#965655 (C++17) No.2703 FizzBuzz Letter Counting

• 問題: No.2703 FizzBuzz Letter Counting
• ユーザー: HIR180
• 提出日時: 2024-03-29 22:06:50
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,781 ms / 3,000 ms
• コード長: 12,954 bytes
• コンパイル時間: 3,911 ms
• コンパイル使用メモリ: 200,192 KB
• 実行使用メモリ: 6,780 KB
• 最終ジャッジ日時: 2024-09-30 16:03:05
• 合計ジャッジ時間: 56,958 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	10 ms; 5,248 KB
testcase_01	AC	23 ms; 5,248 KB
testcase_02	AC	235 ms; 5,248 KB
testcase_03	AC	1,538 ms; 6,652 KB
testcase_04	AC	434 ms; 5,248 KB
testcase_05	AC	449 ms; 5,248 KB
testcase_06	AC	817 ms; 5,760 KB
testcase_07	AC	1,251 ms; 6,524 KB
testcase_08	AC	297 ms; 5,376 KB
testcase_09	AC	1,394 ms; 6,780 KB
testcase_10	AC	848 ms; 5,624 KB
testcase_11	AC	298 ms; 5,248 KB
testcase_12	AC	1,084 ms; 5,880 KB
testcase_13	AC	559 ms; 5,248 KB
testcase_14	AC	1,589 ms; 6,524 KB
testcase_15	AC	1,526 ms; 6,656 KB
testcase_16	AC	1,505 ms; 6,652 KB
testcase_17	AC	399 ms; 5,248 KB
testcase_18	AC	1,171 ms; 6,012 KB
testcase_19	AC	985 ms; 5,880 KB
testcase_20	AC	1,164 ms; 5,976 KB
testcase_21	AC	812 ms; 5,632 KB
testcase_22	AC	554 ms; 5,248 KB
testcase_23	AC	1,648 ms; 6,520 KB
testcase_24	AC	936 ms; 5,880 KB
testcase_25	AC	1,018 ms; 5,756 KB
testcase_26	AC	1,582 ms; 6,656 KB
testcase_27	AC	1,413 ms; 6,780 KB
testcase_28	AC	1,725 ms; 6,776 KB
testcase_29	AC	1,710 ms; 6,648 KB
testcase_30	AC	1,741 ms; 6,648 KB
testcase_31	AC	1,710 ms; 6,652 KB
testcase_32	AC	1,695 ms; 6,648 KB
testcase_33	AC	1,714 ms; 6,528 KB
testcase_34	AC	1,736 ms; 6,656 KB
testcase_35	AC	1,771 ms; 6,656 KB
testcase_36	AC	1,691 ms; 6,780 KB
testcase_37	AC	1,702 ms; 6,524 KB
testcase_38	AC	1,729 ms; 6,780 KB
testcase_39	AC	1,715 ms; 6,580 KB
testcase_40	AC	1,781 ms; 6,652 KB
testcase_41	AC	1,708 ms; 6,548 KB
testcase_42	AC	1,716 ms; 6,776 KB
testcase_43	AC	19 ms; 5,248 KB
testcase_44	AC	3 ms; 5,248 KB
testcase_45	AC	19 ms; 5,248 KB
testcase_46	AC	19 ms; 5,248 KB
testcase_47	AC	22 ms; 5,248 KB
testcase_48	AC	10 ms; 5,248 KB
testcase_49	AC	16 ms; 5,248 KB
testcase_50	AC	18 ms; 5,248 KB
testcase_51	AC	19 ms; 5,248 KB
testcase_52	AC	13 ms; 5,248 KB
testcase_53	AC	19 ms; 5,248 KB
testcase_54	AC	9 ms; 5,248 KB
testcase_55	AC	10 ms; 5,248 KB
testcase_56	AC	16 ms; 5,248 KB
testcase_57	AC	21 ms; 5,248 KB
testcase_58	AC	2 ms; 5,248 KB
testcase_59	AC	3 ms; 5,248 KB
testcase_60	AC	3 ms; 5,248 KB
testcase_61	AC	3 ms; 5,248 KB
testcase_62	AC	3 ms; 5,248 KB

ソースコード

//Let's join Kaede Takagaki Fan Club !!
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cassert>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <functional>
#include <iostream>
#include <map>
#include <set>
//#include <unordered_map>
//#include <unordered_set>
#include <cassert>
#include <iomanip>
#include <chrono>
#include <random>
#include <bitset>
#include <complex>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
//#include <atcoder/convolution>
//#include <atcoder/lazysegtree>
//#include <atcoder/maxflow>
//#include <atcoder/mincostflow>
//#include <atcoder/segtree>
//#include <atcoder/string>
using namespace std;
//using namespace atcoder;
#define int long long
//#define L __int128
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define a first
#define b second
#define fi first
#define sc second
#define rng(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,x) for(int i=0;i<x;i++)
#define gnr(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);i--)
#define per(i,b) gnr(i,0,b)
#define repn(i,x) for(int i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())
#define all(x) x.begin(),x.end()
#define si(x) (int)(x.size())
#define pcnt(x) __builtin_popcountll(x)
#define all(x) x.begin(),x.end()

#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
 
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
 
template<class t> using vc=vector<t>;
 
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.fi<<","<<p.sc<<"}";
}
 
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}
 
 //https://codeforces.com/blog/entry/62393
struct custom_hash {
	static uint64_t splitmix64(uint64_t x) {
		// http://xorshift.di.unimi.it/splitmix64.c
		x += 0x9e3779b97f4a7c15;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
		x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
		return x ^ (x >> 31);
	}
 
	size_t operator()(uint64_t x) const {
		static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x + FIXED_RANDOM);
	}
	//don't make x negative!
	size_t operator()(pair<int,int> x)const{
		return operator()(uint64_t(x.first)<<32|x.second);
	}
};
//unordered_set -> dtype, null_type
//unordered_map -> dtype(key), dtype(value)
using namespace __gnu_pbds;
template<class t,class u>
using hash_table=gp_hash_table<t,u,custom_hash>;

template<class T>
void o(const T &a,bool space=false){
	cout << a << (space?' ':'\n');
}
//ios::sync_with_stdio(false);
const ll mod = 998244353;
//const ll mod = 1000000007;
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());

struct mint{
	ll v;
	mint(ll vv=0){s(vv%mod+mod);}
	mint& s(ll vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	mint operator-()const{return mint()-*this;}
	mint &operator+=(const mint&rhs){return s(v+rhs.v);}
	mint &operator-=(const mint&rhs){return s(v+mod-rhs.v);}
	mint &operator*=(const mint&rhs){v=ll(v)*rhs.v%mod;return *this;}
	mint &operator/=(const mint&rhs){return *this*=rhs.inv();}
	mint operator+(const mint&rhs)const{return mint(*this)+=rhs;}
	mint operator-(const mint&rhs)const{return mint(*this)-=rhs;}
	mint operator*(const mint&rhs)const{return mint(*this)*=rhs;}
	mint operator/(const mint&rhs)const{return mint(*this)/=rhs;}
	mint pow(ll n)const{
		if(n<0)return inv().pow(-n);
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	mint inv()const{return pow(mod-2);}
	friend mint operator+(ll x,const mint&y){
		return mint(x)+y;
	}
	friend mint operator-(ll x,const mint&y){
		return mint(x)-y;
	}
	friend mint operator*(ll x,const mint&y){
		return mint(x)*y;
	}
	friend mint operator/(ll x,const mint&y){
		return mint(x)/y;
	}
	friend ostream& operator<<(ostream&os,const mint&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,mint&m){
		ll x;is>>x;
		m=mint(x);
		return is;
	}
	bool operator<(const mint&r)const{return v<r.v;}
	bool operator==(const mint&r)const{return v==r.v;}
	bool operator!=(const mint&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};
ll modpow(ll x,ll n,ll _md=mod){
	ll res=1;
	while(n>0){
		if(n&1) res=res*x%_md;
		x=x*x%_md;
		n>>=1;
	}
	return res;
}
#define _sz 1
mint F[_sz],R[_sz];
void make(){
	F[0] = 1;
	for(int i=1;i<_sz;i++) F[i] = F[i-1] * i;
	R[_sz-1] = F[_sz-1].pow(mod-2);
	for(int i=_sz-2;i>=0;i--) R[i] = R[i+1] * (i+1);
}
mint C(int a,int b){
	if(b < 0 || a < b) return mint();
	return F[a]*R[b]*R[a-b];
}
using ld=long double;
using vi=vc<int>;
using ull=unsigned long long;
/*int dst(P p, P q){
	return (p.a-q.a)*(p.a-q.a)+(p.b-q.b)*(p.b-q.b);
}*/
/*template<class t>
void add_inplace(t &a, t b){
	if(a.size() < b.size()) swap(a, b);
	for(int i=0;i<si(b);i++){
		a[i] += b[i];
		if(a[i] < 0) a[i] += mod;
		if(a[i] >= mod) a[i] -= mod;
	}
	return ;
}*/
template<class t>
void ov(const vc<t>&a){
	if(a.empty()) return;
	rep(i, si(a)) cout << a[i] << (i+1==si(a)?'\n':' ');
}
//o(ans?"Yes":"No");

template<class T> using mat = vc<vc<T>>;
template<class T=int>
mat<T> make_e(int n, int m, T v = (int)1){
	mat<T>ret(n, vc<T>(m));
	rep(i, min(n, m)) ret[i][i] = v;
	return ret;
}
template<class T>
mat<T> operator+(mat<T> a, mat<T> b){
	assert(a.size() == b.size());
	if(a.size()) assert(a[0].size() == b[0].size());
	
	rep(i, a.size()) rep(j, a[0].size()){
		a[i][j] += b[i][j];
		if(a[i][j] >= mod) a[i][j] -= mod;
	}
	
	return a;
}
template<class T>
mat<T> operator-(mat<T> a, mat<T> b){
	assert(a.size() == b.size());
	if(a.size()) assert(a[0].size() == b[0].size());
	
	rep(i, a.size()) rep(j, a[0].size()){
		a[i][j] += mod - b[i][j];
		if(a[i][j] >= mod) a[i][j] -= mod;
	}
	
	return a;
}
template<class T>
mat<T> operator*(mat<T> a, mat<T> b){
	if(a.empty() || b.empty()) return mat<T>();
	int n = a.size();
	int m = b[0].size();
	int len = a[0].size();
	assert(len == b.size());
	mat<T>ret(n);
	rep(i, n) ret[i] = vc<T>(m);
	
	rep(i, n) rep(j, len) rep(k, m){
		ll add = (ll)(a[i][j]) * b[j][k];
		add %= mod;
		ret[i][k] += add;
		if(ret[i][k] >= mod) ret[i][k] -= mod;
	}
	return ret;
}
template<class T>
vc<T> operator*(mat<T> a, vc<T> b){
	if(a.empty() || b.empty()) return vc<T>();
	assert(si(a[0]) == si(b));
	vc<T>ret(si(a));
	rep(i, si(a)){
		rep(j, si(b)){
			ll add = (ll)a[i][j] * b[j] % mod;
			ret[i] += add;
			if(ret[i] >= mod) ret[i] -= mod;
		}
	}
	return ret;
}
template<class T>
mat<T> modpow(mat<T> a, int n){
	if(a.empty()) return mat<T>();
	mat<T>ret = make_e(a.size(), a[0].size(), (T)(1));
	while(n){
		if(n&1) ret = ret * a;
		a = a * a;
		n /= 2;
	}
	return ret;
}
template<class T>
ll det(mat<T>m){
	int n = m.size();
	assert(n > 0 && m[0].size() == n);
	
	ll ret = 1;
	for(int j=0;j<n;j++){
		int pivot=-1;
		for(int i=j;i<n;i++){
			if(m[i][j]){
				pivot = i; break;
			}
		}
		if(pivot == -1) return 0;
     	if(j != pivot){
			rep(k,n) swap(m[j][k],m[pivot][k]);
        	ret = -ret;
        }
        ret = ret * m[j][j] % mod;
		ll rev = modpow(m[j][j],mod-2);
		for(int i=j+1;i<n;i++){
			if(m[i][j]){
				ll gg = (ll)m[i][j]*rev%mod;
				for(int g=j;g<n;g++){
					m[i][g] -= (ll)m[j][g]*gg%mod;
					if(m[i][g]<0) m[i][g]+=mod;
				}
			}
		}
	}
	return (mod+ret)%mod;
}
//vc<vc<int>>bs;
template<class T>
vc<T>AxB(mat<T>A, vc<T>b){
	int r = A.size(), c = A[0].size();
	assert(b.size() == r);
	
	int nxt = 0, free = 0;
	vc<T>ret(c, 0);
	
	rep(j, c){
		int pivot = -1;
		for(int i=nxt;i<r;i++){
			if(A[i][j]){
				pivot = i; break;
			}
		}
		if(pivot == -1){
			free ++;
			continue;
		}
		if(nxt != pivot){
			rep(k, c) swap(A[nxt][k],A[pivot][k]);
			swap(b[nxt], b[pivot]);
		}
		ll rev = modpow(A[nxt][j],mod-2);
		for(int g=j;g<c;g++){
			A[nxt][g] = A[nxt][g]*rev%mod;
		}
		b[nxt] = b[nxt]*rev%mod;
		rep(i, r){
			if(i != nxt and A[i][j]){
				T gg = A[i][j];
				for(int g=j;g<c;g++){
					A[i][g] -= A[nxt][g]*gg%mod;
					if(A[i][g]<0) A[i][g]+=mod;
				}
				b[i] -= b[nxt]*gg%mod;
				if(b[i]<0) b[i]+=mod;
			}
		}
		nxt ++;
	}
	vc<int>fix(c, 0);
	vc<int>top(nxt);
	rep(i, nxt){
		rep(j, c){
			if(A[i][j] != 0){
				top[i] = j;
				fix[j] = 1;
				ret[j] = b[i];
				break;
			}
		}
	}
	//error
	for(int i=nxt;i<r;i++) if(b[i] != 0) return vc<T>();
	//get basis
	/*vc<vc<T>>basis(free);
	int id = 0;
	rep(j, c){
		if(fix[j] == 1) continue;
		vc<T>tmp(c, 0);
		tmp[j] = 1;
		for(int i=0;i<nxt;i++){
			tmp[top[i]] = (mod-A[i][j])%mod;
		}
		basis[id++] = tmp;
	}
	bs = basis;*/
	return ret;
}
//A...n*n matrix or n*2n matrix, left = A and right = E
template<class T>
mat<T>inv(mat<T>A){
	int r = A.size(), c = A[0].size();
	if(c == r){
		rep(i, r){
			A[i].resize(r+r, 0);
			rep(j, r) A[i][r+j] = (i == j);
		}
		c += r;
	}
	assert(c == r+r);
	rep(j, r){
		int pivot = -1;
		for(int i=j;i<r;i++){
			if(A[i][j]){
				pivot = i; break;
			}
		}
		if(pivot == -1){
			return mat<T>();
		}
		if(j != pivot){
			rep(k, c) swap(A[j][k],A[pivot][k]);
		}
		ll rev = modpow(A[j][j],mod-2);
		for(int g=j;g<c;g++){
			A[j][g] = A[j][g]*rev%mod;
		}
		rep(i, r){
			if(i != j and A[i][j]){
				T gg = A[i][j];
				for(int g=j;g<c;g++){
					A[i][g] -= A[j][g]*gg%mod;
					if(A[i][g]<0) A[i][g]+=mod;
				}
			}
		}
	}
	mat<int>ret = make_e(r, r, 0LL);
	rep(i, r) rep(j, r){
		assert(A[i][j] == (i==j));
		ret[i][j] = A[i][r+j];
	}
	return ret;
}
//B...bitset
//T...int
//F2 /64
template<class B, class T=int>
vc<T>AxB(vc<B>A, vc<T>b){
	int r = A.size(), c = A[0].size();
	assert(b.size() == r);
	
	int nxt = 0;
	vc<T>ret(c);
	
	rep(j, c){
		int pivot = -1;
		for(int i=nxt;i<r;i++){
			if(A[i][j]){
				pivot = i; break;
			}
		}
		if(pivot == -1){
			continue;
		}
		if(nxt != pivot){
			swap(A[nxt], A[pivot]);
			swap(b[nxt], b[pivot]);
		}
		rep(i, r){
			if(i != nxt and A[i][j]){
				A[i] ^= A[nxt];
				b[i] ^= b[nxt];
			}
		}
		nxt ++;
	}
	vc<T>fix(c, 0);
	vc<T>top(nxt);
	rep(i, nxt){
		rep(j, c){
			if(A[i][j] != 0){
				top[i] = j;
				fix[j] = 1;
				ret[j] = b[i];
				break;
			}
		}
	}
	//error
	for(int i=nxt;i<r;i++) if(b[i] != 0) return vc<T>();
	return ret;
}

void solve(){
	mat<int>M[10];
	rep(i,10){
		M[i] = make_e<int>(120, 120, 0);
	}
	rep(now,10){
		rep(m3, 3){
			rep(m5, 5){
				rep(eq, 2){
					rep(isz, 2){
						int id = m3*20 + m5*4 + eq*2 + isz;
						//id -> count
						rep(nxt, 10){
							if(eq == 1 and now < nxt) continue;
							int nid = (m3*10+nxt)%3*20 + (m5*10+nxt)%5*4
							+ (eq == 1 and now == nxt)*2 + (isz == 1 and nxt == 0);
							
							M[now][nid][id] ++;
							if(isz == 1 and nxt == 0);
							else M[now][nid+60][id] ++;
							M[now][nid+60][id+60] ++;
						}
					}
				}
			}
		}
	}
	vi dp(120);
	//0,0,1,1
	dp[3] = 1;
	int m;cin>>m;
	int sum = 0;
	vc<P>vec;
	rep(i,m){
		int v; int len;
		cin>>v>>len;
		sum += len;
		vec.eb(v, len);
		//dp = (modpow(M[v],len)*dp);
	}
	
	dp = modpow(M[9],sum-1)*dp;
	auto get=[&](int t, int add)->mint{
		//10^t+add / 15
		int rem = modpow(10, t, 15) + add;
		rem %= 15;
		
		//10^t+add-rem / 15
		int up = modpow(10, t) + add - rem;
		up *= modpow(15, mod-2);
		
		return mint(up%mod);
	};
	auto get2=[&](int add)->mint{
		//vec+add / 15
		int now = 0;
		for(auto [v, len]:vec){
			now = now * modpow(10, len, 15) % 15;
			//v * (10^len-1) / 9
			int up = v * (modpow(10, len, 135)-1) % 135;
			up /= 9;
			now = (now+up)%15;
		}
		int rem = (now+add)%15;
		//vec+add-rem / 15
		mint ret;
		for(auto [v, len]:vec){
			ret = ret*modpow(10,len);
			ret += v*(modpow(10,len)-1)*modpow(9,mod-2);
		}
		ret += add-rem;
		ret /= mint(15);
		return ret;
	};
	
	mint ans;
	rep(r,15){
		//[10^(sum-1), vec]
		//[10^(sum-1)+15-r, vec+15-r]
		mint now = get2(15-r) - get(sum-1, 14-r);
		
		if(r == 0){
			ans += now * 8;
		}
		else if(r%3 == 0 or r%5 == 0){
			ans += now * 4;
		}
		else{
			ans += now * (sum%mod);
		}
	}
	{
		rep(m3, 3){
			rep(m5, 5){
				rep(eq, 2){
					rep(isz, 2){
						int id = m3*20 + m5*4 + eq*2 + isz;
						if(m3 == 0 and m5 == 0){
							ans += dp[id] * 8 % mod;
						}
						else if(m3 == 0 or m5 == 0){
							ans += dp[id] * 4 % mod;
						}
						else{
							ans += dp[id+60];
						}
					}
				}
			}
		}
	}
	o(ans+mod-8);
}
signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	int t; t=1;//cin >> t;
	while(t--) solve();
}