#pragma region opt #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma endregion opt #pragma region header #include #pragma endregion header #pragma region type using i8 = std::int8_t; using i16 = std::int16_t; using i32 = std::int32_t; using i64 = std::int64_t; using i128 = __int128_t; using u8 = std::uint8_t; using u16 = std::uint16_t; using u32 = std::uint32_t; using u64 = std::uint64_t; using u128 = __uint128_t; template using vec = std::vector; template using vvec = std::vector>; template using vvvec = std::vector>>; #pragma endregion type #pragma region MACRO #define FOR(i,a,b) for(int i=(a), i##_len=(b); i((obj).size())) #define POPCNT32(a) __builtin_popcount((a)) #define POPCNT64(a) __builtin_popcountll((a)) #define CTZ32(a) __builtin_ctz((a)) #define CLZ32(a) __builtin_clz((a)) #define CTZ64(a) __builtin_ctzll((a)) #define CLZ64(a) __builtin_clzll((a)) #define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1)) #define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1)) #define MSB32(a) ((31) - __builtin_clz((a))) #define MSB64(a) ((63) - __builtin_clzll((a))) #define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0)) #define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0)) #define LSBit(a) ((a) & (-(a))) #define CLSBit(a) ((a) & ((a) - (1))) #define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a))))) #define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a))))) #define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a))))) #define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a))))) #define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32)))))) #define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32)))))) #define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s))))) #define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s))))) #define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64)))))) #define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64)))))) #define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s))))) #define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s))))) #pragma endregion MACRO #pragma region io // -2147483648 ~ 2147483647 (> 10 ^ 9) i32 in_i32(void) { i32 c, x = 0, f = 1; while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f; while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return f * x; } static inline void out_i32_inner(i32 x) { if (x >= 10) out_i32_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void out_i32(i32 x) { if (x < 0) { putchar_unlocked('-'); x = -x; } out_i32_inner(x); } // -9223372036854775808 ~ 9223372036854775807 (> 10 ^ 18) i64 in_i64(void) { i64 c, x = 0, f = 1; while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f; while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return f * x; } static inline void out_i64_inner(i64 x) { if (x >= 10) out_i64_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void out_i64(i64 x) { if (x < 0) { putchar_unlocked('-'); x = -x; } out_i64_inner(x); } // 0 ~ 4294967295 (> 10 ^ 9) u32 in_u32(void) { u32 c, x = 0; while (c = getchar_unlocked(), c < 48 || c > 57); while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return x; } void out_u32(u32 x) { if (x >= 10) out_u32(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } // 0 ~ 18446744073709551615 (> 10 ^ 19) u64 in_u64(void) { u64 c, x = 0; while (c = getchar_unlocked(), c < 48 || c > 57); while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return x; } void out_u64(u64 x) { if (x >= 10) out_u64(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void NL(void) { putchar_unlocked('\n'); } void SP(void) { putchar_unlocked(' '); } #pragma endregion io #pragma region util template inline bool chmax(T& a,T b){ if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a,T b){ if (a > b) { a = b; return 1; } return 0; } #pragma endregion util #pragma region runtime montgomery modint struct Runtime_Montgomery_Modint32 { private: using m32 = u32; public: inline static m32 one, r2, n, md; static void set_mod(u32 m) { md = m; one = u32(-1u) % m + 1; r2 = u64(i64(-1)) % m + 1; u32 nn = m; for (int _ = 0; _ < 4; ++_) nn *= 2 - nn * m; n = nn; } static m32 reduce(u64 a) { u32 y = (u32(a >> 32)) - (u32((u64(u32(a) * n) * md) >> 32)); return i32(y) < 0 ? y + md : y; } Runtime_Montgomery_Modint32() : x(0) { } Runtime_Montgomery_Modint32(u32 x) : x(reduce(u64(x) * r2)) { } m32 x; Runtime_Montgomery_Modint32 &operator+=(Runtime_Montgomery_Modint32 y) { x += y.x - md; if (i32(x) < 0) x += md; return *this; } Runtime_Montgomery_Modint32 &operator-=(Runtime_Montgomery_Modint32 y) { if (i32(x -= y.x) < 0) x += 2 * md; return *this; } Runtime_Montgomery_Modint32 &operator*=(Runtime_Montgomery_Modint32 y) { x = reduce(u64(x) * y.x); return *this; } Runtime_Montgomery_Modint32 operator+(Runtime_Montgomery_Modint32 y) const { return Runtime_Montgomery_Modint32(*this) += y; } Runtime_Montgomery_Modint32 operator-(Runtime_Montgomery_Modint32 y) const { return Runtime_Montgomery_Modint32(*this) -= y; } Runtime_Montgomery_Modint32 operator*(Runtime_Montgomery_Modint32 y) const { return Runtime_Montgomery_Modint32(*this) *= y; } bool operator==(Runtime_Montgomery_Modint32 y) const { return (x >= md ? x - md : x) == (y.x >= md ? y.x - md : y.x); } bool operator!=(Runtime_Montgomery_Modint32 y) const { return not operator==(y); } Runtime_Montgomery_Modint32 pow(u64 k) { Runtime_Montgomery_Modint32 y = 1, z = *this; for ( ; k; k >>= 1, z *= z) if (k & 1) y *= z; return y; } Runtime_Montgomery_Modint32 inv() { return (*this).pow(md - 2); } m32 get_raw() { return x; } u32 get_val() { return reduce(u64(x)); } }; struct Runtime_Montgomery_Modint64 { private: using m64 = u64; public: inline static m64 one, r2, n, md; static void set_mod(u64 m) { md = m; one = u64(-1ull) % m + 1; r2 = u128(i128(-1)) % m + 1; u64 nn = m; for (int _ = 0; _ < 5; ++_) nn *= 2 - nn * m; n = nn; } static m64 reduce(u128 a) { u64 y = (u64(a >> 64)) - (u64((u128(u64(a) * n) * md) >> 64)); return i64(y) < 0 ? y + md : y; } Runtime_Montgomery_Modint64() : x(0) { } Runtime_Montgomery_Modint64(u64 x) : x(reduce(u128(x) * r2)) { } m64 x; Runtime_Montgomery_Modint64 &operator+=(Runtime_Montgomery_Modint64 y) { x += y.x - md; if (i64(x) < 0) x += md; return *this; } Runtime_Montgomery_Modint64 &operator-=(Runtime_Montgomery_Modint64 y) { if (i64(x -= y.x) < 0) x += 2 * md; return *this; } Runtime_Montgomery_Modint64 &operator*=(Runtime_Montgomery_Modint64 y) { x = reduce(u128(x) * y.x); return *this; } Runtime_Montgomery_Modint64 operator+(Runtime_Montgomery_Modint64 y) const { return Runtime_Montgomery_Modint64(*this) += y; } Runtime_Montgomery_Modint64 operator-(Runtime_Montgomery_Modint64 y) const { return Runtime_Montgomery_Modint64(*this) -= y; } Runtime_Montgomery_Modint64 operator*(Runtime_Montgomery_Modint64 y) const { return Runtime_Montgomery_Modint64(*this) *= y; } bool operator==(Runtime_Montgomery_Modint64 y) const { return (x >= md ? x - md : x) == (y.x >= md ? y.x - md : y.x); } bool operator!=(Runtime_Montgomery_Modint64 y) const { return not operator==(y); } Runtime_Montgomery_Modint64 pow(u64 k) { Runtime_Montgomery_Modint64 y = 1, z = *this; for ( ; k; k >>= 1, z *= z) if (k & 1) y *= z; return y; } Runtime_Montgomery_Modint64 inv() { return (*this).pow(md - 2); } m64 get_raw() { return x; } u64 get_val() { return reduce(u128(x)); } }; #pragma endregion runtime montgomery modint #pragma region mr u32 is_prime32(u32 n) { using m32 = Runtime_Montgomery_Modint32; m32::set_mod(n); m32 o{1}; m32 r{n - 1}; u32 base[] = { 2u, 7u, 61u }; u32 d = (n - 1) >> __builtin_ctz(n - 1); for (int i = 0; i < 3; i++) { if (n <= base[i]) break; m32 a(base[i]); u32 t = d; m32 y = a.pow(t); while (t != (n - 1) && y != o && y != r) { y *= y; t <<= 1; } if (y != r && (!(t & 1))) return 0; } return 1; } u64 is_prime64(u64 n) { using m64 = Runtime_Montgomery_Modint64; m64::set_mod(n); m64 o{1}; m64 r{n - 1}; u64 base[] = { 2ul, 325ul, 9375ul, 28178ul, 450775ul, 9780504ul, 1795265022ul }; u64 d = (n - 1) >> __builtin_ctzll(n - 1); for (int i = 0; i < 7; i++) { if (n <= base[i]) break; m64 a(base[i]); u64 t = d; m64 y = a.pow(t); while (t != (n - 1) && y != o && y != r) { y *= y; t <<= 1; } if (y != r && (!(t & 1))) return 0; } return 1; } u32 is_prime(u64 n) { if (n <= 1) return 0; if (n <= 3) return 1; if (!(n & 1)) return 0; if (n < (1ull << 30)) return is_prime32(u32(n)); return is_prime64(n); } #pragma endregion mr void Main() { // your source here u64 Q = in_u64(); while (Q--) { u64 x = in_u64(); out_u64(x); SP(); out_u32(is_prime(x)); NL(); } return; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr); std::cout << std::fixed << std::setprecision(13); std::cerr << std::fixed << std::setprecision(3); Main(); }