#include using namespace std; namespace inner { using i32 = int32_t; using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; template T gcd(T a, T b) { while (b) swap(a %= b, b); return a; } uint64_t gcd_impl(uint64_t n, uint64_t m) { constexpr uint64_t K = 5; for (int i = 0; i < 80; ++i) { uint64_t t = n - m; uint64_t s = n - m * K; bool q = t < m; bool p = t < m * K; n = q ? m : t; m = q ? t : m; if (m == 0) return n; n = p ? n : s; } return gcd_impl(m, n % m); } uint64_t gcd_pre(uint64_t n, uint64_t m) { for (int i = 0; i < 4; ++i) { uint64_t t = n - m; bool q = t < m; n = q ? m : t; m = q ? t : m; if (m == 0) return n; } return gcd_impl(n, m); } uint64_t gcd_fast(uint64_t n, uint64_t m) { return n > m ? gcd_pre(n, m) : gcd_pre(m, n); } template T inv(T a, T p) { T b = p, x = 1, y = 0; while (a) { T q = b % a; swap(a, b /= a); swap(x, y -= q * x); } assert(b == 1); return y < 0 ? y + p : y; } template T modpow(T a, U n, T p) { T ret = 1; for (; n; n >>= 1, a = U(a) * a % p) if (n & 1) ret = U(ret) * a % p; return ret; } } // namespace inner using namespace std; unsigned long long rng() { static unsigned long long x_ = 88172645463325252ULL; x_ = x_ ^ (x_ << 7); return x_ = x_ ^ (x_ >> 9); } using namespace std; struct ArbitraryLazyMontgomeryModInt { using mint = ArbitraryLazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static u32 mod; static u32 r; static u32 n2; static u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static void set_mod(u32 m) { assert(m < (1 << 30)); assert((m & 1) == 1); mod = m; n2 = -u64(m) % m; r = get_r(); assert(r * mod == 1); } u32 a; ArbitraryLazyMontgomeryModInt() : a(0) {} ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)) {}; static u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } mint operator+(const mint &b) const { return mint(*this) += b; } mint operator-(const mint &b) const { return mint(*this) -= b; } mint operator*(const mint &b) const { return mint(*this) *= b; } mint operator/(const mint &b) const { return mint(*this) /= b; } bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint() - mint(*this); } mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = ArbitraryLazyMontgomeryModInt(t); return (is); } mint inverse() const { return pow(mod - 2); } u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static u32 get_mod() { return mod; } }; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2; using namespace std; struct montgomery64 { using mint = montgomery64; using i64 = int64_t; using u64 = uint64_t; using u128 = __uint128_t; static u64 mod; static u64 r; static u64 n2; static u64 get_r() { u64 ret = mod; for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret; return ret; } static void set_mod(u64 m) { assert(m < (1LL << 62)); assert((m & 1) == 1); mod = m; n2 = -u128(m) % m; r = get_r(); assert(r * mod == 1); } u64 a; montgomery64() : a(0) {} montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){}; static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; } mint &operator+=(const mint &b) { if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint &operator-=(const mint &b) { if (i64(a -= b.a) < 0) a += 2 * mod; return *this; } mint &operator*=(const mint &b) { a = reduce(u128(a) * b.a); return *this; } mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } mint operator+(const mint &b) const { return mint(*this) += b; } mint operator-(const mint &b) const { return mint(*this) -= b; } mint operator*(const mint &b) const { return mint(*this) *= b; } mint operator/(const mint &b) const { return mint(*this) /= b; } bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint() - mint(*this); } mint pow(u128 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = montgomery64(t); return (is); } mint inverse() const { return pow(mod - 2); } u64 get() const { u64 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static u64 get_mod() { return mod; } }; typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2; using namespace std; namespace fast_factorize { using u64 = uint64_t; template bool miller_rabin(u64 n, vector as) { if (mint::get_mod() != n) mint::set_mod(n); u64 d = n - 1; while (~d & 1) d >>= 1; mint e{1}, rev{int64_t(n - 1)}; for (u64 a : as) { if (n <= a) break; u64 t = d; mint y = mint(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool is_prime(u64 n) { if (~n & 1) return n == 2; if (n <= 1) return false; if (n < (1LL << 30)) return miller_rabin(n, {2, 7, 61}); else return miller_rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}); } template T pollard_rho(T n) { if (~n & 1) return 2; if (is_prime(n)) return n; if (mint::get_mod() != n) mint::set_mod(n); mint R, one = 1; auto f = [&](mint x) { return x * x + R; }; auto rnd = [&]() { return rng() % (n - 2) + 2; }; while (1) { mint x, y, ys, q = one; R = rnd(), y = rnd(); T g = 1; constexpr int m = 128; for (int r = 1; g == 1; r <<= 1) { x = y; for (int i = 0; i < r; ++i) y = f(y); for (int k = 0; g == 1 && k < r; k += m) { ys = y; for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y)); g = inner::gcd_fast(q.get(), n); } } if (g == n) do { g = inner::gcd_fast((x - (ys = f(ys))).get(), n); } while (g == 1); if (g != n) return g; } exit(1); } vector inner_factorize(u64 n) { if (n <= 1) return {}; u64 p; if (n <= (1LL << 30)) p = pollard_rho(n); else p = pollard_rho(n); if (p == n) return {p}; auto l = inner_factorize(p); auto r = inner_factorize(n / p); copy(begin(r), end(r), back_inserter(l)); return l; } vector factorize(u64 n) { auto ret = inner_factorize(n); sort(begin(ret), end(ret)); return ret; } } // namespace fast_factorize using fast_factorize::factorize; using fast_factorize::is_prime; using namespace std; namespace fastio { static constexpr int SZ = 1 << 17; char ibuf[SZ], obuf[SZ]; int pil = 0, pir = 0, por = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } inline void rd(char& c) { c = ibuf[pil++]; } template inline void rd(T& x) { if (pil + 32 > pir) load(); char c; do { c = ibuf[pil++]; } while (c < '-'); bool minus = 0; if (c == '-') { minus = 1; c = ibuf[pil++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = ibuf[pil++]; } if (minus) x = -x; } inline void rd() {} template inline void rd(Head& head, Tail&... tail) { rd(head); rd(tail...); } inline void wt(char c) { obuf[por++] = c; } template inline void wt(T x) { if (por > SZ - 32) flush(); if (!x) { obuf[por++] = '0'; return; } if (x < 0) { obuf[por++] = '-'; x = -x; } int i = 12; char buf[16]; while (x >= 10000) { memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; i -= 4; } if (x < 100) { if (x < 10) { wt(char('0' + char(x))); } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; obuf[por + 0] = '0' + q; obuf[por + 1] = '0' + r; por += 2; } } else { if (x < 1000) { memcpy(obuf + por, pre.num + (x << 2) + 1, 3); por += 3; } else { memcpy(obuf + por, pre.num + (x << 2), 4); por += 4; } } memcpy(obuf + por, buf + i + 4, 12 - i); por += 12 - i; } inline void wt() {} template inline void wt(Head head, Tail... tail) { wt(head); wt(tail...); } template inline void wtn(T x) { wt(x, '\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::wt; using fastio::wtn; using namespace std; int main() { int t; rd(t); while (t--) { int64_t n; rd(n); auto ret = is_prime(n); wt(n); wt(' '); if (ret) wt('1'); else wt('0'); wt('\n'); } }