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 main() {
	var wtr = bufio.NewWriter(os.Stdout)
	var scanner = bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanLines)
	var N, M, C int
	if scanner.Scan() {
		str := scanner.Text()
		cols := strings.Split(str, " ")
		N, _ = strconv.Atoi(cols[0])
		M, _ = strconv.Atoi(cols[1])
		C, _ = strconv.Atoi(cols[2])
	}

	B := make([]int, M)
	if scanner.Scan() {
		str := scanner.Text()
		cols := strings.Split(str, " ")
		for j := 0; j < M; j++ {
			B[j], _ = strconv.Atoi(cols[j])
		}
	}

	var sum int
	for i := 0; i < N; i++ {
		var F int
		if scanner.Scan() {
			str := scanner.Text()
			cols := strings.Split(str, " ")
			for j := 0; j < M; j++ {
				a, _ := strconv.Atoi(cols[j])
				F += B[j] * a
			}
			F += C
		}
		if F > 0 {
			sum++
		}

	}

	fmt.Fprintln(wtr, sum)
	_ = wtr.Flush()
}