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 Go (1.6) (judge verdict: Accepted)

package main
import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var stdin = bufio.NewScanner(os.Stdin)

func Input_int() int {
        stdin.Scan()
        out,err := strconv.Atoi(stdin.Text())
        if err != nil{
                panic(err)
        }
        return out
}

func main(){
	stdin.Split(bufio.ScanWords)
	N,M := Input_int(),Input_int()
	count := 0
	sum := 0
	B := make([]int,M)
	C := Input_int()
	for i:=0;i<M;i++ {
		B[i] = Input_int()
	}

	for n_iter:=0;n_iter<N;n_iter++{
		sum = C
		for m_iter:=0;m_iter<M;m_iter++{
			sum += Input_int()*B[m_iter]
		}
		if sum > 0{
			count++
		}
	}

	fmt.Println(count)
}