub(expr, rhs.expr); } else if (c < 0) { expr = nn_sub(rhs.expr, expr); pos = !pos; } else { expr.clear(); } } return *this; } BigInt &operator*=(const BigInt &rhs) { expr = nn_mul(expr, rhs.expr); pos ^= !rhs.pos; return *this; } friend BigInt operator+(BigInt lhs, const BigInt &rhs) { lhs += rhs; return lhs; } friend BigInt operator-(BigInt lhs, const BigInt &rhs) { lhs -= rhs; return lhs; } friend BigInt operator*(BigInt lhs, const BigInt &rhs) { lhs *= rhs; return lhs; } std::string to_string() const { if (expr.empty()) { return std::string("0"); } std::string ret; if (!pos) { ret.push_back('-'); } for (int i = (int)expr.size() - 1; i >= 0; --i) { std::string s = std::to_string(expr[i]); if (i != (int)expr.size() - 1) { s = std::string(6 - (int)s.size(), '0') + s; } ret += s; } return ret; } }; std::istream &operator>>(std::istream &is, BigInt &v) { std::string s; is >> s; int p = 0; bool pos = true; while (p < (int)s.size() && s[p] == '-') { pos = !pos; ++p; } v = BigInt(s.substr(p)); if (!pos) { v = -v; } return is; } std::ostream &operator<<(std::ostream &os, const BigInt &v) { os << v.to_string(); return os; } // ============ template typename Op::Value weighted_merge(const V &vals) { using Val = typename Op::Value; auto rec = [&](auto rec, i32 l, i32 r) -> Val { if (r - l == 1) { return vals[l]; } i32 s = 0; REP(i, l, r) { s += vals[i].size(); } i32 c = 0; REP(i, l, r) { c += vals[i].size(); if (2 * c >= s) { Val ret = vals[i]; if (i != l) { ret = Op::op(rec(rec, l, i), ret); } if (i != r - 1) { ret = Op::op(ret, rec(rec, i + 1, r)); } return ret; } } assert(false); }; return rec(rec, 0, LEN(vals)); } using bigint = BigInt; struct Affine { bigint a, b; Affine() : a(1LL), b(0LL) {} Affine(bigint a, bigint b) : a(a), b(b) {} i32 size() const { return max(a.size(), b.size()); } }; struct Op { using Value = Affine; static Affine op(const Affine f, const Affine g) { return Affine(f.a * g.a, f.a * g.b + f.b); } }; struct Parser { string s; i32 it; // results VV tree; V val; V op; i32 root; i32 new_node() { i32 v = LEN(tree); tree.push_back(V()); val.push_back(bigint()); op.push_back('!'); return v; } i32 number() { bool pos = true; while (it < (i32)s.size() && s[it] == '-') { pos = !pos; ++it; } string d; while (it < (i32)s.size() && isdigit(s[it])) { d.push_back(s[it]); ++it; } i32 v = new_node(); val[v] = bigint(d); if (!pos) { val[v] = -val[v]; } return v; } i32 factor() { if (s[it] == '(') { ++it; i32 v = expr(); assert(it < (i32)s.size() && s[it] == ')'); ++it; return v; } else { i32 v = number(); return v; } } i32 term() { i32 r = factor(); while (it < (i32)s.size() && s[it] == '*') { ++it; i32 u = r; i32 v = factor(); r = new_node(); op[r] = '*'; tree[r].push_back(u); tree[r].push_back(v); } return r; } i32 expr() { i32 r = term(); while (it < (i32)s.size() && (s[it] == '+' || s[it] == '-')) { if (s[it] == '+') { ++it; i32 u = r; i32 v = term(); r = new_node(); op[r] = '+'; tree[r].push_back(u); tree[r].push_back(v); } else { ++it; i32 v = term(); // negate { i32 m = new_node(); val[m] = bigint(-1LL); i32 t = new_node(); op[t] = '*'; tree[t].push_back(v); tree[t].push_back(m); v = t; } // add i32 u = r; r = new_node(); op[r] = '+'; tree[r].push_back(u); tree[r].push_back(v); } } return r; } Parser(string s) : s(s), it(0), tree(), val(), op(), root(-1) { root = expr(); } }; // 末尾から適用する bigint affine(const V &op, const V &val, const bigint &x) { assert(op.size() == val.size()); /*bigint ans = x; PER(i, op.size()) { if (op[i] == '+') { ans += val[i]; } else if (op[i] == '-') { ans -= val[i]; } else { ans *= val[i]; } } return ans;*/ /*// x -> ax+b auto rec = [&](auto rec, i32 l, i32 r) -> pair { if (r - l == 1) { if (op[l] == '+') { return pair(bigint(1LL), val[l]); } else if (op[l] == '-') { return pair(bigint(1LL), -val[l]); } else { return pair(val[l], bigint()); } } i32 mid = (l + r) / 2; auto [al, bl] = rec(rec, l, mid); auto [ar, br] = rec(rec, mid, r); return pair(al * ar, al * br + bl); }; auto [a, b] = rec(rec, 0, (i32)op.size()); return a * x + b;*/ V funcs; REP(i, LEN(op)) { if (op[i] == '+') { funcs.emplace_back(Affine(bigint(1LL), val[i])); } else if (op[i] == '-') { funcs.emplace_back(Affine(bigint(1LL), -val[i])); } else { funcs.emplace_back(Affine(val[i], bigint(0LL))); } } Affine tot = weighted_merge(funcs); return tot.a * x + tot.b; } int main() { i32 n; cin >> n; string s; cin >> s; Parser parser(s); HeavyLightDecomposition hld(parser.tree, parser.root); V heavy(parser.tree.size(), -1), light(parser.tree.size(), -1); REP(i, parser.tree.size()) { if (parser.tree[i].empty()) { continue; } i32 u = parser.tree[i][0], v = parser.tree[i][1]; if (hld.head(u) == u) { heavy[i] = v; light[i] = u; } else { heavy[i] = u; light[i] = v; } } auto solve = [&](auto solve, i32 v) -> bigint { if (heavy[v] == -1) { return parser.val[v]; } V op; V val; i32 cur = v; while (heavy[cur] != -1) { op.push_back(parser.op[cur]); val.push_back(solve(solve, light[cur])); cur = heavy[cur]; } return affine(op, val, solve(solve, cur)); }; cout << solve(solve, parser.root) << '\n'; }