// {{{ #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define VARGS_(_4, _3, _2, _1, N, ...) N #define VARGS(...) VARGS_(__VA_ARGS__, 4, 3, 2, 1) #define CONCAT_(a, b) a##b #define CONCAT(a, b) CONCAT_(a, b) #define FOR_1(x) for (auto& x) #define FOR_2(i, n) for (auto i = remove_reference_t<decltype(n)>{0}; i < (n); ++i) #define FOR_3(i, b, e) for (auto i = remove_reference_t<decltype(e)>{b}; i < (e); ++i) #define FOR_4(i, b, e, s) for (auto i = remove_reference_t<decltype(e)>{b}; i < (e); i += s) #define FORD_2(i, n) for (auto i = (n) - 1; i >= 0; --i) #define FORD_3(i, b, e) for (auto i = remove_reference_t<decltype(b)>{(e) - 1}; i >= (b); --i) #define FORD_4(i, b, e, s) for (auto i = remove_reference_t<decltype(b)>{(e) - 1}; i >= (b); i -= s) #define FOR(...) CONCAT(FOR_, VARGS(__VA_ARGS__))(__VA_ARGS__) #define FORD(...) CONCAT(FORD_, VARGS(__VA_ARGS__))(__VA_ARGS__) #define B begin() #define E end() #define RB rbegin() #define RE rend() #define A(x) std::begin(x), std::end(x) #define RA(x) std::rbegin(x), std::rend(x) #define RANGE(x, b, e) (std::begin(x) + (b)), (std::begin(x) + (e)) #define MP make_pair #define MT make_tuple #define FS first #define ND second #define G1 get<0> #define G2 get<1> #define G3 get<2> #define G4 get<3> #define G5 get<4> #define PB push_back #define PP pop_back #define PF push_front #define FF pop_front #define RS resize #define INF(T) numeric_limits<T>::max() #define L0(_expr) [&]() { return _expr; } #define L1(_expr) [&](auto&& _1) { return _expr; } #define L2(_expr) [&](auto&& _1, auto&& _2) { return _expr; } #define _ CONCAT(_unused_, __COUNTER__) #define MIN min_element #define MAX max_element #define SUM accumulate using namespace std; using LL = long long; using LD = long double; using ULL = unsigned long long; template<class T1,class T2> using P = pair<T1,T2>; using PII = P<int,int>; using PLL = P<LL,LL>; using PLD = P<LD,LD>; template<class T> using V = vector<T>; using VI = V<int>; using VLL = V<LL>; using VLD = V<LD>; using VB = V<bool>; using VS = V<string>; template<class T,class Comp=greater<T>> using PQ = priority_queue<T,V<T>,Comp>; template<class T> int sz(const T& x) { return size(x); } template<class T> bool amin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template<class T> bool amax(T& a, const T& b) { if (b > a) { a = b; return true; } return false; } /* find_by_order(k) - k'th largest counting from 0; order_of_key(k) - number of items strictly smaller than k; join(other), split(k, other) - all keys in other greater than in *(this). */ template<class K,class V,class Comp=less<K>> using ordered_map = __gnu_pbds::tree<K,V,Comp, __gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; template<class T,class Comp=less<T>> using ordered_set = ordered_map<T,__gnu_pbds::null_type,Comp>; string _sep = " ", _ignore; bool _newline = true; stack<ostream*> _ostack; stack<istream*> _istack; template<class TH> void out(const TH& h) { if (_newline) _newline = false; else *_ostack.top() << _sep; *_ostack.top() << h; } template<class TH,class...TA> void out(const TH& h, const TA&... a) { out(h); out(a...); } void outln() { *_ostack.top() << '\n'; _newline = true; } template<class...TA> void outln(const TA&... a) { out(a...); outln(); } template<class TH> void in(TH& h) { *_istack.top() >> h; } template<class TH,class...TA> void in(TH& h, TA&... a) { in(h); in(a...); } template<class...TA> void EXIT(const TA&... a) { outln(a...); exit(0); } #ifdef SPONGE template<class...TA> void dbg(const TA&... a) { _ostack.push(&cerr); cerr << "\033[1;33m"; outln(a...); cerr << "\033[0m"; _ostack.pop(); } #else #define dbg(...) #endif struct _upgrade_io { _upgrade_io(bool ok) { _ostack.push(&cout); _istack.push(&cin); if (ok) { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout.precision(15); cout.setf(ios::fixed, ios::floatfield); }} } _upgrade_io(true); /* bitset: _Find_first(), _Find_next(i) */ // }}} constexpr int mod = int(1e9) + 7; LL fastpow(LL a, int e) { LL res = 1; while (e) { if (e & 1) res = res * a % mod; a = a * a % mod; e /= 2; } return res; } #define INV(a) fastpow((a), mod - 2) void add(int& a, int b) { a = (a + b) % mod; } array<int,3> ind; int n, rad[3], cnt[4], ans = 0; string str[3]; VI fact, invfact, pref; int nCk(int N, int K) { return 1LL * fact[N] * invfact[K] % mod * invfact[N - K] % mod; } int getpos(int i) { return (str[ind[0]][i] == str[ind[1]][i]) + 2 * (str[ind[1]][i] == str[ind[2]][i]); } int go() { dbg("{"); dbg("ind[] =", ind[0], ind[1], ind[2]); fill(A(cnt), 0); FOR(i, n) cnt[getpos(i)]++; dbg("cnt[] =", cnt[0], cnt[1], cnt[2], cnt[3]); pref.RS(cnt[3] + 1); pref[0] = 1; FOR(i, 1, cnt[3] + 1) { pref[i] = nCk(cnt[3], i); add(pref[i], pref[i - 1]); } int t[3]; int res = 0; FOR(i, cnt[0] + 1) { if (i > rad[ind[1]] || cnt[0] - i > min(rad[ind[0]], rad[ind[2]])) continue; FOR(j, cnt[1] + 1) { t[0] = cnt[0] - i + cnt[1] - j; t[1] = i + cnt[1] - j; t[2] = cnt[0] - i + j; if (t[0] > rad[ind[0]] || t[1] > rad[ind[1]] || t[2] > rad[ind[2]]) continue; FOR(k, cnt[2] + 1) { t[0] = cnt[0] - i + cnt[1] - j + k; t[1] = i + cnt[1] - j + cnt[2] - k; t[2] = cnt[0] - i + j + cnt[2] - k; if (t[0] > rad[ind[0]] || t[1] > rad[ind[1]] || t[2] > rad[ind[2]]) continue; int x = 1LL * nCk(cnt[0], i) * nCk(cnt[1], j) % mod * nCk(cnt[2], k) % mod; x = 1LL * x * pref[min({rad[ind[0]] - t[0], rad[ind[1]] - t[1], rad[ind[2]] - t[2], cnt[3]})] % mod; add(res, x); } } } dbg("res = ", res); dbg("}"); return res; } int main() { in(n); fact.RS(n + 1); invfact.RS(n + 1); fact[0] = invfact[0] = 1; FOR(i, n) { fact[i + 1] = 1LL * fact[i] * (i + 1) % mod; invfact[i + 1] = INV(fact[i + 1]); } FOR(i, 3) in(rad[i], str[i]); ind = { 0, 0, 0 }; add(ans, go()); ind = { 1, 1, 1 }; add(ans, go()); ind = { 2, 2, 2 }; add(ans, go()); ind = { 0, 0, 1 }; add(ans, mod - go()); ind = { 0, 0, 2 }; add(ans, mod - go()); ind = { 1, 1, 2 }; add(ans, mod - go()); ind = { 0, 1, 2 }; add(ans, go()); outln(ans); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 | // {{{ #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define VARGS_(_4, _3, _2, _1, N, ...) N #define VARGS(...) VARGS_(__VA_ARGS__, 4, 3, 2, 1) #define CONCAT_(a, b) a##b #define CONCAT(a, b) CONCAT_(a, b) #define FOR_1(x) for (auto& x) #define FOR_2(i, n) for (auto i = remove_reference_t<decltype(n)>{0}; i < (n); ++i) #define FOR_3(i, b, e) for (auto i = remove_reference_t<decltype(e)>{b}; i < (e); ++i) #define FOR_4(i, b, e, s) for (auto i = remove_reference_t<decltype(e)>{b}; i < (e); i += s) #define FORD_2(i, n) for (auto i = (n) - 1; i >= 0; --i) #define FORD_3(i, b, e) for (auto i = remove_reference_t<decltype(b)>{(e) - 1}; i >= (b); --i) #define FORD_4(i, b, e, s) for (auto i = remove_reference_t<decltype(b)>{(e) - 1}; i >= (b); i -= s) #define FOR(...) CONCAT(FOR_, VARGS(__VA_ARGS__))(__VA_ARGS__) #define FORD(...) CONCAT(FORD_, VARGS(__VA_ARGS__))(__VA_ARGS__) #define B begin() #define E end() #define RB rbegin() #define RE rend() #define A(x) std::begin(x), std::end(x) #define RA(x) std::rbegin(x), std::rend(x) #define RANGE(x, b, e) (std::begin(x) + (b)), (std::begin(x) + (e)) #define MP make_pair #define MT make_tuple #define FS first #define ND second #define G1 get<0> #define G2 get<1> #define G3 get<2> #define G4 get<3> #define G5 get<4> #define PB push_back #define PP pop_back #define PF push_front #define FF pop_front #define RS resize #define INF(T) numeric_limits<T>::max() #define L0(_expr) [&]() { return _expr; } #define L1(_expr) [&](auto&& _1) { return _expr; } #define L2(_expr) [&](auto&& _1, auto&& _2) { return _expr; } #define _ CONCAT(_unused_, __COUNTER__) #define MIN min_element #define MAX max_element #define SUM accumulate using namespace std; using LL = long long; using LD = long double; using ULL = unsigned long long; template<class T1,class T2> using P = pair<T1,T2>; using PII = P<int,int>; using PLL = P<LL,LL>; using PLD = P<LD,LD>; template<class T> using V = vector<T>; using VI = V<int>; using VLL = V<LL>; using VLD = V<LD>; using VB = V<bool>; using VS = V<string>; template<class T,class Comp=greater<T>> using PQ = priority_queue<T,V<T>,Comp>; template<class T> int sz(const T& x) { return size(x); } template<class T> bool amin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template<class T> bool amax(T& a, const T& b) { if (b > a) { a = b; return true; } return false; } /* find_by_order(k) - k'th largest counting from 0; order_of_key(k) - number of items strictly smaller than k; join(other), split(k, other) - all keys in other greater than in *(this). */ template<class K,class V,class Comp=less<K>> using ordered_map = __gnu_pbds::tree<K,V,Comp, __gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; template<class T,class Comp=less<T>> using ordered_set = ordered_map<T,__gnu_pbds::null_type,Comp>; string _sep = " ", _ignore; bool _newline = true; stack<ostream*> _ostack; stack<istream*> _istack; template<class TH> void out(const TH& h) { if (_newline) _newline = false; else *_ostack.top() << _sep; *_ostack.top() << h; } template<class TH,class...TA> void out(const TH& h, const TA&... a) { out(h); out(a...); } void outln() { *_ostack.top() << '\n'; _newline = true; } template<class...TA> void outln(const TA&... a) { out(a...); outln(); } template<class TH> void in(TH& h) { *_istack.top() >> h; } template<class TH,class...TA> void in(TH& h, TA&... a) { in(h); in(a...); } template<class...TA> void EXIT(const TA&... a) { outln(a...); exit(0); } #ifdef SPONGE template<class...TA> void dbg(const TA&... a) { _ostack.push(&cerr); cerr << "\033[1;33m"; outln(a...); cerr << "\033[0m"; _ostack.pop(); } #else #define dbg(...) #endif struct _upgrade_io { _upgrade_io(bool ok) { _ostack.push(&cout); _istack.push(&cin); if (ok) { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout.precision(15); cout.setf(ios::fixed, ios::floatfield); }} } _upgrade_io(true); /* bitset: _Find_first(), _Find_next(i) */ // }}} constexpr int mod = int(1e9) + 7; LL fastpow(LL a, int e) { LL res = 1; while (e) { if (e & 1) res = res * a % mod; a = a * a % mod; e /= 2; } return res; } #define INV(a) fastpow((a), mod - 2) void add(int& a, int b) { a = (a + b) % mod; } array<int,3> ind; int n, rad[3], cnt[4], ans = 0; string str[3]; VI fact, invfact, pref; int nCk(int N, int K) { return 1LL * fact[N] * invfact[K] % mod * invfact[N - K] % mod; } int getpos(int i) { return (str[ind[0]][i] == str[ind[1]][i]) + 2 * (str[ind[1]][i] == str[ind[2]][i]); } int go() { dbg("{"); dbg("ind[] =", ind[0], ind[1], ind[2]); fill(A(cnt), 0); FOR(i, n) cnt[getpos(i)]++; dbg("cnt[] =", cnt[0], cnt[1], cnt[2], cnt[3]); pref.RS(cnt[3] + 1); pref[0] = 1; FOR(i, 1, cnt[3] + 1) { pref[i] = nCk(cnt[3], i); add(pref[i], pref[i - 1]); } int t[3]; int res = 0; FOR(i, cnt[0] + 1) { if (i > rad[ind[1]] || cnt[0] - i > min(rad[ind[0]], rad[ind[2]])) continue; FOR(j, cnt[1] + 1) { t[0] = cnt[0] - i + cnt[1] - j; t[1] = i + cnt[1] - j; t[2] = cnt[0] - i + j; if (t[0] > rad[ind[0]] || t[1] > rad[ind[1]] || t[2] > rad[ind[2]]) continue; FOR(k, cnt[2] + 1) { t[0] = cnt[0] - i + cnt[1] - j + k; t[1] = i + cnt[1] - j + cnt[2] - k; t[2] = cnt[0] - i + j + cnt[2] - k; if (t[0] > rad[ind[0]] || t[1] > rad[ind[1]] || t[2] > rad[ind[2]]) continue; int x = 1LL * nCk(cnt[0], i) * nCk(cnt[1], j) % mod * nCk(cnt[2], k) % mod; x = 1LL * x * pref[min({rad[ind[0]] - t[0], rad[ind[1]] - t[1], rad[ind[2]] - t[2], cnt[3]})] % mod; add(res, x); } } } dbg("res = ", res); dbg("}"); return res; } int main() { in(n); fact.RS(n + 1); invfact.RS(n + 1); fact[0] = invfact[0] = 1; FOR(i, n) { fact[i + 1] = 1LL * fact[i] * (i + 1) % mod; invfact[i + 1] = INV(fact[i + 1]); } FOR(i, 3) in(rad[i], str[i]); ind = { 0, 0, 0 }; add(ans, go()); ind = { 1, 1, 1 }; add(ans, go()); ind = { 2, 2, 2 }; add(ans, go()); ind = { 0, 0, 1 }; add(ans, mod - go()); ind = { 0, 0, 2 }; add(ans, mod - go()); ind = { 1, 1, 2 }; add(ans, mod - go()); ind = { 0, 1, 2 }; add(ans, go()); outln(ans); } |