1 /**************************************************************
2 Problem: 2152
3 User: idy002
4 Language: C++
5 Result: Accepted
6 Time:500 ms
7 Memory:2612 kb
8 ****************************************************************/
9
10 #include <cstdio>
11 #define N 20010
12
13 typedef long long dnt;
14
15 int n;
16 int head[N], dest[N+N], wght[N+N], next[N+N], ntot;
17 int fat[N], vis[N], siz[N], bac[N], dis[N], siz_tot, cur_root;
18 int vv[3], vtot;
19 dnt path_tot, path_ans;
20
21 void insert( int u, int v, int w ) {
22 ntot++;
23 next[ntot] = head[u];
24 wght[ntot] = w;
25 dest[ntot] = v;
26 head[u] = ntot;
27 }
28
29 void dfs_root( int u ) {
30 siz[u] = 1, bac[u] = 0;
31 for( int t=head[u]; t; t=next[t] ) {
32 int v=dest[t];
33 if( vis[v] || v==fat[u] ) continue;
34 fat[v] = u;
35 dfs_root(v);
36 siz[u]+=siz[v];
37 if( siz[v]>bac[u] ) bac[u]=siz[v];
38 }
39 if( siz_tot-siz[u]>bac[u] ) bac[u]=siz_tot-siz[u];
40 if( bac[cur_root]>bac[u] ) cur_root=u;
41 }
42 void dfs_read( int u ) {
43 int a = (3-dis[u]%3)%3;
44 path_ans += vv[a];
45 path_tot += vtot;
46 for( int t=head[u]; t; t=next[t] ) {
47 int v=dest[t], w=wght[t];
48 if( vis[v] || v==fat[u] ) continue;
49 dis[v]=dis[u]+w;
50 fat[v]=u;
51 dfs_read( v );
52 }
53 }
54 void dfs_write( int u ) {
55 int a = dis[u]%3;
56 vv[a]++;
57 vtot++;
58 for( int t=head[u]; t; t=next[t] ) {
59 int v=dest[t];
60 if( vis[v] || v==fat[u] ) continue;
61 dfs_write(v);
62 }
63 }
64 void bfs( int rt ) {
65 siz_tot = siz[rt];
66 cur_root = 0;
67 fat[rt] = rt;
68 dfs_root(rt);
69
70 rt=cur_root;
71 vis[rt] = true;
72 vv[0] = 1;
73 vtot = 1;
74 for( int t=head[rt]; t; t=next[t] ) {
75 int v=dest[t], w=wght[t];
76 if( vis[v] ) continue;
77 dis[v] = w;
78 fat[v] = rt;
79 dfs_read(v);
80 dfs_write(v);
81 }
82 vv[0] = vv[1] = vv[2] = 0;
83 vtot = 0;
84 for( int t=head[rt]; t; t=next[t] ) {
85 int v=dest[t];
86 if( vis[v] ) continue;
87 bfs(v);
88 }
89 }
90 void build_vdcp() {
91 bac[0] = n;
92 siz[1] = n;
93 bfs( 1 );
94 }
95 dnt gcd( dnt a, dnt b ) {
96 return b ? gcd(b,a%b) : a;
97 }
98
99 int main() {
100 scanf( "%d", &n );
101 for( int i=1,u,v,w; i<n; i++ ) {
102 scanf( "%d%d%d", &u, &v, &w );
103 insert( u, v, w );
104 insert( v, u, w );
105 }
106 build_vdcp();
107 path_tot *= 2;
108 path_ans *= 2;
109 path_tot += n;
110 path_ans += n;
111 dnt cd = gcd(path_tot,path_ans);
112 printf( "%lld/%lld\n", path_ans/cd, path_tot/cd );
113 }
