1 #include<iostream>
 2 using namespace std;
 3
 4 const int MAXN = 1000 + 10 ;
 5 const int MAX = 1000000 + 10 ;
 6
 7 int N;
 8 int M;
 9 int dis[MAXN] ;
10 int map[MAXN][MAXN];
11 int used[MAXN];
12 int mark[MAXN];    // 某点到家的符合条件的路径有多少种
13 int flag[MAXN];
14
15 void dijskra(int x)
16 {
17     dis[x] = 0 ;
18     used[x] = 0;
19
20     for(int j = 0 ; j < N ; j ++ )
21     {
22         int mix = MAX;
23         int y;
24
25         for( int i = 1 ; i <= N ; i ++ )
26         {
27             if( !used[i] && dis[i] <= mix )
28             {
29                 mix = dis[i] ;
30                 y = i ;
31             }
32         }
33
34         used[y] = 1;
35
36
37         for( i = 1 ; i <= N ;i ++)
38         {
39             if(!used[i])
40             {
41                 if( dis[i] > dis[y] + map[y][i] && map[y][i]  )
42                 {
43                     dis[i] = dis[y] + map[y][i] ;
44                 }
45             }
46         }
47     }
48 }
49
50 int DFS(int x)
51 {
52     if(x == 2)
53     {
54         return 1;
55     }
56
57     if(mark[x] != 0 )
58     {
59         return mark[x];
60     }
61
62     for( int i = 1 ; i <= N ; i ++ )
63     {
64         if(dis[i] < dis[x] && !flag[i] && map[x][i] )
65         {
66             mark[x] += DFS(i);
67         }
68     }
69     return mark[x];
70 }
71
72
73
74 int main()
75 {
76     while(cin>> N , N )
77     {
78         cin >> M ;
79         memset( map  , 0 ,  sizeof(map)) ;
80         memset( used , 0 , sizeof(used)) ;
81         memset( dis  , MAX, sizeof(dis)) ;
82         memset( mark , 0 , sizeof(mark)) ;
83         memset( flag , 0 , sizeof(flag)) ;
84
85         for(int i = 0 ; i < M ; i++ )
86         {
87             int a;
88             int b;
89             int c;
90             cin>> a >> b >> c ;
91             map[a][b] = c ;
92             map[b][a] = c ;
93         }
94
95         dijskra(2);
96         cout<<DFS(1)<<endl;
97     }
98     return 0;
99 }