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 Rust (1.15.1) (judge verdict: Accepted)

use std::cmp;

fn main(){
    let mut sc = Scanner::new();
    while sc.read() {
        let n = sc.next();
        let m = sc.next();
        let mut es = [(0,0,0); 1000];
        let mut d:[[i32; 100]; 100] = [[i32::max_value() / 4; 100]; 100];
        for i in 0..m {
            let a = sc.next::<usize>() - 1;
            let b = sc.next::<usize>() - 1;
            let c:i32 = sc.next();
            d[a][b] = cmp::min(d[a][b], c);
            d[b][a] = cmp::min(d[b][a], c);
            es[i] = (a, b, c);
        }
        for k in 0..n {
            for i in 0..n {
                for j in 0..n {
                    d[i][j] = cmp::min(d[i][j], d[i][k] + d[k][j]);
                }
            }
        }
        println!("{}", es.iter().take(m).fold(0, |sum, &e| {
            sum + if d[e.0][e.1] < e.2 { 1 } else { 0 }
        }));
    }
}

#[allow(dead_code)]
struct Scanner {
    buf: Vec<u8>, i: usize, next: Option<String>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner { buf: vec![], i: 0, next: None, }
    }

    fn next<T: std::str::FromStr>(&mut self) -> T {
        self.wrapped::<T>().unwrap()
    }

    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut res = Vec::<T>::with_capacity(n);
        for _ in 0..n { res.push(self.next()) }
        res
    }

    fn wrapped<T: std::str::FromStr>(&mut self) -> Option<T> {
        self.read();
        self.next.take().and_then(|s| s.parse::<T>().ok())
    }

    fn read(&mut self) -> bool {
        if self.next.is_some() { return true }
        let mut s = String::with_capacity(16);
        while let Some(c) = self.get_char() {
            if !c.is_whitespace() { s.push(c); }
            else if !s.is_empty() { break; }
        }
        self.next = if !s.is_empty() { Some(s) } else { None };
        self.next.is_some()
    }

    fn get_char(&mut self) -> Option<char> {
        if self.i >= self.buf.len() {
            use std::io::BufRead;
            let reader = std::io::stdin();
            let mut buffer = reader.lock();
            let len = match buffer.fill_buf() {
                Ok(bytes) => {
                    self.buf.resize(bytes.len(), b'\0');
                    // self.buf.copy_from_slice(bytes); // AtCoderのRustには未実装
                    for i in 0..bytes.len() { self.buf[i] = bytes[i]; }
                    Some(bytes.len())
                },
                Err(_) => None,
            };
            self.i = 0;
            if len.is_some() { buffer.consume(len.unwrap()); }
            if len.is_none() || len.unwrap() == 0 { return None }
        }
        self.i += 1;
        Some(self.buf[self.i - 1] as char)
    }
}