B - Can you solve this?

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.

2 3 -10
1 2 3
3 2 1
1 2 2

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.

5 2 -4
-2 5
100 41
100 40
-3 0
-6 -2
18 -13

2

3 3 0
100 -100 0
0 100 100
100 100 100
-100 100 100

0

All of them are Wrong Answer. Except yours.