// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2")
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
//#define int long long
#define SZ(x) ((int)((x).size()))
#define ALL(x) (x).begin(),(x).end()
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	return f?-x:x;
}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

typedef long double db;
const db eps=1e-12,pi=3.14159265358979323846;
int sgn(db x){return x<-eps?-1:x>eps;}
int cmp(db a,db b){return sgn(a-b);}

struct P{
	db x,y; int id;
	P(db x=0,db y=0):x(x),y(y){}
	P&operator +=(P o){return x+=o.x,y+=o.y,*this;}
	P&operator -=(P o){return x-=o.x,y-=o.y,*this;}
	P&operator *=(db o){return x*=o,y*=o,*this;}
	P&operator /=(db o){return x/=o,y/=o,*this;}
	friend P operator +(P a,P b){return a+=b;}
	friend P operator -(P a,P b){return a-=b;}
	friend P operator *(P a,db b){return a*=b;}
	friend P operator /(P a,db b){return a/=b;}
	friend bool operator <(P a,P b){return fabs(a.x-b.x)<eps?a.y<b.y:a.x<b.x;}
	friend bool operator ==(P a,P b){return cmp(a.x,b.x)==0 && cmp(a.y,b.y)==0;}
	friend bool operator !=(P a,P b){return !(a==b);}
	friend db operator %(P a,P b){return a.x*b.x+a.y*b.y;} // dot
	friend db operator *(P a,P b){return a.x*b.y-a.y*b.x;} // cross
	
	P rot(db o){
		db s=sin(o),c=cos(o);
		return P(x*c-y*s,x*s+y*c);
	}
	P rot90(){return P(-y,x);}
	db ang(){return atan2(y,x);}
	db len(){return sqrt(x*x+y*y);}
	db len2(){return x*x+y*y;}
	
	int half(){return sgn(y)==1||(sgn(y)==0&&sgn(x)>=0);}
	P unit(){return ((*this))/len();}
	
	void read(){cin>>x>>y;}
	void out(){cout<<"("<<x<<","<<y<<")"<<endl;}
};
bool cmp_dir(P a,P b){
	if(a.half()!=b.half())return a.half()<b.half();
	return sgn(a*b)>0;
}

db dis(P a,P b){return (a-b).len();}
db cross(P a,P b,P c){
	// (a->b)*(a->c)
	return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);
}
int cmp3(P a,P b,P c){
	return sgn(cross(a,b,c));
}

bool in_tri(P a,P b,P c,P p){
	if(cmp3(a,b,c)<0) swap(b,c);
	return cmp3(a,b,p)>=0 && cmp3(b,c,p)>=0 && cmp3(c,a,p)>=0;
}
db area_tri(P a,P b,P c){
	return fabs(cross(a,b,c))/2;
}

bool paral(P p1,P p2,P q1,P q2){
	// is parallel
	return sgn((p2-p1)*(q2-q1))==0;
}
P interl(P p1,P p2,P q1,P q2){
	// intersect point
	db s1=cross(q1,q2,p1),s2=-cross(q1,q2,p2);
	return (p1*s2+p2*s1)/(s1+s2);
}

bool inter(db l1,db r1,db l2,db r2){
	if(l1>r1)swap(l1,r1); if(l2>r2)swap(l2,r2);
	return !(cmp(r1,l2)==-1||cmp(r2,l1)==-1);
}
bool ismid(db a,db m,db b){
	return sgn(a-m)==0||sgn(b-m)==0||((a<m)!=(b<m));
}
bool ismid(P a,P m,P b){
	return ismid(a.x,m.x,b.x)&&ismid(a.y,m.y,b.y);
}

bool isseg(P p1,P p2,P q1,P q2){
	return inter(p1.x,p2.x,q1.x,q2.x) && inter(p1.y,p2.y,q1.y,q2.y) &&
	cmp3(p1,p2,q1)*cmp3(p1,p2,q2)<=0 && cmp3(q1,q2,p1)*cmp3(q1,q2,p2)<=0;
}
bool isseg_strict(P p1,P p2,P q1,P q2){
	return cmp3(p1,p2,q1)*cmp3(p1,p2,q2)<0 && cmp3(q1,q2,p1)*cmp3(q1,q2,p2)<0;
}

struct L{
	P a,b; int id;
	L(P aa=P(0,0),P bb=P(0,0)){a=aa,b=bb;}
	bool in(P p){return sgn((b-a)*(p-a))>0;}
	int in_sgn(P p){return sgn((b-a)*(p-a));}
	P dir(){return b-a;}
	bool onl(P p){
		return cmp3(a,b,p)==0;
	}
	bool onseg(P p){
		return onl(p)&&ismid(a,p,b);
	}
	bool onseg_strict(P p){
		return onl(p)&&sgn((p-a)%(a-b))*sgn((p-b)%(a-b))<0;
	}
	void out(){cout<<"("<<a.x<<","<<a.y<<")---("<<b.x<<","<<b.y<<")\n";}
};

bool isseg(L a,L b){
	return isseg(a.a,a.b,b.a,b.b);
}
bool isseg_strict(L a,L b){
	return isseg_strict(a.a,a.b,b.a,b.b);
}
bool paral(L a,L b){
	// is parallel
	return paral(a.a,a.b,b.a,b.b);
}
P operator &(L a,L b){
	return interl(a.a,a.b,b.a,b.b);
}
bool samedir(L a,L b){
	return paral(a,b) && sgn(a.dir()%b.dir())==1;
}
bool operator <(L a,L b){
	if(samedir(a,b)) return b.in(a.a);
	return cmp_dir(a.dir(),b.dir());
}

P proj(L a,P b){
	P d=a.dir();
	return a.a+d*((d%(b-a.a))/d.len2());
}
P reflect(L a,P b){
	return proj(a,b)*2-b;
}
db dis(L a,P b){
	db s=abs((b-a.a)*(b-a.b));
	return s/dis(a.a,a.b);
}
db dis_seg(L a,P b){
	if(a.a==a.b) return	dis(a.a,b);
	P h=proj(a,b);
	if(ismid(a.a,h,a.b)) return dis(h,b);
	return min(dis(a.a,b),dis(a.b,b));
}

db rad(P a,P b){
	return atan2l(a*b,a%b);
}

// polygon
db area(vector<P>a){
	db res=0;
	For(i,0,(int)a.size()-1)res+=a[i]*a[(i+1)%a.size()];
	return res/2;
}
int contain(vector<P>a,P p){
	int n=a.size(),res=0;
	For(i,0,n-1){
		P u=a[i],v=a[(i+1)%n];
		if(L(u,v).onseg(p))return 1;
		if(cmp(u.y,v.y)<=0)swap(u,v);
		if(cmp(p.y,u.y)>0 || cmp(p.y,v.y)<=0)continue;
		res^=cmp3(p,u,v)>0;
	}
	return res*2;
}
vector<P>cut(vector<P>&a,P q1,P q2){
	vector<P>b; int n=a.size();
	For(i,0,n-1){
		P p1=a[i],p2=a[(i+1)%n];
		int d1=cmp3(q1,q2,p1),d2=cmp3(q1,q2,p2);
		if(d1>=0)b.pb(p1);
		if(d1*d2<0)b.pb(interl(p1,p2,q1,q2));
	}
	return b;
}
vector<P>cut(vector<P>&a,L l){
	return cut(a,l.a,l.b);
}

vector<P>convex(vector<P>a){
	int n=a.size(),m=0; if(n<=1)return a;
	sort(a.begin(),a.end());
	vector<P>st(n*2); int tp=0;
	For(i,0,n-1){
		while(tp>1 && cmp3(st[tp-2],st[tp-1],a[i])<=0)--tp;
		st[tp++]=a[i];
	}
	int t=tp;
	Rep(i,n-2,0){
		while(tp>t && cmp3(st[tp-2],st[tp-1],a[i])<=0)--tp;
		st[tp++]=a[i];
	}
	st.resize(tp-1);
	return st;
}
db diam(vector<P>a){
	int n=a.size();
	if(n<=1)return 0;
	int ii=0,jj=0;
	For(k,1,n-1){
		if(a[k]<a[ii])ii=k;
		if(a[jj]<a[k])jj=k;
	}
	int i=ii,j=jj;
	db res=dis(a[i],a[j]);
	do{
		if((a[(i+1)%n]-a[i])*(a[(j+1)%n]-a[j])>=0) (++j)%=n;
		else (++i)%=n;
		res=max(res,dis(a[i],a[j]));
	}while(i!=ii||j!=jj);
	return res;
}

bool check(L a,L b,L c){
	return c.in(a&b);
}
int checksgn(L a,L b,L c){
	return c.in_sgn(a&b);
}
vector<P>hpis(vector<L>&l,bool is=0){
	if(!is)sort(l.begin(),l.end());
	deque<L>q;
	For(i,0,(int)l.size()-1){
		if(i&&samedir(l[i],l[i-1]))continue;
		while(q.size()>1 && !check(q[q.size()-2],q[q.size()-1],l[i]))q.pop_back();
		while(q.size()>1 && !check(q[1],q[0],l[i]))q.pop_front();
		q.pb(l[i]);
	}
	while(q.size()>2 && !check(q[q.size()-2],q[q.size()-1],q[0]))q.pop_back();
	while(q.size()>2 && !check(q[1],q[0],q[q.size()-1]))q.pop_front();
	vector<P>res;
	For(i,0,(int)q.size()-1) res.pb(q[i]&q[(i+1)%q.size()]);
	return res;
}

mt19937_64 rnd(64);

vector<L>cut(vector<L>&a,L l){
	vector<L>b; int n=a.size();
	For(i,0,n-1){
		L a1=a[i],a2=a[(i+1)%n],a3=a[(i+2)%n];
		int d1=checksgn(a1,a2,l),d2=checksgn(a2,a3,l);
		if(d1>0 || d2>0 || (d1==0&&d2==0)) b.pb(a2);
		if(d1>=0 && d2<0) b.pb(l);
	}
	return b;
}

#define maxn 500005
#define inf 0x3f3f3f3f

int X;
P s,t,a[5],aa[5],m1,m2,ss,tt;
L mr,l1[6],l2[6],st;

vector< tuple<int,db,int> >e[maxn];
P ps[maxn];
int tot;

void adde(int u,int v,db w,int st){
	e[u].pb({v,w,st});
	e[v].pb({u,w,st});
//	if(st!=3)return;
//	cout<<"add  "<<u<<" "<<v<<"\n";
//	cout<<"add: "<<w<<" "<<st<<"\n";
//	ps[u].out(),ps[v].out();
}

db f[maxn];
bool vis[maxn];
db dij(int sta,int s,int t){
	#define node pair<db,int>
	priority_queue< node,vector<node>,greater<node> >q;
	For(i,1,tot) f[i]=4e18,vis[i]=0; f[s]=0;
	q.push(mkp(f[s],s));
	while(q.size()){
		auto [d,u]=q.top(); q.pop();
		if(vis[u]) continue;
		if(u==t) return f[u];
		vis[u]=1;
		for(auto [v,w,ww]:e[u]){
			if((ww&sta)!=sta) continue;
			if(f[v]>f[u]+w){
				f[v]=f[u]+w;
				q.push(mkp(f[v],v));
			}
		}
	}
	return 4e18;
}
db dij(int sta){
	db res=dij(sta,1,2);
	return res;
}

bool chk(L l){
	For(i,0,2) if(isseg_strict(l,l1[i])) return 0;
	if(isseg_strict(l,mr)) return 0;
	return 1;
}

int add(P u){
	ps[++tot]=u; e[tot].clear();
	return tot;
}
void build1(){
	cerr<<"build1\n";
	add(s),add(t),add(m1),add(m2);
	For(i,0,2)add(a[i]);
	For(i,1,tot) For(j,i+1,tot) {
		if(chk(L(ps[i],ps[j]))){
			adde(i,j,dis(ps[i],ps[j]),0);
		}
	}
}

vector<L>buc;

bool see(P p,P to){
	if(chk(L(p,to))) return 1;
	L l=L(p,reflect(mr,to));
	if(!isseg(l,mr)) return 0;
	For(i,0,2)
		if(isseg_strict(l,l1[i]) || isseg_strict(l,l2[i])) return 0;
	return 1;
}

int is_see(L l,P to){
//	cout<<"is_see: ";
//	l.out(),to.out();
	vector<P>vec={l.a,l.b};
	for(auto ls:buc){
		if(!paral(ls,l)){
			P p=(ls&l);
			if(ismid(l.a,p,l.b)) vec.pb(p);
		}
	}
	sort(ALL(vec),[&](P a,P b){
		return dis(a,l.a)<dis(b,l.a);
	});
//	for(auto ps:vec) ps.out();
	For(i,1,SZ(vec)-1){
		P it=(vec[i]+vec[i-1])*0.5;
		if(!see(it,to)) return 0;
	}
	return 1;
}

void build2(){
	cerr<<"build2\n";
	add(s),add(t);
	for(auto p1:{s,t,ss,tt}) {
		for(auto p2:{m1,m2}) buc.pb(L(p1,p2));
		For(i,0,2) buc.pb(L(p1,a[i]));
		if(p1==ss || p1==tt) {
			For(i,0,2) buc.pb(L(p1,aa[i]));
		}
	}
	For(i,0,SZ(buc)-1){
		For(j,i+1,SZ(buc)-1){
			if(!paral(buc[i],buc[j])){
				P p=(buc[i]&buc[j]);
				if(cmp3(m1,m2,p)<0 && find(ps+1,ps+tot+1,p)==ps+tot+1) add(p);
			}
		}
	}
	sort(ps+3,ps+tot+1);
//	cout<<"tot: "<<tot<<"\n";
	
	For(i,1,tot) For(j,i+1,tot) if(chk(L(ps[i],ps[j]))) {
		L l=L(ps[i],ps[j]);
		int sta=(is_see(l,s))+(is_see(l,t)<<1);
		adde(i,j,dis(ps[i],ps[j]),sta);
	}
}

void work(int ID)
{
	tot=0,buc.clear();
	
	
	X=read();
	s.read(),t.read(),m1.read(),m2.read();
	For(i,0,2) a[i].read();
	
//	if(ID>3){
//		if(ID==20){
//			cout<<X<<"\n";
//			cout<<s.x<<" "<<s.y<<"\n";
//			cout<<t.x<<" "<<t.y<<"\n";
//			cout<<m1.x<<" "<<m1.y<<"\n";
//			cout<<m2.x<<" "<<m2.y<<"\n";
//			For(i,0,2)cout<<a[i].x<<" "<<a[i].y<<"\n";
//		}
//		return;
//	}
	
	mr=L(m1,m2);
	ss=reflect(mr,s);
	tt=reflect(mr,t);
	For(i,0,2) aa[i]=reflect(mr,a[i]);
	For(i,0,2) l1[i]=L(a[i],a[(i+1)%3]),l2[i]=L(aa[i],aa[(i+1)%3]);
	db res=4e18;
	
	if(chk(L(s,t))) res=dis(s,t)*(2*X-1);
	else if(X==1){
		build1();
		res=dij(0);
	}
	else if(cmp3(m1,m2,s)<0 && cmp3(m1,m2,t)<0){
		build2();
		res=dij(1)+dij(3)*(X*2-3)+dij(2);
	}
	
	if(res>1e18)puts("-1");
	else printf("%.12lf\n",(double)res);
}

signed main()
{
//	freopen("my.out","w",stdout);
	int T=read();
	For(_,1,T)work(_);
	return 0;
}
/*
1
2
-4 -8
3 -6
0 0
3 0
2 -7
2 -5
1 -3

*/