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: Wrong Answer)

/*
 *
 *   Author     : Amit Kumar
 *   Date    	: June 5 2019
 * 
 */

#include <bits/stdc++.h>

//#define FAST_INPUT_OUTPUT
//#define MORE_THAN_ONE_TESTCASE // COMMENT IT

#define vi vector<int>
#define vl vector<long long>
#define mii map<int , int>
#define mll map<long long , long long>
#define msi map<string , i>
#define msl map<string , long long>
#define umii unordered_map<int,int>
#define umll unordered_map<long long ,long long>
#define umsi unordered_map<string , int>
#define umsl map<string , long long> 
#define si set<int>
#define sl set<long long>
#define pii pair<int , int >
#define psi pair<string,int>
#define psl pair<string , long > 
#define pll pair<long long , long long>
#define vpii vector<pii>
#define vpll vector<pll>
#define vpsi vector<psi>
#define vpsl vector<psl>
#define pqi priority_queue<int>
#define pql priority_queue<long long>
#define ub upper_bound
#define lb lower_bound
#define bint long long int
#define ff first
#define ss second
#define all(x) x.begin(),x.end()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define iv(v) for(auto &i:v){cin>>i;}
#define ov(v) for(auto i:v){cout<<i<<" ";}cout<<endl;
#define ovn(v) for(auto i:v){cout<<i<<endl;}
#define euv(v) for(auto i:v){cerr<<i<<" ";}cerr<<endl;
#define eovn(v) for(auto i:v){cerr<<i<<endl;}
#define os(s) for(auto itr:s){cout<<itr<<" ";}cout<<endl;
#define osn(s) for(auto itr:s){cout<<itr<<endl;}
#define eos(s) for(auto itr:s){cerr<<itr<<" ";}cerr<<endl;
#define eosn(s) for(auto itr:s){cerr<<itr<<endl;}
#define rep(x) for(auto i=0 ; i<(x); ++i)
#define _rep(a,b) for(auto i=(a); i<(b); ++i)
#define endl '\n'
using namespace std;




auto SOLUTION_FUNCTION( void ) ->void {

    // your solution goes here 

    int n , m , c;

    cin>>n>>m>>c;

    vi b(m);
    iv(b);
    int ans = 0;
    rep(n){
        vi a(m);
        bint counter = 0;
        iv(a);
        for(int j=0; j<m; ++j){
            counter += (a[i]*b[i]);
        }
        counter+=c;
        if(counter>0){
            ans++;
        }
    }

    cout<<ans<<endl;


    return ;
}




int main(void){
#ifdef FAST_INPUT_OUTPUT
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    cout<<setprecision(10);
    cout<<fixed;
    cout<<boolalpha;
#endif
#ifdef MY_LOCAL_PROJECT
    freopen("bin","r",stdin);
    freopen("bout","w",stdout);
#endif
    int testcase = 1;


#ifdef MORE_THAN_ONE_TESTCASE
    cin>>testcase;
#endif
    
    while(testcase--){
        SOLUTION_FUNCTION();
    }

#ifdef MY_LOCAL_PROJECT
    cout<<"Time : "<<1.0*(double)clock()/CLOCKS_PER_SEC<<endl;
#endif
    return 0;
}