// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x,l,r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf = numeric_limits::max()/2-1; auto constexpr INF32 = inf; auto constexpr INF64 = inf; auto constexpr INF = inf; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } const int dx[] = { 1,0,-1,0,1,-1,-1,1 }; const int dy[] = { 0,1,0,-1,1,1,-1,-1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } // [a,b] template Int rand(Int a, Int b) { static mt19937_64 mt{random_device{}()}; return uniform_int_distribution(a,b)(mt); } i64 irand(i64 a, i64 b) { return rand(a,b); } u64 urand(u64 a, u64 b) { return rand(a,b); } template void shuffle(It l, It r) { shuffle(l, r, mt19937_64(random_device{}())); } // <<< // >>> runtime modint template class runtime_modint { using i32 = int32_t; using i64 = int64_t; using M = runtime_modint; i32 x; public: static i32& mod() { static i32 mod = 0; return mod; } runtime_modint(i64 x = 0) : x((assert(mod() > 0), ((x%=mod()) < 0 ? x+mod() : x))) { } i64 val() const { return x; } bool operator==(M const& r) const { return x == r.x; } bool operator!=(M const& r) const { return x != r.x; } M operator+() const { return *this; } M operator-() const { return M()-*this; } M& operator+=(M const& r) { i64 t = i64(x) + r.x; if (t >= mod()) t -= mod(); x = t; return *this; } M& operator-=(M const& r) { i64 t = i64(x) + mod()-r.x; if (t >= mod()) t -= mod(); x = t; return *this; } M& operator*=(M const& r) { return *this = *this * r; } M operator*(M const& r) const { M t; t.x = (i64(x)*r.x) % mod(); return t; } M& operator/=(M const& r) { return *this *= r.inv(); } M operator+(M const& r) const { return M(*this) += r; } M operator-(M const& r) const { return M(*this) -= r; } M operator/(M const& r) const { return M(*this) /= r; } friend M operator+(i64 x, M const& y) { return M(x)+y; } friend M operator-(i64 x, M const& y) { return M(x)-y; } friend M operator*(i64 x, M const& y) { return M(x)*y; } friend M operator/(i64 x, M const& y) { return M(x)/y; } M pow(i64 n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } M inv() const { assert(x > 0); i64 t = 1, v = x, q = 0, r = 0; while (v != 1) { q = mod() / v; r = mod() % v; if (r * 2 < v) { t *= -q; t %= mod(); v = r; } else { t *= q + 1; t %= mod(); v -= r; } } if (t < 0) t += mod(); M y; y.x = t; return y; } static i64 gen() { // assume mod():prime if (mod() == 2) return 1; vector ps; int n = mod()-1; for (int i = 2; i*i <= n; ++i) { if (n % i) continue; ps.push_back(i); do n /= i; while (n % i == 0); } if (n > 1) ps.push_back(n); n = mod()-1; auto check = [&](M g) { for (int p : ps) if (g.pow(n/p) == 1) return false; return true; }; for (int g = 2; g <= n; ++g) if (check(g)) return g; return -1; } int log(M y) { assert(x > 0); assert(gcd(x, mod()) == 1); // int s = 1; while (s*s < mod()) s++; unordered_map m; M c = 1; for (int i = 0; i < s; ++i) { if (!m.count(c.val())) m[c.val()] = i; c *= *this; if (c.val() == 1) return i+1; } M d = pow(-s); c = y; for (int i = 0; i < s; ++i) { if (m.count(c.val())) { int ans = i*s + m[c.val()]; if (ans > 0) return ans; } c *= d; } return -1; } #ifdef LOCAL // friend string to_s(M r) { return to_s(r.val(), M::mod()); } friend string to_s(M r) { return to_s(r.val()); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; using mint = runtime_modint<-1>; // <<< auto solve() { int n; cin >> n; while (n % 2 == 0) n /= 2; while (n % 5 == 0) n /= 5; if (n == 1) { cout << 1 << "\n"; } else { mint::mod() = n; cout << mint(10).log(1) << "\n"; } } int32_t main() { int t; cin >> t; while (t--) { solve(); // cout << (solve() ? "YES" : "NO") << "\n"; debug { cerr << endl; } } }