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)

#include <bits/stdc++.h>
#define SORT(a) sort(a.begin(), a.end())
#define RSORT(a) sort(a.rbegin(), a.rend())
#define REP(i, n) for (int i = 0; i < n; i++)
#define RREP(i, n) for (int i = n; 0 <= i; i--)
#define FOR(i, start, end) for (int i = start; i < end; i++)
#define RFOR(i, start, end) for (int i = start; end <= i; i--)
#define ALL(a) a.begin(), a.end()
#define MOD(a) a %= 1'000'000'007
#define INF32 1'050'000'000
#define INF64 4'000'000'000'000'000'000
using ll = long long;
using namespace std;
template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

class Warshall_floyd {
  private:
    int vertex;
    const int INF = 1'050'000'000;
    vector<vector<int>> cost;

  public:
    Warshall_floyd(int N) {
        vertex = N;
        cost.resize(N, vector<int>(N, INF));
        for (int i = 0; i < vertex; i++) {
            cost[i][i] = 0;
        }
    }
    void update(int x, int y, int weight) {
        cost[x][y] = weight;
        cost[y][x] = weight;
    }
    void calc() {
        for (int k = 0; k < vertex; k++) {
            for (int i = 0; i < vertex; i++) {
                for (int j = 0; j < vertex; j++) {
                    cost[i][j] = min(cost[i][j], cost[i][k] + cost[k][j]);
                }
            }
        }
    }
    int dist(int x, int y) { return cost[x][y]; }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N, M;
    cin >> N >> M;
    auto wf = Warshall_floyd(N);
    vector<int> a(M), b(M), c(M);
    REP(i, M) {
        cin >> a[i] >> b[i] >> c[i];
        a[i]--;
        b[i]--;
        wf.update(a[i], b[i], c[i]);
    }
    wf.calc();
    int ans = 0;
    REP(i, M) {
        if (wf.dist(a[i], b[i]) != c[i])
            ans++;
    }
    std::cout << ans << '\n';

    return 0;
}