Language: C++

#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <algorithm>
#define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = std::int_fast64_t;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-15;
 
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << to_string(v[i]);
    }
    return os;
}
 
struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
 
#define MAX_N 4040404
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}
 
using mi = modint;
 
mi mod_pow(mi a, ll n) {
    mi ret = 1;
    mi tmp = a;
    while(n > 0) {
        if(n % 2) ret *= tmp;
        tmp = tmp * tmp;
        n /= 2;
    }
    return ret;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> a(n);
    REP(i, n) cin >> a[i];
    REP(i, n) a[i]--;
    vector<int> w(n, 1);
    vector<int> d(n, 0);
    vector<int> tmp(n, 0);
    REP(i, n) {
        d[a[i]]++;
        tmp[a[i]]++;
    }
    queue<int> q;
    REP(i, n) if(tmp[i] == 0) q.push(i);
    while(!q.empty()) {
        int p = q.front();
        q.pop();
        if(d[p] > 1) {
            cout << 0 << endl;
            return 0;
        }
        tmp[a[p]]--;
        w[a[p]] += w[p];
        if(tmp[a[p]] == 0) q.push(a[p]);
    }
    mi ans = 1;
    vector<int> c(n + 1, 0);
    REP(i, n) {
        if(tmp[i]) {
            deque<int> deq;
            int p = i, sum = 0;
            while(tmp[p]) {
                tmp[p] = 0;
                deq.push_back(w[p] - 1);
                sum += w[p] - 1;
                p = a[p];
            }
            reverse(ALL(deq));
            int m = (int)deq.size();
            if(sum > m) {
                cout << 0 << endl;
                return 0;
            }
            if(sum == 0) {
                c[m]++;
                continue;
            }
            if(m == 1) continue;
            while(deq.front() == 0) {
                deq.push_back(deq.front());
                deq.pop_front();
            }
            if(sum == deq.front()) {
                if(sum == m) ans *= 1;
                else ans *= 2;
                continue;
            }
            mi co = 1;
            int r = -1;
            for(int j = m - 1; j >= 0; j--) {
                if(deq[j] == 0) continue;
                if(r == -1) {
                    if(m - j > deq[j]) co *= 2;
                } else {
                    if(r - j > deq[j]) co *= 2;
                }
                r = j;
            }
            ans *= co;
        }
    }
    vector<mi> fact(n + 1, 1);
    FOR(i, 1, n + 1) fact[i] = fact[i - 1] * i;
    if(c[1]) assert(false);
    FOR(i, 1, n + 1) {
        if(c[i] == 0) continue;
        mi co = 0;
        for(int j = 0; j <= c[i] / 2; j++) {
            mi tmp2 = mod_comb(c[i], 2 * j) * fact[2 * j];
            tmp2 *= mod_pow(fact[j] * mod_pow(2, j), mod - 2);
            tmp2 *= mod_pow(i, j);
            if(i % 2 && i != 1) tmp2 *= mod_pow(2, c[i] - 2 * j);
            co += tmp2;
        }
        ans *= co;
    }
    cout << ans << endl;
    return 0;
}


Compiler output:
a.cc:13:17: error: 'int_fast64_t' in namespace 'std' does not name a type
   13 | using ll = std::int_fast64_t;
      |                 ^~~~~~~~~~~~
a.cc:14:16: error: 'll' was not declared in this scope
   14 | using P = pair<ll, ll>;
      |                ^~
a.cc:14:20: error: 'll' was not declared in this scope
   14 | using P = pair<ll, ll>;
      |                    ^~
a.cc:14:22: error: template argument 1 is invalid
   14 | using P = pair<ll, ll>;
      |                      ^
a.cc:14:22: error: template argument 2 is invalid
a.cc:15:11: error: 'll' does not name a type
   15 | constexpr ll inf = 1000000000;
      |           ^~
a.cc:16:11: error: 'll' does not name a type
   16 | constexpr ll mod = 1000000007;
      |           ^~
a.cc: In function 'std::ostream& operator<<(std::ostream&, std::vector<_Tp>&)':
a.cc:8:26: error: 'll' was not declared in this scope
    8 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                          ^~
a.cc:9:19: note: in expansion of macro 'FOR'
    9 | #define REP(i, n) FOR(i, 0, n)
      |                   ^~~
a.cc:26:5: note: in expansion of macro 'REP'
   26 |     REP(i, v.size()) {
      |     ^~~
a.cc:26:9: error: 'i' was not declared in this scope
   26 |     REP(i, v.size()) {
      |         ^
a.cc:8:36: note: in definition of macro 'FOR'
    8 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                                    ^
a.cc:26:5: note: in expansion of macro 'REP'
   26 |     REP(i, v.size()) {
      |     ^~~
a.cc: At global scope:
a.cc:34:5: error: 'll' does not name a type
   34 |     ll n;
      |     ^~
a.cc:36:18: error: 'll' does not name a type
   36 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                  ^~
a.cc: In constructor 'modint::modint(int)':
a.cc:36:30: error: class 'modint' does not have any field named 'n'
   36 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                              ^
a.cc:36:37: error: 'mod' was not declared in this scope
   36 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                                     ^~~
a.cc: In member function 'modint modint::operator~() const':
a.cc:49:52: error: 'n' was not declared in this scope
   49 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                    ^
a.cc:49:55: error: 'mod' was not declared in this scope
   49 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                       ^~~
a.cc: In function 'bool operator==(const modint&, const modint&)':
a.cc:51:20: error: 'const struct modint' has no member named 'n'
   51 |         return lhs.n == rhs.n;
      |                    ^
a.cc:51:29: error: 'const struct modint' has no member named 'n'
   51 |         return lhs.n == rhs.n;
      |                             ^
a.cc: In function 'bool operator<(const modint&, const modint&)':
a.cc:54:20: error: 'const struct modint' has no member named 'n'
   54 |         return lhs.n < rhs.n;
      |                    ^
a.cc:54:28: error: 'const struct modint' has no member named 'n'
   54 |         return lhs.n < rhs.n;
      |                            ^
a.cc: In function 'bool operator>(const modint&, const modint&)':
a.cc:57:20: error: 'const struct modint' has no member named 'n'
   57 |         return lhs.n > rhs.n;
      |                    ^
a.cc:57:28: error: 'const struct modint' has no member named 'n'
   57 |         return lhs.n > rhs.n;
      |                            ^
a.cc: In function 'modint& operator+=(modint&, const modint&)':
a.cc:60:13: error: 'struct modint' has no member named 'n'
   60 |         lhs.n += rhs.n;
      |             ^
a.cc:60:22: error: 'const struct modint' has no member named 'n'
   60 |         lhs.n += rhs.n;
      |                      ^
a.cc:61:17: error: 'struct modint' has no member named 'n'
   61 |         if (lhs.n >= mod) lhs.n -= mod;
      |                 ^
a.cc:61:22: error: 'mod' was not declared in this scope
   61 |         if (lhs.n >= mod) lhs.n -= mod;
      |                      ^~~
a.cc:61:31: error: 'struct modint' has no member named 'n'
   61 |         if (lhs.n >= mod) lhs.n -= mod;
      |                               ^
a.cc: In function 'modint& operator-=(modint&, const modint&)':
a.cc:65:13: error: 'struct modint' has no member named 'n'
   65 |         lhs.n -= rhs.n;
      |             ^
a.cc:65:22: error: 'const struct modint' has no member named 'n'
   65 |         lhs.n -= rhs.n;
      |                      ^
a.cc:66:17: error: 'struct modint' has no member named 'n'
   66 |         if (lhs.n < 0) lhs.n += mod;
      |                 ^
a.cc:66:28: error: 'struct modint' has no member named 'n'
   66 |         if (lhs.n < 0) lhs.n += mod;
      |                            ^
a.cc:66:33: error: 'mod' was not declared in this scope
   66 |         if (lhs.n < 0) lhs.n += mod;
      |                                 ^~~
a.cc: In function 'modint& operator*=(modint&, const modint&)':
a.cc:70:13: error: 'struct modint' has no member named 'n'
   70 |         lhs.n = (lhs.n * rhs.n) % mod;
      |             ^
a.cc:70:22: error: 'struct modint' has no member named 'n'
   70 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                      ^
a.cc:70:30: error: 'const struct modint' has no member named 'n'
   70 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                              ^
a.cc:70:35: error: 'mod' was not declared in this scope
   70 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                                   ^~~
a.cc: In function 'modint& operator/=(modint&, const modint&)':
a.cc:74:13: error: 'struct modint' has no member named 'n'
   74 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |             ^
a.cc:74:22: error: 'struct modint' has no member named 'n'
   74 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                      ^
a.cc:74:33: error: 'struct modint' has no member named 'n'
   74 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                 ^
a.cc:74:38: error: 'mod' was not declared in this scope
   74 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                      ^~~
a.cc: In function 'modint operator+(const modint&, const modint&)':
a.cc:78:27: error: 'const struct modint' has no member named 'n'
   78 |         return modint(lhs.n + rhs.n);
      |                           ^
a.cc:78:35: error: 'const struct modint' has no member named 'n'
   78 |         return modint(lhs.n + rhs.n);
      |                                   ^
a.cc: In function 'modint operator-(const modint&, const modint&)':
a.cc:81:27: error: 'const struct modint' has no member named 'n'
   81 |         return modint(lhs.n - rhs.n);
      |                           ^
a.cc:81:35: error: 'const struct modint' has no member named 'n'
   81 |         return modint(lhs.n - rhs.n);
      |                                   ^
a.cc: In function 'modint operator*(const modint&, const modint&)':
a.cc:84:27: error: 'const struct modint' has no member named 'n'
   84 |         return modint(lhs.n * rhs.n);
      |                           ^
a.cc:84:35: error: 'const struct modint' has no member named 'n'
   84 |         return modint(lhs.n * rhs.n);
      |                                   ^
a.cc: In function 'modint operator/(const modint&, const modint&)':
a.cc:87:27: error: 'const struct modint' has no member named 'n'
   87 |         return modint(lhs.n * (~rhs).n);
      |                           ^
a.cc:87:38: error: 'struct modint' has no member named 'n'
   87 |         return modint(lhs.n * (~rhs).n);
      |                                      ^
a.cc: In function 'std::istream& operator>>(std::istream&, modint)':
a.cc:90:54: error: 'struct modint' has no member named 'n'
   90 | istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
      |                                                      ^
a.cc: In function 'std::ostream& operator<<(std::ostream&, modint)':
a.cc:91:54: error: 'struct modint' has no member named 'n'
   91 | ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
      |                                                      ^
a.cc: At global scope:
a.cc:109:33: error: 'inf' was not declared in this scope; did you mean 'int'?
  109 | vector<long long> fact(MAX_N+1, inf);
      |                                 ^~~
      |                                 int
a.cc: In function 'long long int mod_fact(long long int, long long int&)':
a.cc:111:19: error: 'inf' was not declared in this scope; did you mean 'int'?
  111 |     if(fact[0] == inf) {
      |                   ^~~
      |                   int
a.cc:114:13: error: 'll' was not declared in this scope
  114 |         for(ll i = 2; i <= MAX_N; ++i) {
      |             ^~
a.cc:114:23: error: 'i' was not declared in this scope
  114 |         for(ll i = 2; i <= MAX_N; ++i) {
      |                       ^
a.cc:115:41: error: 'mod' was not declared in this scope
  115 |             fact[i] = (fact[i-1] * i) % mod;
      |                                         ^~~
a.cc:120:34: error: 'mod' was not declared in this scope
  120 |     long long res = mod_fact(n / mod, e);
      |                                  ^~~
a.cc: In function 'long long int mod_comb(long long int, long long int)':
a.cc:131:42: error: 'mod' was not declared in this scope
  131 |     return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
      |                                          ^~~
a.cc: At global scope:
a.cc:136:18: error: 'll' has not been declared
  136 | mi mod_pow(mi a, ll n) {
      |                  ^~
a.cc: In function 'int main()':
a.cc:8:26: error: 'll' was not declared in this scope
    8 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                          ^~
a.cc:9:19: note: in expansion of macro 'FOR'
    9 | #define REP(i, n) FOR(i, 0, n)
      |                   ^~~
a.cc:153:5: note: in expansion of macro 'REP'
  153 |     REP(i, n) cin >> a[i];
      |     ^~~
a.cc:153:9: error: 'i' was not