import static java.lang.Math.*; import static java.util.Arrays.*; import java.io.*; import java.lang.reflect.Array; import java.math.BigInteger; import java.util.*; import java.util.concurrent.ThreadLocalRandom; import java.util.function.*; import java.util.stream.IntStream; class Solver{ long st = System.currentTimeMillis(); long elapsed(){ return System.currentTimeMillis() -st; } void reset(){ st = System.currentTimeMillis(); } final static int infI = (1 <<30) -1; final static long infL = 1L <<60; // final static long mod = (int) 1e9 +7; final static long mod = 998244353; final static String yes = "Yes"; final static String no = "No"; MyReader in = new MyReader(System.in); MyWriter out = new MyWriter(System.out); MyWriter log = new MyWriter(System.err){ @Override void println(Object obj){ super.println(obj == null ? "null" : obj); }; @Override protected void ln(){ super.ln(); flush(); }; }; Object solve(){ Prime pm = new Prime(1000_000); int Q = in.it(); while (Q-- > 0) { long n = in.lg(); List list = new ArrayList<>(); for (var f:pm.factorize(n *n +1)) while (f[1]-- > 0) list.add(f[0]); out.println(list.stream().mapToLong(a -> a).toArray()); } return null; } long gcd(final long a,final long b){ return b == 0 ? a : gcd(b,a %b); } int bSearchI(int o,int n,Predicate judge){ if (!judge.test(o)) return o -(n -o) /abs(n -o); for (int c = 0;1 < abs(n -o);) if (judge.test(c = o +n >>1)) o = c; else n = c; return o; } } class Prime{ BitSet primes; int[] spf; BigInteger[] A; Prime(){ this(10_000_000); } Prime(int n){ primes = new BitSet(); primes.set(2,n +1); spf = Util.arrI(n +1,i -> i); for (int p = 2;p *p <= n;p++) if (primes.get(p)) for (int nn = p *p;nn <= n;primes.clear(nn),nn += p) spf[nn] = p; A = IntStream.of(2,325,9375,28178,450775,9780504,1795265022).mapToObj(BigInteger::valueOf) .toArray(nn -> new BigInteger[nn]); } boolean isPrime(long n){ if (n < spf.length) return primes.get((int) n); if ((n &1) == 0) return false; BigInteger bn = BigInteger.valueOf(n); long lsb = Long.lowestOneBit(n -1); BigInteger m = BigInteger.valueOf((n -1) /lsb); a:for (var ba:A) { BigInteger z = ba.modPow(m,bn); if (z.longValue() <= 1) continue; for (long k = 1;k <= lsb;k <<= 1) { if (z.longValue() == n -1) continue a; z = z.modPow(BigInteger.TWO,bn); } return false; } return true; } List factorize(long n){ if (n < 2) return List.of(); Map map = new HashMap<>(); long[] stk = new long[100]; int s = 0; stk[++s] = n; while (0 < s) { long cur = stk[s--]; if (isPrime(cur)) map.merge(cur,1,Integer::sum); else { var p = pollard(cur); stk[++s] = p; stk[++s] = cur /p; } } List ret = new ArrayList<>(); for (var e:map.entrySet()) ret.add(new long[]{e.getKey(), e.getValue()}); ret.sort(Comparator.comparing(t -> t[0])); return ret; } long[] divisors(long n){ List facts = factorize(n); int l = 1; for (var f:factorize(n)) l *= f[1] +1; long[] ret = new long[l]; int id = 1; ret[0] = 1; for (var f:facts) { long p = f[0]; for (;f[1]-- > 0;p *= f[0]) for (int j = 0;ret[j] != f[0];j++) ret[id++] = ret[j] *p; } return ret; } long gcd(final long a,final long b){ return b == 0 ? a : gcd(b,a %b); } long pollard(long n){ if (n < spf.length) return spf[(int) n]; BigInteger bn = BigInteger.valueOf(n); LongUnaryOperator f = x -> x < Solver.infI ? x *x %n : BigInteger.valueOf(x).modPow(BigInteger.TWO,bn).longValue(); long step = 0; while (true) { long x = ++step,y = f.applyAsLong(x); while (true) { long p = gcd(y -x +n,n); if (p == 0 || p == n) break; if (p != 1) return p; x = f.applyAsLong(x); y = f.applyAsLong(f.applyAsLong(y)); } } } } class Combin{ int n = 2; long[] fac,finv,inv; long mod = Solver.mod; Combin(){ fac = finv = inv = new long[]{1, 1}; } void grow(int n){ fac = copyOf(fac,n); finv = copyOf(finv,n); inv = copyOf(inv,n); for (int i = this.n;i < n;i++) { fac[i] = fac[i -1] *i %mod; inv[i] = mod -inv[(int) (mod %i)] *(mod /i) %mod; finv[i] = finv[i -1] *inv[i] %mod; } this.n = n; } long nHr(int n,int r){ return r < 0 ? 0 : nCr(n +r -1,r); } long nCr(int n,int r){ if (r < 0 || n -r < 0) return 0; if (this.n <= n) grow(n <<1); return fac[n] *(finv[r] *finv[n -r] %mod) %mod; } } class Sum{ long[] sum; public Sum(long[] A){ sum = new long[A.length +1]; for (int i = 0;i < A.length;i++) sum[i +1] = (sum[i] +A[i]) %Solver.mod; } long get(int l,int r){ return sum[r] -sum[l]; } } abstract class SegmentTree extends Seg{ SegmentTree(int n,V e){ this(n,e,i -> e); } SegmentTree(int n,V e,IntFunction sup){ super(n,e,sup); } @Override protected F comp(F f0,F f1){ return null; } @Override protected void upd(int i,F f){ super.upd(i,f); up(i,i +1); } } abstract class DualSegmentTree extends Seg{ DualSegmentTree(int n,V e){ this(n,e,i -> e); } DualSegmentTree(int n,V e,IntFunction sup){ super(n,e,sup); } @Override V agg(V v0,V v1){ return null; } @Override protected void rangeMap(int i){} @Override protected void upd(int i,F f){ upd(i,i +1,f); } @Override protected void upd(int l,int r,F f){ down(l,r); super.upd(l,r,f); } @Override protected V get(int i){ down(i,i +1); return super.get(i); } } abstract class LazySegmentTree extends Seg{ LazySegmentTree(int n,V e){ this(n,e,i -> e); } LazySegmentTree(int n,V e,IntFunction sup){ super(n,e,sup); } @Override protected void upd(int i,F f){ upd(i,i +1,f); } @Override protected void upd(int l,int r,F f){ down(l,r); super.upd(l,r,f); up(l,r); } @Override protected V get(int i){ return get(i,i +1); } @Override protected V get(int l,int r){ down(l,r); return super.get(l,r); } } abstract class Seg { protected int n; private V e; private V[] val; private F[] lazy; private int[] l,r,stk; @SuppressWarnings("unchecked") Seg(int n,V e,IntFunction sup){ this.n = n; this.e = e; val = (V[]) new Object[n <<1]; lazy = (F[]) new Object[n]; l = new int[n <<1]; r = new int[n <<1]; stk = new int[100]; for (int i = -1;++i < n;l[i +n] = i,r[i +n] = i +1) val[i +n] = sup.apply(i); for (int i = n;--i > 0;l[i] = l[i <<1],r[i] = r[i <<1 |1]) merge(i); } abstract V agg(V v0,V v1); abstract V map(V v,F f,int l,int r); abstract F comp(F f0,F f1); private void merge(int i){ val[i] = agg(eval(i <<1),eval(i <<1 |1)); } protected void rangeMap(int i){ val[i] = map(val[i],lazy[i],l[i],r[i]); } protected V eval(int i){ if (i < n && lazy[i] != null) { rangeMap(i); prop(i <<1,lazy[i]); prop(i <<1 |1,lazy[i]); lazy[i] = null; } return val[i]; } protected void prop(int i,F f){ if (i < n) lazy[i] = lazy[i] == null ? f : comp(lazy[i],f); else val[i] = map(val[i],f,l[i],r[i]); } protected void up(int l,int r){ l = oddPart(l +n); r = oddPart(r +n); while (1 < l) merge(l >>= 1); while (1 < r) merge(r >>= 1); } protected void down(int l,int r){ int s = 0; stk[++s] = l = oddPart(l +n); stk[++s] = r = oddPart(r +n); while (1 < l) stk[++s] = l >>= 1; while (1 < r) stk[++s] = r >>= 1; while (0 < s) eval(stk[s--]); } private int oddPart(int i){ return i /(i &-i); } protected void upd(int i,F f){ prop(i +n,f); } protected void upd(int l,int r,F f){ l += n; r += n; do { if ((l &1) == 1) prop(l++,f); if ((r &1) == 1) prop(--r,f); } while ((l >>= 1) < (r >>= 1)); } protected V get(int i){ return val[i +n]; } protected V get(int l,int r){ l += n; r += n; V vl = e; V vr = e; do { if ((l &1) == 1) vl = agg(vl,eval(l++)); if ((r &1) == 1) vr = agg(eval(--r),vr); } while ((l >>= 1) < (r >>= 1)); return agg(vl,vr); } } class Util{ static int[] arrI(int N,IntUnaryOperator f){ int[] ret = new int[N]; setAll(ret,f); return ret; } static long[] arrL(int N,IntToLongFunction f){ long[] ret = new long[N]; setAll(ret,f); return ret; } static double[] arrD(int N,IntToDoubleFunction f){ double[] ret = new double[N]; setAll(ret,f); return ret; } static T[] arr(T[] arr,IntFunction f){ setAll(arr,f); return arr; } } class MyReader{ byte[] buf = new byte[1 <<16]; int ptr = 0; int tail = 0; InputStream in; MyReader(InputStream in){ this.in = in; } byte read(){ if (ptr == tail) try { tail = in.read(buf); ptr = 0; } catch (IOException e) {} return buf[ptr++]; } boolean isPrintable(byte c){ return 32 < c && c < 127; } boolean isNum(byte c){ return 47 < c && c < 58; } byte nextPrintable(){ byte ret = read(); while (!isPrintable(ret)) ret = read(); return ret; } int it(){ return toIntExact(lg()); } int[] it(int N){ return Util.arrI(N,i -> it()); } int[][] it(int H,int W){ return Util.arr(new int[H][],i -> it(W)); } int idx(){ return it() -1; } int[] idx(int N){ return Util.arrI(N,i -> idx()); } int[][] idx(int H,int W){ return Util.arr(new int[H][],i -> idx(W)); } long lg(){ byte i = nextPrintable(); boolean negative = i == 45; long n = negative ? 0 : i -'0'; while (isPrintable(i = read())) n = 10 *n +i -'0'; return negative ? -n : n; } long[] lg(int N){ return Util.arrL(N,i -> lg()); } long[][] lg(int H,int W){ return Util.arr(new long[H][],i -> lg(W)); } double dbl(){ return Double.parseDouble(str()); } double[] dbl(int N){ return Util.arrD(N,i -> dbl()); } double[][] dbl(int H,int W){ return Util.arr(new double[H][],i -> dbl(W)); } char[] ch(){ return str().toCharArray(); } char[][] ch(int H){ return Util.arr(new char[H][],i -> ch()); } String line(){ StringBuilder sb = new StringBuilder(); for (byte c;(c = read()) != '\n';) sb.append((char) c); return sb.toString(); } String str(){ StringBuilder sb = new StringBuilder(); sb.append((char) nextPrintable()); for (byte c;isPrintable(c = read());) sb.append((char) c); return sb.toString(); } String[] str(int N){ return Util.arr(new String[N],i -> str()); } } class MyWriter{ OutputStream out; byte[] buf = new byte[1 <<16]; byte[] ibuf = new byte[20]; int tail = 0; MyWriter(OutputStream out){ this.out = out; } void flush(){ try { out.write(buf,0,tail); tail = 0; } catch (IOException e) { e.printStackTrace(); } } protected void ln(){ write((byte) '\n'); } private void write(byte b){ buf[tail++] = b; if (tail == buf.length) flush(); } private void write(byte[] b,int off,int len){ for (int i = off;i < off +len;i++) write(b[i]); } private void write(long n){ if (n < 0) { n = -n; write((byte) '-'); } int i = ibuf.length; do { ibuf[--i] = (byte) (n %10 +'0'); n /= 10; } while (n > 0); write(ibuf,i,ibuf.length -i); } private void print(Object obj){ if (obj instanceof Boolean) print((boolean) obj ? Solver.yes : Solver.no); else if (obj instanceof Character) write((byte) (char) obj); else if (obj instanceof Integer) write((int) obj); else if (obj instanceof Long) write((long) obj); else if (obj instanceof char[]) for (char b:(char[]) obj) write((byte) b); else if (obj.getClass().isArray()) { int l = Array.getLength(obj); for (int i = 0;i < l;i++) { print(Array.get(obj,i)); if (i +1 < l) write((byte) ' '); } } else for (char b:Objects.toString(obj).toCharArray()) write((byte) b); } void printlns(Object... o){ print(Util.arr(new Object[o.length],i -> o[i])); ln(); } void println(Object obj){ if (obj == null) return; if (obj instanceof Collection) for (Object e:(Collection) obj) println(e); else if (obj.getClass().isArray() && Array.getLength(obj) > 0 && !(Array.get(obj,0) instanceof char[]) && Array.get(obj,0).getClass().isArray()) { int l = Array.getLength(obj); for (int i = 0;i < l;i++) println(Array.get(obj,i)); } else { print(obj); ln(); } } } class Main{ public static void main(String[] args) throws Exception{ Solver solver = new Solver(); solver.out.println(solver.solve()); solver.out.flush(); solver.log.println(solver.elapsed()); } }