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>
#include <stdlib.h>//random,NULL
#include <string.h>
#include <time.h>
#include <unistd.h>//sleep()
#include <math.h>
#include <stdbool.h>

#define rep(i,n) for(int i=0; i<((int)n); i++)
#define REP(i,n) for(int i=0; i<=((int)n); i++)
#define srep(i,a,n) for(int i=a; i<((int)n); i++)
#define SREP(i,a,n) for(int i=a; i<=((int)n); i++)
#define rrep(i,n) for(int i=n-1; i>=0; i--)
#define RREP(i,n) for(int i=n; i>=0; i--)
#define INF 1000000000

int main(){
  char buf[1024];
  int N,M,C;

  fgets(buf,sizeof(buf),stdin);
  sscanf(buf, "%d %d %d", &N, &M, &C);

  int *B=(int *)malloc(sizeof(int)*M);
  rep(i,M){
    scanf("%d", &B[i]);
  }

  int **A=(int **)malloc(sizeof(int *)*N);
  rep(i,N){
    A[i]=(int *)malloc(sizeof(int)*M);
  }

  rep(i,N){
    rep(j,M){
      scanf("%d", &A[i][j]);
    }
  }

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

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

  return 0;


}