#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace placeholders; using LL = long long; using ULL = unsigned long long; using VI = vector< int >; using VVI = vector< vector< int > >; using VS = vector< string >; using ISS = istringstream; using OSS = ostringstream; using PII = pair< int, int >; using VPII = vector< pair< int, int > >; template < typename T = int > using VT = vector< T >; template < typename T = int > using VVT = vector< vector< T > >; template < typename T = int > using LIM = numeric_limits< T >; template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; } template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; } template < typename T > struct getv_fmt; template <> struct getv_fmt< int >{ static constexpr const char *fmt = "%d"; }; template <> struct getv_fmt< long long >{ static constexpr const char *fmt = "%lld"; }; template < typename T > void getv( std::vector< T > &v ){ for_each( begin( v ), end( v ), []( T &a ){ scanf( getv_fmt< T >::fmt, &a ); } ); }; template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; } template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); } #define NUMBERED( name, number ) NUMBERED2( name, number ) #define NUMBERED2( name, number ) name ## _ ## number #define REP1( n ) REP2( NUMBERED( REP_COUNTER, __LINE__ ), n ) #define REP2( i, n ) REP3( i, 0, n ) #define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i ) #define GET_REP( a, b, c, F, ... ) F #define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2, REP1 )( __VA_ARGS__ ) #define FOR( e, c ) for ( auto &&e : c ) #define ALL( c ) begin( c ), end( c ) #define AALL( a ) ( remove_all_extents< decltype( a ) >::type * )a, ( remove_all_extents< decltype( a ) >::type * )a + sizeof( a ) / sizeof( remove_all_extents< decltype( a ) >::type ) #define DRANGE( c, p ) begin( c ), begin( c ) + ( p ), end( c ) #define SZ( v ) ( (int)( v ).size() ) #define EXIST( c, e ) ( ( c ).find( e ) != ( c ).end() ) template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; } template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; } #define PB push_back #define EM emplace #define EB emplace_back #define BI back_inserter #define MP make_pair #define fst first #define snd second #define DUMP( x ) cerr << #x << " = " << ( x ) << endl template < typename Number > using Vector = vector< Number >; template < typename Number > using Matrix = vector< vector< Number > >; // 単位行列 // O( N ) template < typename Number > Matrix< Number > identify_matrix( const int N ) { Matrix< Number > res( N, Vector< Number >( N ) ); for ( int i = 0; i < N; ++i ) { res[i][i] = 1; } return res; } // 行列×ベクトル template < typename Number > Vector< Number > operator*( const Matrix< Number > &m, const Vector< Number > &v ) { if ( m[0].size() != v.size() ) { throw "Matrix * Vector : size error"; } Vector< Number > res( m.size() ); for ( int i = 0; i < static_cast( m.size() ); ++i ) { for ( int k = 0; k < static_cast( v.size() ); ++k ) { res[i] += m[i][k] * v[k]; } } return res; } // 行列同士の積 // O( N^3 ) template < typename Number > Matrix< Number > matrix_multiply( const Matrix< Number > &a, const Matrix< Number > &b, unsigned int mod = 0 ) { assert( a[0].size() == b.size() ); Matrix< Number > res( a.size(), Vector< Number >( b[0].size() ) ); for ( int i = 0; i < static_cast( a.size() ); ++i ) { for ( int j = 0; j < static_cast( b[0].size() ); ++j ) { for ( int k = 0; k < static_cast( b.size() ); ++k ) { ( res[i][j] += a[i][k] * b[k][j] ) %= mod; } } } return res; } template < typename Number > inline const Matrix< Number > operator*( const Matrix< Number > &a, const Matrix< Number > &b ) { return matrix_multiply( a, b ); } // 行列累乗 // OO( N^3 log n ) template < typename Number > Matrix< Number > power( Matrix< Number > a, long long n, long long mod = numeric_limits< long long >::max() ) { Matrix< Number > res = identify_matrix< Number >( a.size() ); while ( n ) { if ( n & 1 ) { res = matrix_multiply( res, a, mod ); } a = matrix_multiply( a, a, mod ); n >>= 1; } return res; } template < typename Number > Number solve( const Matrix< Number > &A, const LL N, LL MOD ) { const Matrix< Number > AA = power( A, N, MOD ); return ( AA * VT< LL >( { 1, 1 } ) )[1] % MOD; } int main() { cin.tie( 0 ); ios::sync_with_stdio( false ); cout << setprecision( 12 ) << fixed; LL N; cin >> N; const Matrix< LL > A( { { 1LL, 0LL }, { 1LL, 100LL } } ); cout << solve( A, N - 1, 1000000007 ) << endl; N %= 11; if ( N == 0 ) { cout << 0 << endl; return 0; } REP( i, N - 1 ) { cout << 10; } cout << 1 << endl; return 0; }