1 #include<stdio.h>
 2 #include<stdlib.h>
 3 #include<string.h>
 4 
 5 #define INF 0xfffffff
 6 
 7 
 8 int map[1005][1005], disk[1005], pathnum[1005];
 9 int n, m;
10 
11 int getmin(int x, int y){
12     return x > y ? y : x;
13 }
14 
15 int dis(){
16     int i, j, visit[1005], idmin, min;
17     memset(visit, 0, sizeof(visit));
18     for(i = 1; i <= n; i ++){
19         disk[i] = map[2][i];
20     }
21     disk[2] = 0;
22     for(i = 1; i <= n; i ++){
23         idmin = 0;
24         min = INF;
25         for(j = 1; j <= n; j ++){
26             if(!visit[j] && disk[j] < min){
27                 min = disk[j];
28                 idmin = j;
29             }
30         }
31         visit[idmin] = 1;
32         for(j = 1; j <= n; j ++){
33             if(!visit[j]){
34                 disk[j] = getmin(disk[j], map[idmin][j] + disk[idmin]);
35             }
36         }
37     }
38     return 0;
39 }
40 
41 int dfs(int start){
42     int sum, i;
43     if(start == 2){
44         return 1;
45     }
46     if(pathnum[start] != -1){
47         return pathnum[start];
48     }
49     sum = 0;
50     for(i = 1; i <= n; i ++){
51         if(map[i][start] != INF && map[i][start] == disk[start] - disk[i]){
52             sum += dfs(i);
53         }
54     }
55     pathnum[start] = sum;
56     return pathnum[start];
57 }
58 
59 int main(){
60     int x, y, d, i, j;
61     while(scanf("%d", &n) && n){
62         scanf("%d", &m);
63         for(i = 0; i < 1005; i ++){
64             for(j = 0; j < 1005; j ++){
65                 map[i][j] = INF;
66             }
67         }
68         //printf("%d\n", map[1][1]);
69         for(i = 0; i < m; i ++){
70             scanf("%d %d %d", &x, &y, &d);
71             map[x][y] = map[y][x] = d;
72         }
73         dis();
74         //printf("%d\n", disk[1]);
75         memset(pathnum, -1, sizeof(pathnum));
76         //printf("%d\n", pathnum[1]);
77         printf("%d\n", dfs(1));
78     }
79     return 0;
80 }