#include <iostream>
#include <vector>
#include <map>
#include <string>
#include <iomanip>
#include <algorithm>
using namespace std;
using ll = long long;
using Vector = pair<ll,ll>;
using Koeff = ll;
struct Lizard{
    ll x{};
    ll y{};
    ll h{};
};

int CeilIndex(std::vector<int>& v, int l, int r, int key)
{
    while (r - l > 1) {
        int m = l + (r - l) / 2;
        if (v[m] >= key)
            r = m;
        else
            l = m;
    }

    return r;
}

int LongestIncreasingSubsequenceLength(std::vector<int>& v)
{
    if (v.size() == 0)
        return 0;

    std::vector<int> tail(v.size(), 0);
    int length = 1; // always points empty slot in tail

    tail[0] = v[0];
    for (size_t i = 1; i < v.size(); i++) {

        // new smallest value
        if (v[i] < tail[0])
            tail[0] = v[i];

            // v[i] extends largest subsequence
        else if (v[i] > tail[length - 1])
            tail[length++] = v[i];

            // v[i] will become end candidate of an existing
            // subsequence or Throw away larger elements in all
            // LIS, to make room for upcoming greater elements
            // than v[i] (and also, v[i] would have already
            // appeared in one of LIS, identify the location
            // and replace it)
        else
            tail[CeilIndex(tail, -1, length - 1, v[i])] = v[i];
    }

    return length;
}


int main() {
    constexpr ll largeK = 1000000000ll;
    Vector tv;
    cin >> tv.first >> tv.second;
    ll n;
    cin >> n;
    map<Koeff , vector<Lizard>> lines;
    for (int i=0;i<n;++i){
        ll x;
        ll y;
        ll h;
        cin >> x >> y >> h;
        ll koeff = (x - tv.first != 0) ? (static_cast<double>(y) - tv.second) / (static_cast<double>(x) - tv.first) * largeK
                                       : LLONG_MAX;
        lines[koeff].push_back({x,y,h});
    }

    //cout << "**********" << endl;
    vector<vector<pair<ll,ll>>> linesLizard;
    for (auto& line:lines){
        //cout << "--------" << endl;
        vector<pair<ll,ll>> temp;
        for (auto& liz:line.second){
            temp.push_back({liz.x, liz.h});
        }
        temp.push_back({tv.first, 0});
        sort(temp.begin(),temp.end());
        linesLizard.emplace_back(temp);
        //for (auto v:temp)
          //  cout << v.first << ' ' << v.second << endl;
    }
    //cout << "************" << endl;

    vector<vector<int>> finalLizard;

    for (auto& line:linesLizard){
        vector<int> temp;
        for (auto& liz:line){
            if (liz.second==0){
                reverse(temp.begin(),temp.end());
                if (!temp.empty())
                    finalLizard.emplace_back(temp);
                temp.clear();
                continue;
            }
            temp.push_back(liz.second);
        }
        if (!temp.empty())
            finalLizard.emplace_back(temp);
    }

    ll ans = 0;
    for (auto& line:finalLizard){
        int len = LongestIncreasingSubsequenceLength(line);
        //cout << len << endl;
        ans+=len;
    }
    cout << ans << endl;


}