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::{Write, stdout, BufReader};
struct Read<R: std::io::BufRead> {
    stdin: R,
    v: Vec<String>,
    i: usize,
}
impl<R:std::io::BufRead> Read<R> {
    pub fn new(stdin: R) -> Self {
        Read{
            stdin: stdin,
            v: Vec::new(),
            i: 0,
        }
    }
    pub fn read_until<T: std::str::FromStr>(&mut self) -> T {
        if self.i == self.v.len() {self.read_line();}
        let elem = &self.v[self.i];
        self.i += 1;
        elem.parse().unwrap_or_else(|_| panic!())
    }
    pub fn read_line(&mut self) {
        self.i = 0; self.v.clear();
        let mut buf = String::new();
        self.stdin.read_line(&mut buf).unwrap();
        let buf = buf.trim().to_owned();
        let mut ws = buf.split_whitespace();
        loop {
            let x = ws.next();
            if x.is_none() {break;}
            let x = x.unwrap().to_owned();
            self.v.push(x);
        }
    }
    #[allow(dead_code)]
    pub fn read_i32(&mut self) -> i32 {
        if self.i == self.v.len() {self.read_line();}
        let elem = self.v[self.i].parse().unwrap();
        self.i += 1;
        elem
    }
    #[allow(dead_code)]
    pub fn read_string(&mut self) -> String {
        if self.i == self.v.len() {self.read_line();}
        let elem = &self.v[self.i];
        self.i += 1;
        elem.to_owned()
    }
}
fn main() {
    let stdin = std::io::stdin();
    let stdin = BufReader::new(stdin.lock());
    let stdout = std::io::stdout();
    let stdout = stdout.lock();
    let read = Read::new(stdin);
    solve(read, stdout);
}

fn solve<R: std::io::BufRead>(mut r: Read<R>, mut o: std::io::StdoutLock) {
    let n:usize = r.read_until();
    let m:usize = r.read_until();
    let c:i32 = r.read_until();
    let mut b:Vec<i32> = Vec::new();
    let mut a:Vec<Vec<i32>> = Vec::with_capacity(n * m);
    for i in 0..m {
        b.push(r.read_until());
    }
    for i in 0..n {
        a.push(Vec::new());
        for j in 0..m {
            a[i].push(r.read_until());
        }
    }
    let mut ans = 0;
    for i in 0..n {
        let mut sum:i32 =0;
        for j in 0..m {
            sum+=a[i][j]*b[j];
        }
        if sum + c > 0 {
            ans += 1;
        }
    }
    println!("{}",ans);
}