#include <bits/stdc++.h>

using namespace std;
using ll = long long;

#define int ll
#define pb push_back

int gcd(int x, int y) {
    x = abs(x); y = abs(y);
    while (x) {
        y %= x;
        swap(x, y);
    }
    return y;
}

void solve() {
    int n; cin >> n;
    vector<pair<int, int>> a(n);
    for (int i = 0; i < n; i++) cin >> a[i].first >> a[i].second;
    vector<pair<int, int>> v;
    for (int i = 1; i < n; i++) {
        v.pb({a[i].first - a[0].first, a[i].second - a[0].second});
    }
    bool line = true;
    for (int i = 2; i < n; i++) {
        if ((a[i].first - a[0].first) * (a[1].second - a[0].second) - (a[i].second - a[0].second) * (a[1].first - a[0].first) != 0) line = false;
    }
    if (line) {
        cout << "-1\n";
        return;
    }
    vector<pair<int, int>> newv = {v[0]};
    for (int i = 1; i < n - 1; i++) {
        if (v[i].first * v[0].second - v[i].second * v[0].first != 0) {
            newv.pb(v[i]);
            for (int j = 1; j < n; j++) {
                if (j != i) newv.pb(v[j]);
            }
            break;
        }
    }
    swap(v, newv);
    int cdx, cdy;
    if (v[0].first == 0) {
        cdy = abs(v[0].second);
    } else if (v[1].first == 0) {
        cdy = abs(v[1].second);
    } else {
        cdy = abs(v[0].second * (v[1].first / gcd(v[1].first, v[0].first)) - v[1].second * (v[0].first / gcd(v[1].first, v[0].first)));
    }

    if (v[0].second == 0) {
        cdx = abs(v[0].first);
    } else if (v[1].second == 0) {
        cdx = abs(v[1].first);
    } else {
        cdx = abs(v[0].first * (v[1].second / gcd(v[1].second, v[0].second)) - v[1].first * (v[0].second / gcd(v[1].second, v[0].second)));
    }
    
    int dry = gcd(v[0].first, v[1].first), drx = gcd(v[1].second, v[0].second);
    cout << cdx + cdy - (cdx / dry) << '\n';
}

signed main() {
    int tt = 1;
    #ifdef LOCAL
        freopen("in.txt", "r", stdin);
        freopen("out.txt", "w", stdout);
        cin >> tt;
    #else 
        ios::sync_with_stdio(false); cin.tie(0);
    #endif

    while (tt--) {
        solve();
    }
}