description: <image>
  
  William is not only interested in trading but also in betting on sports matches. n teams participate in each match. Each team is characterized by strength a_i. Each two teams i < j play with each other exactly once. Team i wins with probability (a_i)/(a_i + a_j) and team j wins with probability (a_j)/(a_i + a_j).
  
  The team is called a winner if it directly or indirectly defeated all other teams. Team a defeated (directly or indirectly) team b if there is a sequence of teams c_1, c_2, ... c_k such that c_1 = a, c_k = b and team c_i defeated team c_{i + 1} for all i from 1 to k - 1. Note that it is possible that team a defeated team b and in the same time team b defeated team a.
  
  William wants you to find the expected value of the number of winners.
  
  Input
  
  The first line contains a single integer n (1 ≤ n ≤ 14), which is the total number of teams participating in a match.
  
  The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — the strengths of teams participating in a match.
  
  Output
  
  Output a single integer — the expected value of the number of winners of the tournament modulo 10^9 + 7.
  
  Formally, let M = 10^9+7. It can be demonstrated that the answer can be presented as a irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output a single integer equal to p ⋅ q^{-1} mod M. In other words, output an integer x such that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.
  
  Examples
  
  Input
  
  
  2
  1 2
  
  
  Output
  
  
  1
  
  
  Input
  
  
  5
  1 5 2 11 14
  
  
  Output
  
  
  642377629
  
  Note
  
  To better understand in which situation several winners are possible let's examine the second test:
  
  One possible result of the tournament is as follows (a → b means that a defeated b):
  
    * 1 → 2 
    * 2 → 3 
    * 3 → 1 
    * 1 → 4 
    * 1 → 5 
    * 2 → 4 
    * 2 → 5 
    * 3 → 4 
    * 3 → 5 
    * 4 → 5 
  
  
  
  Or more clearly in the picture:
  
  <image>
  
  In this case every team from the set \{ 1, 2, 3 \} directly or indirectly defeated everyone. I.e.:
  
    * 1st defeated everyone because they can get to everyone else in the following way 1 → 2, 1 → 2 → 3, 1 → 4, 1 → 5. 
    * 2nd defeated everyone because they can get to everyone else in the following way 2 → 3, 2 → 3 → 1, 2 → 4, 2 → 5. 
    * 3rd defeated everyone because they can get to everyone else in the following way 3 → 1, 3 → 1 → 2, 3 → 4, 3 → 5. 
  
  
  
  Therefore the total number of winners is 3.
solution: import java.util.*;
  import java.io.*;
  import java.text.*;
  
  public class CF_1556_F{
      //SOLUTION BEGIN
      long MOD = (long)1e9+7;
      void pre() throws Exception{}
      void solve(int TC) throws Exception{
          int N = ni();
          long[] A = new long[N];
          for(int i = 0; i< N; i++)A[i] = nl();
  
          long[]  P = new long[1<<N];
          long[][] L = new long[N][1<<N];
          //L[i][mask] => Probabilitiy that person i loses to all people in mask. If i is included in mask, L[i][mask] = 0
  
          for(int win = 1; win < 1<<N; win++){
              for(int i = 0; i< N; i++){
                  if(((win>>i)&1)==1)continue;
                  long sum = 1;
                  for(int j = 0; j< N; j++){
                      if(((win>>j)&1)==0)continue;
                      sum *= A[j]*inv(A[i]+A[j])%MOD;
                      if(sum >= MOD)sum %= MOD;
                  }
                  L[i][win] = sum;
              }
          }
  
          int ALL = (1<<N)-1;
          long ans = 0;
          for(int mask = 1; mask < 1<<N; mask++){
              long sum = 0;
              for(int sub = (mask-1)&mask; sub > 0; sub = (sub-1)&mask){
                  sum += P[sub]*G(L, sub, mask^sub)%MOD;//G[sub]%MOD;
  //                sum += F[sub]%MOD;
                  if(sum > 0)sum -= MOD;
              }
              P[mask] = (1+MOD-sum)%MOD;
              ans += (bit(mask))*P[mask]%MOD * G(L, mask, ALL^mask)%MOD;
              if(ans >= MOD)ans -= MOD;
          }
          pn(ans);
      }
      long G(long[][] L, int win, int lose){
          if((win&lose) > 0)return -1;
          long ans = 1;
          for(int i = 0; i< L.length; i++){
              if(((lose>>i)&1)==0)continue;
              ans = ans*L[i][win]%MOD;
          }
          return ans;
      }
      long inv(long a){
          return pow(a, MOD-2);
      }
      long pow(long a, long p){
          long o = 1;
          a %= MOD;
          for(; p>0; p>>=1){
              if((p&1)==1)o = (o*a)%MOD;
              a = (a*a)%MOD;
          }
          return o;
      }
      //SOLUTION END
      void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
      void exit(boolean b){if(!b)System.exit(0);}
      static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
      final long IINF = (long)1e17;
      final int INF = (int)1e9+2;
      DecimalFormat df = new DecimalFormat("0.00000000000");
      double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-8;
      static boolean multipleTC = false, memory = true, fileIO = false;
      FastReader in;PrintWriter out;
      void run() throws Exception{
          long ct = System.currentTimeMillis();
          if (fileIO) {
              in = new FastReader("");
              out = new PrintWriter("");
          } else {
              in = new FastReader();
              out = new PrintWriter(System.out);
          }
          //Solution Credits: Taranpreet Singh
          int T = multipleTC? ni():1;
          pre();
          for (int t = 1; t <= T; t++) solve(t);
          out.flush();
          out.close();
          System.err.println(System.currentTimeMillis() - ct);
      }
      public static void main(String[] args) throws Exception{
          if(memory)new Thread(null, new Runnable() {public void run(){try{new CF_1556_F().run();}catch(Exception e){e.printStackTrace();System.exit(1);}}}, "1", 1 << 28).start();
          else new CF_1556_F().run();
      }
      int[][] make(int n, int e, int[] from, int[] to, boolean f){
          int[][] g = new int[n][];int[]cnt = new int[n];
          for(int i = 0; i< e; i++){
              cnt[from[i]]++;
              if(f)cnt[to[i]]++;
          }
          for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
          for(int i = 0; i< e; i++){
              g[from[i]][--cnt[from[i]]] = to[i];
              if(f)g[to[i]][--cnt[to[i]]] = from[i];
          }
          return g;
      }
      int[][][] makeS(int n, int e, int[] from, int[] to, boolean f){
          int[][][] g = new int[n][][];int[]cnt = new int[n];
          for(int i = 0; i< e; i++){
              cnt[from[i]]++;
              if(f)cnt[to[i]]++;
          }
          for(int i = 0; i< n; i++)g[i] = new int[cnt[i]][];
          for(int i = 0; i< e; i++){
              g[from[i]][--cnt[from[i]]] = new int[]{to[i], i, 0};
              if(f)g[to[i]][--cnt[to[i]]] = new int[]{from[i], i, 1};
          }
          return g;
      }
      int find(int[] set, int u){return set[u] = (set[u] == u?u:find(set, set[u]));}
      int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
      long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
      int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
      int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
      void p(Object... o){for(Object oo:o)out.print(oo+" ");}
      void pn(Object... o){for(int i = 0; i< o.length; i++)out.print(o[i]+(i+1 < o.length?" ":"\n"));}
      void pni(Object... o){for(Object oo:o)out.print(oo+" ");out.println();out.flush();}
      String n()throws Exception{return in.next();}
      String nln()throws Exception{return in.nextLine();}
      int ni()throws Exception{return Integer.parseInt(in.next());}
      long nl()throws Exception{return Long.parseLong(in.next());}
      double nd()throws Exception{return Double.parseDouble(in.next());}
  
      class FastReader{
          BufferedReader br;
          StringTokenizer st;
          public FastReader(){
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          public FastReader(String s) throws Exception{
              br = new BufferedReader(new FileReader(s));
          }
  
          String next() throws Exception{
              while (st == null || !st.hasMoreElements()){
                  try{
                      st = new StringTokenizer(br.readLine());
                  }catch (IOException  e){
                      throw new Exception(e.toString());
                  }
              }
              return st.nextToken();
          }
  
          String nextLine() throws Exception{
              String str;
              try{
                  str = br.readLine();
              }catch (IOException e){
                  throw new Exception(e.toString());
              }
              return str;
          }
      }
  }