#include<bits/stdc++.h>
#define taskname ""
#define el '\n'
#define fi first
#define sc second
#define pii pair<int, int>
#define all(v) v.begin(), v.end()
#define int ll
using namespace std;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
#define Faster ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
const int maxn=5e3+6;
const int INF=6e18;
const int mod=1e9+7;
int n,f[maxn][maxn];
struct P
{
    int x,y;
}p[maxn];
int d(P x,P y)
{
    return (x.x-y.x)*(x.x-y.x)+(x.y-y.y)*(x.y-y.y);
}
int nxt(int i)
{
    return (i+1)%n;
}
void solve()
{
    cin>>n;
    for(int i=0;i<n;i++)
    {
        cin>>p[i].x>>p[i].y;
    }
    for(int i=0;i<n;i++)
    {
        f[i][1]=d(p[i],p[nxt(i)]);
    }
    for(int j=2;j<n;j++)
    {
        for(int i=0;i<n;i++)
        {
            f[i][j]=max({f[i][j-1],f[nxt(i)][j-1],d(p[i],p[(i+j)%n])});
        }
    }
    int ans=INF;
    for(int j=2;j<=n-2;j++)
    {
        for(int i=0;i<n;i++)
        {
            ans=min(ans,f[i][j]+f[(i+j)%n][n-j]);
        }
    }
    cout<<ans<<"\n";
}
signed main()
{
    if (fopen(taskname".INP","r"))
    {
        freopen(taskname".INP","r",stdin);
        freopen(taskname".OUT","w",stdout);
    }
    Faster
    int t;
    cin>>t;
    while(t--)
    {
        solve();
    }

}