/*
ID: LinKArftc
PROG: 1142.cpp
LANG: C++
*/

#include <map>
#include <set>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <cstdio>
#include <string>
#include <utility>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define eps 1e-8
#define randin srand((unsigned int)time(NULL))
#define input freopen("input.txt","r",stdin)
#define debug(s) cout << "s = " << s << endl;
#define outstars cout << "*************" << endl;
const double PI = acos(-1.0);
const double e = exp(1.0);
const int inf = 0x3f3f3f3f;
const int INF = 0x7fffffff;
typedef long long ll;

const int maxn = 1010;
int n, m;
int mp[maxn][maxn];
int dis[maxn];
bool vis[maxn];

void dij(int s) {
    for (int i = 1; i <= n; i ++) dis[i] = mp[s][i];
    memset(vis, 0, sizeof(vis));
    vis[s] = true;
    dis[s] = 0;
    for (int i = 2; i <= n; i ++) {
        int mi = inf;
        int ii = s;//要赋值，因为下一行的for循环可能并不改变ii的值，所以可能会RE
        for (int j = 1; j <= n; j ++) {
            if (!vis[j] && dis[j] < mi) {
                mi = dis[j];
                ii = j;
            }
        }
        vis[ii] = true;
        for (int j = 1; j <= n; j ++) {
            if (!vis[j] && dis[j] > dis[ii] + mp[ii][j]) {
                dis[j] = dis[ii] + mp[ii][j];
            }
        }
    }
}

int cnt[maxn];

int dfs(int cur) {
    if (cnt[cur]) return cnt[cur];
    if (cur == 2) return 1;
    int ret = 0;
    for (int i = 1; i <= n; i ++) {
        if (mp[cur][i] == inf || dis[i] >= dis[cur]) continue;
        ret += dfs(i);
    }
    cnt[cur] = ret;
    return ret;
}

int main() {
    //input;
    int u, v, c;
    while (~scanf("%d", &n) && n) {
        scanf("%d", &m);
        memset(mp, 0x3f, sizeof(mp));
        for (int i = 1; i <= m; i ++) {
            scanf("%d %d %d", &u, &v, &c);
            mp[u][v] = c;
            mp[v][u] = c;
        }
        dij(2);
        //for (int i = 1; i <= n; i ++) printf("dis[%d] = %d\n", i, dis[i]);
        memset(cnt, 0, sizeof(cnt));
        printf("%d\n", dfs(1));
    }

    return 0;
}