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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

using namespace std;
using ll = long long;
using P = pair<int,int>;
using Pl = pair<ll,ll>;
#define REP(i,n) for(ll i = 0;i < (ll)n;i++)
#define REPD(i,n) for(ll i = (ll)n - 1;i >= 0;i--)
#define ALL(x) (x).begin(),(x).end()
#define FILLl(n,first_dimension_size,value) fill((ll*)n,(ll*)(n+first_dimension_size),value)
#define FILL(n,first_dimension_size,value) fill((int*)n,(int*)(n+first_dimension_size),value)
#define INF (1 << 29)
#define MOD 1000000007
//int dx[4] = {1,0,0,-1};
//int dy[4] = {0,1,-1,0};



int main(){

  int n,m,c,res = 0;
  cin >> n >> m >> c;
  vector<int> b(m);
  REP(i,m)cin >> b[i];
  vector<vector<int>> v(n);
  REP(i,n){
    REP(j,m){
      int x;cin >> x;
      v[i].push_back(x);
    }
  }
  REP(i,n){
    int sum = 0; 
    REP(j,m){
      sum += v[i][j]*b[j];
    }
    if(sum > -c)res++;
  }
  cout << res << endl;

  return 0;
}