Language: C++

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <iomanip>
#include <utility>
#include <tuple>
#include <functional>
#include <bitset>
#include <cassert>
#include <complex>
#include <stdio.h>
#include <time.h>
#include <numeric>
#include <random>
#include <unordered_map>
#include <unordered_set>
#define int long long
#define all(a) a.begin(),a.end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define pb push_back
#define debug(x) cerr << #x << ':' << x << '\n'
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef complex<ld> com;
constexpr int inf = 1000000010;
constexpr ll INF = 1000000000000000010;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
template<class T, class U> inline bool chmax(T &a, const U &b) { if (a < b) { a = b; return true; } return false; }
template<class T, class U> inline bool chmin(T &a, const U &b) { if (a > b) { a = b; return true; } return false; }

constexpr ll mod = 1000000007;
vector<ll> fac, inv, facinv;

void modcalc(int modsize) {
	fac.resize(modsize); inv.resize(modsize); facinv.resize(modsize);
	fac[0] = 1; fac[1] = 1; inv[1] = 1;
	facinv[0] = 1; facinv[1] = 1;
	for (ll i = 2; i < modsize; i++) {
		fac[i] = fac[i - 1] * i % mod;
		inv[i] = mod - inv[mod % i] * (mod / i) % mod;
		facinv[i] = facinv[i - 1] * inv[i] % mod;
	}
}

ll modinv(ll a) {
	a %= mod;
	if (a == 0) abort();
	if (a < (ll)inv.size()) return inv[a];
	ll b = mod, u = 1, v = 0;
	while (b) {
		ll t = a / b;
		a -= t * b; swap(a, b);
		u -= t * v; swap(u, v);
	}
	u %= mod;
	if (u < 0) u += mod;
	return u;
}

ll modpow(ll a, ll b) {
	ll ans = 1;
	a %= mod;
	while (b) {
		if (b & 1) ans = ans * a % mod;
		a = a * a % mod;
		b >>= 1;
	}
	return ans;
}

ll modcomb(ll n, ll k) {
	if (n < 0 || k < 0 || n < k) return 0;
	return fac[n] * facinv[k] % mod * facinv[n - k] % mod;
}

ll modperm(ll n, ll k) {
	if (n < 0 || k < 0 || n < k) return 0;
	return fac[n] * facinv[n - k] % mod;
}

ll modhom(ll n, ll k) {
	if (n < 0 || k < 0 || n == 0 && k > 0) return 0;
	if (n == 0 && k == 0) return 1;
	return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod;
}

vector<vector<int>> graph(100010, vector<int>());
vector<int> sz(100010), vis(100010), ver(100010), cnt(100010);

void dfs1(int n, int v) {
	if (vis[n]) return;
	vis[n] = true;
	ver[n] = v;
	for (int i : graph[n]) {
		if (vis[i]) continue;
		dfs1(i, v);
	}
}

void dfs2(int n, int p, int r, set<int> &s) {
	if (n != r) cnt[r]++;
	int c = 0; int v;
	for (int i : graph[n]) {
		if (i == p || s.count(i)) continue;
		else {
			c++;
			v = i;
		}
	}
	if (c > 1) cnt[r] = inf;
	if (c == 1) dfs2(v, n, r, s);
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(20);
	modcalc(200010);

	int n;
	cin >> n;
	vector<int> p(n);
	rep(i, n) {
		cin >> p[i];
		p[i]--;
		graph[i].pb(p[i]);
		graph[p[i]].pb(i);
	}
	rep(i, n) if (!vis[i]) dfs1(i, i);
	vector<int> root = ver;
	root.resize(n);
	sort(all(root)); root.erase(unique(all(root)), root.end());
	vector<int> si(n);
	rep(i, n) si[ver[i]]++;
	vector<int> cycle(n + 1);
	ll ans = 1;
	rep(i, root.size()) {
		int v = root[i];
		int now = v;
		bool flag = true;
		rep(j, si[v]) {
			if (j && now == v) flag = false;
			now = p[now];
		}
		if (flag && now == v) cycle[si[v]]++;
		else {
			set<int> st;
			now = v;
			int start;
			while (true) {
				if (st.count(now)) {
					start = now;
					break;
				}
				st.insert(now);
				now = p[now];
			}
			vector<int> cyc; cyc.pb(start);
			while (p[now] != start) {
				cyc.pb(p[now]);
				now = p[now];
			}
			int cycsz = cyc.size();
			set<int> cycst;
			rep(j, cycsz) cycst.insert(cyc[j]);
			vector<int> check;
			for (int ve : cyc) {
				dfs2(ve, -1, ve, cycst);
				if (cnt[ve] >= inf) ans = 0;
				check.pb(cnt[ve]);
			}
			reverse(all(check));
			vector<int> nonzero(2 * cycsz + 1);
			rep(j, 2 * cycsz) {
				nonzero[j + 1] = nonzero[j];
				if (check[j % cycsz]) nonzero[j + 1]++;
			}
			ll pat = 1;
			rep(j, cycsz) {
				if (!check[j]) continue;
				if (check[j] > cycsz) ans = 0;
				else {
					int x = check[j] - 1;
					int pa = 0;
					if (nonzero[j + 1] == nonzero[j + x + 1]) pa++;
					if (nonzero[j + 1] == nonzero[j + x + 2]) pa++;
					if (pa == 0) ans = 0;
					else if (pa == 2) {
						pat *= 2;
						if (pat >= mod) pat -= mod;
					}
				}
			}
			ans *= pat; ans %= mod;
		}
	}
	rep(i, n + 1) {
		int m = cycle[i];
		ll sum = 0;
		for (int j = 0; j <= m / 2; j++) sum += fac[m] * facinv[m - 2 * j] % mod * modinv(modpow(2, j)) % mod * modpow(i, j) % mod * modpow((i + 1) / 2, m - 2 * j) % mod;
		sum %= mod;
		ans *= sum; ans %= mod;
	}
	assert(0 <= ans && ans < mod);
	cout << ans << '\n';
}

Compiler output:
cc1plus: error: '::main' must return 'int'