Problem:
Score : 400 points

Problem Statement

You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.

The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

A connected graph is a graph where there is a path between every pair of different vertices.

Find the number of the edges that are not contained in any shortest path between any pair of different vertices.

Constraints

2≤N≤100

N-1≤M≤min(N(N-1)/2,1000)

1≤a_i,b_i≤N

1≤c_i≤1000

c_i is an integer.

The given graph contains neither self-loops nor double edges.

The given graph is connected.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.

Sample Input 1

3 3
1 2 1
1 3 1
2 3 3

Sample Output 1

1

In the given graph, the shortest paths between all pairs of different vertices are as follows:

The shortest path from vertex 1 to vertex 2 is: vertex 1 → vertex 2, with the length of 1.

The shortest path from vertex 1 to vertex 3 is: vertex 1 → vertex 3, with the length of 1.

The shortest path from vertex 2 to vertex 1 is: vertex 2 → vertex 1, with the length of 1.

The shortest path from vertex 2 to vertex 3 is: vertex 2 → vertex 1 → vertex 3, with the length of 2.

The shortest path from vertex 3 to vertex 1 is: vertex 3 → vertex 1, with the length of 1.

The shortest path from vertex 3 to vertex 2 is: vertex 3 → vertex 1 → vertex 2, with the length of 2.

Thus, the only edge that is not contained in any shortest path, is the edge of length 3 connecting vertex 2 and vertex 3, hence the output should be 1.

Sample Input 2

3 2
1 2 1
2 3 1

Sample Output 2

0

Every edge is contained in some shortest path between some pair of different vertices.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#define SIZE 300005
#define MOD 1000000007LL
#define EPS 1e-10
#define INF 2147483647
#define LLINF 9223372036854775807
#define REP(i,n) for(int i=0;i<n;i++)
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define DOWN(i,b,a) for(int i=b;i>=a;i--)
#define SET(a,c) memset(a,c,sizeof a)
#define BIT(i,j) ((i)>>(j))&1
#define ALL(o) (o).begin(), (o).end()
#define ERASE(o) (o).erase(unique((o).begin(),(o).end()), (o).end())
#define SQ(x) ((x)*(x))
using namespace std;
typedef long long ll;
typedef pair<ll,ll> Pll;
typedef pair<int, int> Pii;
typedef pair<double, double> Pdd;
typedef complex<double> dcomplex;
template<typename T> inline void priv(vector<T>a){REP(i,a.size()){cerr<<a[i]<<((i==a.size()-1)?"\n":" ");}}
inline void fastio(){cin.tie(nullptr); cout.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15);}
ll gcd(ll a,ll b){int c=max(a,b);int d=min(a,b);return c==0||d==0?c:gcd(c%d,d);}
ll lcm(ll a,ll b){return a==0||b==0?0:a*b/gcd(a,b);}
ll modfact(ll a){ll b=1;FOR(i,2,a)b=b*i%MOD;return b;}
ll modpow(ll a, ll n){ll b=1;while (n>0){if(n&1)b=b*a%MOD;a=a*a%MOD;n>>=1;}return b;}
ll modcomb(ll n, ll k){ll b=1;k=min(n-k,k);DOWN(i,n,n-k+1)b=b*i%MOD;return b*modpow(modfact(k),MOD-2)%MOD;}

int N, M;
int A[1000], B[1000], C[1000];
int dist[100][100];

int main() {
    fastio();
    int N, M;
    int inf = 100000000;
    cin >> N >> M;
    REP(i, N) REP(j, N) dist[i][j] = i == j ? 0 : inf;
    REP(i, M) {
        cin >> A[i] >> B[i] >> C[i];
        A[i]--; B[i]--;
        dist[A[i]][B[i]] = min(dist[A[i]][B[i]], C[i]);
        dist[B[i]][A[i]] = min(dist[B[i]][A[i]], C[i]);
    }
    REP(i, N) REP(j, N) REP(k, N)
        dist[j][k] = min(dist[j][k], dist[j][i] + dist[i][k]);
    int ans = M;
    REP(i, M) {
        REP(s, N) {
            if(dist[s][A[i]] + C[i] == dist[s][B[i]]) {
                ans--; break;
            }
        }
    }
    cout << ans << "\n";
	return 0;
}