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: Runtime Error)

package main

import (
	"fmt"
)

func main() {
	// mainA()
	mainB()
}

func mainA() {
	var numH, numW, h, w int
	fmt.Scan(&numH, &numW, &h, &w)
	var res = solveA(numH, numW, h, w)
	fmt.Print(res)
}

func solveA(numH int, numW int, h int, w int) int {

	var res = 0
	res = (numH - h) * (numW - w)
	return res
}

func mainBInputTest(bArrayArg []int, aArrayArg [][]int, n int, m int, c int) int {

	var bArray []int
	for i := 0; i < m; i++ {
		bArray = append(bArray, bArrayArg[i])
	}
	var aArray [][]int
	for outer := 0; outer < n; outer++ {
		for i := 0; i < m; i++ {
			// aArray[outer][i] = b
			aArray[outer] = append(aArray[outer], aArrayArg[outer][i])

		}
	}

	var res = solveB(bArray, aArray, n, m, c)

	return res
}

func mainB() {
	var n, m, c int
	fmt.Scan(&n, &m, &c)
	var bArray []int
	for i := 0; i < m; i++ {
		var b int
		fmt.Scan(&b)
		bArray = append(bArray, b)
	}
	var aArray [][]int
	for outer := 0; outer < n; outer++ {
		for i := 0; i < m; i++ {
			var b int
			fmt.Scan(&b)
			// aArray[outer][i] = b
			aArray[outer] = append(aArray[outer], b)

		}
	}

	var res = solveB(bArray, aArray, n, m, c)
	fmt.Println(res)
}

func solveB(bArray []int, aArray [][]int, n int, m int, c int) int {
	var res, point = 0, 0
	for outer := 0; outer < n; outer++ {
		point = 0
		for i := 0; i < m; i++ {
			point += aArray[outer][i] * bArray[i]
		}
		if point+c > 0 {
			res++
		}
	}
	return res
}