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 Ruby (2.3.3) (judge verdict: Accepted)

# N  個のソースコードがあり、i 個目のソースコードの特徴は Ai1,Ai2,...,AiM の M 個の整数で表されます。
# また、整数 B1,B2,...,BM と 整数 C が与えられます。
# Ai1B1+Ai2B2+...+AiMBM+C>0 のときに限り、i 個目のソースコードはこの問題に正答するソースコードです。
# N 個のソースコードのうち、この問題に正答するソースコードの個数を求めてください。

nmc = gets.chomp.split
n = nmc[0].to_i
m = nmc[1].to_i
c = nmc[2].to_i

b = gets.chomp.split
m.times do |i|
    b[i] = b[i].to_i
end

a = []
n.times do
    input_a = gets.chomp.split
    m.times do |i|
        input_a[i] = input_a[i].to_i
    end
    a << input_a
end

correct_count = 0
n.times do |i|
    sum = 0
    m.times do |j|
        sum += a[i][j] * b[j]
    end
    sum += c
    correct_count += 1 if sum > 0
end

puts correct_count