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: Accepted)

#include <stdio.h>
#define MAX 200

int main(int argc, const char * argv[]) {
    int n, m, c, i, t, k, l, w, soc=0, clr=0;
    int bsum[MAX];
    int sum[MAX][MAX];
    scanf("%d %d %d", &n, &m, &c);
    //printf("%d %d %d\n", n, m, c);
    
    for(i=0;i<m;i++){
        scanf("%d", &bsum[i]);
        //printf("bsum[0][%d]=%d\n", i, bsum[0][i]);
    }
    
    for(t=0;t<n;t++){
        for(k=0;k<m;k++){
            scanf("%d", &sum[t][k]);
            //printf("sum[%d][%d]=%d\n", t, k, sum[t][k]);
        }
    }
    for(l=0;l<n;l++){
        for(w=0;w<m;w++){
            soc = soc + sum[l][w]*bsum[w];
        }
        if(soc+c>0){
            clr++;
        }
        soc = 0;
    }
    printf("%d\n", clr);
    return 0;
}