#include #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" #define NDEBUG #define SHOW(...) static_cast(0) //!===========================================================!// //! dP dP dP !// //! 88 88 88 !// //! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !// //! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !// //! 88 88 88. ... 88. .88 88. .88 88. ... 88 !// //! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !// //!===========================================================!// using ld = long double; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr unsigned int MOD = 1000000007; template constexpr T INF = std::numeric_limits::max() / 4; template constexpr F PI = static_cast(3.1415926535897932385); std::mt19937 mt{std::random_device{}()}; template bool chmin(T& a, const T& b) { return a = std::min(a, b), a == b; } template bool chmax(T& a, const T& b) { return a = std::max(a, b), a == b; } template std::vector Vec(const std::size_t n, T v) { return std::vector(n, v); } template auto Vec(const std::size_t n, Args... args) { return std::vector(n, Vec(args...)); } template constexpr T popCount(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : (T)__builtin_popcountll(u); #else unsigned long long v = static_cast(u); return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast(v * 0x0101010101010101ULL >> 56 & 0x7f); #endif } template constexpr T log2p1(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : T(64 - __builtin_clzll(u)); #else unsigned long long v = static_cast(u); return v = static_cast(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v); #endif } template constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); } template constexpr T msbp1(const T v) { return log2p1(v); } template constexpr T lsbp1(const T v) { #ifdef __has_builtin return __builtin_ffsll(v); #else return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1); #endif } template constexpr bool ispow2(const T v) { return popCount(v) == 1; } template constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); } template constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); } //!===============================================================!// //! 88888888b dP .88888. a88888b. 888888ba !// //! 88 88 d8' '88 d8' '88 88 '8b !// //! a88aaaa dP. .dP d8888P 88 88 88 88 !// //! 88 '8bd8' 88 88 YP88 88 88 88 !// //! 88 .d88b. 88 Y8. .88 Y8. .88 88 .8P !// //! 88888888P dP' 'dP dP '88888' Y88888P' 8888888P !// //!===============================================================!// template constexpr std::pair extgcd(const T a, const T b) { if (b == 0) { return std::pair{1, 0}; } const auto p = extgcd(b, a % b); return {p.second, p.first - p.second * (a / b)}; } template constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; } //!====================================================================================!// //! .88888. a88888b. 888888ba d88b dP a88888b. 8888ba.88ba !// //! d8' '88 d8' '88 88 '8b 8''8 88 d8' '88 88 '8b '8b !// //! 88 88 88 88 d8b 88 88 88 88 88 !// //! 88 YP88 88 88 88 d8P'8b 88 88 88 88 88 !// //! Y8. .88 Y8. .88 88 .8P d8' '8bP 88 Y8. .88 88 88 88 !// //! '88888' Y88888P' 8888888P '888P''YP 88888888P Y88888P' dP dP dP !// //!====================================================================================!// template constexpr T gcd(const T a, const T b) { return (b != 0) ? gcd(b, a % b) : a; } template constexpr T lcm(const T a, const T b) { return (a == 0 and b == 0) ? (T)0 : (a / gcd(a, b)) * b; } //!========================================================!// //! 8888ba.88ba dP dP dP !// //! 88 '8b '8b 88 88 88 !// //! 88 88 88 .d8888b. .d888b88 88 88d888b. d8888P !// //! 88 88 88 88' '88 88' '88 88 88' '88 88 !// //! 88 88 88 88. .88 88. .88 88 88 88 88 !// //! dP dP dP '88888P' '88888P8 dP dP dP dP !// //!========================================================!// template class ModInt { private: uint v; static uint norm(const uint& x) { return x < mod ? x : x - mod; } static ModInt make(const uint& x) { ModInt m; return m.v = x, m; } static ModInt power(ModInt x, ll n) { ModInt ans = 1; for (; n; n >>= 1, x *= x) { if (n & 1) { ans *= x; } } return ans; } static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; } public: ModInt() : v{0} {} ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {} ModInt(const ModInt& n) : v{n()} {} explicit operator bool() const { return v != 0; } ModInt& operator=(const ModInt& n) { return v = n(), (*this); } ModInt& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); } ModInt operator+() const { return *this; } ModInt operator-() const { return make(norm(mod - v)); } ModInt operator+(const ModInt& val) const { return make(norm(v + val())); } ModInt operator-(const ModInt& val) const { return make(norm(v + mod - val())); } ModInt operator*(const ModInt& val) const { return make((uint)((ll)v * val() % (ll)mod)); } ModInt operator/(const ModInt& val) const { return *this * inv(val()); } ModInt& operator+=(const ModInt& val) { return *this = *this + val; } ModInt& operator-=(const ModInt& val) { return *this = *this - val; } ModInt& operator*=(const ModInt& val) { return *this = *this * val; } ModInt& operator/=(const ModInt& val) { return *this = *this / val; } ModInt operator+(const ll val) const { return ModInt{v + val}; } ModInt operator-(const ll val) const { return ModInt{v - val}; } ModInt operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; } ModInt operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; } template ModInt operator^(const I n) const { return power(v, n); } ModInt& operator+=(const ll val) { return *this = *this + val; } ModInt& operator-=(const ll val) { return *this = *this - val; } ModInt& operator*=(const ll val) { return *this = *this * val; } ModInt& operator/=(const ll val) { return *this = *this / val; } template ModInt& operator^=(const I n) { return (*this) = ((*this) ^ n); } bool operator==(const ModInt& val) const { return v == val.v; } bool operator!=(const ModInt& val) const { return not(*this == val); } bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); } bool operator!=(const ll val) const { return not(*this == val); } uint operator()() const { return v; } }; template inline ModInt operator+(const ll val, const ModInt& n) { return n + val; } template inline ModInt operator-(const ll val, const ModInt& n) { return ModInt{val - (ll)n()}; } template inline ModInt operator*(const ll val, const ModInt& n) { return n * val; } template inline ModInt operator/(const ll val, const ModInt& n) { return ModInt(val) / n; } template inline bool operator==(const ll val, const ModInt& n) { return n == val; } template inline bool operator!=(const ll val, const ModInt& n) { return not(val == n); } template inline std::istream& operator>>(std::istream& is, ModInt& n) { uint v; return is >> v, n = v, is; } template std::ostream& operator<<(std::ostream& os, const ModInt& n) { return (os << n()); } //!============================================!// //! 8888ba.88ba oo !// //! 88 '8b '8b !// //! 88 88 88 .d8888b. dP 88d888b. !// //! 88 88 88 88' '88 88 88' '88 !// //! 88 88 88 88. .88 88 88 88 !// //! dP dP dP '88888P8 dP dP dP !// //!============================================!// int main() { using mint = ModInt; int N; std::cin >> N; std::vector A(N), B(N); for (int i = 0; i < N; i++) { std::cin >> A[i], A[i]--; } for (int i = 0; i < N; i++) { std::cin >> B[i], B[i]--; } std::vector> cycle1; std::vector C1(N, -1), D1(N, -1); for (int i = 0; i < N; i++) { if (C1[i] != -1) { continue; } std::vector c; for (int p = i, d = 0; C1[p] == -1; p = A[p], d++) { C1[p] = (int)cycle1.size(), D1[p] = d, c.push_back(p); } cycle1.push_back(c); } std::vector> cycle2; std::vector C2(N, -1), D2(N, -1); for (int i = 0; i < N; i++) { if (C2[i] != -1) { continue; } std::vector c; for (int p = i, d = 0; C2[p] == -1; p = B[p], d++) { C2[p] = (int)cycle2.size(), D2[p] = d, c.push_back(p); } cycle2.push_back(c); } std::map> ds; for (int i = 0; i < N; i++) { const ll c1 = C1[i], c2 = C2[i], d = D2[i] - D1[i]; const ll S1 = cycle1[c1].size(), S2 = cycle2[c2].size(), G = gcd(S1, S2), D = ((d % G) + G) % G; (D2[i] += S2 - D) %= S2; const ll C = c1 * (N + 1) * (N + 1) + c2 * (N + 1) + D; using P = std::pair; std::vector

mods; ll M1 = S1, V1 = D1[i], M2 = S2, V2 = D2[i]; const auto p = extgcd(M1, M2); const ll M = (M1 * p.first) * (V2 - V1) / (M1 * p.first + M2 * p.second) + V1; const ll S = lcm(S1, S2); ds[C].push_back((M + S) % S); } mint ans = 0; for (auto& p : ds) { const ll code = p.first, c1 = code / (N + 1) / (N + 1), c2 = (code / (N + 1)) % (N + 1), S1 = cycle1[c1].size(), S2 = cycle2[c2].size(); const ll S = lcm(S1, S2); auto& v = p.second; std::sort(v.begin(), v.end()); const int V = v.size(); for (int i = 0; i < V; i++) { const mint dis = (i == V - 1 ? v[0] + S - v[i] - 1 : v[i + 1] - v[i] - 1); ans += ((dis) * (dis + 1)) / 2; } } std::cout << ans << std::endl; return 0; }