#include using namespace std; typedef long long ll; typedef pair p_ll; template void debug(T itr1, T itr2) { auto now = itr1; while(now=0; i--) const ll MOD = pow(10,9)+7; const ll LLINF = pow(2,61)-1; const int INF = pow(2,30)-1; vector fac; void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; } ll modpow(ll x, ll p) { ll result = 1, now = 1, pm = x; while (now<=p) { if (p&now) { result = result * pm % MOD; } now*=2; pm = pm*pm % MOD; } return result; } ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; } ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; } ll gcd(ll a, ll b) { if (a> N; double A[N]; rep(i,N) cin >> A[i]; ll p3[N+1] = {}; rep(i,N+1) p3[i] = i==0 ? 1 : p3[i-1]*3; ll ma = p3[N]; double dp[ma][2] = {}; per(i,ma) { ll ti = i, c0 = 0, xsum = 0, ysum = 0, now[N]; rep(j,N) { now[j] = ti%3; ti/=3; if (now[j]==0) c0++; else if (now[j]==1) xsum += A[j]; else if (now[j]==2) ysum += A[j]; } // cout << i << " " << c0 << " " << xsum << " " << ysum << endl; if (c0==0) { if (xsum>ysum) { dp[i][0] = 1; dp[i][1] = 1; } else { dp[i][0] = 0; dp[i][1] = 0; } } else { double rxy0 = 0, rxy1 = 0; rep(x,N) { if (now[x]) continue; double rx0 = 1, rx1 = 1; rep(y,N) { if (now[y]) continue; double r0 = (A[y]*dp[i+p3[x]][1]+(A[x]-1)*dp[i+p3[y]*2][0]) / (A[x]+A[y]-1); double r1 = ((A[y]-1)*dp[i+p3[x]][1]+A[x]*dp[i+p3[y]*2][0]) / (A[x]+A[y]-1); // cout << i << "->" << x << " " << y << " " << result << endl; rx0 = min(rx0,r0); rx1 = min(rx1,r1); } rxy0 = max(rxy0, rx0); rxy1 = max(rxy1, rx1); } dp[i][0] = rxy0; dp[i][1] = rxy1; } } // rep(i,ma) cout << dp[i][0] << " "; cout << endl; // rep(i,ma) cout << dp[i][1] << " "; cout << endl; double result = dp[0][0]; cout << setprecision(10) << result << endl; return 0; }