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)

fn main() {
    let s = {
        use std::io::Read;
        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    };
    let mut iter = s.split_whitespace();
    let n = iter.next().unwrap().parse::<usize>().expect("Parse error");
    let m = iter.next().unwrap().parse::<usize>().expect("Parse error");
    let c = iter.next().unwrap().parse::<i32>().expect("Parse error");
    let b = (0..m).map(|_| iter.next().unwrap().parse::<i32>().expect("Parse error")).collect::<Vec<_>>();
    let a = (0..n).map(|_| (0..m).map(|_| iter.next().unwrap().parse::<i32>().expect("Parse error")).collect::<Vec<_>>()).collect::<Vec<_>>();
    println!("{}", solve(n, m, c, b, a));
}

fn solve(n: usize, m: usize, c: i32, b: Vec<i32>, a: Vec<Vec<i32>>) -> i32 {
    // write solution here
    let mut counter = 0;
    for n in 0..n {
        let mut line_sum = 0;
        for m in 0..m{
            line_sum += a[n][m] * b[m];
        }
        line_sum += c;
        if line_sum > 0{
            counter += 1;
        }
    }
    // return answer
    counter
}