1 #include <bits/stdc++.h>
 2 using namespace std;
 3 #define ll long long
 4 #define mst(a,b) memset((a),(b),sizeof(a))
 5 #define pi acos(-1)
 6 #define pii pair<int,int>
 7 const int INF = 0x3f3f3f3f;
 8 const double eps = 1e-3;
 9 const int MAXN = 1e5 + 10;
10 const int MAXM = 2e6 + 10;
11 const ll mod = 1e9 + 9;
12
13 int n;
14 ll x[25],y[25],r[25];
15 ll inv[25],st[25];
16 ll dp[1<<21];
17 bool vis[25];
18
19 ll pow_mod(ll a,ll m) {
20     ll res = 1;
21     while(m) {
22         if(m & 1) res = res * a % mod;
23         a = a * a % mod;
24         m /= 2;
25     }
26     return res;
27 }
28
29 ll dis(int i,int j) {
30     return (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]);
31 }
32
33 ll num;
34
35 void dfs(int u) {
36     num |= 1<<u;
37     vis[u] = true;
38     for(int i=0; i<n; i++) {
39         if(vis[i] || dis(u,i)>r[u]*r[u]) continue;
40         dfs(i);
41     }
42 }
43
44 int main()
45 {
46 #ifdef local
47     freopen("data.txt","r",stdin);
48 //    freopen("data.txt","w",stdout);
49 #endif
50     inv[0] = 1;
51     for(int i=1; i<=20; i++)
52         inv[i] = pow_mod(i,mod-2);
53     while(~scanf("%d",&n)) {
54         for(int i=0; i<n; i++)
55             scanf("%lld%lld%lld",&x[i],&y[i],&r[i]);
56         for(int i=0; i<n; i++) {
57             mst(vis,false);
58             num = 0;
59             dfs(i);
60             st[i] = num;
61         }
62         dp[(1<<n)-1] = 0;
63         for(ll i=(1<<n)-2; i>=0; i--) {
64             dp[i] = 0;
65             num = 0;
66             for(ll j=0; j<n; j++) {
67                 if((1<<j)&i) {
68                     num++;
69                     continue;
70                 }
71                 dp[i] = (dp[i] + dp[i|st[j]]) % mod;
72             }
73             dp[i] = (dp[i] + n) % mod;
74             dp[i] = (dp[i] * inv[n-num]) % mod;
75         }
76         printf("%lld\n",dp[0]);
77     }
78     return 0;
79 }