// #define _GLIBCXX_DEBUG // #pragma GCC optimize("O2,unroll-loops") #include using namespace std; #define rep(i, n) for (int i = 0; i < int(n); i++) #define per(i, n) for (int i = (n)-1; 0 <= i; i--) #define rep2(i, l, r) for (int i = (l); i < int(r); i++) #define per2(i, l, r) for (int i = (r)-1; int(l) <= i; 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() 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'; } using ll = long long; using pii = pair; using pll = pair; 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 using minheap = std::priority_queue, std::greater>; template using maxheap = std::priority_queue; 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)); } // __int128_t gcd(__int128_t a, __int128_t b) { // if (a == 0) // return b; // if (b == 0) // return a; // __int128_t cnt = a % b; // while (cnt != 0) { // a = b; // b = cnt; // cnt = a % b; // } // return b; // } struct Union_Find_Tree { vector data; const int n; int cnt; Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {} int root(int x) { if (data[x] < 0) return x; return data[x] = root(data[x]); } int operator[](int i) { return root(i); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; // if (data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; cnt--; return true; } int size(int x) { return -data[root(x)]; } int count() { return cnt; }; bool same(int x, int y) { return root(x) == root(y); } void clear() { cnt = n; fill(begin(data), end(data), -1); } }; 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; } }; ll mpow(ll x, ll n, ll mod) { ll ans = 1; x %= mod; while (n != 0) { if (n & 1) ans = ans * x % mod; x = x * x % mod; n = n >> 1; } ans %= mod; return ans; } template T modinv(T a, const T &m) { T b = m, u = 1, v = 0; while (b > 0) { T t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return u >= 0 ? u % m : (m - (-u) % m) % m; } ll divide_int(ll a, ll b) { if (b < 0) a = -a, b = -b; return (a >= 0 ? a / b : (a - b + 1) / b); } // const int MOD = 1000000007; const int MOD = 998244353; using mint = Mod_Int; // ----- library ------- template struct Lazy_Segment_Tree { using Monoid = typename Acted_Monoid::Monoid; using Operator = typename Acted_Monoid::Operator; using M = typename Monoid::V; using O = typename Operator::V; int n, m, height; vector seg; vector lazy; // f(f(a,b),c) = f(a,f(b,c)), f(e1,a) = f(a,e1) = a // h(h(p,q),r) = h(p,h(q,r)), h(e2,p) = h(p,e2) = p // g(f(a,b),p) = f(g(a,p),g(b,p)) // g(g(a,p),q) = g(a,h(p,q)) Lazy_Segment_Tree(const vector &v) : n(v.size()) { m = 1, height = 0; while (m < n) m <<= 1, height++; seg.assign(2 * m, Monoid::id), lazy.assign(2 * m, Operator::id); copy(begin(v), end(v), begin(seg) + m); build(); } Lazy_Segment_Tree(int n, M x = Monoid::id) : Lazy_Segment_Tree(vector(n, x)) {} void set(int i, const M &x) { seg[m + i] = x; } void build() { for (int i = m - 1; i > 0; i--) seg[i] = Monoid::merge(seg[2 * i], seg[2 * i + 1]); } inline M reflect(int i) const { return Acted_Monoid::merge(seg[i], lazy[i]); } inline void recalc(int i) { while (i >>= 1) seg[i] = Monoid::merge(reflect(2 * i), reflect(2 * i + 1)); } inline void eval(int i) { lazy[2 * i] = Operator::merge(lazy[2 * i], lazy[i]); lazy[2 * i + 1] = Operator::merge(lazy[2 * i + 1], lazy[i]); seg[i] = reflect(i); lazy[i] = Operator::id; } inline void thrust(int i) { for (int j = height; j > 0; j--) eval(i >> j); } void update(int l, int r, const O &x) { l = max(l, 0), r = min(r, n); if (l >= r) return; l += m, r += m; thrust(l), thrust(r - 1); int a = l, b = r; while (l < r) { if (l & 1) lazy[l] = Operator::merge(lazy[l], x), l++; if (r & 1) r--, lazy[r] = Operator::merge(lazy[r], x); l >>= 1, r >>= 1; } recalc(a), recalc(b - 1); } M query(int l, int r) { l = max(l, 0), r = min(r, n); if (l >= r) return Monoid::id; l += m, r += m; thrust(l), thrust(r - 1); M L = Monoid::id, R = Monoid::id; while (l < r) { if (l & 1) L = Monoid::merge(L, reflect(l++)); if (r & 1) R = Monoid::merge(reflect(--r), R); l >>= 1, r >>= 1; } return Monoid::merge(L, R); } M operator[](int i) { return query(i, i + 1); } template int find_subtree(int i, const C &check, M &x, int type) { while (i < m) { eval(i); M nxt = type ? Monoid::merge(reflect(2 * i + type), x) : Monoid::merge(x, reflect(2 * i + type)); if (check(nxt)) { i = 2 * i + type; } else { x = nxt; i = 2 * i + (type ^ 1); } } return i - m; } // check(区間 [l,r] での演算結果) を満たす最小の r (なければ n) template int find_first(int l, const C &check) { M L = Monoid::id; int a = l + m, b = 2 * m; thrust(a); while (a < b) { if (a & 1) { M nxt = Monoid::merge(L, reflect(a)); if (check(nxt)) return find_subtree(a, check, L, 0); L = nxt; a++; } a >>= 1, b >>= 1; } return n; } // check(区間 [l,r) での演算結果) を満たす最大の l (なければ -1) template int find_last(int r, const C &check) { M R = Monoid::id; int a = m, b = r + m; thrust(b - 1); while (a < b) { if ((b & 1) || a == 1) { M nxt = Monoid::merge(reflect(--b), R); if (check(nxt)) return find_subtree(b, check, R, 1); R = nxt; } a >>= 1, b >>= 1; } return -1; } }; struct Monoid_1 { using V = int; static V merge(V a, V b) { int val = a + b; return val >= MOD ? val - MOD : val; } static const V id; }; constexpr Monoid_1::V Monoid_1::id = 0; struct Func_1 { int base, add; Func_1(int base, int add) : base(base), add(add) {} constexpr Func_1() : base(-1), add(0) {} }; struct Operator_1 { using V = Func_1; static V merge(V a, V b) { if (b.base != -1) return b; int val = a.add + b.add; return Func_1(a.base, val >= MOD ? val - MOD : val); } static const V id; }; constexpr Operator_1::V Operator_1::id = Func_1(); struct Acted_Monoid_1 { using Monoid = Monoid_1; using Operator = Operator_1; using M = typename Monoid::V; using O = typename Operator::V; static M merge(M a, O b) { int val = (b.base == -1 ? a : b.base) + b.add; return val >= MOD ? val - MOD : val; } }; // ----- library ------- int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); int n; cin >> n; vector ps; rep2(i, 2, 100) { bool f = true; for (int j = 2; j * j <= i; j++) { if (i % j == 0) f = false; } if (f) ps.eb(i); } int m = sz(ps); vector a(n); rep(i, n) cin >> a[i]; int q; cin >> q; vector> pa(m, vector(n, 0)); rep(i, n) rep(j, m) while (a[i] % ps[j] == 0) a[i] /= ps[j], pa[j][i]++; vector> seg; rep(i, m) seg.eb(pa[i]); while (q--) { int type; cin >> type; if (type == 1) { ll l, r, x; cin >> l >> r >> x; l--; rep(i, m) { int c = 0; while (x % ps[i] == 0) x /= ps[i], c++; seg[i].update(l, r, Func_1(c, 0)); } } if (type == 2) { ll l, r, x; cin >> l >> r >> x; l--; rep(i, m) { int c = 0; while (x % ps[i] == 0) x /= ps[i], c++; seg[i].update(l, r, Func_1(-1, c)); } } if (type == 3) { ll l, r, x; cin >> l >> r >> x; l--; mint ans = 1; rep(i, m) { if (ps[i] >= x) continue; ans *= seg[i].query(l, r) + 1; } cout << ans << '\n'; } } }