【ZJOI2019】麻将

【ZJOI2019】麻将

dp套dp+自动机。

/*
{
######################
#       Author       #
#        Gary        #
#        2021        #
######################
*/
#include<bits/stdc++.h>
#define rb(a,b,c) for(int a=b;a<=c;++a)
#define rl(a,b,c) for(int a=b;a>=c;--a)
#define LL long long
#define ULL unsigned long long
#define IT iterator
#define PB push_back
#define II(a,b) make_pair(a,b)
#define FIR first
#define SEC second
#define FREO freopen("check.out","w",stdout)
#define rep(a,b) for(int a=0;a<b;++a)
#define SRAND mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define random(a) rng()%a
#define ALL(a) a.begin(),a.end()
#define POB pop_back
#define ff fflush(stdout)
#define fastio ios::sync_with_stdio(false)
#define check_min(a,b) a=min(a,b)
#define check_max(a,b) a=max(a,b)
using namespace std;
//inline int read(){
//    int x=0;
//    char ch=getchar();
//    while(ch<'0'||ch>'9'){
//        ch=getchar();
//    }
//    while(ch>='0'&&ch<='9'){
//        x=(x<<1)+(x<<3)+(ch^48);
//        ch=getchar();
//    }
//    return x;
//}
const int INF=0x3f3f3f3f;
typedef pair<int,int> mp;
/*}
*/
struct state{
	int cnt,f[2][3][3];
	state(){cnt=0;rep(i,2) rep(j,3) rep(k,3) f[i][j][k]=-1;f[0][0][0]=0;}
	ULL get_hash(){
		ULL num=0;
		ULL z=1;
		rep(i,2)
			rep(j,3)
				rep(k,3)
				{
					num+=z*(f[i][j][k]>=0 ? f[i][j][k]:5);
					z*=10;
				}
		num+=z*cnt;
		return num;
	}
	state tran(int x){
		state ret;
		int nxtcnt,nxtf[2][3][3];
		nxtcnt=cnt;
		rep(i,2) rep(j,3) rep(k,3) nxtf[i][j][k]=-1;
		nxtcnt += x>=2;
		check_min(nxtcnt,7);
		rep(i,2) rep(j,3) rep(k,3){
			if(f[i][j][k]==-1) continue;
			if(j+k<=x){
				int rest=x-j-k;
				rb(l,0,min(2,rest)){
					check_max(nxtf[i|((rest-l)>=2)][k][l],f[i][j][k]+j);
					check_min(nxtf[i|((rest-l)>=2)][k][l],4);
					check_max(nxtf[i][k][l],f[i][j][k]+j+(rest-l)/3);
					check_min(nxtf[i][k][l],4);
				}
			}
		}
		ret.cnt=nxtcnt;
		rep(i,2) rep(j,3) rep(k,3) ret.f[i][j][k]=nxtf[i][j][k];
		return ret;
	}
	bool ok(){
		if(cnt==7||f[1][0][0]==4) return true;
		return false;
	}
};
unordered_map<ULL,int> id;
int trans[10000][5];
int cnt=0;
struct Mahjong{
	void dfs(state s){
		id[s.get_hash()]=++cnt;
		int now=cnt;
		rb(i,0,4){
			state nxt=s.tran(i);
			if(nxt.ok()) continue;
			if(id.find(nxt.get_hash())==id.end()){
				dfs(nxt);
			}
			trans[now][i]=id[nxt.get_hash()];
		}
	}
	void init(){
		dfs(state());
	}
}Mj;
const int MOD=998244353;
int c[5][5];
void add(int & A,int B){
	A+=B;
	if(A>=MOD) A-=MOD;
}
int need[101];
int quick(int A,int B){
	if(B==0) return 1;
	int tmp=quick(A,B>>1);
	tmp=1ll*tmp*tmp%MOD;
	if(B&1) tmp=1ll*tmp*A%MOD;
	return tmp;
}
int dp[101][401][2099];
int fact[401];
int main(){
	Mj.init();
	rb(i,0,4) c[0][i]=1;
	rb(i,1,4)
		rb(j,1,4) c[i][j]=c[i-1][j-1]+c[i][j-1];
	int n;
	scanf("%d",&n);
	rb(i,1,13){
		int a,b;
		scanf("%d%d",&a,&b);
		need[a]++;
	}
	dp[0][0][1]=1;
	rb(i,1,n){
		rb(k,0,4*(i-1)){
			rb(s,1,cnt){
				rb(j,need[i],4){
					int nxt=trans[s][j];
					if(nxt){
						add(dp[i][k+j][nxt],1ll*c[j-need[i]][4-need[i]]*dp[i-1][k][s]%MOD);
					}
				}
			}
		}
	}
	fact[0]=1;
	rb(i,1,4*n) fact[i]=1ll*fact[i-1]*i%MOD;
	int rest=0;
	rb(k,13,4*n){
		int sum=0;
		rb(i,1,cnt){
			add(sum,dp[n][k][i]);
		}
		sum=1ll*sum*fact[k-13]%MOD;
		sum=1ll*sum*fact[4*n-k]%MOD;
		add(rest,sum);
	}
	cout<<1ll*rest*quick(fact[4*n-13],MOD-2)%MOD<<endl;
	return 0;
}