#include<bits/stdc++.h>
using namespace std;
#define rep(i,x,y) for (int i=(x);i<=(y);i++)
#define drep(i,y,x) for (int i=(y);i>=(x);i--)
#define pii pair<int,int>
#define fir first
#define sec second
#define MP make_pair
template<typename T> bool chkmin(T &x,T y){return x>y?x=y,1:0;}
const double eps=1e-10;
bool chkmin(double &x,double y){return x>y+eps?x=y,1:0;}
template<typename T> bool chkmax(T &x,T y){return x<y?x=y,1:0;}
void file() {
    #ifdef zqj
    freopen("a.in","r",stdin);
    #endif
}
typedef long long ll;
typedef double db;
#define sz 5555

int n;
int h[sz];

db dp[sz][sz];

bool IN(int x,int y,int z){return x>=min(y,z)&&x<=max(y,z);}
db dis(int x,int y){return sqrt((x-y)*(x-y)+(h[x]-h[y])*(h[x]-h[y]));}
db dis(db x1,db y1,db x2,db y2) {
    return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}

void work() {
    cin>>n;
    rep(i,0,n) cin>>h[i];
    h[n+1]=h[n];
    rep(i,0,n) rep(j,0,n) dp[i][j]=1e18;
    dp[0][n]=0;
    priority_queue<pair<db,pii>,vector<pair<db,pii>>,greater<pair<db,pii>>>q;
    q.push({0.,{0,n}});
    while (!q.empty()) {
        auto [x,y]=q.top().sec; auto w=q.top().fir;
        q.pop();
        if (dp[x][y]!=w) continue;
        if (x==y) return printf("%.10lf\n",2*w),void();
        if (h[y]==h[x]&&chkmin(dp[y][x],w)) q.push({w,{y,x}});
        if (h[y]!=h[y+1]&&h[y+1]==h[x]) {
            if (chkmin(dp[x][y+1],w)) q.push({w,{x,y+1}});
            continue;
        }
        db yX=y;
        if (h[y]!=h[y+1]) yX=1.0*(h[x]-h[y])/(h[y+1]-h[y])+y; // CHECK
        for (auto xx:{x-1,x+1}) {
            if (xx<0||xx>n) continue;
            if (IN(h[xx],h[y],h[y+1])) {
                db ww=dis(x,xx);
                if (h[y]==h[y+1]) {
                    if (chkmin(dp[xx][y],w+ww)) q.push({w+ww,{xx,y}});
                }
                else {
                    db _yX=1.0*(h[xx]-h[y])/(h[y+1]-h[y])+y;
                    ww+=dis(yX,h[x],_yX,h[xx]);
                    if (chkmin(dp[xx][y],w+ww)) q.push({w+ww,{xx,y}});
                }
            }
            if (h[x]==h[y]&&h[xx]!=h[x]&&IN(h[xx],h[y],h[y-1])) {
                db ww=dis(x,xx);
                if (h[y]==h[y-1]) {
                    
                }
                else {
                    db _yX=-1.0*(h[xx]-h[y])/(h[y-1]-h[y])+y;
                    ww+=dis(yX,h[x],_yX,h[xx]);
                    if (chkmin(dp[xx][y-1],w+ww)) q.push({w+ww,{xx,y-1}});
                }
            }
            {
                if (h[y]==h[y+1]) continue;
                for (auto yy:{y,y+1}) {
                    if (yy>n) continue;
                    
                    if (IN(h[yy],h[x],h[xx])) {
                        db ww=dis(yX,h[x],yy,h[yy]);
                        db xX=x;
                        if (h[x]!=h[xx]) xX=(xx-x)*1.0*(h[yy]-h[x])/(h[xx]-h[x])+x;
                        ww+=dis(x,h[x],xX,h[yy]);
                        int _x=min(x,xx); if (h[x]==h[xx]) _x=x;
                        if (chkmin(dp[yy][_x],w+ww)) q.push({w+ww,{yy,_x}});
                    }
                }
            }
        }
    }
    assert(0);
}

int main() {
    file();
    int T; cin>>T;
    while (T--) work();
    return 0;
}