結果
| 問題 | No.2595 Parsing Challenge |
| ユーザー |
👑  p-adic
|
| 提出日時 | 2023-12-23 23:17:55 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 36,021 bytes |
| コンパイル時間 | 7,332 ms |
| コンパイル使用メモリ | 325,308 KB |
| 実行使用メモリ | 36,444 KB |
| 最終ジャッジ日時 | 2024-09-27 12:41:05 |
| 合計ジャッジ時間 | 20,693 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
| testcase_03 | RE | - |
| testcase_04 | RE | - |
| testcase_05 | RE | - |
| testcase_06 | RE | - |
| testcase_07 | RE | - |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | RE | - |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | RE | - |
| testcase_24 | RE | - |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | TLE | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
ソースコード
#ifdef INCLUDE_MAIN
struct Compare
{
inline bool operator()( const bigint& n , const bigint& m ) { return n.a.d.size() < m.a.d.size(); }
};
const Compare compare{};
inline void Debug( ... ){}
// inline void Debug( const char& type , const string& s , const int& i_start , const int& i_final ){ cerr << "SyntaxAnalysis " << type << ": " << s.substr( i_start , i_final - i_start + 1 ) << endl; }
// inline void Debug( const char& type , const string& s , const int& i_start , const int& i_final , const bigint& n ){ cerr << "Evaluate " << type << ": " << s.substr( i_start , i_final - i_start + 1 ) << " == " << n << endl; }
bigint& Sum( list<bigint>& a )
{
a.sort( compare );
while( a.size() > 1 ){
auto itr = a.begin();
bigint temp0 = move( *itr );
itr = a.erase( itr );
bigint temp1 = move( *itr );
itr = a.erase( itr );
temp0 += temp1;
a.merge( { move( temp0 ) } , compare );
}
return a.front();
}
bigint& Prod( list<bigint>& a )
{
a.sort( compare );
while( a.size() > 1 ){
auto itr = a.begin();
bigint temp0 = move( *itr );
itr = a.erase( itr );
bigint temp1 = move( *itr );
itr = a.erase( itr );
temp0 *= temp1;
a.merge( { move( temp0 ) } , compare );
}
return a.front();
}
inline bool Digit( const char& c ) { return '0' <= c && c <= '9'; }
inline bigint Number( const string& s , const int& i_start , const int& i_final ) { return bigint( s.substr( i_start , i_final - i_start + 1 ) ); }
using Data = tuple<char,int,int,int,list<int>>;
CEXPR( char , expression , 'e' );
CEXPR( char , number , 'n' );
CEXPR( char , term , 't' );
void SetMatchingParenthesis( const string& s , const int& n , vector<int>& syntax )
{
CEXPR( int , not_searching , 0 );
CEXPR( int , searching_num , 1 );
CEXPR( int , searching_minus , 2 );
int searching_mode = not_searching;
list<int> parenthesis{};
FOR( i , 0 , n ){
if( s[i] == '(' ){
assert( searching_mode == not_searching );
parenthesis.push_back( i );
} else if( s[i] == ')' ){
assert( searching_mode == not_searching );
syntax[syntax[i] = parenthesis.back()] = i;
parenthesis.pop_back();
} else if( Digit( s[i] ) ){
if( searching_mode != searching_num ){
parenthesis.push_back( i );
searching_mode = searching_num;
}
if( i + 1 == n ? true : ! Digit( s[i+1] ) ){
syntax[syntax[i] = parenthesis.back()] = i;
parenthesis.pop_back();
searching_mode = not_searching;
}
} else if( s[i] == '-' ){
if( searching_mode != searching_minus ){
parenthesis.push_back( i );
searching_mode = searching_minus;
}
if( i + 1 == n ? true : s[i+1] != '-' ){
syntax[syntax[i] = parenthesis.back()] = i;
parenthesis.pop_back();
searching_mode = not_searching;
}
}
}
}
void Term( const string& s , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , list<int>& child , int& val_num , list<T2<int>>& factors )
{
FOR_ITR( factors ){
auto& [i,i_final] = *itr;
int j = i_final;
int count = 0;
while( s[j] == ')' ){
assert( i + 1 < j );
if( s[i] == '-' ){
assert( i <= syntax[i] );
count += syntax[i] - i;
i = syntax[i] + 1;
}
if( i == syntax[j] ){
assert( s[i] == '(' );
i++;
j--;
} else {
break;
}
}
child.push_back( val_num );
stack.push_back( { j == i_final ? number : expression , i , j , val_num , {} } );
if( stack.size() > 10000000 ){
while( true ){
COUT( "一体どこでTLEしてるのよ！" );
}
}
val_num++;
neg.push_back( count % 2 == 1 );
}
}
void Expression( const string& s , const int& i_start , const int& i_final , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , list<int>& child , int& val_num )
{
int js = i_final;
list<tuple<int,int,int,list<T2<int>>>> terms{};
terms.push_back( { 0 , 0 , js , {} } );
while( true ){
auto& [count,i,j,factors] = terms.back();
const int& is = syntax[js];
i = is;
if( i_start < i ){
if( s[i-1] == '-' ){
count += i - syntax[i-1];
i = syntax[i-1];
}
}
factors.push_back( { is , js } );
if( i_start == i ){
break;
}
assert( i_start < i );
if( s[i-1] == '+' ){
js = i - 2;
terms.push_back( { 0 , 0 , js , {} } );
} else if( s[i-1] == ')' || Digit( s[i-1] ) ){
js = i - 1;
terms.push_back( { 0 , 0 , js , {} } );
} else {
assert( s[i-1] == '*' );
js = i - 2;
}
}
FOR_ITR( terms ){
auto& [count,i,j,factors] = *itr;
child.push_back( val_num );
stack.push_back( { term , i , j , val_num , {} } );
val_num++;
neg.push_back( count % 2 == 1 );
Term( s , syntax , stack , neg , get<4>( stack.back() ) , val_num , factors );
}
}
void SyntaxAnalysis( const string& s , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , int& val_num )
{
AUTO_ITR( stack );
while( itr_stack != end_stack ){
auto& [type,i_start,i_final,self,child] = *itr_stack;
if( type == expression ){
Expression( s , i_start , i_final , syntax , stack , neg , child , val_num );
}
Debug( type , s , i_start , i_final );
itr_stack++;
}
}
void Evaluate( const string& s , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , vector<list<bigint>>& value )
{
while( !stack.empty() ){
auto& [type,i_start,i_final,self,child] = stack.back();
if( type == expression ){
list<bigint> a{};
while( !child.empty() ){
int& temp = child.back();
bigint& prod = Prod( value[temp] );
if( neg[temp] ){
prod.neg = !prod.neg;
}
a.push_back( move( prod ) );
child.pop_back();
}
value[self] = { move( Sum( a ) ) };
} else if( type == term ){
while( !child.empty() ){
int& temp = child.back();
if( neg[temp] ){
neg[self] = !neg[self];
}
value[self].splice( value[self].begin() , move( value[temp] ) );
child.pop_back();
}
} else if( type == number ){
assert( child.size() == 0 );
value[self] = { move( Number( s , i_start , i_final ) ) };
}
Debug( type , s , i_start , i_final , value[self] );
stack.pop_back();
}
}
inline void Solve()
{
CIN( int , N );
CIN( string , S );
vector<int> syntax( N );
SetMatchingParenthesis( S , N , syntax );
// abort(); // TLEなし。ここまではOK。
list<Data> stack{};
vector<bool> neg{};
int val_num = 0;
stack.push_back( { expression , 0 , N - 1 , val_num , {} } );
neg.push_back( false );
val_num++;
SyntaxAnalysis( S , syntax , stack , neg , val_num );
abort(); // testcase_30でTLE。
vector<list<bigint>> value( val_num );
Evaluate( S , syntax , stack , neg , value );
RETURN( value[0].front() );
}
REPEAT_MAIN(1);
#else // INCLUDE_MAIN
#ifdef INCLUDE_SUB
template <typename PATH> list<PATH> E( const int& i )
{
// list<PATH> answer{};
list<PATH> answer = e<PATH>[i];
// VVV 入力によらない処理は以下に挿入する。
// AAA 入力によらない処理は以上に挿入する。
return answer;
}
template <typename T> inline T F( const T& t ){ return f<T>[t]; }
template <typename T> inline T G( const int& i ){ return g<T>[i]; }
// COMPAREに使用。圧縮時は削除する。
ll Naive( int N , int M , int K )
{
ll answer = N + M + K;
return answer;
}
// COMPAREに使用。圧縮時は削除する。
ll Answer( ll N , ll M , ll K )
{
// START_WATCH;
ll answer = N + M + K;
// // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。
// CEXPR( double , TL , 2000.0 );
// while( CHECK_WATCH( TL ) ){
// }
return answer;
}
// 圧縮時は中身だけ削除する。
inline void Experiment()
{
// CEXPR( int , bound , 10 );
// FOREQ( N , 0 , bound ){
// FOREQ( M , 0 , bound ){
// FOREQ( K , 0 , bound ){
// COUT( N , M , K , ":" , Naive( N , M , K ) );
// }
// }
// // cout << Naive( N ) << ",\n"[N==bound];
// }
}
// 圧縮時は中身だけ削除する。
inline void SmallTest()
{
// CEXPR( int , bound , 10 );
// FOREQ( N , 0 , bound ){
// FOREQ( M , 0 , bound ){
// FOREQ( K , 0 , bound ){
// COMPARE( N , M , K );
// }
// }
// // COMPARE( N );
// }
}
#define INCLUDE_MAIN
#include __FILE__
#else // INCLUDE_SUB
#ifdef INCLUDE_LIBRARY
/*
C-x 3 C-x o C-x C-fによるファイル操作用
BFS:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt
CoordinateCompress:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt
DFSOnTree
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp
Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt
Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt
UnionFind
c:/Users/user/Documents/Programming/Utility/VLTree/UnionFindForest/compress.txt
*/
// VVV 常設でないライブラリは以下に挿入する。
// https://yukicoder.me/problems/no/2595
// で指定されたライブラリ
// https://github.com/SSRS-cp/yuki2595-bigint-lib
// を添付。
#include <vector>
#include <string>
#include <atcoder/convolution>
const int DIGIT = 6;
const int BASE = 1000000;
struct positive_bigint{
std::vector<int> d;
positive_bigint(){
}
positive_bigint(long long X){
while (X > 0){
d.push_back(X % BASE);
X /= BASE;
}
}
positive_bigint(std::string S){
if (S == "0"){
S = "";
}
int L = S.size();
d.resize((L + DIGIT - 1) / DIGIT, 0);
for (int i = L - 1; i >= 0; i -= 6){
for (int j = std::max(i - 5, 0); j <= i; j++){
d[i / DIGIT] *= 10;
d[i / DIGIT] += S[j] - '0';
}
}
std::reverse(d.begin(), d.end());
}
bool empty() const {
return d.empty();
}
int size() const {
return d.size();
}
int& operator [](int i){
return d[i];
}
int operator [](int i) const {
return d[i];
}
};
std::string to_string(const positive_bigint &A){
int N = A.size();
std::string ans;
for (int i = N - 1; i >= 0; i--){
std::string tmp = std::to_string(A[i]);
if (i < N - 1){
ans += std::string(DIGIT - tmp.size(), '0');
}
ans += tmp;
}
if (ans.empty()){
ans = "0";
}
return ans;
}
std::istream& operator >>(std::istream &is, positive_bigint &A){
std::string S;
is >> S;
A = positive_bigint(S);
return is;
}
std::ostream& operator <<(std::ostream &os, positive_bigint &A){
os << to_string(A);
return os;
}
int cmp(const positive_bigint &A, const positive_bigint &B){
int N = A.size();
int M = B.size();
if (N < M){
return -1;
} else if (N > M){
return 1;
} else {
for (int i = N - 1; i >= 0; i--){
if (A[i] < B[i]){
return -1;
}
if (A[i] > B[i]){
return 1;
}
}
return 0;
}
}
bool operator ==(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) == 0;
}
bool operator !=(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) != 0;
}
bool operator <(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) < 0;
}
bool operator >(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) > 0;
}
bool operator <=(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) <= 0;
}
bool operator >=(const positive_bigint &A, const positive_bigint &B){
return cmp(A, B) >= 0;
}
positive_bigint& operator +=(positive_bigint &A, const positive_bigint &B){
int N = A.size();
int M = B.size();
while (N < M){
A.d.push_back(0);
N++;
}
for (int i = 0; i < M; i++){
A[i] += B[i];
}
for (int i = 0; i < N - 1; i++){
if (A[i] >= BASE){
A[i] -= BASE;
A[i + 1]++;
}
}
if (N > 0){
if (A[N - 1] >= BASE){
A.d.push_back(1);
A[N - 1] -= BASE;
}
}
return A;
}
positive_bigint operator +(const positive_bigint &A, const positive_bigint &B){
positive_bigint A2 = A;
A2 += B;
return A2;
}
positive_bigint& operator -=(positive_bigint &A, const positive_bigint &B){
int N = A.size();
int M = B.size();
for (int i = 0; i < M; i++){
A[i] -= B[i];
}
for (int i = 0; i < N - 1; i++){
if (A[i] < 0){
A[i] += BASE;
A[i + 1]--;
}
}
while (!A.empty()){
if (A.d.back() == 0){
A.d.pop_back();
} else {
break;
}
}
return A;
}
positive_bigint operator -(const positive_bigint &A, const positive_bigint &B){
positive_bigint A2 = A;
A2 -= B;
return A2;
}
positive_bigint operator *(const positive_bigint &A, const positive_bigint &B){
if (A.empty() || B.empty()){
return 0;
}
int N = A.size();
int M = B.size();
std::vector<long long> a(N);
for (int i= 0; i < N; i++){
a[i] = A[i];
}
std::vector<long long> b(M);
for (int i = 0; i < M; i++){
b[i] = B[i];
}
std::vector<long long> C = atcoder::convolution_ll(a, b);
for (int i = 0; i < N + M - 2; i++){
C[i + 1] += C[i] / BASE;
C[i] %= BASE;
}
if (C[N + M - 2] >= BASE){
C.resize(N + M);
C[N + M - 1] += C[N + M - 2] / BASE;
C[N + M - 2] %= BASE;
}
positive_bigint ans;
ans.d.resize(C.size());
for (int i = 0; i < C.size(); i++){
ans[i] = C[i];
}
return ans;
}
positive_bigint operator *=(positive_bigint &A, const positive_bigint &B){
A = A * B;
return A;
}
struct bigint{
bool neg = false;
positive_bigint a;
bigint(){
}
bigint(long long X): neg(X < 0), a(abs(X)){
}
bigint(const positive_bigint &X, bool neg = false): neg(neg), a(X){
}
bigint(const std::string &s){
if (!s.empty()){
if (s[0] == '-'){
neg = true;
a = positive_bigint(s.substr(1, s.size() - 1));
} else {
a = positive_bigint(s);
}
}
}
bool empty() const {
return a.empty();
}
int size() const {
return a.size();
}
int& operator [](int i){
return a[i];
}
};
std::string to_string(const bigint &A){
std::string ans;
if (A.neg){
ans += '-';
}
ans += to_string(A.a);
return ans;
}
std::istream& operator >>(std::istream &is, bigint &A){
std::string S;
is >> S;
if (S != "0"){
A = bigint(S);
}
return is;
}
std::ostream& operator <<(std::ostream &os, bigint A){
os << to_string(A);
return os;
}
positive_bigint abs(const bigint &A){
return A.a;
}
int cmp(const bigint &A, const bigint &B){
if (!A.neg){
if (!B.neg){
return cmp(A.a, B.a);
} else {
return 1;
}
} else {
if (!B.neg){
return -1;
} else {
return cmp(B.a, A.a);
}
}
}
bool operator ==(const bigint &A, const bigint &B){
return cmp(A, B) == 0;
}
bool operator !=(const bigint &A, const bigint &B){
return cmp(A, B) != 0;
}
bool operator <(const bigint &A, const bigint &B){
return cmp(A, B) < 0;
}
bool operator >(const bigint &A, const bigint &B){
return cmp(A, B) > 0;
}
bool operator <=(const bigint &A, const bigint &B){
return cmp(A, B) <= 0;
}
bool operator >=(const bigint &A, const bigint &B){
return cmp(A, B) >= 0;
}
bigint operator +(const bigint &A){
return A;
}
bigint operator -(const bigint &A){
bigint A2 = A;
if (!A2.empty()){
A2.neg = !A2.neg;
}
return A2;
}
bigint& operator +=(bigint &A, const bigint &B){
if (A.neg == B.neg){
A.a += B.a;
} else {
int c = cmp(A.a, B.a);
if (c > 0){
A.a -= B.a;
} else if (c < 0){
A.a = B.a - A.a;
A.neg = !A.neg;
} else {
A = 0;
}
}
return A;
}
bigint operator +(const bigint &A, const bigint &B){
bigint A2 = A;
A2 += B;
return A2;
}
bigint& operator -=(bigint &A, const bigint &B){
if (A.neg != B.neg){
A.a += B.a;
} else {
int c = cmp(A.a, B.a);
if (c > 0){
A.a -= B.a;
} else if (c < 0){
A.a = B.a - A.a;
A.neg = !A.neg;
} else {
A = 0;
}
}
return A;
}
bigint operator -(const bigint &A, const bigint &B){
bigint A2 = A;
A2 -= B;
return A2;
}
bigint operator *=(bigint &A, const bigint &B){
if (A.empty() || B.empty()){
A = 0;
} else {
if (B.neg){
A.neg = !A.neg;
}
A.a *= B.a;
}
return A;
}
bigint operator *(const bigint &A, const bigint &B){
bigint A2 = A;
A2 *= B;
return A2;
}
// AAA 常設でないライブラリは以上に挿入する。
#define INCLUDE_SUB
#include __FILE__
#else // INCLUDE_LIBRARY
// #define REACTIVE
// #define USE_GETLINE
#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); if( exec_mode == sample_debug_mode || exec_mode == submission_debug_mode || exec_mode == library_search_mode ){ return 0; } else if( exec_mode == experiment_mode ){ Experiment(); return 0; } else if( exec_mode == small_test_mode ){ SmallTest(); return 0; }; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if( exec_mode == solve_mode ){ if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); } FINISH_MAIN
#define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
#define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
#define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { assert( false ); }
#define SOLVE_ONLY static_assert( __FUNCTION__[0] == 'S' )
#define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
#define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
#define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
#define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
#define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
#define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
#else
#pragma GCC optimize ( "O3" )
#pragma GCC optimize ( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
#define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
#define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
#define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
#define SOLVE_ONLY
#define CERR( ... )
#define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
#define CERR_A( A , N )
#define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
#define CERR_ITR( A )
#define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL
#endif
#ifdef REACTIVE
#define ENDL endl
#else
#define ENDL "\n"
#endif
#ifdef USE_GETLINE
#define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
#define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
#define SET_LL( A ) cin >> A
#define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
#define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
#define CIN_A( LL , A , N ) vector<LL> A( N ); SET_A( A , N );
#endif
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using lld = __float128;
template <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now()
#define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- )
#define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS
#define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); return
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ return; }
// 入出力用
template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const vector<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }
// 算術用
template <typename T> constexpr T PositiveBaseResidue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
template <typename T> constexpr T Residue( const T& a , const T& p ){ return PositiveBaseResidue( a , p < 0 ? -p : p ); }
template <typename T> constexpr T PositiveBaseQuotient( const T& a , const T& p ){ return ( a - PositiveBaseResidue( a , p ) ) / p; }
template <typename T> constexpr T Quotient( const T& a , const T& p ){ return p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); }
#define POWER( ANSWER , ARGUMENT , EXPONENT ) \
static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
TYPE_OF( ARGUMENT ) ANSWER{ 1 }; \
{ \
TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \
TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \
while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \
if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \
ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \
} \
ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \
EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \
} \
} \
#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO ) \
ll ANSWER{ 1 }; \
{ \
ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \
ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \
TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \
while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \
if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \
ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
} \
ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \
} \
} \
#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
ll ANSWER[CONSTEXPR_LENGTH]; \
ll ANSWER_INV[CONSTEXPR_LENGTH]; \
ll INVERSE[CONSTEXPR_LENGTH]; \
{ \
ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \
FOREQ( i , 1 , MAX_INDEX ){ \
ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
} \
ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
FOREQ( i , 2 , MAX_INDEX ){ \
ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
} \
} \
// 二分探索用
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CONST_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CONST_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
static_assert( ! is_same<TYPE_OF( CONST_TARGET ),uint>::value && ! is_same<TYPE_OF( CONST_TARGET ),ull>::value ); \
ll ANSWER = MINIMUM; \
{ \
ll L_BS = MINIMUM; \
ll U_BS = MAXIMUM; \
ANSWER = UPDATE_ANSWER; \
ll EXPRESSION_BS; \
const ll CONST_TARGET_BS = ( CONST_TARGET ); \
ll DIFFERENCE_BS; \
while( L_BS < U_BS ){ \
DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CONST_TARGET_BS; \
CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "-" , #CONST_TARGET , "=" , EXPRESSION_BS , "-" , CONST_TARGET_BS , "=" , DIFFERENCE_BS ); \
if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \
U_BS = UPDATE_U; \
} else { \
L_BS = UPDATE_L; \
} \
ANSWER = UPDATE_ANSWER; \
} \
if( L_BS > U_BS ){ \
CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \
ANSWER = MAXIMUM + 1; \
} else { \
CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS" ); \
CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \
EXPRESSION_BS = ( EXPRESSION ); \
CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CONST_TARGET_BS ? ">" : EXPRESSION_BS < CONST_TARGET_BS ? "<" : "=" ) , CONST_TARGET_BS ); \
if( EXPRESSION_BS DESIRED_INEQUALITY CONST_TARGET_BS ){ \
CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER ); \
} else { \
CERR( "二分探索失敗：" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \
ANSWER = MAXIMUM + 1; \
} \
} \
} \
// 単調増加の時にEXPRESSION >= CONST_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) \
BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) \
// 単調増加の時にEXPRESSION <= CONST_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) \
BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) \
// 単調減少の時にEXPRESSION >= CONST_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) \
BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) \
// 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) \
BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) \
// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return S.lower_bound( t ); }
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); }
// データ構造用
template <typename T> inline T Add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T XorAdd( const T& t0 , const T& t1 ){ return t0 ^ t1; }
template <typename T> inline T Multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
template <typename T> inline const T& Zero() { static const T z = 0; return z; }
template <typename T> inline const T& One() { static const T o = 1; return o; }\
template <typename T> inline T AddInv( const T& t ) { return -t; }
template <typename T> inline T Id( const T& v ) { return v; }
template <typename T> inline T Min( const T& a , const T& b ){ return a < b ? a : b; }
template <typename T> inline T Max( const T& a , const T& b ){ return a < b ? b : a; }
// グリッド問題用
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline T2<int> EnumHW( const int& v ) { return { v / W , v % W }; }
inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; }
const string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// v->wの方向番号を取得
inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back(v);}if(j>0){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back(v);}}}}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<path> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back({v,1});}if(j>0){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back({v,1});}}}}
inline void SetWallOnGrid( const string& Si , const int& i , vector<vector<bool> >& non_wall , const char& walkable = '.' , const char& unwalkable = '#' ){non_wall.push_back(vector<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}
// グラフ用
template <typename PATH> vector<list<PATH> > e;
template <typename T> map<T,T> f;
template <typename T> vector<T> g;
// デバッグ用
#ifdef DEBUG
inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
void AutoCheck( int& exec_mode , const bool& use_getline );
inline void Solve();
inline void Experiment();
inline void SmallTest();
inline void RandomTest();
ll GetRand( const ll& Rand_min , const ll& Rand_max );
int exec_mode;
CEXPR( int , solve_mode , 0 );
CEXPR( int , sample_debug_mode , 1 );
CEXPR( int , submission_debug_mode , 2 );
CEXPR( int , library_search_mode , 3 );
CEXPR( int , experiment_mode , 4 );
CEXPR( int , small_test_mode , 5 );
CEXPR( int , random_test_mode , 6 );
#ifdef USE_GETLINE
CEXPR( bool , use_getline , true );
#else
CEXPR( bool , use_getline , false );
#endif
#else
ll GetRand( const ll& Rand_min , const ll& Rand_max ) { ll answer = time( NULL ); return answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#endif
// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
// VVV 常設ライブラリは以下に挿入する。
// AAA 常設ライブラリは以上に挿入する。
#define INCLUDE_LIBRARY
#include __FILE__
#endif // INCLUDE_LIBRARY
#endif // INCLUDE_SUB
#endif // INCLUDE_MAIN