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};
use std::iter::FromIterator;

trait Source {
    fn next_chr(&mut self) -> char;
    fn next_str(&mut self) -> String;
}

#[allow(dead_code)]
fn from_stdin() -> SourceImpl {
    let mut data = String::new();
    io::stdin().read_to_string(&mut data).expect("Input error");
    from_str(&data)
}

fn from_str(s: &str) -> SourceImpl {
    let data = String::from(s);
    let chars = data.chars().collect::<Vec<char>>().into_iter();
    SourceImpl { chars: chars }
}

struct SourceImpl {
    chars: std::vec::IntoIter<char>,
}

impl Source for SourceImpl {
    fn next_chr(&mut self) -> char {
        self.chars
            .by_ref()
            .skip_while(|c| char::is_whitespace(*c))
            .next()
            .expect("eof")
    }

    fn next_str(&mut self) -> String {
        let it = self
            .chars
            .by_ref()
            .skip_while(|c| char::is_whitespace(*c))
            .take_while(|c| !char::is_whitespace(*c));
        let s = String::from_iter(it);
        if s.is_empty() {
            panic!("eof")
        } else {
            s
        }
    }
}

#[allow(unused_macros)]
macro_rules! input {
    ($src:expr; $($elem:tt)*) => {
        input_inner!($src, $($elem)*)
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($src:expr) => {};
    ($src:expr,) => {};
    ($src:expr, $var:ident : mut $ty:tt $($rest:tt)*) => {
        let mut $var = parse!($src, $ty);
        input_inner!($src $($rest)*)
    };
    ($src:expr, $var:ident : $ty:tt $($rest:tt)*) => {
        let $var = parse!($src, $ty);
        input_inner!($src $($rest)*)
    };
}

#[allow(unused_macros)]
macro_rules! parse {
    ($src:expr, ( $($ty:tt),* )) => {
        ( $(parse!($src,$ty)),* )
    };
    ($src:expr, char) => {
        $src.next_chr()
    };
    ($src:expr, [ $ty:tt; $len:expr ]) => {
        (0..$len).map(|_| parse!($src,$ty)).collect::<Vec<_>>()
    };
    ($src:expr, $ty:tt) => {
        parse_str!($src,$ty)
    };
}

#[allow(unused_macros)]
macro_rules! parse_str {
    ($src:expr, chars) => {
        $src.next_str().chars().collect::<Vec<char>>()
    };
    ($src:expr, $ty:ty) => {
        $src.next_str().parse::<$ty>().expect("Parse error")
    };
}

fn main() {
    let mut src = from_stdin();
    input! { src;
             n: usize, m: usize,
             c: i32, b: [i32; m],
             testcases: [[i32; m]; n]
    }

    let res = testcases
        .iter()
        .filter(|t| {
            let v = t.iter().zip(b.iter()).fold(c, |x, (a, b)| x + a * b);
            v > 0
        })
        .count();

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