Language: C++

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep2(i, n) for (ll i = n - 1; i >= 0; i--)
const int mod = 998244353;

ll gcd(ll a, ll b)
{
	ll c = a % b;
	while (c != 0)
	{
		a = b;
		b = c;
		c = a % b;
	}
	return b;
}

long long extGCD(long long a, long long b, long long &x, long long &y)
{
	if (b == 0)
	{
		x = 1;
		y = 0;
		return a;
	}
	long long d = extGCD(b, a % b, y, x);
	y -= a / b * x;
	return d;
}

struct UnionFind
{
	vector<ll> data;

	UnionFind(int sz)
	{
		data.assign(sz, -1);
	}

	bool unite(int x, int y)
	{
		x = find(x), y = find(y);
		if (x == y)
			return (false);
		if (data[x] > data[y])
			swap(x, y);
		data[x] += data[y];
		data[y] = x;
		return (true);
	}

	int find(int k)
	{
		if (data[k] < 0)
			return (k);
		return (data[k] = find(data[k]));
	}

	ll size(int k)
	{
		return (-data[find(k)]);
	}
};

ll M = 1000000007;

vector<ll> fac(2000011);  //n!(mod M)
vector<ll> ifac(2000011); //k!^{M-2} (mod M)

ll mpow(ll x, ll n)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % M;
		x = x * x % M;
		n = n >> 1;
	}
	return ans;
}
ll mpow2(ll x, ll n, ll mod)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % mod;
		x = x * x % mod;
		n = n >> 1;
	}
	return ans;
}
void setcomb()
{
	fac[0] = 1;
	ifac[0] = 1;
	for (ll i = 0; i < 2000010; i++)
	{
		fac[i + 1] = fac[i] * (i + 1) % M; // n!(mod M)
	}
	ifac[2000010] = mpow(fac[2000010], M - 2);
	for (ll i = 2000010; i > 0; i--)
	{
		ifac[i - 1] = ifac[i] * i % M;
	}
}
ll comb(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	ll tmp = ifac[a - b] * ifac[b] % M;
	return tmp * fac[a] % M;
}
ll perm(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a)
{
	long long b = M, u = 1, v = 0;
	while (b)
	{
		long long t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= M;
	if (u < 0)
		u += M;
	return u;
}
ll modinv2(ll a, ll mod)
{
	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;
}

template <int mod>
struct ModInt
{
	int x;

	ModInt() : x(0) {}

	ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

	ModInt &operator+=(const ModInt &p)
	{
		if ((x += p.x) >= mod)
			x -= mod;
		return *this;
	}

	ModInt &operator-=(const ModInt &p)
	{
		if ((x += mod - p.x) >= mod)
			x -= mod;
		return *this;
	}

	ModInt &operator*=(const ModInt &p)
	{
		x = (int)(1LL * x * p.x % mod);
		return *this;
	}

	ModInt &operator/=(const ModInt &p)
	{
		*this *= p.inverse();
		return *this;
	}

	ModInt operator-() const { return ModInt(-x); }

	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

	bool operator==(const ModInt &p) const { return x == p.x; }

	bool operator!=(const ModInt &p) const { return x != p.x; }

	ModInt inverse() const
	{
		int a = x, b = mod, u = 1, v = 0, t;
		while (b > 0)
		{
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}

	ModInt pow(int64_t n) const
	{
		ModInt ret(1), mul(x);
		while (n > 0)
		{
			if (n & 1)
				ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}

	friend ostream &operator<<(ostream &os, const ModInt &p)
	{
		return os << p.x;
	}

	friend istream &operator>>(istream &is, ModInt &a)
	{
		int64_t t;
		is >> t;
		a = ModInt<mod>(t);
		return (is);
	}

	static int get_mod() { return mod; }
};

using mint = ModInt<mod>;

vector<vector<mint>> mul(vector<vector<mint>> a, vector<vector<mint>> b)
{
	int i, j, k;
	mint t;
	int n = a.size(), m = b[0].size(), l = a[0].size();
	vector<vector<mint>> c(n, vector<mint>(m));
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < m; j++)
		{
			t = 0;
			for (k = 0; k < l; k++)
				t += a[i][k] * b[k][j];
			c[i][j] = t;
		}
	}
	return c;
}

vector<vector<mint>> mat_pow(vector<vector<mint>> x, ll n)
{
	ll k = x.size();
	vector<vector<mint>> ans(k, vector<mint>(k, 0));
	for (int i = 0; i < k; i++)
		ans[i][i] = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = mul(ans, x);
		x = mul(x, x);
		n = n >> 1;
	}
	return ans;
}

template <int mod>
struct NumberTheoreticTransform
{

	vector<int> rev, rts;
	int base, max_base, root;

	NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1}
	{
		assert(mod >= 3 && mod % 2 == 1);
		auto tmp = mod - 1;
		max_base = 0;
		while (tmp % 2 == 0)
			tmp >>= 1, max_base++;
		root = 2;
		while (mod_pow(root, (mod - 1) >> 1) == 1)
			++root;
		assert(mod_pow(root, mod - 1) == 1);
		root = mod_pow(root, (mod - 1) >> max_base);
	}

	inline int mod_pow(int x, int n)
	{
		int ret = 1;
		while (n > 0)
		{
			if (n & 1)
				ret = mul(ret, x);
			x = mul(x, x);
			n >>= 1;
		}
		return ret;
	}

	inline int inverse(int x)
	{
		return mod_pow(x, mod - 2);
	}

	inline unsigned add(unsigned x, unsigned y)
	{
		x += y;
		if (x >= mod)
			x -= mod;
		return x;
	}

	inline unsigned mul(unsigned a, unsigned b)
	{
		return 1ull * a * b % (unsigned long long)mod;
	}

	void ensure_base(int nbase)
	{
		if (nbase <= base)
			return;
		rev.resize(1 << nbase);
		rts.resize(1 << nbase);
		for (int i = 0; i < (1 << nbase); i++)
		{
			rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
		}
		assert(nbase <= max_base);
		while (base < nbase)
		{
			int z = mod_pow(root, 1 << (max_base - 1 - base));
			for (int i = 1 << (base - 1); i < (1 << base); i++)
			{
				rts[i << 1] = rts[i];
				rts[(i << 1) + 1] = mul(rts[i], z);
			}
			++base;
		}
	}

	void ntt(vector<int> &a)
	{
		const int n = (int)a.size();
		assert((n & (n - 1)) == 0);
		int zeros = __builtin_ctz(n);
		ensure_base(zeros);
		int shift = base - zeros;
		for (int i = 0; i < n; i++)
		{
			if (i < (rev[i] >> shift))
			{
				swap(a[i], a[rev[i] >> shift]);
			}
		}
		for (int k = 1; k < n; k <<= 1)
		{
			for (int i = 0; i < n; i += 2 * k)
			{
				for (int j = 0; j < k; j++)
				{
					int z = mul(a[i + j + k], rts[j + k]);
					a[i + j + k] = add(a[i + j], mod - z);
					a[i + j] = add(a[i + j], z);
				}
			}
		}
	}

	vector<int> multiply(vector<int> a, vector<int> b)
	{
		int need = a.size() + b.size() - 1;
		int nbase = 1;
		while ((1 << nbase) < need)
			nbase++;
		ensure_base(nbase);
		int sz = 1 << nbase;
		a.resize(sz, 0);
		b.resize(sz, 0);
		ntt(a);
		ntt(b);
		int inv_sz = inverse(sz);
		for (int i = 0; i < sz; i++)
		{
			a[i] = mul(a[i], mul(b[i], inv_sz));
		}
		reverse(a.begin() + 1, a.end());
		ntt(a);
		a.resize(need);
		return a;
	}

	vector<int> pol_pow(vector<int> a, int n)
	{
		int need = a.size() * n - (n - 1);
		int nbase = 1;
		while ((1 << nbase) < need)
			nbase++;
		ensure_base(nbase);
		int sz = 1 << nbase;
		a.resize(sz, 0);
		ntt(a);
		int inv_sz = inverse(sz);
		for (int i = 0; i < sz; i++)
		{
			a[i] = mul(mpow(a[i], n), inv_sz);
		}
		reverse(a.begin() + 1, a.end());
		ntt(a);
		a.resize(need);
		return a;
	}
};

#include<atcoder/all>
using namespace atcoder;
int main()
{
	M = 998244353;
	setcomb();
	ll n, cnt[111111] = {};
	cin >> n;
	ll h;
	rep(i, n * 2) cin >> h, cnt[--h]++;
	sort(cnt, cnt + 100000);
	ll cnt2;
	NumberTheoreticTransform<mod> ntt;
	vector<int> x(n + 1, 0);
	x[0] = 1;
	rep(i, 100000){
		if(i==0)
			cnt2 = 1;
		else{
			if(cnt[i]!=cnt[i-1]){
				vector<int> p(cnt[i - 1] / 2 + 1, 0);
				rep(j, cnt[i - 1] / 2 + 1) p[j] = comb(cnt[i - 1], j * 2);
				x = ntt.multiply(x, ntt.pol_pow(p, cnt2));
				cnt2 = 1;
			}
			else
				cnt2++;
		}
	}
	vector<int> pl(cnt[99999] / 2 + 1, 0);
	rep(j, cnt[99999] / 2 + 1) pl[j] = comb(cnt[99999], j * 2);
	x = ntt.multiply(x, ntt.pol_pow(pl, cnt2));
	mint k[55555];
	k[0] = 1;
	rep(i, n) k[(i + 1) * 2] = k[i * 2] / (i+1) * comb((i + 1) * 2, 2);
	mint ans = 0;
	rep(i,n+1){
		if(i%2==0)
			ans += k[2 * (n - i)] * x[i];
		else
			ans -= k[2 * (n - i)] * x[i];
	}
	cout << ans << endl;
}


Compiler output:
a.cc:441:9: fatal error: atcoder/all: No such file or directory
  441 | #include<atcoder/all>
      |         ^~~~~~~~~~~~~
compilation terminated.