///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

template <typename TT, typename T>
void incr_m(map<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(V<ll> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(V<t2> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(V<t3> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(V<t4> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(V<ll> &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

template <typename T>
void _debug_print(T x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

template <typename TT, typename T>
void _debug_print(const map<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
#if DEBUG
    struct tm *tm = localtime(&tv.tv_sec);
#endif
    debug_printf("-- %s %02d:%02d:%02d.%06ld\n",
                 prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}



// #define MOD   (1000000007LL)
#define MOD   (998244353LL)

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
    }

    perm_invs[size-1] = mod_inv(perms[size-1], mod);
    rrep (i, size-1) {
        perm_invs[i] = perm_invs[i+1LL] * (i+1LL);
        perm_invs[i] %= mod;
    }
}







// #define MOD (998244353LL)
#define SZ (1048576LL)
#define ROOT (646LL)

S map<ll, ll> units;
S map<ll, ll> units_inv;
S ll *buf = NULL;
S ll buf_offset;

void _ntt(ll coefs[], ll n, bool inverse, bool top)
{
    // pow of 2
    assert(((n - 1LL) & n) == 0LL);

    if (n == 1) return;

    ll *ncoefs[2];
    rep (i, 2) {
        // ncoefs[i] = new ll[n/2LL];
        ncoefs[i] = buf + buf_offset;
        buf_offset += n/2LL;
    }
    rep (i, n) ncoefs[i & 1LL][i/2LL] = coefs[i];

    _ntt(ncoefs[0], n/2LL, inverse, false);
    _ntt(ncoefs[1], n/2LL, inverse, false);

    ll unit;
    if (inverse) unit = units_inv[n];
    else unit = units[n];
    ll now = 1;

    rep (i, n) {
        coefs[i] = ncoefs[0][i%(n/2LL)];
        coefs[i] %= MOD;
        coefs[i] += now * ncoefs[1][i%(n/2LL)];
        coefs[i] %= MOD;
        now = now * unit;
        now %= MOD;
    }

    if (inverse && top) {
        ll mlt = mod_inv(n, MOD);
        rep (i, n) {
            coefs[i] = coefs[i] * mlt;
            coefs[i] %= MOD;
        }
    }
}

void ntt(ll coefs[], ll n, bool inverse)
{
    if (!buf) buf = new ll[30LL * 1024LL * 1024LL];
    buf_offset = 0;
    return _ntt(coefs, n, inverse, true);
}

void convolution(ll results[], const ll alist[], ll an, const ll blist[], ll bn)
{
    // must search appropriate root if an + bn > 1048576
    assert(an + bn <= SZ);

    ll sz = 1;
    while (sz < an + bn) sz <<= 1LL;
    ll unit = ROOT;
    rep (i, llround(log2(SZ / sz))) {
        unit *= unit;
        unit %= MOD;
    }
    ll unit_inv = mod_pow(unit, sz-1LL, MOD);

    ll ssz = sz;
    while (ssz > 1) {
        units[ssz] = unit;
        units_inv[ssz] = unit_inv;
        ssz >>= 1LL;
        unit *= unit;
        unit %= MOD;
        unit_inv *= unit_inv;
        unit_inv %= MOD;
    }

    ll *acs = new ll[sz];
    memset(acs, 0, sizeof(ll) * sz);
    rep (i, an) acs[i] = alist[i] % MOD;
    ntt(acs, sz, false);

    ll *bcs = new ll[sz];
    memset(bcs, 0, sizeof(ll) * sz);
    rep (i, bn) bcs[i] = blist[i] % MOD;
    ntt(bcs, sz, false);

    ll *mlts = new ll[sz];
    rep (i, sz) mlts[i] = (acs[i] * bcs[i]) % MOD;
    ntt(mlts, sz, true);

    rep (i, an+bn) results[i] = mlts[i] % MOD;

    delete [] acs;
    delete [] bcs;
    delete [] mlts;
}






///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

void _main()
{
    ll n1; llin(n1);
    V<ll> hlist; llina(hlist, n1 * 2);
    ll n2 = n1 * 2;

    S ll perms[200'010];
    S ll perm_invs[200'010];
    make_perms(perms, perm_invs, 200'010, MOD);

    S ll pps[200'010];
    pps[0] = pps[1] = 1;
    pps[2] = 2;
    srep (i, 3, 200'010) {
        pps[i] = pps[i-2] * i;
        pps[i] %= MOD;
    }

    S ll cnts[100'010] = {};
    for (auto h : hlist) cnts[h]++;

    S V<ll> cntlist;
    rep (h, 100'010) if (cnts[h]) cntlist.pb(cnts[h]);
    sort(cntlist);

    debug_printf("---- cntlist\n");
    debug_print(cntlist);

    S deque< V<ll> > cmbq;
    for (auto cnt : cntlist) {
        V<ll> cmbs;
        rep (cmbcnt, cnt/2LL+1LL) {
            ll cmb = 1;
            cmb *= perms[cnt];
            cmb %= MOD;
            cmb *= perm_invs[cmbcnt*2LL];
            cmb %= MOD;
            cmb *= perm_invs[cnt-cmbcnt*2LL];
            cmb %= MOD;
            if (cmbcnt) cmb *= pps[cmbcnt*2LL-1LL];
            cmb %= MOD;
            cmbs.pb(cmb);
        }
        cmbq.push_back(cmbs);
    }

#if 0
    debug_printf("-------------------- cmblist\n");
    for (auto cmbs : cmblist) {
        debug_printf("----\n");
        debug_print(cmbs);
    }
#endif

    while (cmbq.size() > 1) {
        V<ll> cmb0 = cmbq.front(); cmbq.pop_front();
        V<ll> cmb1 = cmbq.front(); cmbq.pop_front();
        debug_printf("---- cmb0\n");
        debug_print(cmb0);
        debug_printf("---- cmb1\n");
        debug_print(cmb1);
        S ll alist0[100'010];
        S ll alist1[100'010];
        rep (i, cmb0.size()) alist0[i] = cmb0[i];
        rep (i, cmb1.size()) alist1[i] = cmb1[i];
        S ll results[100'010];
        convolution(results, alist0, cmb0.size(), alist1, cmb1.size());
        V<ll> cmb_result;
        rep (i, cmb0.size() + cmb1.size() - 1) cmb_result.pb(results[i]);
        cmbq.push_back(cmb_result);
    }

    V<ll> last_cmb = cmbq.front();

    debug_printf("------- last_cmb\n");
    debug_print(last_cmb);

    ll ans = 0;

    rep (cnt, last_cmb.size()) {
        ll diff = last_cmb[cnt];
        ll remain = n2 - cnt * 2LL;
        if (remain) diff *= pps[remain-1LL];
        diff %= MOD;
        if (cnt & 1LL) ans -= diff;
        else ans += diff;
        if (ans < 0) ans += MOD;
        ans %= MOD;
    }

    debug_printf("---- ans\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////


Measured memory_bytes: 22356