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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.TreeSet;
 
 
 
public class Main {
  public static void main(String[] args) {
    InputReader sc = new InputReader(System.in);
 
    int n = sc.nextInt();
    int m = sc.nextInt();

    int[][] graph = new int[n][n];
    for(int i = 0; i< n; i++){
      for(int j = 0; j < n; j++){
        if(i == j){
          graph[i][j] = 0;
        }else{
          graph[i][j] = 1000001;
        }
      }
    }

    for(int i = 0; i < m; i++){
      int a = sc.nextInt() - 1;
      int b = sc.nextInt() - 1;
      int c = sc.nextInt();
      graph[a][b] = c;
      graph[b][a] = c;
    }

    int[][] shortest = new int[n][n];
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        shortest[i][j] = graph[i][j];
      }
    }

    //わーしゃるふろいど
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        for(int k = 0; k < n; k++){
          if(shortest[j][k] > shortest[j][i] + shortest[i][k]){
            shortest[j][k] = shortest[j][i] + shortest[i][k];
            shortest[k][j] = shortest[j][i] + shortest[i][k];
          }
        }
      }
    }

    int count = 0;
    for(int i = 0; i < n; i++){
      for(int j = i + 1; j < n; j++){
        if(graph[i][j] > shortest[i][j] && graph[i][j] <= 1000){//<=1000で、辺があるかどうか判定(条件より)
          count++;
        }
      }
    }

    System.out.println(count);
 
  }
 
 //ここからテンプレ
  static class InputReader {
      private InputStream stream;
      private byte[] buf = new byte[1024];
      private int curChar;
      private int numChars;
      private SpaceCharFilter filter;
 
      public InputReader(InputStream stream) {
          this.stream = stream;
      }
 
      public int next() {
          if (numChars == -1)
              throw new InputMismatchException();
          if (curChar >= numChars) {
              curChar = 0;
              try {
                  numChars = stream.read(buf);
              } catch (IOException e) {
                  throw new InputMismatchException();
              }
              if (numChars <= 0)
                  return -1;
          }
          return buf[curChar++];
      }
 
      public String nextStr() {
        int c = next();
        while(isSpaceChar(c)){c = next();}
        StringBuffer str = new StringBuffer();
        do{
          str.append((char)c);
          c = next();
        }while(!isSpaceChar(c));
        return str.toString();
      }
 
      public char nextChar() {
        int c = next();
        while(isSpaceChar(c)){c = next();}
        char ret;
        do{
          ret = (char)c;
          c = next();
        }while(!isSpaceChar(c));
        return ret;
      }
 
      public int nextInt() {
          int c = next();
          while (isSpaceChar(c))
              c = next();
          int sgn = 1;
          if (c == '-') {
              sgn = -1;
              c = next();
          }
          int res = 0;
          do {
              if (c < '0' || c > '9')
                  throw new InputMismatchException();
              res *= 10;
              res += c - '0';
              c = next();
          } while (!isSpaceChar(c));
          return res * sgn;
      }
 
      public boolean isSpaceChar(int c) {
          if (filter != null)
              return filter.isSpaceChar(c);
          return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
      }
 
      public interface SpaceCharFilter {
          public boolean isSpaceChar(int ch);
      }
  }
}