結果
| 問題 |
No.3316 Make 81181819 with only 0,1,or 8
|
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2025-11-01 14:18:06 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 172 ms / 6,000 ms |
| コード長 | 31,994 bytes |
| コンパイル時間 | 6,421 ms |
| コンパイル使用メモリ | 327,900 KB |
| 実行使用メモリ | 7,720 KB |
| 最終ジャッジ日時 | 2025-11-01 14:18:19 |
| 合計ジャッジ時間 | 10,448 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 22 |
コンパイルメッセージ
main.cpp: In function ‘std::pair<std::vector<Matrix<atcoder::static_modint<998244353> > >, std::vector<atcoder::static_modint<998244353> > > embed_coefs(int, int, int)’:
main.cpp:554:1: warning: control reaches end of non-void function [-Wreturn-type]
554 | }
| ^
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 int 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); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif
//【任意文字列の列挙】O(n |cs|^n)
/*
* 文字集合 cs の要素からなる長さ n の文字列全てを格納したリストを返す．
*/
vector<string> enumerate_all_strings(int n, const string& cs) {
// verify : https://yukicoder.me/problems/no/3015
vector<string> strs;
string s;
// l : 長さ
function<void(int)> rf = [&](int l) {
// 長さが n の場合は記録
if (l == n) {
strs.push_back(s);
return;
}
// c : s[l]
repe(c, cs) {
s.push_back(c);
rf(l + 1);
s.pop_back();
}
};
rf(0);
return strs;
}
// 愚直
constexpr int N_MAX = 100000000;
int ans[N_MAX + 1];
void init() {
vi cand;
auto ss = enumerate_all_strings(8, "018");
repe(s, ss) cand.push_back(stoi(s));
sort(all(cand));
ans[0] = 0;
repi(i, 1, N_MAX) ans[i] = INF;
repi(i, 0, N_MAX) {
if (i % 1000000 == 0) dump("i:", i);
repe(x, cand) {
if (i + x > N_MAX) break;
chmin(ans[i + x], ans[i] + 1);
}
}
}
// 愚直解を返す
mint naive(const string& s) {
int n = stoi("0" + s);
if (n > N_MAX) exit(-1);
return mint(ans[n]);
}
//【行列】
/*
* Matrix<T>(int n, int m) : O(n m)
* n×m 零行列で初期化する．
*
* Matrix<T>(int n) : O(n^2)
* n×n 単位行列で初期化する．
*
* Matrix<T>(vvT a) : O(n m)
* 二次元配列 a[0..n)[0..m) の要素で初期化する．
*
* bool empty() : O(1)
* 行列が空かを返す．
*
* A + B : O(n m)
* n×m 行列 A, B の和を返す．+= も使用可．
*
* A - B : O(n m)
* n×m 行列 A, B の差を返す．-= も使用可．
*
* c * A ／ A * c : O(n m)
* n×m 行列 A とスカラー c のスカラー積を返す．*= も使用可．
*
* A * x : O(n m)
* n×m 行列 A と n 次元列ベクトル x の積を返す．
*
* x * A : O(n m)（やや遅い）
* m 次元行ベクトル x と n×m 行列 A の積を返す．
*
* A * B : O(n m l)
* n×m 行列 A と m×l 行列 B の積を返す．
*
* Mat pow(ll d) : O(n^3 log d)
* 自身を d 乗した行列を返す．
*/
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) {
// verify : https://judge.yosupo.jp/problem/matrix_product
// inline を付けて [] でアクセスするとなぜか v[] への直接アクセスより速くなった．
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 {
// verify : https://judge.yosupo.jp/problem/matrix_product
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 {
// verify : https://judge.yosupo.jp/problem/pow_of_matrix
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))
/*
* 行基本変形（行交換なし）で n×m 行列 A を行簡約形に変形し，ピボット位置のリストを返す．
*/
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)
/*
* n 次正方行列 mat の逆行列を返す（存在しなければ空）
*/
template <class T>
Matrix<T> inverse_matrix(const Matrix<T>& mat) {
// verify : https://judge.yosupo.jp/problem/inverse_matrix
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;
}
// 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 len_max とか LB_max とかを指定する．
pair<vector<Matrix<mint>>, vm> embed_coefs(int COL, int len_max = INF, int LB_max = INF) {
vector<string> ss{ "" };
int idx = 0;
vector<pii> piv_prv;
repi(len, 0, INF) {
dump("----------- len:", len, "--------------");
int L = sz(ss); int LB = min(L, LB_max);
dump("L:", L);
// (i,j) 成分が naive(ss[i] + ss[j]) であるような行列 mat を得る．
Matrix<mint> mat(L, LB);
rep(i, L) rep(j, LB) mat[i][j] = naive(ss[i] + ss[j]);
//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);
dump("piv[0.." + to_string(sz(piv)) + "):"); 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．
if (len == len_max || (sz(piv) > 0 && sz(piv) == sz(piv_prv))) { // たまに失敗する．
int DIM = sz(piv);
// 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));
// 基底の変換行列 P を得る．
Matrix<mint> matP(DIM, DIM);
rep(i, DIM) rep(j, DIM) matP[i][j] = naive(ss[is[i]] + ss[js[j]]);
// P の逆行列 P_inv を得る．
auto matP_inv = inverse_matrix(matP);
// 各文字に対応する表現行列を得る．
vector<Matrix<mint>> matAs(COL, Matrix<mint>(DIM, DIM));
rep(c, COL) {
char ch = '0' + c;
rep(i, DIM) rep(j, DIM) matAs[c][i][j] = naive(ss[is[i]] + ch + ss[js[j]]);
matAs[c] = matAs[c] * matP_inv;
}
// 右端を閉じるためのベクトルを得る．
vm vecP(DIM);
rep(i, DIM) vecP[i] = matP[i][0];
// スパース埋め込み用の文字列を出力する．
vector<tuple<int, int, mint>> elems; vi offsets{ 0 };
rep(c, COL) {
rep(i, DIM) rep(j, DIM) {
if (matAs[c][i][j] != 0) elems.emplace_back(i, j, matAs[c][i][j]);
}
offsets.push_back(sz(elems));
}
auto to_signed_string = [](mint x) {
int v = x.val();
int mod = mint::mod();
if (2 * v > mod) v -= mod;
return to_string(v);
};
string eb = "constexpr int DIM = ";
eb += to_string(DIM);
eb += ";\n";
eb += "constexpr int COL = ";
eb += to_string(COL);
eb += ";\n";
eb += "tuple<int, int, VTYPE> matAs[] = {";
for (auto [i, j, v] : elems) {
eb += "{";
eb += to_string(i);
eb += ",";
eb += to_string(j);
eb += ",";
eb += to_signed_string(v);
eb += "},";
}
eb.pop_back();
eb += "};\n";
eb += "int offset[COL + 1] = {";
repi(c, 0, COL) eb += to_string(offsets[c]) + ",";
eb.pop_back();
eb += "};\n";
eb += "VTYPE vecP[DIM] = {";
rep(i, DIM) eb += to_signed_string(vecP[i]) + ",";
eb.pop_back();
eb += "};\n";
cout << eb;
exit(0);
return { matAs, vecP };
}
// 基底ガチャ
mt19937_64 mt((int)time(NULL)); shuffle(ss.begin() + idx, ss.end(), mt);
// 次に長い文字列たちを ss に追加する．
int nidx = sz(ss);
repi(i, idx, nidx - 1) rep(c, COL) {
ss.push_back(ss[i]);
ss.back().push_back('0' + c);
}
idx = nidx;
piv_prv = move(piv);
}
}
template <class VTYPE>
VTYPE solve(const string& s) {
// --------------- embed_coefs() からの出力を貼る ----------------
constexpr int DIM = 31;
constexpr int COL = 10;
tuple<int, int, VTYPE> matAs[] = { {0,0,1},{1,1,1},{2,9,1},{3,4,1},{3,9,-1},{3,11,1},{4,4,1},{5,12,-249561087},{6,2,-1},{6,6,1},{6,9,1},{7,12,1},{8,8,1},{8,10,-1},{8,12,-249561087},{9,9,1},{10,12,-249561087},{11,11,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,15,1},{16,12,1},{17,2,1},{17,3,1},{17,9,-1},{17,12,2},{17,13,-1},{17,16,-1},{17,17,1},{17,18,-1},{18,4,1},{18,9,-1},{18,11,1},{19,19,1},{20,12,1},{21,12,1},{22,19,1},{23,8,1},{23,10,-1},{23,12,-249561087},{24,1,1},{24,3,-1},{24,6,-1},{24,9,1},{24,12,-249561088},{24,13,1},{24,16,1},{24,17,-1},{24,18,1},{24,19,-1},{25,1,1},{25,3,-1},{25,6,-1},{25,9,1},{25,12,-249561088},{25,13,1},{25,16,1},{25,17,-1},{25,18,1},{25,19,-1},{26,10,1},{27,12,-249561087},{28,12,-249561087},{29,10,1},{30,25,1},{0,6,1},{1,6,1},{2,9,1},{3,3,1},{4,4,1},{4,9,-1},{4,11,1},{5,10,1},{6,2,-1},{6,6,1},{6,9,1},{7,12,1},{8,14,1},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{16,12,1},{17,2,1},{17,12,1},{17,13,-1},{18,3,1},{19,13,1},{20,12,1},{21,12,1},{22,13,1},{23,14,1},{24,28,1},{25,28,1},{26,5,1},{26,10,-1},{26,12,-499122174},{26,14,-1},{27,12,-249561087},{28,12,-249561087},{29,5,1},{29,10,-1},{29,12,-499122174},{29,14,-1},{30,12,-499122175},{0,9,1},{1,9,1},{2,9,1},{3,16,1},{4,4,1},{4,9,-1},{4,11,1},{5,22,1},{6,9,1},{7,12,1},{8,19,1},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,19,1},{15,9,1},{16,12,1},{17,9,1},{18,16,1},{19,12,1},{20,7,1},{20,12,1},{20,16,-1},{21,7,1},{21,12,1},{21,16,-1},{22,12,1},{23,12,-249561087},{24,12,-249561087},{24,19,-1},{24,22,1},{25,29,1},{26,1,1},{26,3,-1},{26,6,-1},{26,9,1},{26,12,-249561088},{26,13,1},{26,16,1},{26,17,-1},{26,18,1},{26,19,-1},{27,12,-249561087},{28,12,-249561087},{29,24,1},{30,1,1},{30,3,-1},{30,6,-1},{30,9,1},{30,12,-249561088},{30,13,1},{30,16,1},{30,17,-1},{30,18,1},{30,19,-1},{0,4,1},{1,4,1},{2,4,1},{3,12,1},{4,4,1},{4,9,-1},{4,11,1},{5,21,1},{6,4,1},{7,7,1},{7,12,1},{7,16,-1},{8,21,1},{9,4,1},{10,12,-249561087},{11,4,1},{12,12,1},{13,12,1},{14,21,1},{15,4,1},{16,12,1},{17,4,1},{18,12,1},{19,12,1},{20,8,1},{20,10,-1},{20,12,-249561087},{21,8,1},{21,10,-1},{21,12,-249561087},{22,12,1},{23,12,-249561087},{24,12,-249561087},{25,30,1},{26,12,-249561087},{27,10,1},{28,10,1},{29,25,1},{30,12,-249561087},{0,3,1},{1,3,1},{2,3,1},{3,2,1},{3,3,1},{3,4,1},{3,9,-2},{3,12,2},{3,13,-1},{3,16,-1},{3,17,1},{3,18,-1},{4,4,1},{4,9,-1},{4,11,1},{5,23,1},{6,3,1},{7,4,1},{7,9,-1},{7,15,1},{8,2,-1},{8,3,-1},{8,9,1},{8,12,-1},{8,13,1},{8,15,1},{8,16,1},{8,17,-1},{8,18,1},{9,4,1},{9,9,-1},{9,11,1},{10,12,-249561087},{11,4,1},{11,9,-1},{11,11,1},{12,12,1},{13,12,1},{14,23,1},{15,3,1},{16,2,1},{16,3,1},{16,4,1},{16,9,-2},{16,12,2},{16,13,-1},{16,16,-1},{16,17,1},{16,18,-1},{17,4,1},{17,9,-1},{17,11,1},{18,12,1},{19,12,1},{20,19,1},{21,14,1},{22,12,1},{23,19,1},{24,27,1},{25,25,1},{26,12,-249561087},{27,12,-249561087},{27,19,-1},{27,22,1},{28,5,1},{28,10,-1},{28,12,-499122174},{28,14,-1},{29,1,1},{29,3,-1},{29,6,-1},{29,9,1},{29,12,-249561088},{29,13,1},{29,16,1},{29,17,-1},{29,18,1},{29,19,-1},{30,27,1},{0,7,1},{1,7,1},{2,7,1},{3,18,1},{4,3,1},{5,14,1},{6,7,1},{7,12,-1},{7,13,1},{7,18,1},{8,13,1},{9,3,1},{10,12,-249561087},{11,3,1},{12,12,1},{13,7,1},{13,12,1},{13,16,-1},{14,14,1},{15,16,1},{16,18,1},{17,3,1},{18,12,1},{19,7,1},{19,12,1},{19,16,-1},{20,13,1},{21,12,-249561087},{22,7,1},{22,12,1},{22,16,-1},{23,13,1},{24,26,1},{25,12,-499122175},{26,12,-249561087},{27,12,-249561087},{28,24,1},{29,12,-249561087},{30,26,1},{0,8,1},{1,8,1},{2,15,1},{3,4,1},{3,9,-1},{3,17,1},{4,17,1},{5,12,-249561087},{6,15,1},{7,16,1},{8,20,1},{9,17,1},{10,12,-249561087},{11,4,1},{11,9,-1},{11,17,1},{12,12,1},{13,2,-1},{13,3,-1},{13,9,1},{13,12,-1},{13,13,1},{13,15,1},{13,16,1},{13,17,-1},{13,18,1},{14,12,-249561087},{15,7,1},{15,12,1},{15,16,-1},{16,16,1},{17,16,1},{18,2,1},{18,3,1},{18,4,1},{18,9,-2},{18,12,2},{18,13,-1},{18,16,-1},{18,17,1},{18,18,-1},{19,8,1},{19,10,-1},{19,12,-249561087},{20,12,1},{21,19,1},{22,8,1},{22,10,-1},{22,12,-249561087},{23,20,1},{24,24,1},{25,12,-499122175},{26,12,-249561087},{27,12,-249561087},{28,1,1},{28,3,-1},{28,6,-1},{28,9,1},{28,12,-249561088},{28,13,1},{28,16,1},{28,17,-1},{28,18,1},{28,19,-1},{29,12,-249561087},{30,24,1},{0,5,1},{1,5,1},{1,10,-1},{1,12,-249561087},{2,2,1},{2,4,1},{2,9,-1},{3,2,1},{3,4,1},{3,9,-2},{3,11,1},{3,12,1},{3,13,-1},{4,2,1},{4,4,1},{4,9,-1},{4,12,1},{4,13,-1},{5,10,1},{6,2,1},{6,4,1},{6,9,-1},{7,12,1},{8,8,1},{8,10,-1},{8,12,-249561087},{9,2,1},{9,4,1},{9,9,-1},{9,12,1},{9,13,-1},{10,12,-249561087},{11,2,1},{11,4,1},{11,9,-2},{11,11,1},{11,12,1},{11,13,-1},{12,12,1},{13,13,1},{14,12,-249561087},{15,8,1},{15,10,-1},{15,12,-249561087},{16,12,1},{17,12,1},{18,2,1},{18,4,1},{18,9,-2},{18,11,1},{18,12,1},{18,13,-1},{19,14,1},{20,12,1},{21,13,1},{22,10,1},{22,12,249561087},{22,14,1},{23,8,1},{23,10,-1},{23,12,-249561087},{24,25,1},{25,12,-499122175},{26,10,1},{27,12,-249561087},{28,12,-249561087},{29,10,1},{30,25,1},{0,1,1},{1,1,1},{2,11,1},{3,3,1},{4,4,1},{4,9,-1},{4,11,1},{5,5,1},{5,10,-1},{5,12,-499122174},{5,14,-1},{6,2,-1},{6,6,1},{6,11,1},{7,12,1},{8,14,1},{9,11,1},{10,12,-249561087},{11,11,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{15,3,1},{15,9,-1},{15,12,1},{15,13,-1},{15,16,-1},{15,17,1},{15,18,-1},{15,19,1},{16,12,1},{17,2,1},{17,3,1},{17,9,-1},{17,12,2},{17,13,-1},{17,16,-1},{17,17,1},{17,18,-1},{18,3,1},{19,19,1},{20,12,1},{21,12,1},{22,22,1},{23,14,1},{24,12,-499122175},{25,12,-499122175},{26,5,1},{26,10,-1},{26,12,-499122174},{26,14,-1},{27,12,-249561087},{28,12,-249561087},{29,5,1},{29,10,-1},{29,12,-499122174},{29,14,-1},{30,12,-499122175},{0,2,1},{1,2,1},{2,9,1},{3,16,1},{4,4,1},{4,9,-1},{4,11,1},{5,24,1},{6,9,1},{7,7,1},{7,12,1},{7,16,-1},{8,12,-249561087},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{16,12,1},{17,2,1},{17,12,1},{17,13,-1},{18,16,1},{19,13,1},{20,7,1},{20,12,1},{20,16,-1},{21,7,1},{21,12,1},{21,16,-1},{22,13,1},{23,12,-249561087},{24,12,-499122175},{25,12,-499122175},{26,24,1},{27,12,-249561087},{28,12,-249561087},{29,24,1},{30,12,-499122175} };
int offset[COL + 1] = { 0,66,109,166,205,284,323,389,457,516,557 };
VTYPE vecP[DIM] = { 0,1,2,4,3,7,1,5,6,2,6,2,4,4,5,2,4,2,4,4,5,5,4,5,6,6,6,6,6,6,6 };
// --------------------------------------------------------------
// ここ以降は書き換えなくて良い．
array<VTYPE, DIM> dp;
dp.fill(0);
dp[0] = 1;
auto apply = [&](const array<VTYPE, DIM>& x, int col) {
array<VTYPE, DIM> z;
z.fill(0);
repi(pt, offset[col], offset[col + 1] - 1) {
auto [i, j, v] = matAs[pt];
z[j] += x[i] * v;
}
return z;
};
repe(c, s) {
dp = apply(dp, c - '0');
}
VTYPE res = 0;
rep(i, DIM) res += dp[i] * vecP[i];
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行列を復元する．
//【使い方】
// 1. mint naive(文字列) を実装する．
// 2. embed_coefs(文字の種類数); を実行する．
// 3. 出力を solve() 内に貼る．
// 4. auto dp = solve<答えの型>(文字列) で勝手に DP してくれる．
// init(); embed_coefs(10, 4, INF);
vi cand;
auto ss = enumerate_all_strings(8, "018");
repe(s, ss) cand.push_back(stoi(s));
int T;
cin >> T;
rep(hoge, T) {
int n;
cin >> n;
n = 81181819 - n;
int cnt = solve<mint>(to_string(n)).val();
dump(cnt);
vi res;
while (cnt > 0) {
repe(x, cand) {
int ncnt = solve<mint>(to_string(n - x)).val();
if (ncnt == cnt - 1) {
res.push_back(x);
n -= x;
cnt = ncnt;
break;
}
}
}
cout << sz(res) << endl;
repe(x, res) cout << x << endl;
}
}
/*
----------- len: 0 --------------
L: 1
piv[0..0):
----------- len: 1 --------------
L: 11
piv[0..10):
(0,2) (2,0) (3,3) (4,4) (5,1) (6,5) (7,6) (8,7) (9,8) (10,10)
----------- len: 2 --------------
L: 111
piv[0..24):
(0,1) (1,0) (2,2) (3,3) (4,4) (6,5) (7,6) (8,8) (9,9) (10,10) (18,11) (27,13) (29,14) (33,15) (34,16) (35,31) (37,36) (63,17) (64,21) (65,33) (66,35) (70,18) (93,56) (97,101)
----------- len: 3 --------------
L: 1111
piv[0..29):
(0,1) (1,0) (2,2) (3,3) (4,4) (6,5) (7,6) (8,8) (9,9) (10,10) (11,11) (18,12) (19,13) (22,14) (23,15) (24,16) (30,46) (32,22) (40,911) (51,23) (56,19) (74,35) (93,25) (95,36) (104,30) (1042,20) (1045,34) (1046,21) (1048,28)
----------- len: 4 --------------
L: 11111
piv[0..31):
(0,1) (1,0) (2,2) (3,3) (4,4) (6,5) (7,6) (8,8) (9,9) (10,10) (11,11) (18,12) (19,13) (22,14) (23,15) (24,16) (30,46) (32,22) (40,610) (51,23) (56,19) (74,35) (93,25) (95,36) (104,30) (129,20) (253,21) (324,28) (1031,34) (1293,38) (1294,31)
constexpr int DIM = 31;
constexpr int COL = 10;
tuple<int, int, VTYPE> matAs[] = {{0,0,1},{1,1,1},{2,9,1},{3,4,1},{3,9,-1},{3,11,1},{4,4,1},{5,12,-249561087},{6,2,-1},{6,6,1},{6,9,1},{7,12,1},{8,8,1},{8,10,-1},{8,12,-249561087},{9,9,1},{10,12,-249561087},{11,11,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,15,1},{16,12,1},{17,2,1},{17,3,1},{17,9,-1},{17,12,2},{17,13,-1},{17,16,-1},{17,17,1},{17,18,-1},{18,4,1},{18,9,-1},{18,11,1},{19,19,1},{20,12,1},{21,12,1},{22,19,1},{23,8,1},{23,10,-1},{23,12,-249561087},{24,1,1},{24,3,-1},{24,6,-1},{24,9,1},{24,12,-249561088},{24,13,1},{24,16,1},{24,17,-1},{24,18,1},{24,19,-1},{25,1,1},{25,3,-1},{25,6,-1},{25,9,1},{25,12,-249561088},{25,13,1},{25,16,1},{25,17,-1},{25,18,1},{25,19,-1},{26,10,1},{27,12,-249561087},{28,12,-249561087},{29,10,1},{30,25,1},{0,6,1},{1,6,1},{2,9,1},{3,3,1},{4,4,1},{4,9,-1},{4,11,1},{5,10,1},{6,2,-1},{6,6,1},{6,9,1},{7,12,1},{8,14,1},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{16,12,1},{17,2,1},{17,12,1},{17,13,-1},{18,3,1},{19,13,1},{20,12,1},{21,12,1},{22,13,1},{23,14,1},{24,28,1},{25,28,1},{26,5,1},{26,10,-1},{26,12,-499122174},{26,14,-1},{27,12,-249561087},{28,12,-249561087},{29,5,1},{29,10,-1},{29,12,-499122174},{29,14,-1},{30,12,-499122175},{0,9,1},{1,9,1},{2,9,1},{3,16,1},{4,4,1},{4,9,-1},{4,11,1},{5,22,1},{6,9,1},{7,12,1},{8,19,1},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,19,1},{15,9,1},{16,12,1},{17,9,1},{18,16,1},{19,12,1},{20,7,1},{20,12,1},{20,16,-1},{21,7,1},{21,12,1},{21,16,-1},{22,12,1},{23,12,-249561087},{24,12,-249561087},{24,19,-1},{24,22,1},{25,29,1},{26,1,1},{26,3,-1},{26,6,-1},{26,9,1},{26,12,-249561088},{26,13,1},{26,16,1},{26,17,-1},{26,18,1},{26,19,-1},{27,12,-249561087},{28,12,-249561087},{29,24,1},{30,1,1},{30,3,-1},{30,6,-1},{30,9,1},{30,12,-249561088},{30,13,1},{30,16,1},{30,17,-1},{30,18,1},{30,19,-1},{0,4,1},{1,4,1},{2,4,1},{3,12,1},{4,4,1},{4,9,-1},{4,11,1},{5,21,1},{6,4,1},{7,7,1},{7,12,1},{7,16,-1},{8,21,1},{9,4,1},{10,12,-249561087},{11,4,1},{12,12,1},{13,12,1},{14,21,1},{15,4,1},{16,12,1},{17,4,1},{18,12,1},{19,12,1},{20,8,1},{20,10,-1},{20,12,-249561087},{21,8,1},{21,10,-1},{21,12,-249561087},{22,12,1},{23,12,-249561087},{24,12,-249561087},{25,30,1},{26,12,-249561087},{27,10,1},{28,10,1},{29,25,1},{30,12,-249561087},{0,3,1},{1,3,1},{2,3,1},{3,2,1},{3,3,1},{3,4,1},{3,9,-2},{3,12,2},{3,13,-1},{3,16,-1},{3,17,1},{3,18,-1},{4,4,1},{4,9,-1},{4,11,1},{5,23,1},{6,3,1},{7,4,1},{7,9,-1},{7,15,1},{8,2,-1},{8,3,-1},{8,9,1},{8,12,-1},{8,13,1},{8,15,1},{8,16,1},{8,17,-1},{8,18,1},{9,4,1},{9,9,-1},{9,11,1},{10,12,-249561087},{11,4,1},{11,9,-1},{11,11,1},{12,12,1},{13,12,1},{14,23,1},{15,3,1},{16,2,1},{16,3,1},{16,4,1},{16,9,-2},{16,12,2},{16,13,-1},{16,16,-1},{16,17,1},{16,18,-1},{17,4,1},{17,9,-1},{17,11,1},{18,12,1},{19,12,1},{20,19,1},{21,14,1},{22,12,1},{23,19,1},{24,27,1},{25,25,1},{26,12,-249561087},{27,12,-249561087},{27,19,-1},{27,22,1},{28,5,1},{28,10,-1},{28,12,-499122174},{28,14,-1},{29,1,1},{29,3,-1},{29,6,-1},{29,9,1},{29,12,-249561088},{29,13,1},{29,16,1},{29,17,-1},{29,18,1},{29,19,-1},{30,27,1},{0,7,1},{1,7,1},{2,7,1},{3,18,1},{4,3,1},{5,14,1},{6,7,1},{7,12,-1},{7,13,1},{7,18,1},{8,13,1},{9,3,1},{10,12,-249561087},{11,3,1},{12,12,1},{13,7,1},{13,12,1},{13,16,-1},{14,14,1},{15,16,1},{16,18,1},{17,3,1},{18,12,1},{19,7,1},{19,12,1},{19,16,-1},{20,13,1},{21,12,-249561087},{22,7,1},{22,12,1},{22,16,-1},{23,13,1},{24,26,1},{25,12,-499122175},{26,12,-249561087},{27,12,-249561087},{28,24,1},{29,12,-249561087},{30,26,1},{0,8,1},{1,8,1},{2,15,1},{3,4,1},{3,9,-1},{3,17,1},{4,17,1},{5,12,-249561087},{6,15,1},{7,16,1},{8,20,1},{9,17,1},{10,12,-249561087},{11,4,1},{11,9,-1},{11,17,1},{12,12,1},{13,2,-1},{13,3,-1},{13,9,1},{13,12,-1},{13,13,1},{13,15,1},{13,16,1},{13,17,-1},{13,18,1},{14,12,-249561087},{15,7,1},{15,12,1},{15,16,-1},{16,16,1},{17,16,1},{18,2,1},{18,3,1},{18,4,1},{18,9,-2},{18,12,2},{18,13,-1},{18,16,-1},{18,17,1},{18,18,-1},{19,8,1},{19,10,-1},{19,12,-249561087},{20,12,1},{21,19,1},{22,8,1},{22,10,-1},{22,12,-249561087},{23,20,1},{24,24,1},{25,12,-499122175},{26,12,-249561087},{27,12,-249561087},{28,1,1},{28,3,-1},{28,6,-1},{28,9,1},{28,12,-249561088},{28,13,1},{28,16,1},{28,17,-1},{28,18,1},{28,19,-1},{29,12,-249561087},{30,24,1},{0,5,1},{1,5,1},{1,10,-1},{1,12,-249561087},{2,2,1},{2,4,1},{2,9,-1},{3,2,1},{3,4,1},{3,9,-2},{3,11,1},{3,12,1},{3,13,-1},{4,2,1},{4,4,1},{4,9,-1},{4,12,1},{4,13,-1},{5,10,1},{6,2,1},{6,4,1},{6,9,-1},{7,12,1},{8,8,1},{8,10,-1},{8,12,-249561087},{9,2,1},{9,4,1},{9,9,-1},{9,12,1},{9,13,-1},{10,12,-249561087},{11,2,1},{11,4,1},{11,9,-2},{11,11,1},{11,12,1},{11,13,-1},{12,12,1},{13,13,1},{14,12,-249561087},{15,8,1},{15,10,-1},{15,12,-249561087},{16,12,1},{17,12,1},{18,2,1},{18,4,1},{18,9,-2},{18,11,1},{18,12,1},{18,13,-1},{19,14,1},{20,12,1},{21,13,1},{22,10,1},{22,12,249561087},{22,14,1},{23,8,1},{23,10,-1},{23,12,-249561087},{24,25,1},{25,12,-499122175},{26,10,1},{27,12,-249561087},{28,12,-249561087},{29,10,1},{30,25,1},{0,1,1},{1,1,1},{2,11,1},{3,3,1},{4,4,1},{4,9,-1},{4,11,1},{5,5,1},{5,10,-1},{5,12,-499122174},{5,14,-1},{6,2,-1},{6,6,1},{6,11,1},{7,12,1},{8,14,1},{9,11,1},{10,12,-249561087},{11,11,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{15,3,1},{15,9,-1},{15,12,1},{15,13,-1},{15,16,-1},{15,17,1},{15,18,-1},{15,19,1},{16,12,1},{17,2,1},{17,3,1},{17,9,-1},{17,12,2},{17,13,-1},{17,16,-1},{17,17,1},{17,18,-1},{18,3,1},{19,19,1},{20,12,1},{21,12,1},{22,22,1},{23,14,1},{24,12,-499122175},{25,12,-499122175},{26,5,1},{26,10,-1},{26,12,-499122174},{26,14,-1},{27,12,-249561087},{28,12,-249561087},{29,5,1},{29,10,-1},{29,12,-499122174},{29,14,-1},{30,12,-499122175},{0,2,1},{1,2,1},{2,9,1},{3,16,1},{4,4,1},{4,9,-1},{4,11,1},{5,24,1},{6,9,1},{7,7,1},{7,12,1},{7,16,-1},{8,12,-249561087},{9,9,1},{10,12,-249561087},{11,9,1},{12,12,1},{13,12,1},{14,12,-249561087},{15,2,1},{16,12,1},{17,2,1},{17,12,1},{17,13,-1},{18,16,1},{19,13,1},{20,7,1},{20,12,1},{20,16,-1},{21,7,1},{21,12,1},{21,16,-1},{22,13,1},{23,12,-249561087},{24,12,-499122175},{25,12,-499122175},{26,24,1},{27,12,-249561087},{28,12,-249561087},{29,24,1},{30,12,-499122175}};
int offset[COL + 1] = {0,66,109,166,205,284,323,389,457,516,557};
VTYPE vecP[DIM] = {0,1,2,4,3,7,1,5,6,2,6,2,4,4,5,2,4,2,4,4,5,5,4,5,6,6,6,6,6,6,6};
*/