1137.cpp

// Ivan Carvalho
// Solution to https://www.beecrowd.com.br/judge/problems/view/1137
#include <algorithm>
#include <iostream>
#define MAXN 201
using namespace std;
typedef long long ll;
ll X[MAXN], Y[MAXN], squared[MAXN], resp, n, sqy[MAXN][MAXN], sqx[MAXN][MAXN],
    xy[MAXN][MAXN];
void addCircle(ll A, ll B, ll C) {
    ll cof1 = X[A] * (Y[B] - Y[C]) - Y[A] * (X[B] - X[C]) + xy[B][C];
    if (cof1 == 0) return;
    ll cof2 = squared[A] * (Y[B] - Y[C]) - Y[A] * (squared[B] - squared[C]) +
              sqy[B][C];
    ll cof3 = squared[A] * (X[B] - X[C]) - X[A] * (squared[B] - squared[C]) +
              sqx[B][C];
    ll cof4 = squared[A] * (xy[B][C]) - X[A] * (sqy[B][C]) + Y[A] * (sqx[B][C]);
    ll temp = 0;
    for (ll i = 1; i <= n; i++) {
        ll val = cof1 * squared[i] - cof2 * X[i] + cof3 * Y[i] - cof4;
        if (val == 0) temp++;
    }
    resp = max(temp, resp);
}
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    while (cin >> n && n) {
        resp = min(n, 2LL);
        for (ll i = 1; i <= n; i++) {
            cin >> X[i] >> Y[i];
            squared[i] = X[i] * X[i] + Y[i] * Y[i];
        }
        for (ll i = 1; i <= n - 1; i++) {
            for (ll j = i + 1; j <= n; j++) {
                xy[i][j] = X[i] * Y[j] - X[j] * Y[i];
                sqx[i][j] = squared[i] * X[j] - squared[j] * X[i];
                sqy[i][j] = squared[i] * Y[j] - squared[j] * Y[i];
            }
        }
        for (ll i = 1; i <= n - 2; i++) {
            for (ll j = i + 1; j <= n - 1; j++) {
                for (ll k = j + 1; k <= n; k++) {
                    addCircle(i, j, k);
                }
            }
        }
        cout << resp << '\n';
    }
    return 0;
}