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"
	"strings"
)

func readLine(sc *bufio.Scanner) string {
	sc.Scan()
	return sc.Text()
}

func lineToInts(line string) []int {
	var res []int
	for _, s := range strings.Split(line, " ") {
		i, _ := strconv.Atoi(s)
		res = append(res, i)
	}
	return res
}

func judge(as, bs []int, m, c int) bool {
	calc := 0
	for j := 0; j < m; j++ {
		calc += as[j] * bs[j]
	}
	calc += c
	return calc > 0
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	line1 := lineToInts(readLine(sc))
	n, m, c := line1[0], line1[1], line1[2]

	bs := lineToInts(readLine(sc))
	res := 0
	for i := 0; i < n; i++ {
		as := lineToInts(readLine(sc))
		if judge(as, bs, m, c) {
			res++
		}
	}
	fmt.Println(res)
}