結果
問題 | No.2892 Lime and Karin |
ユーザー |
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提出日時 | 2024-09-13 21:55:27 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 4,289 ms / 8,000 ms |
コード長 | 35,615 bytes |
コンパイル時間 | 4,602 ms |
コンパイル使用メモリ | 280,328 KB |
実行使用メモリ | 27,188 KB |
最終ジャッジ日時 | 2024-09-13 21:56:16 |
合計ジャッジ時間 | 17,360 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 52 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"using namespace std;#include<bits/stdc++.h>#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"namespace noya2 {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p){os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p){is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v){int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v){for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &...u){cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &...u){cout << t;if (sizeof...(u)) cout << sep;out(u...);}template<typename T>void out(const vector<vector<T>> &vv){int s = (int)vv.size();for (int i = 0; i < s; i++) out(vv[i]);}struct IoSetup {IoSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetup_noya2;} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"namespace noya2{const int iinf = 1'000'000'007;const long long linf = 2'000'000'000'000'000'000LL;const long long mod998 = 998244353;const long long mod107 = 1000000007;const long double pi = 3.14159265358979323;const vector<int> dx = {0,1,0,-1,1,1,-1,-1};const vector<int> dy = {1,0,-1,0,1,-1,-1,1};const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string alp = "abcdefghijklmnopqrstuvwxyz";const string NUM = "0123456789";void yes(){ cout << "Yes\n"; }void no(){ cout << "No\n"; }void YES(){ cout << "YES\n"; }void NO(){ cout << "NO\n"; }void yn(bool t){ t ? yes() : no(); }void YN(bool t){ t ? YES() : NO(); }} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"namespace noya2{unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){if (a == 0 || b == 0) return a + b;int n = __builtin_ctzll(a); a >>= n;int m = __builtin_ctzll(b); b >>= m;while (a != b) {int mm = __builtin_ctzll(a - b);bool f = a > b;unsigned long long c = f ? a : b;b = f ? b : a;a = (c - b) >> mm;}return a << std::min(n, m);}template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }long long sqrt_fast(long long n) {if (n <= 0) return 0;long long x = sqrt(n);while ((x + 1) * (x + 1) <= n) x++;while (x * x > n) x--;return x;}template<typename T> T floor_div(const T n, const T d) {assert(d != 0);return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);}template<typename T> T ceil_div(const T n, const T d) {assert(d != 0);return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);}template<typename T> void uniq(std::vector<T> &v){std::sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }} // namespace noya2#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)#define all(v) (v).begin(),(v).end()using ll = long long;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pii = pair<int,int>;using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;namespace noya2{/* ~ (. _________ . /) */}using namespace noya2;#line 2 "c.cpp"#line 2 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"#include<ranges>#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"namespace noya2::internal {template<class E>struct csr {csr () {}csr (int _n) : n(_n) {}csr (int _n, int m) : n(_n){start.reserve(m);elist.reserve(m);}// ACL style constructor (do not have to call build)csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {for (auto &[i, e] : idx_elem){start[i + 2]++;}for (int i = 1; i < n; i++){start[i + 2] += start[i + 1];}for (auto &[i, e] : idx_elem){elist[start[i + 1]++] = e;}prepared = true;}int add(int idx, E elem){int eid = start.size();start.emplace_back(idx);elist.emplace_back(elem);return eid;}void build(){if (prepared) return ;int m = start.size();std::vector<E> nelist(m);std::vector<int> nstart(n + 2, 0);for (int i = 0; i < m; i++){nstart[start[i] + 2]++;}for (int i = 1; i < n; i++){nstart[i + 2] += nstart[i + 1];}for (int i = 0; i < m; i++){nelist[nstart[start[i] + 1]++] = elist[i];}swap(elist,nelist);swap(start,nstart);prepared = true;}const auto operator[](int idx) const {return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);}auto operator[](int idx){return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);}const auto operator()(int idx, int l, int r) const {return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);}auto operator()(int idx, int l, int r){return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);}int n;std::vector<int> start;std::vector<E> elist;bool prepared = false;};} // namespace noya2::internal#line 5 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"namespace noya2 {struct simple_tree {internal::csr<int> g;simple_tree () {}simple_tree (int _n) : g(_n, (_n - 1)*2) {if (_n == 1){g.build();}}void add_edge(int u, int v){g.add(u, v);int id = g.add(v, u);if (id + 1 == (g.n - 1)*2) g.build();}void input(int indexed = 1){for (int i = 0; i < g.n - 1; i++){int u, v; cin >> u >> v;u -= indexed, v -= indexed;add_edge(u, v);}}void input_parents(int indexed = 1){for (int i = 0; i < g.n - 1; i++){int v; cin >> v;v -= indexed;add_edge(i + 1, v);}}const auto operator[](int v) const {return g[v];}auto operator[](int v){return g[v];}int size() const {return g.n;}};} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/tree/centroid_decomposition.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/tree/centroid_decomposition.hpp"namespace noya2 {std::vector<int> centroid_decomposition(const auto &g){int n = g.size();if (n == 0){return {};}std::vector<int> sub(n), order;order.reserve(n);auto subtree = [&](auto sfs, int v, int f) -> void {sub[v] = 1;for (int u : g[v]){if (u == f) continue;sfs(sfs, u, v);sub[v] += sub[u];}};subtree(subtree,0,-1);auto fixed_root = [&](auto self, int root, int par, int cur_size) -> void {auto dfs = [&](auto sfs, int v, int f, int sz) -> int {int heavy = 0, child = -1;for (int u : g[v]){if (u == f) continue;if (heavy < sub[u]){heavy = sub[u];child = u;}}if (heavy > sz/2){int ret = sfs(sfs, child, v, sz);sub[v] -= ret;return ret;}else {order.emplace_back(v);for (int u : g[v]){if (u == f) continue;self(self, u, v, sub[u]);}int ret = sub[v];sub[v] = 0;return ret;}};while (cur_size > 0){cur_size -= dfs(dfs, root, par, cur_size);}};fixed_root(fixed_root, 0, -1, n);return order;}std::vector<int> centroid_decomposition_tree(const auto &g){int n = g.size();if (n == 0){return {};}std::vector<int> sub(n), par_tree(n);auto subtree = [&](auto sfs, int v, int f) -> void {sub[v] = 1;for (int u : g[v]){if (u == f) continue;sfs(sfs, u, v);sub[v] += sub[u];}};subtree(subtree,0,-1);auto fixed_root = [&](auto self, int root, int par, int cur_size, int cpre) -> void {auto dfs = [&](auto sfs, int v, int f, int sz) -> int {int heavy = 0, child = -1;for (int u : g[v]){if (u == f) continue;if (heavy < sub[u]){heavy = sub[u];child = u;}}if (heavy > sz/2){int ret = sfs(sfs, child, v, sz);sub[v] -= ret;return ret;}else {par_tree[v] = cpre;for (int u : g[v]){if (u == f) continue;self(self, u, v, sub[u], v);}int ret = sub[v];cpre = v;sub[v] = 0;return ret;}};while (cur_size > 0){cur_size -= dfs(dfs, root, par, cur_size);}};fixed_root(fixed_root, 0, -1, n, -1);return par_tree;}} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint4724.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"namespace noya2 {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);// constexpr long long primitive_root_constexpr(long long m){// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;// return primitive_root_constexpr(static_cast<int>(m));// }} // namespace noya2#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"namespace noya2{struct barrett {unsigned int _m;unsigned long long im;explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);unsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};template <int m>struct static_modint {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<std::signed_integral T>constexpr static_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>constexpr static_modint(T v){_v = (unsigned int)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (uint)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = is_prime_flag<m>;};template <int id> struct dynamic_modint {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template<std::signed_integral T>dynamic_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>dynamic_modint(T v){_v = (unsigned int)(v % umod());}uint val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = noya2::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;template<typename T>concept Modint = requires (T &a){T::mod();a.inv();a.val();a.pow(declval<int>());};} // namespace noya2#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint4724.hpp"namespace noya2 {template<>struct static_modint<-4724> {static constexpr unsigned long long mod(){return m;}static constexpr unsigned long long cal_mod(unsigned long long x){unsigned long long xu = x >> 47;unsigned long long xd = x & MASK47;unsigned long long res = (xu << 24) + xd - xu;if (res >= m) res -= m;return res;}constexpr static_modint() : _v(0) {}constexpr static_modint(long long x){if (x < 0){_v = cal_mod(-x);if (_v != 0){_v = m - _v;}}else {_v = cal_mod(x);}}constexpr static_modint(unsigned long long x){_v = cal_mod(x);}template<std::signed_integral T>constexpr static_modint(T x) : static_modint((long long)x) {}template<std::unsigned_integral T>constexpr static_modint(T x) : static_modint((unsigned long long)x) {}using modint4724 = static_modint;constexpr modint4724 &operator+=(const modint4724 &p){_v += p._v;if (_v >= m) _v -= m;return *this;}constexpr modint4724 &operator-=(const modint4724 &p){_v += m - p._v;if (_v >= m) _v -= m;return *this;}constexpr modint4724 &operator*=(const modint4724 &p){unsigned long long a = _v, b = p._v;unsigned long long au = a >> 24, ad = a & MASK24;unsigned long long bu = b >> 24, bd = b & MASK24;unsigned long long X = (au + ad) * (bu + bd);unsigned long long Y = ad * bd;unsigned long long Z = au * bu;unsigned long long A = X - Y + Z, B = Y + m4 - 2*Z;unsigned long long Au = A >> 23, Ad = A & MASK23;_v = cal_mod(((Au + Ad) << 24) + B + m - Au);return *this;}constexpr modint4724 &operator/=(const modint4724 &p){*this *= p.inv();return *this;}friend constexpr modint4724 operator+(const modint4724 &lhs, const modint4724 &rhs){return modint4724(lhs) += rhs;}friend constexpr modint4724 operator-(const modint4724 &lhs, const modint4724 &rhs){return modint4724(lhs) -= rhs;}friend constexpr modint4724 operator*(const modint4724 &lhs, const modint4724 &rhs){return modint4724(lhs) *= rhs;}friend constexpr modint4724 operator/(const modint4724 &lhs, const modint4724 &rhs){return modint4724(lhs) /= rhs;}constexpr modint4724 operator+() const {return *this;}constexpr modint4724 operator-() const {return modint4724() - *this;}constexpr modint4724 inv() const {long long a = _v, b = m, u = 1, v = 0;while (b > 0){long long t = a / b;std::swap(a -= t * b, b);std::swap(u -= t * v, v);}return modint4724(u);}constexpr modint4724 pow(long long n) const {modint4724 ret(1ULL), mul(_v);while (n != 0){if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend std::istream &operator>>(std::istream &is, modint4724 &p){unsigned long long x;is >> x;p = modint4724(x);return is;}friend std::ostream &operator<<(std::ostream &os, const modint4724 &p){return os << p._v;}constexpr unsigned long long val() const {return _v;}constexpr auto operator<=>(const modint4724 &) const = default;private:unsigned long long _v;static constexpr unsigned long long m = (1ULL << 47) - (1ULL << 24) + 1;static constexpr unsigned long long m4 = m << 2;static constexpr unsigned long long MASK23 = (1ULL << 23) - 1;static constexpr unsigned long long MASK24 = (1ULL << 24) - 1;static constexpr unsigned long long MASK47 = (1ULL << 47) - 1;};using modint4724 = static_modint<-4724>;} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"namespace noya2{template<typename T>concept Field = requires (T a, T b){a + b; a - b; a / b; a * b;T(0); T(1);};template<class Info>concept Fps_Info = requires {typename Info::value_type;requires Field<typename Info::value_type>;{Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typenameInfo::value_type>>;{Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;{Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;};template<Fps_Info Info>struct FormalPowerSeries : vector<typename Info::value_type> {using T = typename Info::value_type;using vector<T>::vector;using vector<T>::operator=;using FPS = FormalPowerSeries;FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }FPS &operator+=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const T &r){for (auto &x : *this) x *= r;return *this;}FPS &operator/=(const T &r){(*this) *= T(1)/r;return *this;}FPS &operator<<=(const int &d){(*this).insert((*this).begin(),d,T(0));return *this;}FPS &operator>>=(const int &d){if ((int)(*this).size() <= d) (*this).clear();else (*this).erase((*this).begin(),(*this).begin()+d);return *this;}FPS &operator+=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];return *this;}FPS &operator-=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];return *this;}FPS &operator*=(const FPS &r){if ((*this).empty() || r.empty()){(*this).clear();return *this;}(*this) = Info::multiply(*this,r);return *this;}FPS operator+(const T &r) const { return FPS(*this) += r; }FPS operator-(const T &r) const { return FPS(*this) -= r; }FPS operator*(const T &r) const { return FPS(*this) *= r; }FPS operator/(const T &r) const { return FPS(*this) /= r; }FPS operator<<(const int &d) const { return FPS(*this) <<= d; }FPS operator>>(const int &d) const { return FPS(*this) >>= d; }FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator+() const { return *this; }FPS operator-() const {FPS res(*this);for (auto &x : res) x = -x;return res;}T eval(const T &x) const {T res = T(0), w = T(1);for (auto &e : *this) res += e * w, w *= x;return res;}static FPS dot(const FPS &lhs, const FPS &rhs){FPS res(min(lhs.size(),rhs.size()));for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];return res;}FPS pre(int siz) const {FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));if ((int)ret.size() < siz) ret.resize(siz);return ret;}FPS rev() const {FPS ret(*this);reverse(ret.begin(), ret.end());return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));T one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {FPS ret = Info::integral(*this);return ret;}FPS inv(int d = -1) const {FPS ret = Info::inv(*this,d);return ret;}FPS exp(int d = -1) const {const int n = (*this).size();if (d == -1) d = n;FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};for (int sz = 2; sz < d; sz <<= 1){f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));if ((int)f.size() < sz*2) f.resize(sz*2);res = res * (f - res.log(2*sz));res.resize(sz*2);}res.resize(d);return res;}FPS log(int d = -1) const {assert(!(*this).empty() && (*this)[0] == T(1));if (d == -1) d = (*this).size();return (this->diff() * this->inv(d)).pre(d - 1).integral();}};} // namespace noya2#line 8 "c.cpp"namespace noya2{consteval unsigned long long primitive_root_4724(unsigned long long p){if (p == modint4724::mod()){return 3;}throw ;}template<Modint mint>struct number_theoretic_transform {static constexpr mint pr = primitive_root_4724(mint::mod());static constexpr int level = std::countr_zero(mint::mod() - 1);static constexpr std::array<mint,level+1> wgen(mint r){std::array<mint,level+1> ret;ret[level] = r;for (int i = level-1; i >= 0; i--){ret[i] = ret[i+1] * ret[i+1];}return ret;}static constexpr std::array<mint,level+1> wp = wgen(pr.pow((mint::mod()-1) >> level));static constexpr std::array<mint,level+1> wm = wgen(pr.pow((mint::mod()-1) >> level).inv());void fft2(std::vector<mint> &a){if (a.empty()) return ;int n = a.size();int k = std::countr_zero((unsigned int)(n));assert(n == (1 << k));for (int t = 1, v = 1<<(k-1), wi = k; v > 0; t <<= 1, v >>= 1, wi -= 1){mint ww = 1;int pl = 1<<wi;for (int j = 0; j < v; j++, ww *= wm[wi]){int j0 = j, j1 = j0+v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl){mint a1 = a[j1];a[j1] = (a[j0] - a1) * ww;a[j0] += a1;}}}}void ifft2(std::vector<mint> &a){if (a.empty()) return ;int n = a.size();int k = std::countr_zero((unsigned int)(n));assert(n == (1 << k));for (int v = 1, t = 1<<(k-1), wi = 1; t > 0; v <<= 1, t >>= 1, wi += 1){mint ww = 1;int pl = 1<<wi;for (int j = 0; j < v; j++, ww *= wp[wi]){int j0 = j, j1 = j0+v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl){mint a1 = a[j1] * ww;a[j1] = a[j0] - a1;a[j0] += a1;}}}}std::vector<mint> multiply(const std::vector<mint> &a, const std::vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40){std::vector<mint> s(l);for (int i = 0; i < (int)a.size(); i++) for (int j = 0; j < (int)b.size(); j++) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;std::vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft2(s);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];}else {std::vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft2(t);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft2(s);s.resize(l);mint invm = mint(M).inv();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}};} // namespace noya2struct fps4724info {using value_type = modint4724;using mint = modint4724;static std::vector<mint> multiply(const std::vector<mint> &a, const std::vector<mint> &b){static number_theoretic_transform<mint> ntt;return ntt.multiply(a,b);}static std::vector<mint> inv(const std::vector<mint> &a, int d = -1){assert(false);}static std::vector<mint> integral(const std::vector<mint> &a){assert(false);}};using mint = modint4724;using fps = FormalPowerSeries<fps4724info>;void solve(){int n; in(n);simple_tree g(n);g.input();string s; in(s);vector<bool> done(n,false);mint ans = 0;mint i2 = mint(2).inv();for (int ctr : centroid_decomposition(g)){fps f;auto depth = [&](auto sfs, int v, int ff) -> int {int ret = (s[v] == '1' ? 1 : -1);int mi = 0;for (int u : g[v]){if (u == ff) continue;if (done[u]) continue;int dp = sfs(sfs,u,v);chmin(mi,dp);}return mi + ret;};auto dfs = [&](auto sfs, int v, int ff, int d) -> void {d += (s[v] == '1' ? 1 : -1);for (int u : g[v]){if (u == ff) continue;if (done[u]) continue;sfs(sfs,u,v,d);}if ((int)f.size() <= d){f.resize(d+1);}f[d] += 1;};fps sum, sq;int geta = 0;for (int v : g[ctr]){if (done[v]) continue;int d = depth(depth,v,ctr);int gg = (d < 0 ? -d : 0);chmax(geta,gg);}for (int v : g[ctr]){if (done[v]) continue;dfs(dfs,v,ctr,geta);sum += f;sq += f*f;f = {};}sq = (sum*sum - sq) * i2;for (int i = (s[ctr] == '1' ? 0 : 2); ; i++){int r = i+geta*2;if (r >= (int)(sq.size())) break;ans += sq[r];}for (int i = (s[ctr] == '1' ? 0 : 2); ; i++){int r = i+geta;if (r >= (int)(sum.size())) break;ans += sum[r];}if (s[ctr] == '1'){ans += 1;}// out(ctr,ans,geta);done[ctr] = true;}out(ans);}int main(){int t = 1; //in(t);while (t--) { solve(); }}