#include <iostream>
#include <vector>
#include <queue>
using namespace std;
using ll = long long;
using ull = unsigned long long;
#define rep(i,n) for(int i=0; i<(n); i++)

template<class T>
using nega_queue = priority_queue<T,vector<T>,greater<T>>;

const int INF = 1001001001;

const int W = 600;
const int H = 600;
const int NV = W * H; // number of vertices
const int maxV = 7;

struct Start{ int id,v; };

int pos2id(int y,int x){ return y * W + x; }

int X,Y;
int N;
vector<Start> hikyaku;
double dt[maxV];
double V[maxV];
double T[maxV][NV];
vector<int> E[NV];

double D[maxV][NV];

int main(){
  cin >> X >> Y; X--; Y--;
  cin >> N;

  rep(y,H) rep(x,W-1) E[pos2id(y,x)].push_back(pos2id(y,x+1));
  rep(y,H) rep(x,W-1) E[pos2id(y,x+1)].push_back(pos2id(y,x));
  rep(y,H-1) rep(x,W) E[pos2id(y,x)].push_back(pos2id(y+1,x));
  rep(y,H-1) rep(x,W) E[pos2id(y+1,x)].push_back(pos2id(y,x));

  hikyaku.resize(N);
  rep(i,N){
    int x,y,v; cin >> x >> y >> v;
    x--; y--; v--;
    hikyaku[i] = { pos2id(y,x),v };
  }

  rep(v,maxV) V[v] = 1+v;
  rep(v,maxV) dt[v] = 1000.0 / (1+v);
  
  rep(v,maxV) rep(i,NV) T[v][i] = INF;

  {
    vector<vector<int>> I(maxV);
    for(auto a : hikyaku){
      I[a.v].push_back(a.id);
      T[a.v][a.id] = 0;
    }
    rep(v,maxV){
      rep(i,I[v].size()){
        int p = I[v][i];
        for(int e : E[p]) if(T[v][e] >= INF - 1.0){
          T[v][e] = T[v][p] + dt[v];
          I[v].push_back(e);
        }
      }
    }
  }
  
  rep(v,maxV) rep(i,NV) D[v][i] = INF;

  nega_queue<pair<double,pair<int,int>>> Q;
  D[hikyaku[0].v][hikyaku[0].id] = 0.0;
  Q.push(make_pair(0.0,make_pair(hikyaku[0].v,hikyaku[0].id)));

  while(Q.size()){
    double d = Q.top().first;
    int v = Q.top().second.first;
    int p = Q.top().second.second;
    Q.pop();
    if(D[v][p] != d) continue;
    for(int nxv=v+1; nxv<maxV; nxv++) if(D[nxv][p] > max(T[nxv][p],d)){
      D[nxv][p] = max(T[nxv][p],d);
      Q.push(make_pair(D[nxv][p],make_pair(nxv,p)));
    }
    for(int e : E[p]){
      if(D[v][e] > d + dt[v]){
        D[v][e] = d + dt[v];
        Q.push(make_pair(D[v][e],make_pair(v,e)));
      }
      double nxd = dt[v];
      int pv = v;
      for(int nxv=v+1; nxv<maxV; nxv++){
        double t0 = d + nxd - max(d - dt[nxv], T[nxv][e]);
        //cout << "p = " << p << ", e = " << e << ", pv = " << pv << ", nxv = " << nxv << ", t0 = " << t0 << endl;
        if(t0 < 0) continue;
        t0 = min(t0,dt[pv]+dt[nxv]);
        double t = nxd - t0 * (V[nxv] - V[pv]) / (V[nxv] + V[pv]);
        nxd = t; pv = nxv;
        if(D[nxv][e] <= d+nxd) continue;
        D[nxv][e] = d+nxd;
        Q.push(make_pair(d+nxd,make_pair(nxv,e)));
      }
    }
  }

  double ans = INF;
  rep(v,maxV) ans = min(ans,D[v][pos2id(Y,X)]);
  cout.precision(10); cout << fixed;
  cout << ans << endl;
  return 0;
}

struct ios_do_not_sync{
  ios_do_not_sync(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
  }
} ios_do_not_sync_inst;