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#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<queue>
#include<map>
#include<stack>
#include<cmath>
#include<set>
#include<bitset>
#include<complex>
#include<assert.h>
#define inc(i,l,r) for(int i=l;i<=r;i++)
#define dec(i,l,r) for(int i=l;i>=r;i--)
#define link(x) for(edge *j=h[x];j;j=j->next)
#define mem(a) memset(a,0,sizeof(a))
#define ll long long
#define eps 1e-10
#define succ(x) (1<<(x))
#define lowbit(x) (x&(-x))
#define sqr(x) ((x)*(x))
#define mid (x+y)/2
#define NM 15
#define nm 5005
using namespace std;
const double pi=acos(-1);
const int inf=1e9+7;
ll read(){
ll x=0,f=1;char ch=getchar();
while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
return f*x;
}
int n,m,tot,a[NM],p[nm],ans,b[NM];
double d[nm],g[nm];
vector<int>c[NM];
bool _check(double t){
double s=0;
inc(i,1,tot-1)s+=asin(b[i]/t/2);
return s>asin(b[tot]/t/2);
}
bool check(double t){
double s=0;
inc(i,1,tot)s+=asin(b[i]/t/2);
return s<pi;
}
int main(){
int _=read();while(_--){
n=read();inc(i,1,n)a[i]=read();
sort(a+1,a+1+n);
m=succ(n)-1;
inc(i,7,m){
tot=0;d[i]=g[i]=0;
inc(j,1,n)if(i&succ(j-1))b[++tot]=a[j];
if(tot<3)continue;
double R=0;int cnt=0;
inc(j,1,tot-1)cnt+=b[j];
if(cnt<b[tot])continue;
cnt=0;
if(!check(b[tot]/2.0)){
for(double x=b[tot]/2.0,y=10000;cnt<=100;cnt++)
if(check(mid))R=y=mid;else x=mid;
inc(j,1,tot)g[i]+=sqrt(sqr(R)-sqr(b[j])/4.0)*b[j]/2;
}else{
for(double x=b[tot]/2.0,y=10000;cnt<=100;cnt++)
if(_check(mid))R=y=mid;else x=mid;
inc(j,1,tot-1)g[i]+=sqrt(sqr(R)-sqr(b[j])/4.0)*b[j]/2;
g[i]-=sqrt(sqr(R)-sqr(b[tot])/4.0)*b[tot]/2;
}
}
d[0]=1;
inc(i,0,m)if(d[i]>eps){
for(int t=m^i,j=t;j;j=(j-1)&t)if(g[j]>eps){
double cnt=d[i]*g[j];
if(d[i|j]<cnt)d[i|j]=cnt,p[i|j]=i;
}
}
ans=1;tot=0;d[0]=0;
inc(i,1,m)if(d[i]>d[ans])ans=i;
printf("%.10lf\n",d[ans]);
for(;ans;ans=p[ans]){
int t=ans^p[ans];
if(g[t]<eps)continue;
c[++tot].clear();
inc(i,1,n)if(t&succ(i-1))c[tot].push_back(i);
}
printf("%d\n",tot);
inc(i,1,tot){printf("%d",(int)c[i].size());for(int&j:c[i])printf(" %d",a[j]);putchar('\n');}
}
return 0;
}
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