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! read_line {
    () => {{
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim_right().to_owned()
    }};
}

macro_rules! parse_next {
    ($ws:expr) => {
        $ws.next().unwrap().parse().unwrap();
    };
}

fn main() {
    let (n, m, c) = {
        let line = read_line!();
        let mut ws = line.split_whitespace();
        let n: i32 = parse_next!(ws);
        let m: i32 = parse_next!(ws);
        let c: i32 = parse_next!(ws);
        (n, m, c)
    };
    let b: Vec<i32> = read_line!()
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect();

    let mut ans = 0;

    for _ in 0..n {
        let a: Vec<i32> = read_line!()
            .split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect();
        let w: i32 = (0..m as usize).map(|mi| a[mi] * b[mi]).sum();
        if w + c > 0 {
            ans += 1;
        }
    }

    println!("{}", ans);
}