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.