#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

#define ll long long
#define pb push_back
#define f first
#define s second
#define sz(x) (int)(x).size()
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define ios ios_base::sync_with_stdio(false);cin.tie(NULL)
#define ld long double
#define li __int128

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>; ///find_by_order(),order_of_key()
template<int D, typename T>struct vec : public vector<vec<D - 1, T>> {template<typename... Args>vec(int n = 0, Args... args) : vector<vec<D - 1, T>>(n, vec<D - 1, T>(args...)) {}};
template<typename T>struct vec<1, T> : public vector<T> {vec(int n = 0, T val = T()) : vector<T>(n, val) {}};
template<class T1,class T2> ostream& operator<<(ostream& os, const pair<T1,T2>& a) { os << '{' << a.f << ", " << a.s << '}'; return os; }
template<class T> ostream& operator<<(ostream& os, const vector<T>& a){os << '{';for(int i=0;i<sz(a);i++){if(i>0&&i<sz(a))os << ", ";os << a[i];}os<<'}';return os;}
template<class T> ostream& operator<<(ostream& os, const deque<T>& a){os << '{';for(int i=0;i<sz(a);i++){if(i>0&&i<sz(a))os << ", ";os << a[i];}os<<'}';return os;}
template<class T> ostream& operator<<(ostream& os, const set<T>& a) {os << '{';int i=0;for(auto p:a){if(i>0&&i<sz(a))os << ", ";os << p;i++;}os << '}';return os;}
template<class T> ostream& operator<<(ostream& os, const set<T,greater<T> >& a) {os << '{';int i=0;for(auto p:a){if(i>0&&i<sz(a))os << ", ";os << p;i++;}os << '}';return os;}
template<class T> ostream& operator<<(ostream& os, const multiset<T>& a) {os << '{';int i=0;for(auto p:a){if(i>0&&i<sz(a))os << ", ";os << p;i++;}os << '}';return os;}
template<class T> ostream& operator<<(ostream& os, const multiset<T,greater<T> >& a) {os << '{';int i=0;for(auto p:a){if(i>0&&i<sz(a))os << ", ";os << p;i++;}os << '}';return os;}
template<class T1,class T2> ostream& operator<<(ostream& os, const map<T1,T2>& a) {os << '{';int i=0;for(auto p:a){if(i>0&&i<sz(a))os << ", ";os << p;i++;}os << '}';return os;}
int ri(){int x;scanf("%i",&x);return x;}
void rd(int&x){scanf("%i",&x);}
void rd(long long&x){scanf("%lld",&x);}
void rd(double&x){scanf("%lf",&x);}
void rd(long double&x){scanf("%Lf",&x);}
void rd(string&x){cin>>x;}
void rd(char*x){scanf("%s",x);}
template<typename T1,typename T2>void rd(pair<T1,T2>&x){rd(x.first);rd(x.second);}
template<typename T>void rd(vector<T>&x){for(T&p:x)rd(p);}
template<typename C,typename...T>void rd(C&a,T&...args){rd(a);rd(args...);}
//istream& operator>>(istream& is,__int128& a){string s;is>>s;a=0;int i=0;bool neg=false;if(s[0]=='-')neg=true,i++;for(;i<s.size();i++)a=a*10+s[i]-'0';if(neg)a*=-1;return is;}
//ostream& operator<<(ostream& os,__int128 a){bool neg=false;if(a<0)neg=true,a*=-1;ll high=(a/(__int128)1e18);ll low=(a-(__int128)1e18*high);string res;if(neg)res+='-';if(high>0){res+=to_string(high);string temp=to_string(low);res+=string(18-temp.size(),'0');res+=temp;}else res+=to_string(low);os<<res;return os;}

void test(){
	int n=ri();
	vector<pair<int,int>> c(n);
	rd(c);
	for(int i=0;i<n;i++){
		c.pb(c[i]);
	}
	auto dist=[&](int a,int b){
		return (ll)(c[a].f-c[b].f)*(c[a].f-c[b].f)+(ll)(c[a].s-c[b].s)*(c[a].s-c[b].s);
	};
	int N=2*n;
	vector<vector<ll>> dp(N,vector<ll>(N));
	for(int i=0;i<N;i++){
		for(int j=i-1;j>=0;j--){
			//printf("%i %i: %lld\n",j,i,dist(i,j));
			dp[j][i]=max(dp[j][i],dist(i,j));
			dp[j][i]=max(dp[j][i],dp[j+1][i]);
			dp[j][i]=max(dp[j][i],dp[j][i-1]);
		}
	}
	ll oo=LLONG_MAX/3;
	for(int i=0;i<N;i++){
		dp[i][i]=oo;
		dp[i][i+1]=oo;
		for(int j=i+2;j<N;j++){
			ll x1=c[j].f-c[i].f,y1=c[j].s-c[i].s,x2=c[i+1].f-c[i].f,y2=c[i+1].s-c[i].s;
			ll crs=x1*y2-x2*y1;
			if(crs==0){
				dp[i][j]=oo;
			}
			else{
				break;
			}
		}
	}
	ll mn=LLONG_MAX;
	for(int i=0;i<n;i++){
		for(int j=i+2;j<n;j++){
			if(i==0&&j==n-1){
				continue;
			}
			ll val=dp[i][j]+dp[j][i+n];
			//printf("%i %i: %lld   %lld  %lld\n",i,j,val,dp[i][j],dp[j][i+n]);
			mn=min(mn,val);
		}
	}
	printf("%lld\n",mn);
}
int main()
{
	int t=ri();
	while(t--){
		test();
	}
	return 0;
}