1 #include <bits/stdc++.h>
 2 
 3 #define MP make_pair
 4 
 5 using namespace std;
 6 
 7 const double eps = 1e-8;
 8 const int N = 1e5+10;
 9 
10 int n,cnt[N];
11 int cr[N][2],r[N];
12 pair<int,int>pt[N];
13 double curx;
14 
15 struct node
16 {
17     int id,f;
18     bool operator < (const node &ta) const
19     {
20         double y1 = cr[id][1] + f * sqrt(1.0 *r[id]*r[id]-1.0*(curx-cr[id][0])*(curx-cr[id][0]));
21         double y2 = cr[ta.id][1] + ta.f * sqrt(1.0 *r[ta.id]*r[ta.id]-1.0*(curx-cr[ta.id][0])*(curx-cr[ta.id][0]));
22         if(fabs(y1-y2)<eps)
23             return f<ta.f;
24         return y1<y2;
25     }
26 };
27 set<node >st;
28 
29 int main(void)
30 {
31     int n;
32     while(~scanf("%d",&n))
33     {
34         st.clear();
35         int tot=0,ans=1;
36         for(int i=1;i<=n;i++)
37         {
38             scanf("%d%d%d",&cr[i][0],&cr[i][1],r+i);
39             pt[tot++]=MP(cr[i][0]-r[i],i);
40             pt[tot++]=MP(cr[i][0]+r[i],i-n);
41             cnt[i]=0;
42         }
43         sort(pt,pt+tot);
44         for(int i=0;i<tot;i++)
45         {
46             int k=pt[i].second,up=0,dw=0;
47             curx = pt[i].first;
48             if(k<=0)
49                 k+=n,st.erase((node){k,-1}),st.erase((node){k,1});
50             else
51             {
52                 auto it=st.insert((node){k,-1}).first;
53                 it++;
54                 if(it!=st.end())    up = it->id;
55                 it--;
56                 if(it!=st.begin())  dw = (--it)->id;
57                 if(up==dw&&up)
58                     ans=max(ans,cnt[k]=cnt[up]+1);
59                 else if(up&&dw)
60                     ans=max(ans,cnt[k]=max(cnt[up],cnt[dw]));
61                 else
62                     cnt[k]=1;
63                 st.insert((node){k,1});
64             }
65         }
66         printf("%d\n",ans);
67     }
68 
69     return 0;
70 }