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() {
	nextReader = NewScanner()
	line1 := nextInt()
	N := line1[0]
	C := line1[2]

	var ints [][]int
	B := nextInt()
	for i := 0; i < N; i++ {
		ints = append(ints, nextInt())
	}

	var count int
	for _, v := range ints {
		var sum int
		for i := 0; i < len(v); i++ {
			sum += v[i] * B[i]
		}
		if sum+C > 0 {
			count++
		}
	}

	fmt.Println(count)
}

// ------ Mathライブラリ ---------------------------------//
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}

func maxIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}

func minIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func sum(a []int) (r int) {
	for i := range a {
		r += a[i]
	}
	return r
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// ------ Mathライブラリ ---------------------------------//

// ----- 標準入力用の関数 ----------------------------------//
var nextReader func() []string

func NewScanner() func() []string {
	r := bufio.NewScanner(os.Stdin)
	r.Buffer(make([]byte, 1024), int(1e+11))
	return func() []string {
		r.Scan()
		return strings.Fields(r.Text())
	}
}

func nextString() []string {
	return nextReader()
}

func nextInt() []int {
	var intArray []int
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.Atoi(v)
		intArray = append(intArray, i)
	}
	return intArray
}

func nextFloat64() []float64 {
	var floatArray []float64
	strArray := nextReader()
	for _, v := range strArray {
		f, _ := strconv.ParseFloat(v, 64)
		floatArray = append(floatArray, f)
	}
	return floatArray
}

// ------ 標準入力用の関数 ---------------------------------//

// ------ あまり使わない -----------------------------------//
func nextInt64() []int64 {
	var int64Array []int64
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.ParseInt(v, 10, 64)
		int64Array = append(int64Array, i)
	}
	return int64Array
}

// ------ あまり使わない -----------------------------------//