Problem10564--ABC121 —— B - Can you solve this?

10564: ABC121 —— B - Can you solve this?

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

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.

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.

Constraints

-   All values in input are integers.
-   $1 \leq N, M \leq 20$
-   $-100 \leq A_{ij} \leq 100$
-   $-100 \leq B_i \leq 100$
-   $-100 \leq C \leq 100$

Sample 1 Input

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

Sample 1 Output

1

Only the second code correctly solves this problem, as follows:

  • Since 3×1+2×2+1×3+(−10)=0≤0, the first code does not solve this problem.
  • 1×1+2×2+2×3+(−10)=1>0, the second code solves this problem.

Sample 2 Input

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

Sample 2 Output

2

Sample 3 Input

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

Sample 3 Output

0
All of them are Wrong Answer. Except yours.

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