//Make CSP great again
//Vengeance
#include <bits/stdc++.h>
#define TASK "TESTCODE"
using namespace std;
const int N = 5e3;
int n;
long long res, l[N], r[N], dp_l[N], dp_r[N];
struct TPoint
{
    int x, y;
} p[N];
using TVector = TPoint;
TVector operator - (TPoint a, TPoint b)
{
    return {b.x - a.x, b.y - a.y};
}
long long dis (TPoint a, TPoint b) // dis
{
    return 1LL * (a.x - b.x) * (a.x - b.x) + 1LL * (a.y - b.y) * (a.y - b.y);
}
long long operator * (TVector a, TVector b)
{
    return 1LL * a.x * b.y - 1LL * a.y * b.x;
}
bool Straight(TPoint a, TPoint b, TPoint c)
{
    return (b - a) * (c - b) == 0;
}
int nxt(int i)
{
    if (i == n - 1)
    {
        return 0;
    }
    return i + 1;
}
int pre(int i)
{
    if (i == 0)
    {
        return n - 1;
    }
    return i - 1;
}
void read()
{   
    res = 1e18;
    cin >> n;
    for (int i = 0; i < n; ++ i)
    {
        cin >> p[i].x >> p[i].y;
    }
}
void solve()
{
    for (int i = 0; i < n; ++ i)
    {
        int k = nxt(i);
        for (int j = nxt(i); j != i; j = nxt(j))
        {
            while(k != i && dis(p[j], p[nxt(k)]) >= dis(p[j], p[k]))
            {
                k = nxt(k);
            }
            l[j] = dis(p[j], p[k]);
        }
        k = pre(i);
        for (int j = pre(i); j != i; j = pre(j))
        {
            while(k != i && dis(p[j], p[pre(k)]) >= dis(p[j], p[k]))
            {
                k = pre(k);
            }
            r[j] = dis(p[j], p[k]);
        }
        long long mx = 0;
        for (int j = pre(i); j != i; j = pre(j))
        {
            mx = max(mx, l[j]);
            dp_l[j] = mx;
        }
        mx = 0;
        for (int j = nxt(i); j != i; j = nxt(j))
        {
            mx = max(mx, r[j]);
            dp_r[j] = mx;
            if (!Straight(p[i], p[j], p[nxt(i)]) && !Straight(p[j], p[pre(i)], p[i]))
            {   
                res = min(res, dp_l[j] + dp_r[j]);
            }
        }
    }
    cout << res << '\n';
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    if (fopen(TASK".INP", "r"))
    {
        freopen(TASK".INP", "r", stdin);
        //freopen(TASK".OUT", "w", stdout);
    }
    int t = 1;
    bool typetest = true;
    if (typetest)
    {
        cin >> t;
    }
    for (int __ = 1; __ <= t; ++ __)
    {
        //cout << "Case " << __ << ": ";
        read();
        solve();
    }
}