#pragma GCC optimize("Ofast") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx") #include using namespace std; using ull = unsigned long long; using ll = long long; #define mod 1000000007ll #define loop(i, n) for (int i = 0; i < n; i++) #define flagcount(bit) __builtin_popcount(bit) #define flag(x) (1ll << x) #define flagadd(bit, x) bit |= flag(x) #define flagpop(bit, x) bit &= ~flag(x) #define flagon(bit, i) bit &flag(i) #define flagoff(bit, i) !(bit & (1ll << i)) #define all(v) v.begin(), v.end() #define putout(a) cout << a << '\n' template bool chmax(T &a, const T &b) { if (a < b) { a = b; // aをbで更新 return true; } return false; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; // aをbで更新 return true; } return false; } void AS(ll X, ll L, ll R) { assert(L <= X && X <= R); } template bool primejudge(T n) { if (n < 2) return false; else if (n == 2) return true; else if (n % 2 == 0) return false; double sqrtn = sqrt(n); for (T i = 3; i < sqrtn + 1; i++) { if (n % i == 0) { return false; } i++; } return true; } //modかけ算 inline ull modd(ull a, ull m) { return (a % m + m) % m; } unsigned long long mul(unsigned long long a, unsigned long long b, unsigned long long p) { long long ret = a * b - p * (unsigned long long)((long double)(a) * (long double)(b) / (long double)(p)); return ret + p * (ret < 0) - p * (ret >= (long long)p); } //modpow ull modp(ull a, ull n, ull p) { ull res = 1; while (n > 0) { if (n & 1) res = mul(res, a, p); a = mul(a, a, p); n >>= 1ll; } return res; } //素数ならtrue,合成数ならfalseを返す bool MR(ull X) { if (X < 10000) return primejudge(X); if (X % 2 == 0) return false; ull Z = X - 1; ull s = 0, t = 0; while (Z % 2 == 0) { s++; Z /= 2; } t = Z; vector A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}; for (auto a : A) { bool ok = true; if (modp(a, t, X) == 1) { ok = false; continue; } ll Z = modp(a, t, X); for (ull i = 0; i < s; i++) { if (Z == X - 1) { ok = false; break; } Z %= X; Z = mul(Z, Z, X); } if (ok) { return false; //条件を満たすものが存在しなかった } } return true; } static struct IO { char tmp[1 << 10]; // fast input routines char cur; //#define nextChar() (cur = getc_unlocked(stdin)) //#define peekChar() (cur) inline char nextChar() { return cur = getc_unlocked(stdin); } inline char peekChar() { return cur; } inline operator bool() { return peekChar(); } inline static bool isBlank(char c) { return (c < '!' && c); } inline bool skipBlanks() { while (isBlank(nextChar())) ; return peekChar() != 0; } inline IO &operator>>(char &c) { c = nextChar(); return *this; } inline IO &operator>>(char *buf) { if (skipBlanks()) { if (peekChar()) { *(buf++) = peekChar(); while (!isBlank(nextChar())) *(buf++) = peekChar(); } *(buf++) = 0; } return *this; } inline IO &operator>>(string &s) { if (skipBlanks()) { s.clear(); s += peekChar(); while (!isBlank(nextChar())) s += peekChar(); } return *this; } inline IO &operator>>(double &d) { if ((*this) >> tmp) sscanf(tmp, "%lf", &d); return *this; } #define defineInFor(intType) \ inline IO &operator>>(intType &n) \ { \ if (skipBlanks()) \ { \ int sign = +1; \ if (peekChar() == '-') \ { \ sign = -1; \ n = nextChar() - '0'; \ } \ else \ n = peekChar() - '0'; \ while (!isBlank(nextChar())) \ { \ n += n + (n << 3) + peekChar() - 48; \ } \ n *= sign; \ } \ return *this; \ } defineInFor(int) defineInFor(unsigned int) defineInFor(long long) // fast output routines //#define putChar(c) putc_unlocked((c), stdout) inline void putChar(char c) { putc_unlocked(c, stdout); } inline IO &operator<<(char c) { putChar(c); return *this; } inline IO &operator<<(const char *s) { while (*s) putChar(*s++); return *this; } inline IO &operator<<(const string &s) { for (int i = 0; i < (int)s.size(); ++i) putChar(s[i]); return *this; } char *toString(double d) { sprintf(tmp, "%lf%c", d, '\0'); return tmp; } inline IO &operator<<(double d) { return (*this) << toString(d); } #define defineOutFor(intType) \ inline char *toString(intType n) \ { \ char *p = (tmp + 30); \ if (n) \ { \ bool isNeg = 0; \ if (n < 0) \ isNeg = 1, n = -n; \ while (n) \ *--p = (n % 10) + '0', n /= 10; \ if (isNeg) \ *--p = '-'; \ } \ else \ *--p = '0'; \ return p; \ } \ inline IO &operator<<(intType n) { return (*this) << toString(n); } defineOutFor(int) defineOutFor(long long) #define endl ('\n') #define cout __io__ #define cin __io__ } __io__; int main() { ll Q; cin >> Q; loop(i, Q) { ll X; cin >> X; if (MR(X)) cout << X << " " << 1 << '\n'; else cout << X << " " << 0 << '\n'; } return 0; }