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)

(*
ocamlfind ocamlopt -package batteries -linkpkg main.ml -o a.out
*)
open Batteries

let n, m, c = Scanf.sscanf (read_line ()) "%d %d %d" (
        fun n m c -> 
                n, m, c
)
let blst = 
        Str.split (Str.regexp " ") (read_line ())
        |> List.map int_of_string
let alst =
        List.init n (
                fun _ -> 
                        Str.split (Str.regexp " ") (read_line ())
                        |> List.map int_of_string
        )

let dot_product = List.fold_left2 (fun a b c -> a + b * c) 0
let rec f lst =
        match lst with
                [] -> 0
                | first :: rest -> 
                        let fdot = c + dot_product first blst in
                                if fdot > 0 then
                                        1 + (f rest)
                                else
                                        f rest

let () =
        f alst
      |> Printf.printf "%d\n"