/**
 *    author:  otera
 *    created: 12.02.2021 22:28:34 
**/
#include<bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
const int inf=1e9+7;
const ll INF=1LL<<60;
#define rep(i, n) for(int i = 0; i < n; ++ i)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
#define pb push_back
#define eb emplace_back
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define si(c) (int)(c).size()
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
#define tpow(n) (1LL<<(n))
#define unless(A) if(!(A))
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template<class T> void scan(T& a){ cin >> a; }
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ cout << ' '; }
template<class T> void print(const T& a){ cout << a; }
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } }
int out(){ cout << '\n'; return 0; }
template<class T> int out(const T& t){ print(t); cout << '\n'; return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; }
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,a4,x,...) x
#define debug_1(x1) cout<<#x1<<": "<<x1<<endl
#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl
#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl
#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl
#define debug_5(x1,x2,x3,x4,x5) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<", "#x5<<": "<<x5<<endl
#ifdef DEBUG
#define debug(...) CHOOSE((__VA_ARGS__,debug_5,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)
#define dump(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...)
#define dump(...)
#endif

#define int long long

// modint: mod 計算を int を扱うように扱える構造体
template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD>& x) noexcept {
        return is >> x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

// 二項係数ライブラリ
template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if(n == k) return 1;
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
};

//const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Fp<MOD>;
BiCoef<mint> bc;

struct UnionFind {
    vector<int> par, w;
    
    UnionFind(int n) : par(n, -1), w(n, 0) { }
    void init(int n) { par.assign(n, -1); w.assign(n, 0); }
    
    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool issame(int x, int y) {
        return root(x) == root(y);
    }
    
    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) {
            ++w[x];
            return false;
        }
        if (par[x] > par[y]) swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        w[x] += w[y];
        ++w[x];
        return true;
    }
    
    int size(int x) {
        return -par[root(x)];
    }
 
    int wei(int x) {
        return w[root(x)];
    }
};

mint dp[5050][5050][2];

void solve() {
    INT(n, m);
    VEC(int, p, n);
    vec(int, deg, n, 0);
    vvc<int> g(n, vc<int>());
    UnionFind uf(n);
    int cnt2 = n;
    rep(i, n) {
        -- p[i];
        ++ deg[i], ++ deg[p[i]];
        g[i].pb(p[i]);
        g[p[i]].pb(i);
        if(uf.merge(i, p[i])) -- cnt2;
    }
    queue<int> que;
    vc<bool> used(n, 0);
    rep(i, n) if(deg[i] == 1) que.push(i);
    int cnt = n;
    while(que.size()) {
        int v = que.front(); que.pop();
        used[v] = 1;
        -- cnt;
        for(int nv: g[v]) {
            if(deg[nv] > 1) {
                -- deg[nv];
                if(deg[nv] == 1) {
                    que.push(nv);
                }
            }
        }
    }
    debug(cnt, cnt2);
    // cnt個で構成された閉路
    rep(i, 5050) rep(j, 5050) rep(k, 2) dp[i][j][k] = 0;
    // rep(i, 5050) rep(j, 5050) sdp[i][j] = 0;
    // dp[1][1][1] = 1;
    // for(int i = 1; i <= cnt; ++ i) {
    //     for(int j = 1; j <= i; ++ j) {
    //         dp[i + 1][j + 1][0] += dp[i][j][0] + dp[i][j][1];
    //         dp[i + 1][j][1] += dp[i][j][0];
    //         dp[i + 1][j][0] += dp[i][j][1] * (j - 1);
    //         if(j >= 2) dp[i + 1][j][0] += dp[i][j][0] * (j - 2);
    //     }
    // }
    // for(int j = 1; j <= cnt; ++ j) {
    //     sdp[cnt][j] = dp[cnt][j][0];
    // }
    int cnt3 = 0;
    auto dfs = [&](auto &&self, int v) -> void {
        used[v] = 1;
        ++ cnt3;
        for(int nv: g[v]) {
            if(!used[nv]) self(self, nv);
        }
    };  
    int cur = 0;
    // sdp[0][0] = 1;
    rep(v, n) {
        if(!used[v]) {
            cnt3 = 0;
            dfs(dfs, v);
            debug(cnt3, cur);
            // cnt3個ののloop
            for(int j = 0; j <= cur; ++ j) {
                // dp[cur + 1][j][1] += sdp[cur][j] * j;
                // dp[cur + 1][j + 1][1] += sdp[cur][j];
            }
            //
            for(int i = 1; i < cnt3; ++ i) {
                for(int j = 0; j <= cur + i; ++ j) {
                    dp[cur + i + 1][j + 1][0] += dp[cur + i][j][0] + dp[cur + i][j][1];
                    dp[cur + i + 1][j][1] += dp[cur + i][j][0];
                    dp[cur + i + 1][j][0] += dp[cur + i][j][1] * (j - 1);
                    if(j >= 2) dp[cur + i + 1][j][0] += dp[cur + i][j][0] * (j - 2);
                }
            }
            //
            cur += cnt3;
            for(int j = 0; j <= cur; ++ j) {
                //sdp[cur][j] = dp[cur][j][0];
                //debug(sdp[cur][j]);
            }
        }
    }
    debug(cur);
    // n - cnt個で構成された木の部分
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    // cout << fixed << setprecision(20);
    // INT(t); rep(i, t)solve();
    solve();
    return 0;
}