#include <bits/stdc++.h>
#ifdef dbg
#define D(...) fprintf(stderr, __VA_ARGS__)
#define DD(...) D(#__VA_ARGS__ " = "), debug_helper::debug(__VA_ARGS__), D("\n")
#include "C:\Users\wsyear\Desktop\OI\templates\debug.hpp"
#else
#define D(...) ((void)0)
#define DD(...) ((void)0)
#endif
#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

using namespace std;

const int N = 5010;

int n;
pll a[N];
ll f[N][N];

ll pw(ll x) { return x * x; }
ll dis(pll x, pll y) { return pw(x.fi - y.fi) + pw(x.se - y.se); }
int get(int x) { x = x % n; if (!x) x = n; return x; }
pll operator-(pll x, pll y) { return pll(x.fi - y.fi, x.se - y.se); }
ll cross(pll x, pll y) { return x.fi * y.se - x.se * y.fi; }

void work() {
  cin >> n;
  rep (i, 1, n) cin >> a[i].fi >> a[i].se;
  rep (len, 2, n) rep (l, 1, n) {
    int r = get(l + len - 1);
    f[l][r] = max(dis(a[l], a[r]), max(f[l][get(r - 1)], f[get(l + 1)][r]));
  }
  ll ans = 5e18;
  rep (i, 1, n) rep (j, i + 1, n) if (i != j) {
    if (cross(a[j] - a[i], a[get(i + 1)] - a[i]) == 0) continue;
    if (cross(a[j] - a[i], a[get(i - 1)] - a[i]) == 0) continue;
    ans = min(ans, f[i][j] + f[j][i]);
  }
  cout << ans << '\n';
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  int t; cin >> t;
  while (t--) work();
}