Red Huang

//============================================================================  
// Name        : How Big Is It.cpp  
// Date : 2013/4/26 下午1:30:18  
// Author : GCA  
//============================================================================  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 55  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo INT\_MAX  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
double r\[M\];  
bool vis\[M\];  
double pos\[M\];  
double dfsr\[M\];  
double minans;  
int n;  
void dfs(int depth){  
    if(depth==n){  
        double xl=oo;  
        double xr=0;  
        for(int i=0;i<n;i++){  
            xl=min(xl,(pos\[i\]-dfsr\[i\]));  
            xr=max(xr,(pos\[i\]+dfsr\[i\]));  
        }  
        minans=min(minans,xr-xl);  
        return;  
    }  
    for(int i=0;i<n;i++){  
        if(!vis\[i\]){  
            dfsr\[depth\]=r\[i\];  
            pos\[depth\]=0;  
            for(int j=0;j<depth;j++){  
                double c=dfsr\[j\]+r\[i\];  
                double a=fabs(dfsr\[j\]-r\[i\]);  
                double b=sqrt(c\*c-a\*a);  
                pos\[depth\]=max(pos\[depth\],b+pos\[j\]);  
            }  
            vis\[i\]=1;  
            dfs(depth+1);  
            vis\[i\]=0;  
        }  
    }  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    int test;  
    scanf("%d",&test);  
    while(test--){  
        scanf("%d",&n);  
        for(int i=0;i<n;i++)scanf("%lf",&r\[i\]);  
        Set(vis,0);  
        minans=oo;  
        for(int i=0;i<n;i++){  
            dfsr\[0\]=r\[i\];  
            pos\[0\]=r\[i\];  
            vis\[i\]=1;  
            dfs(1);  
            vis\[i\]=0;  
        }  
        printf("%.3f\\n",minans);  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}