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)

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>

#define FOR(i, a, b) for (int i = (a); i < int(b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= int(a); --i)
#define REP(i, n) FOR(i, 0, n)
#define REP1(i, n) FOR(i, 1, int(n) + 1)
#define RREP(i, n) RFOR(i, 0, n)
#define RREP1(i, n) RFOR(i, 1, int(n) + 1)
#define ALL(c) begin(c), end(c)

int _ = (
#ifndef LOCAL
    std::cin.tie(nullptr), std::ios::sync_with_stdio(false),
#endif
    std::cout.precision(10), std::cout.setf(std::ios::fixed));

using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T> using vec = std::vector<T>;
using namespace std;

int main() {
  ll N, M, C;
  cin >> N >> M >> C;

  vec<ll> B(M);
  REP(i, M) { cin >> B[i]; }

  ll answer = 0;
  ll Aij;
  REP(i, N) {
    ll lhs = C;
    REP(j, M) {
      cin >> Aij;
      lhs += Aij * B[j];
    }
    if (lhs > 0) {
      answer++;
    }
  }
  cout << answer << endl;
  return 0;
}