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)

use std::io;

fn can_solve(av: &Vec<i32>, bv: &Vec<i32>, c: i32) -> bool {
    av.iter().zip(bv.iter()).map(|(a, b)| a * b).sum::<i32>() + c > 0
}

#[test]
fn test_can_solve_1() {
    assert!(!can_solve(&vec![3, 2, 1], &vec![1, 2, 3], -10));
    assert!(can_solve(&vec![1, 2, 2], &vec![1, 2, 3], -10));
}

fn main() {
    let mut input = String::new();
    io::stdin().read_line(&mut input).unwrap();
    let mut iter = input.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let m: usize = iter.next().unwrap().parse().unwrap();
    let c: i32 = iter.next().unwrap().parse().unwrap();
    let mut input = String::new();
    io::stdin().read_line(&mut input).unwrap();
    let mut iter = input.split_whitespace();
    let bv: Vec<i32> = (0..m).map(|_| { iter.next().unwrap().parse().unwrap() }).collect();
    let mut a_matrix: Vec<Vec<i32>> = Vec::with_capacity(n);
    for _ in 0..n {
        let mut input = String::new();
        io::stdin().read_line(&mut input).unwrap();
        let mut iter = input.split_whitespace();
        let av: Vec<i32> = (0..m).map(|_| { iter.next().unwrap().parse().unwrap() }).collect();
        a_matrix.push(av);
    }
    let count = a_matrix.iter().filter(|av| { can_solve(av, &bv, c) }).count();
    println!("{}", count);
}