結果
| 問題 | No.2892 Lime and Karin |
| ユーザー |
 noya2
|
| 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 |
（要ログイン）
| 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<typename Info::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 noya2
struct 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(); }
}