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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>

int main(void){
    int M, N, C;
    scanf("%d%d%d", &N, &M, &C);

    int **A;
    int *B;
    int i, j;

    B = (int*)malloc(sizeof(int) * N);
    for(i=0; i<M; i++) {
    		scanf("%d", &B[i]);
    }

    A = (int**)malloc(sizeof(int*) * N);
    for(i=0; i<N; i++) {
    	A[i] = malloc(sizeof(int) * N);
    }
    

    for(i=0;i<N;i++) {
    	for(j=0; j<M; j++) {
    		scanf("%d", &A[i][j]);
    	}
    }

    int count = 0;
    for(i=0;i<N;i++) {
        int sum = 0;
    	for(j=0; j<M; j++) {
            sum += A[i][j] * B[j];
    	}
        if(sum + C > 0) {
            count++;
        }
    }

    printf("%d\n", count);

    for (i=0; i<N; i++) {
    	free(A[i]);
    }

    free(A);
    free(B);
    return 0;
}