Problem:
Score : 200 points

Problem Statement

There are N pieces of source code. The characteristics of the i-th code is represented by M integers A_{i1}, A_{i2}, ..., A_{iM}.

Additionally, you are given integers B_1, B_2, ..., B_M and C.

The i-th code correctly solves this problem if and only if A_{i1} B_1 + A_{i2} B_2 + ... + A_{iM} B_M + C > 0.

Among the N codes, find the number of codes that correctly solve this problem.

Constraints

All values in input are integers.

1 \leq N, M \leq 20

-100 \leq A_{ij} \leq 100

-100 \leq B_i \leq 100

-100 \leq C \leq 100

Input

Input is given from Standard Input in the following format:

N M C
B_1 B_2 ... B_M
A_{11} A_{12} ... A_{1M}
A_{21} A_{22} ... A_{2M}
\vdots
A_{N1} A_{N2} ... A_{NM}

Output

Print the number of codes among the given N codes that correctly solve this problem.

Sample Input 1

2 3 -10
1 2 3
3 2 1
1 2 2

Sample Output 1

1

Only the second code correctly solves this problem, as follows:

Since 3 \times 1 + 2 \times 2 + 1 \times 3 + (-10) = 0 \leq 0, the first code does not solve this problem.

1 \times 1 + 2 \times 2 + 2 \times 3 + (-10) = 1 > 0, the second code solves this problem.

Sample Input 2

5 2 -4
-2 5
100 41
100 40
-3 0
-6 -2
18 -13

Sample Output 2

2

Sample Input 3

3 3 0
100 -100 0
0 100 100
100 100 100
-100 100 100

Sample Output 3

0

All of them are Wrong Answer. Except yours.

Solution in Rust (1.15.1) (judge verdict: Accepted)

macro_rules! bind_from_vec {
    ( $($variable:ident),+ = $vector:expr ) => {
        let mut v = $vector.clone().into_iter();
        $(let $variable = v.next().unwrap();)+
    };
}
macro_rules! read_line {
    () => {{
        let mut input = String::new();
        std::io::stdin().read_line(&mut input).unwrap();
        input
    }};
}
pub fn read_to_vec<T: std::str::FromStr>() -> Vec<T> {
    read_line!().split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
fn main() {
    bind_from_vec!(n, m, c = read_to_vec());
    let b = read_to_vec::<i32>();
    let mut a = Vec::with_capacity(n as usize);
    for _ in 0..n {a.push(read_to_vec::<i32>());}
    let a = a;

    println!("{}", a.iter().filter(|code| code.iter().zip(&b).fold(0, |acc, (&a, &b)| acc + a*b) + c > 0).count());
}