TLE 49

#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <cmath>
#include <map>
#include <cstring>
#include <iomanip>

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#define forr(i,x,n) for(int i=(x); i<int(n); i++)
#define forn(i,n) forr(i,0,n)

using namespace std;

typedef long long ll;
typedef double real;

const ll MAXN = 2005;
const real INF = 1e9;

ll N;
vector<real> C(MAXN);
real LSUM[MAXN];
real RSUM[MAXN];

real DP[MAXN][MAXN][2];

real f(int s, int e, int b){
    if(DP[s][e][b] >= 0) return DP[s][e][b];

    real ans = INF;
    real denom = LSUM[s-1] + RSUM[e];

    if(b == 0){
        if(s > 0) ans = min(ans, (1 - C[s-1]/denom) * ( f(s-1, e, 0) + 1 ) + 1 * C[s-1]/denom);
        if(e < 2*N) ans = min(ans, ( f(s, e+1, 1) + (e-s+1) ) * (1 - C[e]/denom) + (e-s+1) * C[e]/denom);
    }else{
        if(s > 0) ans = min(ans, (1 - C[s-1]/denom) * ( f(s-1, e, 0) + (e-s+1) ) + (e-s+1) * C[s-1]/denom);
        if(e < 2*N) ans = min(ans, ( f(s, e+1, 1) + 1 ) * (1 - C[e]/denom) + C[e]/denom);
    }

    return DP[s][e][b] = ans;
}

int main(){
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    //freopen("in.txt", "r", stdin);

    cin>>N;

    forn(i,2*N+1) forn(j,2*N+1) forn(b,2) DP[i][j][b] = -1;
    forn(b,2) DP[0][2*N][b] = 0;

    forn(i, 2*N) cin >> C[i];
    LSUM[0] = C[0];
    forr(i, 1, 2*N)
        LSUM[i] = LSUM[i-1] + C[i];

    RSUM[2*N-1] = C[2*N-1];
    for(int i = 2*N-2; i >=0; i--)
        RSUM[i] = RSUM[i+1] + C[i];

    cout << fixed << showpoint << setprecision(6) << f(N, N, 0) << endl;

    return 0;
}