#include <bits/stdc++.h>
using namespace std;
typedef long double lf;
lf read(){
    int x;cin>>x;return (lf)x;
}
const lf inf =1e9;
lf dis[3000][3000];
struct point {
    lf x,y;
};
int equal(lf x,lf y){
    return fabs(x-y)<=1e-9;
}
lf dist(point a,point b){
    return sqrtl((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
struct kkk{
    int x,y;
    lf len;
    bool operator<(kkk k1)const{
        return len>k1.len;
    }
};
lf solve()
{
    int n;cin>>n;
    vector<int> a(n+1);
    for(int i=0;i<=n;i++)cin>>a[i];
    vector<point>p;
    for(int i=0;i<n;i++){
        p.push_back(point{(lf)i,(lf)a[i]});
        if(a[i]<a[i+1]){
            for(int j=a[i]+1;j<a[i+1];j++){
                p.push_back(point{(lf)i+(lf)(j-a[i])/((lf)(a[i+1]-a[i])),(lf)j});
            }
        }
        if(a[i]>a[i+1]){
            for(int j=a[i]-1;j>a[i+1];j--){
                p.push_back(point{(lf)i+(lf)(a[i]-j)/((lf)(a[i]-a[i+1])),(lf)j});
            }
        }
    }
    p.push_back(point{(lf)n,(lf)a[n]});
    vector<pair<int,int>> vis;
    priority_queue<kkk,vector<kkk>> qu;
    qu.push(kkk{0,(int)p.size()-1,0.});
    while(!qu.empty()){
        kkk k1=qu.top();qu.pop();
        if(dis[k1.x][k1.y]!=inf)continue;
        vis.emplace_back(k1.x,k1.y);
        dis[k1.x][k1.y]=k1.len;
        for(int i=-1;i<=1;i++){
            for(int j=-1;j<=1;j++)if((!(i==0&&j==0))&&(i+k1.x>=0&&i+k1.x<p.size()&&j+k1.y>=0&&j+k1.y<p.size())){
                if(equal(p[i+k1.x].y,p[j+k1.y].y)){
                    qu.push(kkk{i+k1.x,j+k1.y,k1.len+dist(p[k1.x],p[i+k1.x])+dist(p[k1.y],p[k1.y+j])});
                }
            }
        }
    }
    lf ans=dis[p.size()-1][0];
    for(auto [x,y]:vis)dis[x][y]=inf;
    return ans;
}
int main()
{
    for(int i=0;i<3000;i++){
        for(int j=0;j<3000;j++)dis[i][j]=inf;
    }
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(10);
    int T;cin>>T;while(T--)cout<<solve()<<"\n";
    return 0;
}