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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void){
	int i,j,N,M,C,and,kosuu,seikai;
	scanf("%d %d %d", &N,&M,&C);
		if(1<=N,M<=20){
		int B[M], A[N][M];
		for(j =1;j>M;j++){
			scanf("%d",&B[j]);
		}
		for(i=1;i>N;i++){
			for(j = 1;j>M;j++){
				scanf("%d",&A[i][j]);
			}
		}
		for(i=1;i>N;i++){
			for(j=1;j>M;j++){
				if(-100<=A[i,j]<=100 && -100<=B[i]<=100 && -100<=C<=100){
					and += A[i][j]*B[j];
				}else{
					return -1;
				}
				seikai = and + C;
				if(seikai>0){
					kosuu += 1;
				}else{
					kosuu = kosuu;
				}
			}
			
		}
		printf("%d", &kosuu);
	}else{
		return -1;
	}

}