package contest170331; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.Comparator; import java.util.InputMismatchException; import java.util.List; public class F2 { InputStream is; PrintWriter out; String INPUT = ""; void add(List res, LongHashSet cache, long[] f) { long h = f[0]*1000000009 + f[1]; if(!cache.add(h))return; res.add(f); } void solve() { int n = ni(); int[] a = na(n); List> dp = new ArrayList<>(); dp.add(new ArrayList<>()); for(int i = 1;i < (1< res = new ArrayList<>(); if(Integer.bitCount(i) == 1){ res.add(new long[]{a[Integer.numberOfTrailingZeros(i)], 1}); }else{ LongHashSet cache = new LongHashSet(); for(int j = 1;j < i;j++){ if((i&j) == j){ int k = i^j; // j,k for(long[] s : dp.get(j)){ for(long[] t : dp.get(k)){ if(j < k){ add(res, cache, add(s, t)); add(res, cache, sub(s, t)); add(res, cache, mul(s, t)); } if(t[0] != 0)add(res, cache, div(s, t)); // res.add(add(s, t)); // res.add(sub(s, t)); // res.add(mul(s, t)); // if(t[0] != 0){ // res.add(div(s, t)); // } } } } } // tr(i, res.size()); } dp.add(res); } for(int i = 1;i < (1<>>16; // x *= 0x85ebca6b; // x ^= x>>>13; // x *= 0xc2b2ae35; // x ^= x>>>16; // return x; // } private int h(long x) { x ^= x>>>33; x *= 0xff51afd7ed558ccdL; x ^= x>>>33; x *= 0xc4ceb9fe1a85ec53L; x ^= x>>>33; return (int)(x^x>>>32); } @Override public String toString() { StringBuilder sb = new StringBuilder(); for(int i = next(0);i < scale;i = next(i+1)){ sb.append(","); sb.append(keys[i]); } return sb.length() == 0 ? "" : sb.substring(1); } } public static long[] reduce(long[] f) { if(f[1] == 0) { // n/0 f[0] = 1; }else if(f[0] == 0) { // 0/n f[1] = 1; }else { if(f[1] < 0) { // -a/-b ->a/b f[0] = -f[0]; f[1] = -f[1]; } long a = Math.abs(f[0]), b = f[1]; while (b > 0) { long c = a; a = b; b = c % b; } f[0] /= a; f[1] /= a; } return f; } public static long[] add(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1]+a[1]*b[0], a[1]*b[1]}); } public static long[] sub(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1]-a[1]*b[0], a[1]*b[1]}); } public static long[] mul(long[] a, long[] b){ return reduce(new long[]{a[0]*b[0], a[1]*b[1]}); } public static long[] div(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1], a[1]*b[0]}); } public static int compare(long[] a, long[] b){return Long.signum(a[0] * b[1] - a[1] * b[0]);} public static long[] min(long[] a, long[] b){ return compare(a, b) <= 0 ? a : b; } public static long[] max(long[] a, long[] b){ return compare(a, b) >= 0 ? a : b; } public static int lowerBound(long[][] es, int p, long[] r) { int low = -1, high = p; while(high-low > 1){ int h = high+low>>>1; if(Long.compare(r[0]*es[h][1], r[1]*es[h][0]) <= 0){ high = h; }else{ low = h; } } return high; } public static Comparator comp = (a, b) -> Long.signum(a[0]*b[1]-a[1]*b[0]); void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new F2().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }