#include using namespace std; using LL = long long int; #define incII(i, l, r) for(LL i = (l) ; i <= (r); i++) #define incIX(i, l, r) for(LL i = (l) ; i < (r); i++) #define incXI(i, l, r) for(LL i = (l) + 1; i <= (r); i++) #define incXX(i, l, r) for(LL i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(LL i = (r) ; i >= (l); i--) #define decIX(i, l, r) for(LL i = (r) - 1; i >= (l); i--) #define decXI(i, l, r) for(LL i = (r) ; i > (l); i--) #define decXX(i, l, r) for(LL i = (r) - 1; i > (l); i--) #define inc(i, n) incIX(i, 0, n) #define dec(i, n) decIX(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto x, auto l, auto r) { return (l <= x && x <= r); }; auto inIX = [](auto x, auto l, auto r) { return (l <= x && x < r); }; auto inXI = [](auto x, auto l, auto r) { return (l < x && x <= r); }; auto inXX = [](auto x, auto l, auto r) { return (l < x && x < r); }; auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(c) c.begin(), c.end() #define RALL(c) c.rbegin(), c.rend() #define RV(c) reverse(ALL(c)) #define SC static_cast #define SI(c) SC(c.size()) #define SL(c) SC(c.size()) #define RF(e, c) for(auto & e: c) #define SF(c, ...) for(auto & [__VA_ARGS__]: c) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) auto * IS = & cin; auto * OS = & cout; array SEQ = { "", " ", "" }; // input template T in() { T a; (* IS) >> a; return a; } // input: tuple template void tin_(istream & is, U & t) { if constexpr(I < tuple_size::value) { is >> get(t); tin_(is, t); } } template istream & operator>>(istream & is, tuple & t) { tin_<0>(is, t); return is; } template auto tin() { return in>(); } // input: array template istream & operator>>(istream & is, array & a) { RF(e, a) { is >> e; } return is; } template auto ain() { return in>(); } // input: multi-dimensional vector template T vin() { T v; (* IS) >> v; return v; } template auto vin(N n, M ... m) { vector(m ...))> v(n); inc(i, n) { v[i] = vin(m ...); } return v; } // input: multi-column (tuple) template void colin_([[maybe_unused]] U & t) { } template void colin_(U & t) { get(t).PB(in()); colin_(t); } template auto colin(int n) { tuple ...> t; inc(i, n) { colin_ ...>, 0, T ...>(t); } return t; } // output void out_([[maybe_unused]] string s) { } template void out_([[maybe_unused]] string s, A && a) { (* OS) << a; } template void out_(string s, A && a, B && ... b) { (* OS) << a << s; out_(s, b ...); } auto outF = [](auto x, auto y, auto z, auto ... a) { (* OS) << x; out_(y, a ...); (* OS) << z << flush; }; auto out = [](auto ... a) { outF("", " " , "\n", a ...); }; auto outS = [](auto ... a) { outF("", " " , " " , a ...); }; auto outL = [](auto ... a) { outF("", "\n", "\n", a ...); }; auto outN = [](auto ... a) { outF("", "" , "" , a ...); }; // output: multi-dimensional vector template ostream & operator<<(ostream & os, vector const & v) { os << SEQ[0]; inc(i, SI(v)) { os << (i == 0 ? "" : SEQ[1]) << v[i]; } return (os << SEQ[2]); } template void vout_(T && v) { (* OS) << v; } template void vout_(T && v, A a, B ... b) { inc(i, SI(v)) { (* OS) << (i == 0 ? "" : a); vout_(v[i], b ...); } } template void vout (T && v, A a, B ... b) { vout_(v, a, b ...); (* OS) << a << flush; } template void voutN(T && v, A a, B ... b) { vout_(v, a, b ...); (* OS) << flush; } // ---- ---- template class ModInt { private: LL v; pair ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } LL val() { return v; } static LL mod() { return M; } ModInt inv() { return ext_gcd(M, v).SE; } ModInt exp(LL b) { ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); } friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); } friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); } friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); } friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); } friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); } friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); } friend ModInt operator- (ModInt a ) { return ModInt(-a.v); } friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); } friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); } friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); } friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); } friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); } friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); } friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); } friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); } friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); } friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; } friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); } }; // ---- using MI = ModInt<1'000'000'007>; template pair, vector> factorial(int n) { vector f(n + 1), r(n + 1); inc(i, n + 1) { f[i] = (i == 0 ? 1 : f[i - 1] * i ); } dec(i, n + 1) { r[i] = (i == n ? 1 / f[n] : r[i + 1] * (i + 1)); } return { f, r }; } int main() { auto cycle_decomposition = [](vector const & p) -> vector> { int n = SI(p); { auto pp = p; sort(ALL(pp)); inc(i, n) { assert(pp[i] == i); } } vector> ans; vector rem(n, true); inc(i, n) { if(! rem[i]) { continue; } ans.PB({}); int j = i; while(rem[j]) { ans.BA.PB(j); rem[j] = false; j = p[j]; } } return ans; }; auto n = in(); auto p = vin(n); RF(e, p) { e--; } auto [f, r] = factorial(n); auto cs = cycle_decomposition(p); MI ans = f[n]; map mp; RF(c, cs) { ans /= SI(c); mp[SI(c)]++; } bool flag = false; SF(mp, len, cnt) { ans *= r[cnt]; flag |= (len % 2 == 0 || cnt >= 2); } if(! flag) { ans /= 2; } out(ans); }