#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define rep(i, a, b) for(int i = (a); i <= (b); i++)
#define per(i, a, b) for(int i = (a); i >= (b); i--)
#define rept(i, a, ne) for(int i = (a); ~i ; i=ne[i])
#define debug(x) cout<<#x<<": "<<x<<endl
#define fi first
#define sec second
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
typedef long long LL;
typedef long double  LD;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef pair<int,int>PII;
const int N=50+10;
bool bo[N][N][N];
LD d[N][N][N];
int a[N];
LD pd[N][N];
LD eps=1e-10;
struct A
{
    int x,y,h;
    LD d;

    bool operator<(const A& a)const 
    {
        return d>a.d;
    }
};

void ud(priority_queue<A>&q,int x,int y,int h,LD di)
{
    if (d[x][y][h]>di)
    {
        d[x][y][h]=di;
        q.push({x,y,h,di});
    }
}
void slove()
{
    int n;
    cin>>n;

    rep(i,0,N-1)
    rep(j,0,N-1)
    rep(k,0,53)
    {
       bo[i][j][k]=0; 
       d[i][j][k]=1e18;
    }
    
    rep(i,0,n)
    cin>>a[i];
    a[n+1]=0;
    priority_queue<A> q;

    d[0][n][0] = 0;
    q.push({0,n,0,0});      

    while (q.size())
    {
        auto [x,y,h,di] = q.top();
        q.pop();
  
        if (bo[x][y][h]) continue;
        bo[x][y][h] = 1;
        //  cout<<x<<' '<<y<<' '<<h<<' '<<di<<endl;
        if(x>0&&a[x]==h)
        ud(q,x-1,y,h,(a[x-1]==a[x])+di);
        if(x<n&&a[x+1]==h)
        ud(q,x+1,y,h,(a[x]==a[x+1])+di);

        if(y>0&&a[y]==h)
        ud(q,x,y-1,h,(a[y-1]==a[y])+di);
        if(y<n&&a[y+1]==h)
        ud(q,x,y+1,h,(a[y]==a[y+1])+di);


        if(h<max(a[x],a[x+1])&&h<max(a[y],a[y+1]))
        {
            LD nd=pd[a[x]][a[x+1]]+pd[a[y]][a[y+1]];
            ud(q,x,y,h+1,nd+di);
        }  
        if(h>min(a[x],a[x+1])&&h>min(a[y],a[y+1]))
        {
            LD nd=pd[a[x]][a[x+1]]+pd[a[y]][a[y+1]];
            ud(q,x,y,h-1,nd+di);
        }  
    }
    cout<<d[n][0][0]<<endl;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
	cout << fixed << setprecision(10);
    int t=1;
	cin>>t;
    rep(i,0,50)
    rep(j,0,50)
    if(i!=j)
    pd[i][j]=sqrtl((i-j)*(i-j)+1)/fabsl(i-j);
    
    while(t--)
    {
        slove();
    }


    return 0;
}
//#pragma GCC optimize(2)