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)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stderr, stdin, stdout, BufWriter, StdoutLock, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! input_inner { ( $ next : expr ) => { } ; ( $ next : expr , ) => { } ; ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; ( $ next : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! read_value { ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) } ; ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ next : expr , [ $ t : tt ] ) => { { let len = read_value ! ( $ next , usize ) ; ( 0 .. len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } } ; ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ next : expr , bytes ) => { read_value ! ( $ next , String ) . into_bytes ( ) } ; ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 } ; ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) } ; }
#[allow(dead_code)]
struct Writer {
    s: String,
}
#[allow(unused_imports)]
use std::fmt::Display;
#[allow(dead_code)]
#[doc = " let mut writer = Writer::new();"]
#[doc = " writer.writeln(hoge);"]
#[doc = " writer.flush()"]
impl Writer {
    #[allow(dead_code)]
    pub fn new() -> Writer {
        Writer { s: String::new() }
    }
    #[allow(dead_code)]
    pub fn flush(&mut self) {
        print!("{}", self.s);
        self.s.clear();
    }
    pub fn write<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
    }
    pub fn writeln<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
        self.s.push('\n');
    }
    #[allow(dead_code)]
    pub fn write_vec<T: Display>(&mut self, xs: &Vec<T>) {
        if xs.len() == 0 {
            self.writeln("");
            return;
        }
        self.write(&format!("{}", xs[0]));
        for i in 1..xs.len() {
            self.write(&format!(" {}", xs[i]));
        }
        self.writeln("");
    }
}
#[allow(unused_macros)]
macro_rules ! dbg { ( $ ( $ a : expr ) ,* ) => { writeln ! ( & mut stderr ( ) , concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) . unwrap ( ) ; } }
use std::u64;
#[allow(dead_code)]
fn main() {
    input!{
        n: usize,
        m: usize,
        abc: [(usize1, usize1, u64); m]
    }
    let mut graph = vec![vec![1_000_000_000; n]; n];
    for &(a, b, c) in &abc {
        graph[a][b] = c;
        graph[b][a] = c;
    }
    for i in 0..n {
        graph[i][i] = 0;
    }
    let mut dist = graph.clone();
    for k in 0..n {
        for i in 0..n {
            for j in 0..n {
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
    let mut ans: u64 = 0;
    for &(a, b, c) in &abc {
        if dist[a][b] < c {
            ans += 1;
        }
    }
    println!("{}", ans);
}