#pragma GCC optimize ("O3")
#pragma GCC target ("avx2")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
template<class S, class T> inline S min_L(S a,T b){
  return a<=b?a:b;
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void rd(double &x){
  int k;
  int m=0;
  int p=0;
  double r = 1;
  x = 0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m = 1;
      break;
    }
    if(k=='.'){
      p = 1;
      break;
    }
    if('0'<=k&&k<='9'){
      x = k - '0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k=='.'){
      p = 1;
      continue;
    }
    if(k<'0'||k>'9'){
      break;
    }
    if(p){
      r *= 0.1;
      x += r * (k - '0');
    }
    else{
      x = x * 10 + k - '0';
    }
  }
  if(m){
    x = -x;
  }
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
int WRITER_DOUBLE_DIGIT = 15;
inline int writerDigit_double(){
  return WRITER_DOUBLE_DIGIT;
}
inline void writerDigit_double(int d){
  WRITER_DOUBLE_DIGIT = d;
}
inline void wt_L(double x){
  const int d = WRITER_DOUBLE_DIGIT;
  int k;
  int r;
  double v;
  if(x!=x || (x==x+1 && x==2*x)){
    my_putchar_unlocked('E');
    my_putchar_unlocked('r');
    my_putchar_unlocked('r');
    return;
  }
  if(x < 0){
    my_putchar_unlocked('-');
    x = -x;
  }
  x += 0.5 * pow(0.1, d);
  r = 0;
  v = 1;
  while(x >= 10*v){
    v *= 10;
    r++;
  }
  while(r >= 0){
    r--;
    k = floor(x / v);
    if(k >= 10){
      k = 9;
    }
    if(k <= -1){
      k = 0;
    }
    x -= k * v;
    v *= 0.1;
    my_putchar_unlocked(k + '0');
  }
  if(d > 0){
    my_putchar_unlocked('.');
    v = 1;
    for(r=(0);r<(d);r++){
      v *= 0.1;
      k = floor(x / v);
      if(k >= 10){
        k = 9;
      }
      if(k <= -1){
        k = 0;
      }
      x -= k * v;
      my_putchar_unlocked(k + '0');
    }
  }
}
int n;
int m;
int x[14];
int y[14];
int p;
int q;
double w[13];
double dp[1 << 13][13];
double dist(int i, int j){
  return abs(x[i] - x[j]) + abs(y[i] - y[j]);
}
double calc(int i, int j, double weight){
  return (weight + 100.0) / 120.0 * dist(i, j);
}
int main(){
  int i, s, v;
  rd(p);
  rd(q);
  rd(n);
  {
    int Nzj9Y0kE;
    for(Nzj9Y0kE=(0);Nzj9Y0kE<(n);Nzj9Y0kE++){
      rd(x[Nzj9Y0kE]);
      rd(y[Nzj9Y0kE]);
      rd(w[Nzj9Y0kE]);
    }
  }
  x[n] = p;
  y[n] = q;
  m = 1 << n;
  for(i=(0);i<(m);i++){
    int j;
    for(j=(0);j<(n);j++){
      dp[i][j] = 4611686016279904256LL;
    }
  }
  for(v=(0);v<(n);v++){
    dp[m - 1][v] = dist(v, n) * 5.0 / 6;
  }
  for(s=(m - 1)-1;s>=(0);s--){
    double k = 0;
    for(v=(0);v<(n);v++){
      if (!(s & 1 << v)){
        k += w[v];
      }
    }
    k = (k + 100) / 120;
    for(v=(0);v<(n);v++){
      int u;
      for(u=(0);u<(n);u++){
        if (!(s & 1 << u)){
          dp[s][v] =min_L(dp[s][v], dp[s | 1 << u][u] + dist(v, u) * k + w[u]);
        }
      }
    }
  }
  double ans = 4611686016279904256LL;
  int RlTT0MFE;
  double ClGtuHe4;
  if(n==0){
    ClGtuHe4 = 0;
  }
  else{
    ClGtuHe4 = w[0];
    for(RlTT0MFE=(1);RlTT0MFE<(n);RlTT0MFE++){
      ClGtuHe4 += w[RlTT0MFE];
    }
  }
  double k = (ClGtuHe4+ 100) / 120;
  for(i=(0);i<(n);i++){
    ans =min_L(ans, dp[0][i] + k * dist(i, n));
  }
  wt_L(ans);
  wt_L('\n');
  return 0;
}
// cLay varsion 20200509-1

// --- original code ---
// int n, m, x[14], y[14], p, q;
// double w[13], dp[1 << 13][13];
// double dist(int i, int j) {
// 	return abs(x[i] - x[j]) + abs(y[i] - y[j]);
// }
// double calc(int i, int j, double weight) {
// 	return (weight + 100.0) / 120.0 * dist(i, j);
// }
// {
// 	rd(p, q, n, (x, y, w)(n));
// 	x[n] = p;
// 	y[n] = q;
// 	m = 1 << n;
// 	rep(i, m) rep(j, n) dp[i][j] = ll_inf;
// 	rep(v, n) dp[m - 1][v] = dist(v, n) * 5.0 / 6;
// 	rrep(s, m - 1) {
// 		double k = 0;
// 		rep(v, n) if (!(s & 1 << v)) k += w[v];
// 		k = (k + 100) / 120;
// 		rep(v, n) rep(u, n) {
// 			if (!(s & 1 << u)) {
// 				dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + dist(v, u) * k + w[u]);
// 			}
// 		}
// 	}
// 	double ans = ll_inf, k = (sum(w(n)) + 100) / 120;
// 	rep(i, n) ans = min(ans, dp[0][i] + k * dist(i, n));
// 	wt(ans);
// }