Problem: Example

Input

4
5
8
58
85


Output

2970.000000000

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

typedef long double D;

const int LOOP=100;
const D PI=acos(-1);
const D EPS=1e-8;
D calc(vint r){
    int n=r.size();

    D ret=0.0;
    do{

        vint rr(n);
        rep(i,n)rr[i]=r[i]*r[(i+1)%n];

        int ei=LLONG_MAX;
        rep(i,n)chmin(ei,rr[i]);
        D lb=-ei;
        D ub=ei;

        rep(i,LOOP){
            D mid=(lb+ub)/2.0;
            D sum=0.0;
            rep(j,n)sum+=acos(mid/rr[j]);
            if(sum>2*PI)lb=mid;
            else ub=mid;
        }
        D sum=0.0;
        rep(j,n)sum+=acos(lb/rr[j]);
        if(abs(sum-2*PI)>EPS){
            continue; //???????
        }
        sum=0.0;
        rep(i,n)sum+=rr[i]*sin(acos(lb/rr[i]));
        chmax(ret,sum);
    }while(next_permutation(all(r)));
    return ret;
}

signed main(){
    int N;
    cin>>N;
    vint R(N);rep(i,N)cin>>R[i];

    sort(all(R));

    D ans=0.0;

    rep(i,1<<N){
        int num=__builtin_popcount(i);
        if(num<=2)continue;
        vint r;
        rep(j,N)if(i>>j&1)r.pb(R[j]);
        chmax(ans,calc(r));
    }

    printf("%.20Lf\n",ans/2.0);
    return 0;
}