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 OCaml (4.02.3) (judge verdict: Accepted)

(* 本当に辛い *)
let array_map2 f a b =
    let l = Array.length a in
    if l = 0 then [||] else begin
        let r = Array.make l (f (Array.unsafe_get a 0) (Array.unsafe_get b 0)) in
        for i = 0 to l - 1 do
            Array.unsafe_set r i (f (Array.unsafe_get a i) (Array.unsafe_get b i))
        done;
        r
    end

let () = Scanf.scanf "%d %d %d\n" @@ fun n m c ->
    let b = Array.init m (fun _ ->
        Scanf.scanf " %d" (fun b -> b)) in
    Array.init n (fun _ ->
        Scanf.scanf "\n" (fun _ -> ()) 0;
        let a = Array.init m (fun _ ->
            Scanf.scanf " %d" (fun a -> a)) in
        let t = array_map2 (fun a b -> a * b) a b
        |> Array.fold_left (+) 0 in
        if t + c > 0
        then 1
        else 0)
    |> Array.fold_left (+) 0
    |> Printf.printf "%d"