結果
| 問題 | No.3412 Christmas Tree Coloring |
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2025-12-20 17:15:30 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 443 ms / 2,000 ms |
| コード長 | 34,014 bytes |
| 記録 | |
| コンパイル時間 | 8,290 ms |
| コンパイル使用メモリ | 342,636 KB |
| 実行使用メモリ | 22,720 KB |
| 最終ジャッジ日時 | 2025-12-20 17:15:46 |
| 合計ジャッジ時間 | 14,864 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 * 2 |
| other | AC * 20 |
ソースコード
#ifndef HIDDEN_IN_VS // 折りたたみ用
// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS
// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;
// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -2^31 ～ 2^31 = 2e9）
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定
// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod
// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif // 折りたたみ用
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<(int)1e9+7>;
//using mint = modint; // mint::set_mod(m);
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
int mute_dump = 0;
int frac_print = 0;
#if __has_include(<atcoder/all>)
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
#endif
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); rep(i,9)cout<<MLE[i]; } } // RE の代わりに MLE を出す
#endif
// n 頂点の森 g に対する愚直解を返す．
mint naive_forest(int n, Graph g) {
// ------------------ 辺 (u[j]-v[j]) のリストに直す ------------------
vi u, v;
rep(s, n) repe(t, g[s]) {
if (s < t) {
u.push_back(s);
v.push_back(t);
}
}
int m = sz(u);
// -------------------------------------------------------------------
mint res = 0;
rep(s, n) { // O(2^n n^2)
repb(set, n) {
if (getb(set, s)) continue;
bool ok = true;
rep(j, m) {
if (u[j] == s) continue;
if (v[j] == s) continue;
if (getb(set, u[j]) == getb(set, v[j])) ok = false;
}
bool ex0 = false, ex1 = false;
rep(t, n) {
if (t == s) continue;
if (!getb(set, t)) ex0 = true;
if (getb(set, t)) ex1 = true;
}
if (ok && ex0 && ex1) res++;
}
}
return res;
}
// 仮根 0 をもつ n 頂点の木 g に対する愚直解を返す．
mint naive_virtual_tree(int n, Graph g) {
mint res = 0;
// set : 黒で塗る頂点の集合
repb(set, n) {
// 根は黒で塗れないとする．
if (getb(set, 0)) continue;
bool ok = true;
rep(s, n) repe(t, g[s]) if (getb(set, s) && getb(set, t)) ok = false;
if (ok) res++;
}
return res;
}
// 頂点 0 を virtual な根とする木 par に対する愚直解を計算する．
// virtual な根を考えたくなければ，頂点 0 と接続辺を無視して森として扱えばいい．
mint naive(const vi& par) {
// 森として扱う
if (1) {
int n = sz(par);
Graph g(n);
rep(i, n) {
if (par[i] == 0) continue;
g[i].push_back(par[i] - 1);
g[par[i] - 1].push_back(i);
}
return naive_forest(n, g);
}
// 仮根をもつ木として扱う
else {
int n = sz(par) + 1;
Graph g(n);
rep(i, n - 1) {
g[i + 1].push_back(par[i]);
g[par[i]].push_back(i + 1);
}
return naive_virtual_tree(n, g);
}
}
//【グラフの入力】O(n + m)
Graph read_Graph(int n, int m = -1, bool directed = false, bool zero_indexed = false) {
Graph g(n);
if (m == -1) m = n - 1;
rep(j, m) {
int a, b;
cin >> a >> b;
if (!zero_indexed) { --a; --b; }
g[a].push_back(b);
if (!directed && a != b) g[b].push_back(a);
}
return g;
}
// (グラフ, 根) を naive() への入力形式に直す．
vi inputform(const Graph& g, int r) {
int n = sz(g);
vi par(n);
function<void(int, int)> dfs = [&](int s, int p) {
par[s] = { p + 1 };
repe(t, g[s]) {
if (t == p) continue;
dfs(t, s);
}
};
dfs(r, -1);
return par;
}
//【行列】
template <class T>
struct Matrix {
int n, m; // 行列のサイズ（n 行 m 列）
vector<vector<T>> v; // 行列の成分
// n×m 零行列で初期化する．
Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}
// n×n 単位行列で初期化する．
Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }
// 二次元配列 a[0..n)[0..m) の要素で初期化する．
Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
Matrix() : n(0), m(0) {}
// 代入
Matrix(const Matrix&) = default;
Matrix& operator=(const Matrix&) = default;
// アクセス
inline vector<T> const& operator[](int i) const { return v[i]; }
inline vector<T>& operator[](int i) {return v[i];}
// 入力
friend istream& operator>>(istream& is, Matrix& a) {
rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
return is;
}
// 行の追加
void push_back(const vector<T>& a) {
Assert(sz(a) == m);
v.push_back(a);
n++;
}
// 行の削除
void pop_back() {
Assert(n > 0);
v.pop_back();
n--;
}
// サイズ変更
void resize(int n_) {
v.resize(n_);
n = n_;
}
void resize(int n_, int m_) {
n = n_;
m = m_;
v.resize(n);
rep(i, n) v[i].resize(m);
}
// 空か
bool empty() const { return min(n, m) == 0; }
// 比較
bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
bool operator!=(const Matrix& b) const { return !(*this == b); }
// 加算，減算，スカラー倍
Matrix& operator+=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] += b[i][j];
return *this;
}
Matrix& operator-=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] -= b[i][j];
return *this;
}
Matrix& operator*=(const T& c) {
rep(i, n) rep(j, m) v[i][j] *= c;
return *this;
}
Matrix operator+(const Matrix& b) const { return Matrix(*this) += b; }
Matrix operator-(const Matrix& b) const { return Matrix(*this) -= b; }
Matrix operator*(const T& c) const { return Matrix(*this) *= c; }
friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
Matrix operator-() const { return Matrix(*this) *= T(-1); }
// 行列ベクトル積 : O(m n)
vector<T> operator*(const vector<T>& x) const {
vector<T> y(n);
rep(i, n) rep(j, m) y[i] += v[i][j] * x[j];
return y;
}
// ベクトル行列積 : O(m n)
friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
vector<T> y(a.m);
rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
return y;
}
// 積：O(n^3)
Matrix operator*(const Matrix& b) const {
Matrix res(n, b.m);
rep(i, res.n) rep(k, m) rep(j, res.m) res[i][j] += v[i][k] * b[k][j];
return res;
}
Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }
// 累乗：O(n^3 log d)
Matrix pow(ll d) const {
Matrix res(n), pow2 = *this;
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d >>= 1;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Matrix& a) {
rep(i, a.n) {
os << "[";
rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
if (i < a.n - 1) os << "\n";
}
return os;
}
#endif
};
//【行簡約形（行交換なし）】O(n m min(n, m))
template <class T>
vector<pii> row_reduced_form(Matrix<T>& A) {
int n = A.n, m = A.m;
vector<pii> piv;
piv.reserve(min(n, m));
// 未確定の列を記録しておくリスト
list<int> rjs;
rep(j, m) rjs.push_back(j);
rep(i, n) {
// 第 i 行の係数を左から走査し非 0 を見つける．
auto it = rjs.begin();
for (; it != rjs.end(); it++) if (A[i][*it] != 0) break;
// 第 i 行の全てが 0 なら無視する．
if (it == rjs.end()) continue;
// A[i][j] をピボットに選択する．
int j = *it;
rjs.erase(it);
piv.emplace_back(i, j);
// A[i][j] が 1 になるよう行全体を A[i][j] で割る．
T Aij_inv = T(1) / A[i][j];
repi(j2, j, m - 1) A[i][j2] *= Aij_inv;
// 第 i 行以外の第 j 列の成分が全て 0 になるよう第 i 行を定数倍して減じる．
rep(i2, n) if (A[i2][j] != 0 && i2 != i) {
T mul = A[i2][j];
repi(j2, j, m - 1) A[i2][j2] -= A[i][j2] * mul;
}
}
return piv;
}
//【逆行列】O(n^3)
template <class T>
Matrix<T> inverse_matrix(const Matrix<T>& mat) {
int n = mat.n;
// 元の行列 mat と単位行列を繋げた拡大行列 v を作る．
vector<vector<T>> v(n, vector<T>(2 * n));
rep(i, n) rep(j, n) {
v[i][j] = mat[i][j];
if (i == j) v[i][n + j] = 1;
}
int m = 2 * n;
// 注目位置を (i, j)（i 行目かつ j 列目）とする．
int i = 0, j = 0;
// 拡大行列に対して行基本変形を行い，左側を単位行列にすることを目指す．
while (i < n && j < m) {
// 同じ列の下方の行から非 0 成分を見つける．
int i2 = i;
while (i2 < n && v[i2][j] == T(0)) i2++;
// 見つからなかったら全て 0 の列があったので mat は非正則
if (i2 == n) return Matrix<T>();
// 見つかったら i 行目とその行を入れ替える．
if (i != i2) swap(v[i], v[i2]);
// v[i][j] が 1 になるよう行全体を v[i][j] で割る．
T vij_inv = T(1) / v[i][j];
repi(j2, j, m - 1) v[i][j2] *= vij_inv;
// v[i][j] と同じ列の成分が全て 0 になるよう i 行目を定数倍して減じる．
rep(i2, n) {
// i 行目だけは引かない．
if (i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, m - 1) v[i2][j2] -= v[i][j2] * mul;
}
// 注目位置を右下に移す．
i++; j++;
}
// 拡大行列の右半分が mat の逆行列なのでコピーする．
Matrix<T> mat_inv(n, n);
rep(i, n) rep(j, n) mat_inv[i][j] = v[i][n + j];
return mat_inv;
}
//【根付き木の同型類】O(n log n)
vi rooted_tree_classification(const Graph& g, int r) {
int n = sz(g);
static map<vi, int> to_id;
vi id(n);
function<int(int s, int p)> dfs = [&](int s, int p) {
vi ch;
repe(t, g[s]) {
if (t == p) continue;
ch.push_back(dfs(t, s));
}
sort(all(ch));
if (to_id.count(ch)) id[s] = to_id[ch];
else id[s] = to_id[ch] = sz(to_id);
return id[s];
};
dfs(r, -1);
return id;
}
// 遷移行列の係数を計算し，埋め込み用のコードを出力する．
// 待てない場合は lv_max や LB_max を指定する．
void embed_coefs(int lv_max = INF, int LB_max = INF) {
using TREE = vi; // 木は親の列 p[1..n) で表す．
vector<TREE> trees{ {} };
int idx = 0;
int ID = -1;
int PDIM = -1;
repi(lv, 1, INF) {
dump("----------- lv:", lv, "--------------");
// 上用の木（位置指定子追加）と下用の木（そのまま）に整形する．
vector<TREE> treesT, treesB(trees);
rep(i, idx) repi(p, 0, sz(trees[i])) {
treesT.push_back(trees[i]);
treesT.back().push_back(p);
}
int LT = sz(treesT); int LB = min(sz(treesB), LB_max);
dump("LT:", LT, "LB:", LB);
// (i,j) 成分が naive(treesT[i] join treesB[j]) であるような行列 mat を得る．
Matrix<mint> mat(LT, LB);
rep(i, LT) rep(j, LB) {
TREE tree(treesT[i]);
int p0 = tree.back();
tree.pop_back();
int offset = sz(tree);
repe(p, treesB[j]) {
int np = (p == 0 ? p0 : p + offset);
tree.push_back(np);
}
mat[i][j] = naive(tree);
}
//dump("mat:"); dump(mat);
// mat に対して行基本変形を行いピボット位置のリスト piv を得る．
auto piv = row_reduced_form(mat);
int DIM = sz(piv);
dump("piv(", DIM, "):"); dump(piv);
// rank の更新がなかったら必要な情報は揃ったとみなして打ち切る（たまにミスる）
if (lv == lv_max || (DIM > 0 && DIM == PDIM)) {
// 選択した行と列をそれぞれ昇順に並べて is, js とする（0 始まりのはず）
vi is(DIM), js(DIM);
rep(r, DIM) tie(is[r], js[r]) = piv[r];
sort(all(js));
// js : 本質的に区別しなければならない木のリスト
// is : js を区別するのに必要最低限の接ぎ木のリスト
// 基底の変換行列 P を得る．
Matrix<mint> P(DIM, DIM);
rep(i_, DIM) rep(j_, DIM) {
int i = is[i_];
int j = js[j_];
TREE tree(treesT[i]);
int p0 = tree.back();
tree.pop_back();
int offset = sz(tree);
repe(p, treesB[j]) {
int np = (p == 0 ? p0 : p + offset);
tree.push_back(np);
}
P[i_][j_] = naive(tree);
}
// P の逆行列 P_inv を得る．
auto P_inv = inverse_matrix(P);
// apply の表現行列を得る．
Matrix<mint> matA(DIM, DIM);
rep(i_, DIM) rep(j_, DIM) {
int i = is[i_];
int j = js[j_];
TREE tree(treesT[i]);
int offset = sz(tree);
repe(p, treesB[j]) {
int np = p + offset;
tree.push_back(np);
}
matA[i_][j_] = naive(tree);
}
matA = P_inv * matA;
// merge の表現テンソルを得る．
vvvm tsrM(DIM, vvm(DIM, vm(DIM)));
rep(j1_, DIM) rep(j2_, DIM) {
if (j1_ > j2_) {
// 子の順序は無視する．
rep(i_, DIM) {
tsrM[j1_][j2_][i_] = tsrM[j2_][j1_][i_];
}
}
else {
rep(i_, DIM) {
int i = is[i_];
int j1 = js[j1_];
int j2 = js[j2_];
TREE tree(treesT[i]);
int p0 = tree.back();
tree.pop_back();
int offset = sz(tree);
repe(p, treesB[j1]) {
int np = (p == 0 ? p0 : p + offset);
tree.push_back(np);
}
offset = sz(tree);
repe(p, treesB[j2]) {
int np = (p == 0 ? p0 : p + offset);
tree.push_back(np);
}
tsrM[j1_][j2_][i_] = naive(tree);
}
tsrM[j1_][j2_] = P_inv * tsrM[j1_][j2_];
}
}
// 根を閉じるためのベクトルを得る．
vm vecP(DIM);
rep(i, DIM) vecP[i] = P[0][i];
// スパース埋め込み用の文字列を出力する．
auto to_signed_string = [](mint x) {
int v = x.val();
int mod = mint::mod();
if (v > mod / 2) v -= mod;
return to_string(v);
};
string eb;
eb += "constexpr int DIM = ";
eb += to_string(DIM);
eb += ";\n";
eb += "tuple<int, int, VTYPE> matA[] = {";
rep(i, DIM) rep(j, DIM) {
if (matA[i][j] == 0) continue;
eb += "{";
eb += to_string(i);
eb += ",";
eb += to_string(j);
eb += ",";
eb += to_signed_string(matA[i][j]);
eb += "},";
}
eb.pop_back();
eb += "};\n";
eb += "tuple<int, int, int, VTYPE> tsrM[] = {";
rep(i, DIM) rep(j1, DIM) rep(j2, DIM) {
if (tsrM[j1][j2][i] == 0) continue;
eb += "{";
eb += to_string(i);
eb += ",";
eb += to_string(j1);
eb += ",";
eb += to_string(j2);
eb += ",";
eb += to_signed_string(tsrM[j1][j2][i]);
eb += "},";
}
eb.pop_back();
eb += "};\n";
eb += "VTYPE vecP[DIM] = {";
rep(j, DIM) eb += to_signed_string(vecP[j]) + ",";
eb.pop_back();
eb += "};\n";
cout << eb;
exit(0);
}
// 基底ガチャ
//mt19937_64 mt((int)time(NULL)); shuffle(trees.begin() + idx, trees.end(), mt);
// 次に大きい木たちを trees に追加する．
int nidx = sz(trees);
repi(i, idx, nidx - 1) rep(p, lv) {
trees.push_back(trees[i]);
trees.back().push_back(p);
Graph g(lv + 1);
rep(j, lv) {
g[j + 1].push_back(trees.back()[j]);
g[trees.back()[j]].push_back(j + 1);
}
auto hash = rooted_tree_classification(g, 0);
if (hash[0] <= ID) {
trees.pop_back();
continue;
}
ID = hash[0];
}
idx = nidx;
PDIM = DIM;
}
}
template <class VTYPE>
vector<VTYPE> solve(const Graph& g, int r) {
// --------------- embed_coefs() からの出力を貼る ----------------
constexpr int DIM = 9;
vector<tuple<int, int, VTYPE>> matA = { {1,0,1},{2,3,-499122176},{2,4,-4},{2,5,-499122176},{2,6,499122174},{2,7,-11},{2,8,499122173},{3,1,1},{3,3,499122176},{3,4,499122176},{3,5,499122175},{3,6,499122176},{3,7,499122175},{3,8,-2},{4,3,499122176},{4,4,-499122169},{4,5,499122176},{4,6,-499122171},{4,7,-499122156},{4,8,7},{5,3,1},{5,4,-3},{5,5,1},{5,6,-2},{5,7,-8},{5,8,-2},{6,2,1},{6,3,-499122176},{6,4,-499122175},{6,5,-499122175},{6,6,-499122176},{6,7,-499122174},{6,8,2},{7,4,499122173},{7,6,-3},{7,7,499122167},{7,8,499122173},{8,4,3},{8,6,3},{8,7,8},{8,8,3} };
vector<tuple<int, int, int, VTYPE>> tsrM = { {0,0,0,1},{1,0,1,1},{1,1,0,1},{2,0,2,1},{2,1,1,1},{2,1,6,-1},{2,1,7,1},{2,1,8,499122176},{2,2,0,1},{2,2,4,1},{2,2,5,499122176},{2,2,6,-3},{2,2,7,2},{2,2,8,-3},{2,3,3,-499122174},{2,3,4,499122176},{2,3,5,1},{2,3,6,-1},{2,3,7,-3},{2,3,8,499122174},{2,4,2,1},{2,4,3,499122176},{2,4,4,2},{2,4,5,-3},{2,4,6,499122169},{2,4,7,-1},{2,4,8,499122165},{2,5,2,499122176},{2,5,3,1},{2,5,4,-3},{2,5,5,499122174},{2,5,6,499122172},{2,5,7,499122165},{2,5,8,-11},{2,6,1,-1},{2,6,2,-3},{2,6,3,-1},{2,6,4,499122169},{2,6,5,499122172},{2,6,6,499122172},{2,6,7,-18},{2,6,8,-12},{2,7,1,1},{2,7,2,2},{2,7,3,-3},{2,7,4,-1},{2,7,5,499122165},{2,7,6,-18},{2,7,7,-20},{2,7,8,-36},{2,8,1,499122176},{2,8,2,-3},{2,8,3,499122174},{2,8,4,499122165},{2,8,5,-11},{2,8,6,-12},{2,8,7,-36},{2,8,8,499122145},{3,0,3,1},{3,1,6,499122176},{3,1,7,-499122176},{3,1,8,249561089},{3,2,4,-499122176},{3,2,5,249561089},{3,2,6,-499122176},{3,2,7,3},{3,2,8,-499122173},{3,3,0,1},{3,3,3,249561087},{3,3,4,249561089},{3,3,5,499122176},{3,3,6,-1},{3,3,7,-499122173},{3,3,8,249561090},{3,4,2,-499122176},{3,4,3,249561089},{3,4,4,3},{3,4,5,-499122173},{3,4,6,-249561085},{3,4,7,-499122165},{3,4,8,-249561077},{3,5,2,249561089},{3,5,3,499122176},{3,5,4,-499122173},{3,5,5,249561090},{3,5,6,249561089},{3,5,7,-249561077},{3,5,8,-499122169},{3,6,1,499122176},{3,6,2,-499122176},{3,6,3,-1},{3,6,4,-249561085},{3,6,5,249561089},{3,6,6,-249561089},{3,6,7,10},{3,6,8,5},{3,7,1,-499122176},{3,7,2,3},{3,7,3,-499122173},{3,7,4,-499122165},{3,7,5,-249561077},{3,7,6,10},{3,7,7,36},{3,7,8,31},{3,8,1,249561089},{3,8,2,-499122173},{3,8,3,249561090},{3,8,4,-249561077},{3,8,5,-499122169},{3,8,6,5},{3,8,7,31},{3,8,8,-249561067},{4,0,4,1},{4,1,2,1},{4,1,6,-499122174},{4,1,7,499122174},{4,1,8,249561090},{4,2,1,1},{4,2,4,499122174},{4,2,5,249561090},{4,2,6,-499122169},{4,2,7,-3},{4,2,8,-499122167},{4,3,3,249561084},{4,3,4,249561090},{4,3,5,499122176},{4,3,6,3},{4,3,7,-499122167},{4,3,8,249561097},{4,4,0,1},{4,4,2,499122174},{4,4,3,249561090},{4,4,4,-3},{4,4,5,-499122167},{4,4,6,-249561069},{4,4,7,-499122166},{4,4,8,-249561054},{4,5,2,249561090},{4,5,3,499122176},{4,5,4,-499122167},{4,5,5,249561097},{4,5,6,249561100},{4,5,7,-249561054},{4,5,8,-499122145},{4,6,1,-499122174},{4,6,2,-499122169},{4,6,3,3},{4,6,4,-249561069},{4,6,5,249561100},{4,6,6,-249561078},{4,6,7,47},{4,6,8,31},{4,7,1,499122174},{4,7,2,-3},{4,7,3,-499122167},{4,7,4,-499122166},{4,7,5,-249561054},{4,7,6,47},{4,7,7,72},{4,7,8,103},{4,8,1,249561090},{4,8,2,-499122167},{4,8,3,249561097},{4,8,4,-249561054},{4,8,5,-499122145},{4,8,6,31},{4,8,7,103},{4,8,8,-249561002},{5,0,5,1},{5,1,3,1},{5,1,6,-1},{5,1,7,-2},{5,1,8,-4},{5,2,4,-2},{5,2,5,-4},{5,2,6,-6},{5,2,7,-12},{5,2,8,-16},{5,3,1,1},{5,3,3,2},{5,3,4,-4},{5,3,5,-2},{5,3,6,-2},{5,3,7,-16},{5,3,8,-12},{5,4,2,-2},{5,4,3,-4},{5,4,4,-12},{5,4,5,-16},{5,4,6,-18},{5,4,7,-46},{5,4,8,-48},{5,5,0,1},{5,5,2,-4},{5,5,3,-2},{5,5,4,-16},{5,5,5,-12},{5,5,6,-10},{5,5,7,-48},{5,5,8,-36},{5,6,1,-1},{5,6,2,-6},{5,6,3,-2},{5,6,4,-18},{5,6,5,-10},{5,6,6,-6},{5,6,7,-46},{5,6,8,-28},{5,7,1,-2},{5,7,2,-12},{5,7,3,-16},{5,7,4,-46},{5,7,5,-48},{5,7,6,-46},{5,7,7,-144},{5,7,8,-128},{5,8,1,-4},{5,8,2,-16},{5,8,3,-12},{5,8,4,-48},{5,8,5,-36},{5,8,6,-28},{5,8,7,-128},{5,8,8,-92},{6,0,6,1},{6,1,6,-499122176},{6,1,7,499122176},{6,1,8,-249561089},{6,2,4,499122176},{6,2,5,-249561089},{6,2,6,499122176},{6,2,7,-3},{6,2,8,499122173},{6,3,3,-249561087},{6,3,4,-249561089},{6,3,5,-499122176},{6,3,6,1},{6,3,7,499122173},{6,3,8,-249561090},{6,4,2,499122176},{6,4,3,-249561089},{6,4,4,-3},{6,4,5,499122173},{6,4,6,249561085},{6,4,7,499122165},{6,4,8,249561077},{6,5,2,-249561089},{6,5,3,-499122176},{6,5,4,499122173},{6,5,5,-249561090},{6,5,6,-249561089},{6,5,7,249561077},{6,5,8,499122169},{6,6,0,1},{6,6,1,-499122176},{6,6,2,499122176},{6,6,3,1},{6,6,4,249561085},{6,6,5,-249561089},{6,6,6,249561089},{6,6,7,-10},{6,6,8,-5},{6,7,1,499122176},{6,7,2,-3},{6,7,3,499122173},{6,7,4,499122165},{6,7,5,249561077},{6,7,6,-10},{6,7,7,-36},{6,7,8,-31},{6,8,1,-249561089},{6,8,2,499122173},{6,8,3,-249561090},{6,8,4,249561077},{6,8,5,499122169},{6,8,6,-5},{6,8,7,-31},{6,8,8,249561067},{7,0,7,1},{7,1,4,1},{7,1,6,499122175},{7,1,7,-499122174},{7,1,8,249561087},{7,2,2,1},{7,2,4,-499122174},{7,2,5,249561087},{7,2,6,499122172},{7,2,7,2},{7,2,8,499122170},{7,3,3,249561090},{7,3,4,249561087},{7,3,5,499122176},{7,3,6,-2},{7,3,7,499122170},{7,3,8,249561082},{7,4,1,1},{7,4,2,-499122174},{7,4,3,249561087},{7,4,4,2},{7,4,5,499122170},{7,4,6,-249561100},{7,4,7,499122168},{7,4,8,-249561111},{7,5,2,249561087},{7,5,3,499122176},{7,5,4,499122170},{7,5,5,249561082},{7,5,6,249561081},{7,5,7,-249561111},{7,5,8,499122156},{7,6,1,499122175},{7,6,2,499122172},{7,6,3,-2},{7,6,4,-249561100},{7,6,5,249561081},{7,6,6,-249561094},{7,6,7,-29},{7,6,8,-19},{7,7,0,1},{7,7,1,-499122174},{7,7,2,2},{7,7,3,499122170},{7,7,4,499122168},{7,7,5,-249561111},{7,7,6,-29},{7,7,7,-51},{7,7,8,-67},{7,8,1,249561087},{7,8,2,499122170},{7,8,3,249561082},{7,8,4,-249561111},{7,8,5,499122156},{7,8,6,-19},{7,8,7,-67},{7,8,8,-249561143},{8,0,8,1},{8,1,5,1},{8,1,6,2},{8,1,7,2},{8,1,8,5},{8,2,3,1},{8,2,4,2},{8,2,5,5},{8,2,6,7},{8,2,7,12},{8,2,8,17},{8,3,2,1},{8,3,3,-1},{8,3,4,5},{8,3,5,3},{8,3,6,3},{8,3,7,17},{8,3,8,13},{8,4,2,2},{8,4,3,5},{8,4,4,12},{8,4,5,17},{8,4,6,19},{8,4,7,46},{8,4,8,49},{8,5,1,1},{8,5,2,5},{8,5,3,3},{8,5,4,17},{8,5,5,13},{8,5,6,11},{8,5,7,49},{8,5,8,37},{8,6,1,2},{8,6,2,7},{8,6,3,3},{8,6,4,19},{8,6,5,11},{8,6,6,7},{8,6,7,47},{8,6,8,29},{8,7,1,2},{8,7,2,12},{8,7,3,17},{8,7,4,46},{8,7,5,49},{8,7,6,47},{8,7,7,144},{8,7,8,129},{8,8,0,1},{8,8,1,5},{8,8,2,17},{8,8,3,13},{8,8,4,49},{8,8,5,37},{8,8,6,29},{8,8,7,129},{8,8,8,93} };
vector<VTYPE> vecP = { 0,0,0,0,6,6,6,24,20 };
// --------------------------------------------------------------
// 木 DP
int n = sz(g);
vector<array<VTYPE, DIM>> dp(n);
rep(s, n) {
dp[s].fill(0);
dp[s][0] = 1;
}
auto apply = [&](const array<VTYPE, DIM>& x) {
array<VTYPE, DIM> z; z.fill(0);
for (auto [i, j, v] : matA) z[i] += v * x[j];
return z;
};
auto merge = [&](const array<VTYPE, DIM>& x, const array<VTYPE, DIM>& y) {
array<VTYPE, DIM> z; z.fill(0);
for (auto [i, j1, j2, v] : tsrM) z[i] += v * x[j1] * y[j2];
return z;
};
function<void(int, int)> dfs = [&](int s, int p) {
bool first_call = true;
repe(t, g[s]) {
if (t == p) continue;
dfs(t, s);
if (first_call) {
dp[s] = dp[t];
first_call = false;
}
else {
dp[s] = merge(dp[s], dp[t]);
}
}
dp[s] = apply(dp[s]);
};
dfs(r, -1);
vector<VTYPE> res(n, 0);
rep(s, n) rep(j, DIM) res[s] += vecP[j] * dp[s][j];
return res;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
//【方法】
// 愚直を書いて集めたデータをもとに遷移テンソルを復元する．
//【使い方】
// 1. mint naive(親の列) を実装する．
// 2. embed_coefs(); を実行する．
// 3. 出力を solve() 内に貼る．
// 4. auto dp = solve<答えの型>(グラフ, 根) で勝手に DP してくれる．
// embed_coefs(INF, INF);
int n;
cin >> n;
auto g = read_Graph(n);
dump("naive:", naive(inputform(g, 0))); dump("======");
auto dp = solve<mint>(g, 0);
cout << dp[0].val() << "\n"; // スパースにして 624 ms → 463 ms
}
/*
----------- lv: 1 --------------
LT: 0 LB: 1
piv( 0 ):
----------- lv: 2 --------------
LT: 1 LB: 2
piv( 0 ):
----------- lv: 3 --------------
LT: 3 LB: 4
piv( 1 ):
(1,2)
----------- lv: 4 --------------
LT: 9 LB: 8
piv( 5 ):
(0,4) (1,2) (2,5) (3,1) (4,3)
----------- lv: 5 --------------
LT: 25 LB: 17
piv( 9 ):
(0,4) (1,2) (2,5) (3,1) (4,3) (6,8) (9,0) (10,6) (13,9)
----------- lv: 6 --------------
LT: 70 LB: 37
piv( 9 ):
(0,4) (1,2) (2,5) (3,1) (4,3) (6,8) (9,0) (10,6) (13,9)
constexpr int DIM = 9;
tuple<int, int, VTYPE> matA[] = {{1,0,1},{2,3,-499122176},{2,4,-4},{2,5,-499122176},{2,6,499122174},{2,7,-11},{2,8,499122173},{3,1,1},{3,3,499122176},{3,4,499122176},{3,5,499122175},{3,6,499122176},{3,7,499122175},{3,8,-2},{4,3,499122176},{4,4,-499122169},{4,5,499122176},{4,6,-499122171},{4,7,-499122156},{4,8,7},{5,3,1},{5,4,-3},{5,5,1},{5,6,-2},{5,7,-8},{5,8,-2},{6,2,1},{6,3,-499122176},{6,4,-499122175},{6,5,-499122175},{6,6,-499122176},{6,7,-499122174},{6,8,2},{7,4,499122173},{7,6,-3},{7,7,499122167},{7,8,499122173},{8,4,3},{8,6,3},{8,7,8},{8,8,3}};
tuple<int, int, int, VTYPE> tsrM[] = {{0,0,0,1},{1,0,1,1},{1,1,0,1},{2,0,2,1},{2,1,1,1},{2,1,6,-1},{2,1,7,1},{2,1,8,499122176},{2,2,0,1},{2,2,4,1},{2,2,5,499122176},{2,2,6,-3},{2,2,7,2},{2,2,8,-3},{2,3,3,-499122174},{2,3,4,499122176},{2,3,5,1},{2,3,6,-1},{2,3,7,-3},{2,3,8,499122174},{2,4,2,1},{2,4,3,499122176},{2,4,4,2},{2,4,5,-3},{2,4,6,499122169},{2,4,7,-1},{2,4,8,499122165},{2,5,2,499122176},{2,5,3,1},{2,5,4,-3},{2,5,5,499122174},{2,5,6,499122172},{2,5,7,499122165},{2,5,8,-11},{2,6,1,-1},{2,6,2,-3},{2,6,3,-1},{2,6,4,499122169},{2,6,5,499122172},{2,6,6,499122172},{2,6,7,-18},{2,6,8,-12},{2,7,1,1},{2,7,2,2},{2,7,3,-3},{2,7,4,-1},{2,7,5,499122165},{2,7,6,-18},{2,7,7,-20},{2,7,8,-36},{2,8,1,499122176},{2,8,2,-3},{2,8,3,499122174},{2,8,4,499122165},{2,8,5,-11},{2,8,6,-12},{2,8,7,-36},{2,8,8,499122145},{3,0,3,1},{3,1,6,499122176},{3,1,7,-499122176},{3,1,8,249561089},{3,2,4,-499122176},{3,2,5,249561089},{3,2,6,-499122176},{3,2,7,3},{3,2,8,-499122173},{3,3,0,1},{3,3,3,249561087},{3,3,4,249561089},{3,3,5,499122176},{3,3,6,-1},{3,3,7,-499122173},{3,3,8,249561090},{3,4,2,-499122176},{3,4,3,249561089},{3,4,4,3},{3,4,5,-499122173},{3,4,6,-249561085},{3,4,7,-499122165},{3,4,8,-249561077},{3,5,2,249561089},{3,5,3,499122176},{3,5,4,-499122173},{3,5,5,249561090},{3,5,6,249561089},{3,5,7,-249561077},{3,5,8,-499122169},{3,6,1,499122176},{3,6,2,-499122176},{3,6,3,-1},{3,6,4,-249561085},{3,6,5,249561089},{3,6,6,-249561089},{3,6,7,10},{3,6,8,5},{3,7,1,-499122176},{3,7,2,3},{3,7,3,-499122173},{3,7,4,-499122165},{3,7,5,-249561077},{3,7,6,10},{3,7,7,36},{3,7,8,31},{3,8,1,249561089},{3,8,2,-499122173},{3,8,3,249561090},{3,8,4,-249561077},{3,8,5,-499122169},{3,8,6,5},{3,8,7,31},{3,8,8,-249561067},{4,0,4,1},{4,1,2,1},{4,1,6,-499122174},{4,1,7,499122174},{4,1,8,249561090},{4,2,1,1},{4,2,4,499122174},{4,2,5,249561090},{4,2,6,-499122169},{4,2,7,-3},{4,2,8,-499122167},{4,3,3,249561084},{4,3,4,249561090},{4,3,5,499122176},{4,3,6,3},{4,3,7,-499122167},{4,3,8,249561097},{4,4,0,1},{4,4,2,499122174},{4,4,3,249561090},{4,4,4,-3},{4,4,5,-499122167},{4,4,6,-249561069},{4,4,7,-499122166},{4,4,8,-249561054},{4,5,2,249561090},{4,5,3,499122176},{4,5,4,-499122167},{4,5,5,249561097},{4,5,6,249561100},{4,5,7,-249561054},{4,5,8,-499122145},{4,6,1,-499122174},{4,6,2,-499122169},{4,6,3,3},{4,6,4,-249561069},{4,6,5,249561100},{4,6,6,-249561078},{4,6,7,47},{4,6,8,31},{4,7,1,499122174},{4,7,2,-3},{4,7,3,-499122167},{4,7,4,-499122166},{4,7,5,-249561054},{4,7,6,47},{4,7,7,72},{4,7,8,103},{4,8,1,249561090},{4,8,2,-499122167},{4,8,3,249561097},{4,8,4,-249561054},{4,8,5,-499122145},{4,8,6,31},{4,8,7,103},{4,8,8,-249561002},{5,0,5,1},{5,1,3,1},{5,1,6,-1},{5,1,7,-2},{5,1,8,-4},{5,2,4,-2},{5,2,5,-4},{5,2,6,-6},{5,2,7,-12},{5,2,8,-16},{5,3,1,1},{5,3,3,2},{5,3,4,-4},{5,3,5,-2},{5,3,6,-2},{5,3,7,-16},{5,3,8,-12},{5,4,2,-2},{5,4,3,-4},{5,4,4,-12},{5,4,5,-16},{5,4,6,-18},{5,4,7,-46},{5,4,8,-48},{5,5,0,1},{5,5,2,-4},{5,5,3,-2},{5,5,4,-16},{5,5,5,-12},{5,5,6,-10},{5,5,7,-48},{5,5,8,-36},{5,6,1,-1},{5,6,2,-6},{5,6,3,-2},{5,6,4,-18},{5,6,5,-10},{5,6,6,-6},{5,6,7,-46},{5,6,8,-28},{5,7,1,-2},{5,7,2,-12},{5,7,3,-16},{5,7,4,-46},{5,7,5,-48},{5,7,6,-46},{5,7,7,-144},{5,7,8,-128},{5,8,1,-4},{5,8,2,-16},{5,8,3,-12},{5,8,4,-48},{5,8,5,-36},{5,8,6,-28},{5,8,7,-128},{5,8,8,-92},{6,0,6,1},{6,1,6,-499122176},{6,1,7,499122176},{6,1,8,-249561089},{6,2,4,499122176},{6,2,5,-249561089},{6,2,6,499122176},{6,2,7,-3},{6,2,8,499122173},{6,3,3,-249561087},{6,3,4,-249561089},{6,3,5,-499122176},{6,3,6,1},{6,3,7,499122173},{6,3,8,-249561090},{6,4,2,499122176},{6,4,3,-249561089},{6,4,4,-3},{6,4,5,499122173},{6,4,6,249561085},{6,4,7,499122165},{6,4,8,249561077},{6,5,2,-249561089},{6,5,3,-499122176},{6,5,4,499122173},{6,5,5,-249561090},{6,5,6,-249561089},{6,5,7,249561077},{6,5,8,499122169},{6,6,0,1},{6,6,1,-499122176},{6,6,2,499122176},{6,6,3,1},{6,6,4,249561085},{6,6,5,-249561089},{6,6,6,249561089},{6,6,7,-10},{6,6,8,-5},{6,7,1,499122176},{6,7,2,-3},{6,7,3,499122173},{6,7,4,499122165},{6,7,5,249561077},{6,7,6,-10},{6,7,7,-36},{6,7,8,-31},{6,8,1,-249561089},{6,8,2,499122173},{6,8,3,-249561090},{6,8,4,249561077},{6,8,5,499122169},{6,8,6,-5},{6,8,7,-31},{6,8,8,249561067},{7,0,7,1},{7,1,4,1},{7,1,6,499122175},{7,1,7,-499122174},{7,1,8,249561087},{7,2,2,1},{7,2,4,-499122174},{7,2,5,249561087},{7,2,6,499122172},{7,2,7,2},{7,2,8,499122170},{7,3,3,249561090},{7,3,4,249561087},{7,3,5,499122176},{7,3,6,-2},{7,3,7,499122170},{7,3,8,249561082},{7,4,1,1},{7,4,2,-499122174},{7,4,3,249561087},{7,4,4,2},{7,4,5,499122170},{7,4,6,-249561100},{7,4,7,499122168},{7,4,8,-249561111},{7,5,2,249561087},{7,5,3,499122176},{7,5,4,499122170},{7,5,5,249561082},{7,5,6,249561081},{7,5,7,-249561111},{7,5,8,499122156},{7,6,1,499122175},{7,6,2,499122172},{7,6,3,-2},{7,6,4,-249561100},{7,6,5,249561081},{7,6,6,-249561094},{7,6,7,-29},{7,6,8,-19},{7,7,0,1},{7,7,1,-499122174},{7,7,2,2},{7,7,3,499122170},{7,7,4,499122168},{7,7,5,-249561111},{7,7,6,-29},{7,7,7,-51},{7,7,8,-67},{7,8,1,249561087},{7,8,2,499122170},{7,8,3,249561082},{7,8,4,-249561111},{7,8,5,499122156},{7,8,6,-19},{7,8,7,-67},{7,8,8,-249561143},{8,0,8,1},{8,1,5,1},{8,1,6,2},{8,1,7,2},{8,1,8,5},{8,2,3,1},{8,2,4,2},{8,2,5,5},{8,2,6,7},{8,2,7,12},{8,2,8,17},{8,3,2,1},{8,3,3,-1},{8,3,4,5},{8,3,5,3},{8,3,6,3},{8,3,7,17},{8,3,8,13},{8,4,2,2},{8,4,3,5},{8,4,4,12},{8,4,5,17},{8,4,6,19},{8,4,7,46},{8,4,8,49},{8,5,1,1},{8,5,2,5},{8,5,3,3},{8,5,4,17},{8,5,5,13},{8,5,6,11},{8,5,7,49},{8,5,8,37},{8,6,1,2},{8,6,2,7},{8,6,3,3},{8,6,4,19},{8,6,5,11},{8,6,6,7},{8,6,7,47},{8,6,8,29},{8,7,1,2},{8,7,2,12},{8,7,3,17},{8,7,4,46},{8,7,5,49},{8,7,6,47},{8,7,7,144},{8,7,8,129},{8,8,0,1},{8,8,1,5},{8,8,2,17},{8,8,3,13},{8,8,4,49},{8,8,5,37},{8,8,6,29},{8,8,7,129},{8,8,8,93}};
VTYPE vecP[DIM] = {0,0,0,0,6,6,6,24,20};
*/