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 contest::io::Scanner;

fn main() {
    let mut sc = Scanner::new(std::io::stdin());
    let n = sc.next::<usize>();
    let m = sc.next::<usize>();
    let c = sc.next::<i32>();
    let mut b = vec![];
    for _ in 0..m {
        b.push(sc.next::<i32>());
    }

    let mut res = 0;
    for _ in 0..n {
        let mut v = c;
        for i in 0..m {
            let a = sc.next::<i32>();
            v += a * b[i];
        }
        if v > 0 {
            res += 1;
        }
    }
    println!("{}", res);
}
pub mod contest {
pub mod io {
/// Scanner
///
/// # Example
/// ```
/// use contest::io::Scanner;
/// let mut sc = Scanner::new("1 2 \n\n \r\t \n 3.5".as_bytes());
/// assert_eq!("1".to_string(), sc.next::<String>());
/// assert_eq!(2, sc.next());
/// assert_eq!(3.5, sc.next());
///
/// // To create a scanner from stdin:
/// Scanner::new(std::io::stdin());
/// ```

use std;
use std::io;
use std::io::BufRead;

pub struct Scanner<R: io::Read> {
    br: io::BufReader<R>,
    // Read tokens are stored in reversed order per line.
    buf: Vec<String>,
}

pub fn new<R: io::Read>(r: R) -> Scanner<R> {
    Scanner::new(r)
}

impl<R: io::Read> Scanner<R> {
    #[inline]
    pub fn new(r: R) -> Scanner<R> {
        Scanner {
            br: io::BufReader::new(r),
            buf: vec![],
        }
    }
    #[inline]
    pub fn next<T>(&mut self) -> T
        where T: std::str::FromStr,
              T::Err: std::fmt::Debug
    {
        self.next_string().map(|s| s.parse::<T>().expect("Parse failed: ")).expect("Unexpected EOF")
    }
    #[inline]
    pub fn next2<T1,T2>(&mut self) -> (T1,T2)
        where T1: std::str::FromStr,
              T2: std::str::FromStr,
              T1::Err: std::fmt::Debug,
              T2::Err: std::fmt::Debug
    {
        (self.next(), self.next())
    }
    fn next_string(&mut self) -> Option<String> {
        self.buf.pop().or_else(|| match self.update() {
            true => self.next_string(),
            false => None,
        })
    }
    #[inline]
    fn update(&mut self) -> bool {
        let mut s = String::new();
        let res = self.br.read_line(&mut s);
        match res.expect("I/O error.") {
            0 => false,
            _ => {
                self.buf = s.split_whitespace().map(|x| x.to_string()).rev().collect();
                true
            }
        }
    }
}

#[test]
fn test_next() {
    let mut sc = new("hoge".as_bytes());
    let s: String = sc.next();
    assert_eq!("hoge", s);
}
}
}