[模板]三维凸包(无讲解)

// luogu-judger-enable-o2
#include<bits/stdc++.h>
using namespace std;
typedef long double ld;
const int maxn=2E3+5;
const ld eps=1E-9;
int n;
bool vis[maxn][maxn];
struct pt
{
    ld x,y,z;
    pt(ld a=0,ld b=0,ld c=0):x(a),y(b),z(c){}
    pt operator+(const pt&A){return pt(x+A.x,y+A.y,z+A.z);}
    pt operator-(const pt&A){return pt(x-A.x,y-A.y,z-A.z);}
    pt operator*(const pt&A){return pt(y*A.z-z*A.y,z*A.x-x*A.z,x*A.y-y*A.x);}
    ld operator&(const pt&A){return x*A.x+y*A.y+z*A.z;}
    ld len(){return sqrt(x*x+y*y+z*z);}
}a[maxn];
struct face
{
    int v[3];
    pt normal(){return (a[v[1]]-a[v[0]])*(a[v[2]]-a[v[0]]);}
    ld area(){return normal().len()/2;}
}f[maxn],wait[maxn];
int cnt;
inline int see(face A,pt B)
{
    return ((B-a[A.v[0]])&A.normal())>0;
}
void solve()
{
    f[++cnt]=(face){1,2,3};
    f[++cnt]=(face){3,2,1};
    for(int i=4;i<=n;++i)
    {
        int tot=0;
        for(int j=1;j<=cnt;++j)
        {
            if(!see(f[j],a[i]))
            {
                wait[++tot]=f[j];
                for(int k=0;k<3;++k)
                    vis[f[j].v[k]][f[j].v[(k+1)%3]]=0;
            }
            else
            {
                for(int k=0;k<3;++k)
                    vis[f[j].v[k]][f[j].v[(k+1)%3]]=1;
            }
        }
        for(int j=1;j<=cnt;++j)
            for(int k=0;k<3;++k)
            {
                int x=f[j].v[k],y=f[j].v[(k+1)%3];
                if(vis[x][y]&&(!vis[y][x]))
                    wait[++tot]=(face){x,y,i};
            }
        for(int j=1;j<=tot;++j)
            f[j]=wait[j];
        cnt=tot;
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin>>n;
    for(int i=1;i<=n;++i)
        cin>>a[i].x>>a[i].y>>a[i].z;
    solve();
    ld ans=0;
    for(int i=1;i<=cnt;++i)
        ans+=f[i].normal().len()/2;
    cout<<fixed<<setprecision(3)<<ans<<endl;
    return 0;
}