#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r)-1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; // const int MOD = 1000000007; const int MOD = 998244353; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template vector divisors(const T &n) { vector ret; for (T i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(begin(ret), end(ret)); return ret; } template vector> prime_factor(T n) { vector> ret; for (T i = 2; i * i <= n; i++) { int cnt = 0; while (n % i == 0) cnt++, n /= i; if (cnt > 0) ret.emplace_back(i, cnt); } if (n > 1) ret.emplace_back(n, 1); return ret; } template bool is_prime(const T &n) { if (n == 1) return false; for (T i = 2; i * i <= n; i++) { if (n % i == 0) return false; } return true; } // 1,2,...,n のうち k と互いに素である自然数の個数 template T coprime(T n, T k) { vector> ps = prime_factor(k); int m = ps.size(); T ret = 0; for (int i = 0; i < (1 << m); i++) { T prd = 1; for (int j = 0; j < m; j++) { if ((i >> j) & 1) prd *= ps[j].first; } ret += (__builtin_parity(i) ? -1 : 1) * (n / prd); } return ret; } vector Eratosthenes(const int &n) { vector ret(n + 1, true); if (n >= 0) ret[0] = false; if (n >= 1) ret[1] = false; for (int i = 2; i * i <= n; i++) { if (!ret[i]) continue; for (int j = i + i; j <= n; j += i) ret[j] = false; } return ret; } vector Eratosthenes2(const int &n) { vector ret(n + 1); iota(begin(ret), end(ret), 0); if (n >= 0) ret[0] = -1; if (n >= 1) ret[1] = -1; for (int i = 2; i * i <= n; i++) { if (ret[i] < i) continue; for (int j = i + i; j <= n; j += i) ret[j] = min(ret[j], i); } return ret; } int main() { int N; cin >> N; vector a(N); rep(i, N) cin >> a[i]; int MAX = 1000000; vector dp(MAX + 1, 0); auto ps = Eratosthenes2(MAX); vector c(MAX + 1, 0); c[1] = -1; rep2(i, 2, MAX + 1) { int p = ps[i]; if (ps[i / p] == p) { c[i] = 0; } else { c[i] = -c[i / p]; } } c[1] = 0; rep(i, N) { auto ds = divisors(a[i]); mint tmp = 1; each(e, ds) tmp += dp[e] * c[e]; each(e, ds) dp[e] += tmp; } cout << dp[1] << '\n'; }