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::{self, Read};

fn main() {
    let mut input = "".to_owned();
    io::stdin().read_to_string(&mut input).unwrap();
    let mut input = input.split_whitespace();
    macro_rules! read {
        ([$tt:tt]) => (read!([$tt; read!(usize)]));
        ([$tt:tt; $n:expr]) => ((0..$n).map(|_| read!($tt)).collect::<Vec<_>>());
        (($($tt:tt),+)) => (($(read!($tt)),*));
        ($ty:ty) => (input.next().unwrap().parse::<$ty>().unwrap());
    }

    let (n, m, c) = read!((usize, usize, i32));
    let (b, a) = read!(([i32; m], [[i32; m]; n]));

    let ans = a
        .into_iter()
        .filter(|a| a.iter().zip(&b).map(|(a, b)| a * b).sum::<i32>() + c > 0)
        .count();
    println!("{}", ans);
}