import java.io.BufferedInputStream; import java.io.IOException; import java.io.PrintWriter; import java.math.BigInteger; import java.util.*; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; import java.util.stream.Collectors; import java.util.stream.IntStream; import java.util.stream.StreamSupport; import static java.lang.Math.*; public class Main { static In in = new In(); static Out out = new Out(false, false); static final long inf = 0x1fffffffffffffffL; static final int iinf = 0x3fffffff; static final double eps = 1e-9; static long mod = 998244353; void solve() { int n = in.nextInt(); for (int i = 0; i < n; i++) { long x = in.nextLong(); if (x < 1L << 62) { out.println(x, PrimeUtils.isPrime(x) ? 1 : 0); } else { out.println(x, BigInteger.valueOf(x).isProbablePrime(Integer.MAX_VALUE) ? 1 : 0); } } } public static void main(String... args) { new Main().solve(); out.flush(); } } class BigMontgomery { private final long n, r2, nInv; public BigMontgomery(long n) { long r2 = (1L << 62) % n; for (int i = 0; i < 66; i++) { r2 <<= 1; if (r2 >= n) { r2 -= n; } } long nInv = n; for (int i = 0; i < 5; ++i) { nInv *= 2 - n * nInv; } this.n = n; this.r2 = r2; this.nInv = nInv; } private static long high(long x, long y) { return multiplyHigh(x, y) + ((x >> 63) & y) + ((y >> 63) & x); } private long mr(long x) { return high(-nInv * x, n) + (x == 0 ? 0 : 1); } private long mr2(long x, long y) { return high(x, y) + high(-nInv * x * y, n) + (x * y == 0 ? 0 : 1); } public long mul(long x, long y) { long r = mr2(mr2(x, r2), y); return r < n ? r : r - n; } public long pow(long x, long y) { long z = mr2(x, r2); long r = 1; while (y > 0) { if ((y & 1) == 1) { r = mr2(r, z); } z = mr2(z, z); y >>= 1; } return r < n ? r : r - n; } } class PrimeUtils { private static final int[] bases = {15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560, 3128, 5212, 2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763, 4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113, 7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556, 2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344, 17, 15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903, 737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875, 3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315, 978, 233, 3003, 2562, 2994, 10587, 10030, 2377, 1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784, 1661, 524, 3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031, 2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336, 579, 165, 1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727, 3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183, 8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674, 411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785, 1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42, 4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197, 13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194}; private static final SieveOfEratosthenes sieve = new SieveOfEratosthenes(); private static final int USE_SIEVE_LIMIT = 5000000; public static int getMinPrimeFactor(int n) { return sieve.minPrimeFactor(n); } public static int getNthPrime(int n) { return sieve.nthPrime(n); } public static boolean isPrime(int n) { if (n == 2 || n == 3 || n == 5 || n == 7) { return true; } if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) { return false; } if (n < 121) { return n > 1; } long h = n; h = ((h >> 16) ^ h) * 0x45D9F3B; h = ((h >> 16) ^ h) * 0x45D9F3B; h = ((h >> 16) ^ h) & 0xFF; int a = bases[(int)h]; return millerRabin(n, a); } private static boolean millerRabin(long n, long a) { long d = n - 1; int s = 0; while ((d & 1) == 0) { s++; d >>= 1; } long x = pow(a, d, n); if (x == 1) { return true; } for (int r = 0; r < s; r++) { if (x == n - 1) { return true; } x = x * x % n; } return false; } public static long pow(long a, long b, long mod) { long x = 1; while (b > 0) { if ((b & 1) == 1) { x = x * a % mod; } a = a * a % mod; b >>= 1; } return x; } private static boolean millerRabinBm(long n, long a, BigMontgomery bm) { long d = n - 1; int s = 0; while ((d & 1) == 0) { s++; d >>= 1; } long x = bm.pow(a, d); if (x == 1) { return true; } for (int r = 0; r < s; r++) { if (x == n - 1) { return true; } x = bm.mul(x, x); } return false; } private static boolean millerRabinBi(long n, long a) { long d = n - 1; int s = 0; while ((d & 1) == 0) { s++; d >>= 1; } BigInteger bn = BigInteger.valueOf(n); BigInteger bn1 = bn.subtract(BigInteger.ONE); BigInteger x = BigInteger.valueOf(a).modPow(BigInteger.valueOf(d), bn); if (x.equals(BigInteger.ONE)) { return true; } for (int r = 0; r < s; r++) { if (x.equals(bn1)) { return true; } x = x.multiply(x).mod(bn); } return false; } public static boolean isPrime(long n) { if (n <= Integer.MAX_VALUE) { return isPrime((int)n); } if (n < 1L << 62) { BigMontgomery bm = new BigMontgomery(n); for (long a : new long[] {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (!millerRabinBm(n, a, bm)) { return false; } } } else { for (long a : new long[] {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (!millerRabinBi(n, a)) { return false; } } } return true; } public static List getPrimesLessThan(int n) { List primes = new ArrayList<>(); for (int prime : sieve) { if (prime >= n) { break; } primes.add(prime); } return primes; } public static List getNPrimes(int n) { List primes = new ArrayList<>(); for (int i = 0; i < n; i++) { primes.add(sieve.nthPrime(i)); } return primes; } public static Map factorize(int n) { if (n <= USE_SIEVE_LIMIT) { return factorize0(n); } else { return factorize1(n); } } // O(N + Q * logN) private static Map factorize0(int n) { Map primeFactors = new LinkedHashMap<>(); while (n > 1) { int primeFactor = getMinPrimeFactor(n); int count = 0; while (getMinPrimeFactor(n) == primeFactor) { count++; n /= primeFactor; } primeFactors.put(primeFactor, count); } return primeFactors; } // O(√N + Q * √N / logN) private static Map factorize1(int n) { Map primeFactors = new LinkedHashMap<>(); int c = n; for (int prime : sieve) { int count = 0; while (c % prime == 0) { count++; c /= prime; } if (count > 0) { primeFactors.put(prime, count); } if (prime * prime >= n) { break; } } if (c > 1) { primeFactors.put(c, 1); } return primeFactors; } public static List divisors(int n) { List divisors = new ArrayList<>(); divisors.add(1); Map primeFactors = factorize(n); for (Map.Entry entry : primeFactors.entrySet()) { int exp = entry.getValue(); int s = divisors.size(); for (int i = 0; i < s; i++) { int v = 1; for (int j = 0; j < exp; j++) { v *= entry.getKey(); divisors.add(divisors.get(i) * v); } } } Collections.sort(divisors); return divisors; } } class SieveOfEratosthenes implements Iterable { private final List primes = new ArrayList<>(); private int[] table; public SieveOfEratosthenes() { this(1000); } public SieveOfEratosthenes(int initialCapacity) { calcTable(initialCapacity); } private void calcTable(int n) { int oldCapacity = 0; int[] newTable = new int[n]; if (table != null) { oldCapacity = table.length; System.arraycopy(table, 0, newTable, 0, oldCapacity); } table = newTable; for (int i = oldCapacity; i < n; i++) { table[i] = i; } for (int i = 2; i < n; i++) { if (i >= oldCapacity && table[i] == i) { primes.add(i); } for (int prime : primes) { if (prime > table[i] || (long)prime * i >= n) { break; } table[prime * i] = prime; } } } private void grow(int minCapacity) { int oldCapacity = table.length; int newCapacity = (int)min(Integer.MAX_VALUE, max(minCapacity, (long)oldCapacity + (oldCapacity >> 1))); calcTable(newCapacity); } public int minPrimeFactor(int n) { if (table.length <= n) { grow(n + 1); } return table[n]; } public int nthPrime(int n) { while (primes.size() <= n) { grow(table.length + 1); } return primes.get(n); } public int countLessThan(int n) { while (primes.get(primes.size() - 1) < n) { grow(table.length + 1); } int left = -1; int right = primes.size(); while (right - left > 1) { int mid = (left + right) / 2; if (primes.get(mid) < n) { left = mid; } else { right = mid; } } return right; } public Map factorize(int n) { Map primeFactors = new LinkedHashMap<>(); while (n > 1) { int primeFactor = minPrimeFactor(n); int exp = 0; while (n % primeFactor == 0) { n /= primeFactor; exp++; } primeFactors.put(primeFactor, exp); } return primeFactors; } public long sumOfDivisors(int n) { long prod = 1; while (n > 1) { int primeFactor = minPrimeFactor(n); int factor = 1; long sum = 1; while (n % primeFactor == 0) { n /= primeFactor; factor *= primeFactor; sum += factor; } prod *= sum; } return prod; } public List divisors(int n) { List divisors = new ArrayList<>(); divisors.add(1); Map primeFactors = factorize(n); for (Map.Entry entry : primeFactors.entrySet()) { int exp = entry.getValue(); int s = divisors.size(); for (int i = 0; i < s; i++) { int v = 1; for (int j = 0; j < exp; j++) { v *= entry.getKey(); divisors.add(divisors.get(i) * v); } } } Collections.sort(divisors); return divisors; } public IntStream stream() { int characteristics = Spliterator.ORDERED | Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.NONNULL | Spliterator.IMMUTABLE; Spliterator.OfInt spliterator = Spliterators.spliteratorUnknownSize(iterator(), characteristics); return StreamSupport.intStream(spliterator, false); } @Override public PrimitiveIterator.OfInt iterator() { return new PrimitiveIterator.OfInt() { private int i = 0; @Override public int nextInt() { return nthPrime(i++); } @Override public boolean hasNext() { return true; } }; } } class In { private final BufferedInputStream reader = new BufferedInputStream(System.in); private final byte[] buffer = new byte[0x10000]; private int i = 0; private int length = 0; public int read() { if (i == length) { i = 0; try { length = reader.read(buffer); } catch (IOException ignored) { } if (length == -1) { return 0; } } if (length <= i) { throw new RuntimeException(); } return buffer[i++]; } public String next() { StringBuilder builder = new StringBuilder(); int b = read(); while (b < '!' || '~' < b) { b = read(); } while ('!' <= b && b <= '~') { builder.appendCodePoint(b); b = read(); } return builder.toString(); } public String nextLine() { StringBuilder builder = new StringBuilder(); int b = read(); while (b != 0 && b != '\r' && b != '\n') { builder.appendCodePoint(b); b = read(); } if (b == '\r') { read(); } return builder.toString(); } public int nextInt() { long val = nextLong(); if (val < Integer.MIN_VALUE || Integer.MAX_VALUE < val) { throw new NumberFormatException(); } return (int)val; } public long nextLong() { int b = read(); while (b < '!' || '~' < b) { b = read(); } boolean neg = false; if (b == '-') { neg = true; b = read(); } long n = 0; int c = 0; while ('0' <= b && b <= '9') { n = n * 10 + b - '0'; b = read(); c++; } if (c == 0 || c >= 2 && n == 0) { throw new NumberFormatException(); } return neg ? -n : n; } public double nextDouble() { return Double.parseDouble(next()); } public char[] nextCharArray() { return next().toCharArray(); } public String[] nextStringArray(int n) { String[] s = new String[n]; for (int i = 0; i < n; i++) { s[i] = next(); } return s; } public char[][] nextCharMatrix(int n, int m) { char[][] a = new char[n][m]; for (int i = 0; i < n; i++) { a[i] = next().toCharArray(); } return a; } public int[] nextIntArray(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) { a[i] = nextInt(); } return a; } public int[] nextIntArray(int n, IntUnaryOperator op) { int[] a = new int[n]; for (int i = 0; i < n; i++) { a[i] = op.applyAsInt(nextInt()); } return a; } public int[][] nextIntMatrix(int h, int w) { int[][] a = new int[h][w]; for (int i = 0; i < h; i++) { a[i] = nextIntArray(w); } return a; } public long[] nextLongArray(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) { a[i] = nextLong(); } return a; } public long[] nextLongArray(int n, LongUnaryOperator op) { long[] a = new long[n]; for (int i = 0; i < n; i++) { a[i] = op.applyAsLong(nextLong()); } return a; } public long[][] nextLongMatrix(int h, int w) { long[][] a = new long[h][w]; for (int i = 0; i < h; i++) { a[i] = nextLongArray(w); } return a; } public List> nextGraph(int n, int m, boolean directed) { List> res = new ArrayList<>(); for (int i = 0; i < n; i++) { res.add(new ArrayList<>()); } for (int i = 0; i < m; i++) { int u = nextInt() - 1; int v = nextInt() - 1; res.get(u).add(v); if (!directed) { res.get(v).add(u); } } return res; } } class Out { private final PrintWriter out = new PrintWriter(System.out); private final PrintWriter err = new PrintWriter(System.err); public boolean autoFlush; public boolean enableDebug; public Out(boolean autoFlush, boolean enableDebug) { this.autoFlush = autoFlush; this.enableDebug = enableDebug; } public void debug(Object... args) { if (!enableDebug) { return; } if (args == null || args.getClass() != Object[].class) { args = new Object[] {args}; } StackTraceElement stackTrace = Thread.currentThread().getStackTrace()[2]; err.print(String.format("[%40s] ", stackTrace.toString())); err.println(Arrays.stream(args).map(obj -> format(obj, true)).collect(Collectors.joining(" "))); err.flush(); } private String format(Object obj, boolean canMultiline) { if (obj == null) return "null"; Class clazz = obj.getClass(); if (clazz == Double.class) return String.format("%.10f", obj); if (clazz == int[].class) return Arrays.toString((int[])obj); if (clazz == long[].class) return Arrays.toString((long[])obj); if (clazz == char[].class) return String.valueOf((char[])obj); if (clazz == boolean[].class) return IntStream.range(0, ((boolean[])obj).length).mapToObj(i -> ((boolean[])obj)[i] ? "1" : "0").collect(Collectors.joining()); if (clazz == double[].class) return Arrays.toString(Arrays.stream((double[])obj).mapToObj(a -> format(a, false)).toArray()); if (canMultiline && clazz.isArray() && clazz.componentType().isArray()) return Arrays.stream((Object[])obj).map(a -> format(a, false)).collect(Collectors.joining("\n")); if (clazz == Object[].class) return Arrays.toString(Arrays.stream((Object[])obj).map(a -> format(a, false)).toArray()); if (clazz.isArray()) return Arrays.toString((Object[])obj); return String.valueOf(obj); } public void println(Object... args) { if (args == null || args.getClass() != Object[].class) { args = new Object[] {args}; } out.println(Arrays.stream(args) .map(obj -> obj instanceof Double ? String.format("%.10f", obj) : String.valueOf(obj)) .collect(Collectors.joining(" "))); if (autoFlush) { out.flush(); } } public void println(char a) { out.println(a); if (autoFlush) { out.flush(); } } public void println(int a) { out.println(a); if (autoFlush) { out.flush(); } } public void println(long a) { out.println(a); if (autoFlush) { out.flush(); } } public void println(double a) { out.println(String.format("%.10f", a)); if (autoFlush) { out.flush(); } } public void println(String s) { out.println(s); if (autoFlush) { out.flush(); } } public void println(char[] s) { out.println(String.valueOf(s)); if (autoFlush) { out.flush(); } } public void println(int[] a) { StringJoiner joiner = new StringJoiner(" "); for (int i : a) { joiner.add(Integer.toString(i)); } out.println(joiner); if (autoFlush) { out.flush(); } } public void println(long[] a) { StringJoiner joiner = new StringJoiner(" "); for (long i : a) { joiner.add(Long.toString(i)); } out.println(joiner); if (autoFlush) { out.flush(); } } public void flush() { err.flush(); out.flush(); } }