#line 1 "Main.cpp" #line 2 "nachia\\math\\prime-sieve-explicit.hpp" #include #include #include #include namespace nachia{ namespace prime_sieve_explicit_internal{ std::vector isprime = { false }; // a[x] := isprime(2x+1) void CalcIsPrime(int z){ if((int)isprime.size() *2+1 < z+1){ int new_z = isprime.size(); while(new_z*2+1 < z+1) new_z *= 2; z = new_z-1; isprime.resize(z+1, true); for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){ for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false; } } } std::vector prime_list = {2}; int prime_list_max = 0; void CalcPrimeList(int z){ while((int)prime_list.size() < z){ if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } void CalcPrimeListUntil(int z){ if(prime_list_max < z){ CalcIsPrime(z); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } } bool IsprimeExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n == 2) return true; if(n % 2 == 0) return false; CalcIsPrime(n); return isprime[(n-1)/2]; } int NthPrimeExplicit(int n){ using namespace prime_sieve_explicit_internal; CalcPrimeList(n); return prime_list[n]; } int PrimeCountingExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n < 2) return 0; CalcPrimeListUntil(n); auto res = ::std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin(); return (int)res; } // [l, r) ::std::vector SegmentedSieveExplicit(long long l, long long r){ assert(0 <= l); assert(l <= r); long long d = r - l; if(d == 0) return {}; ::std::vector res(d, true); for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){ long long il = (l+p-1)/p, ir = (r+p-1)/p; if(il <= p) il = p; for(long long i=il; i> 1) & (~0ull/3)); c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5)); c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17)); c = (c * (~0ull/257)) >> 56; return c; #endif } // please ensure x != 0 int MsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return 63 - __builtin_clzll(x); #else int res = 0; for(int d=32; d>=0; d>>=1) if(x >> d){ res |= d; x >>= d; } return res; #endif } // please ensure x != 0 int LsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return __builtin_ctzll(x); #else return msb_idx(x & -x); #endif } } #line 4 "Main.cpp" #line 6 "Main.cpp" #include #line 9 "Main.cpp" #include #include using namespace std; using i32 = int32_t; using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; #define rep(i,n) for(int i=0; i<(int)(n); i++) using Modint = atcoder::static_modint<998244353>; int main(){ int N; cin >> N; vector A(N); rep(i,N) cin >> A[i]; int maxA = *max_element(A.begin(), A.end()); vector> P(maxA+1); for(int p=1; p<=maxA; p++) if(nachia::IsprimeExplicit(p)) for(int q=p; q<=maxA; q+=p) P[q].push_back(p); vector> divs(maxA+1); auto QueryDivs = [&](int a) -> vector { if(divs[a].size()) return divs[a]; divs[a] = {1}; for(int p : P[a]){ int z = divs[a].size(); rep(i,z) divs[a].push_back(divs[a][i] * p); } return divs[a]; }; Modint ans = 0; vector dp(maxA+1, 0); for(int a : A){ Modint c = 0; auto D = QueryDivs(a); for(int d : D) if(d != 1) c += dp[d]; c += 1; rep(i,D.size()) if(i != 0) dp[D[i]] += ((nachia::Popcount(i)%2) ? c : -c); if(a == 1) ans += 1; } for(auto a : dp) ans += a; cout << ans.val() << '\n'; return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } } ios_do_not_sync_instance;