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 _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#if defined(_MSC_VER) || defined(ONLINE_JUDGE)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
using namespace std;
#define rep(i, n) for(int i=0; i<(n); ++i)
#define FOR(i, m, n) for(int i=(m); i<(n); ++i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define mp make_pair
#define pb push_back
#define dump(x) cerr << #x << " = " << (x) << endl;
using LL=long long;
using VS=vector<string>;   using VD=vector<double>;
using VI=vector<int>;      using VL=vector<LL>;
using VVI=vector<VI>;      using VVL=vector<VL>;
using PII=pair<int, int>;  using PLL=pair<LL, LL>;
const int inf = (int)1e9;  const double pi = acos(-1.0);
const LL MOD = 1000000007; const string Snum = "0123456789";
const int dx[] = { -1,0,1,0,-1,-1,1,1 }, dy[] = { 0,1,0,-1,-1,1,-1,1 };
template<class T>void Sort(T& a) { sort(a.begin(), a.end()); }
template<class T>void ReSort(T& a) { sort(a.rbegin(), a.rend()); }
template<class T>void Reverse(T& a) { reverse(a.begin(), a.end()); }
template<class T>void Unique(T& a) { a.erase(unique(a.begin(), a.end()), a.end()); }
template<class T>auto Max(const T& a) { return *max_element(a.begin(), a.end()); }
template<class T>auto Min(const T& a) { return *min_element(a.begin(), a.end()); }
template<class T, class U>int Count(const T& a, U c) { return count(a.begin(), a.end(), c); }
template<class T, class U>U Sum(const T& a, U init = 0) { return accumulate(a.begin(), a.end(), init); }
template<class T, class U>int Lower(const T& a, U s) { return lower_bound(a.begin(), a.end(), s) - a.begin(); }
template<class T, class U>int Upper(const T& a, U s) { return upper_bound(a.begin(), a.end(), s) - a.begin(); }
template<class T>T Age(T a, T b) { return (a + b - 1) / b; }
template<class T>T gcd(T n, T m) { return m == 0 ? n : gcd(m, n % m); }
template<class T>T lcm(T n, T m) { return n / gcd(n, m) * m; }

/* INPUT */
template<class T>T GetInput() { return 0; }
template<> char GetInput() {
	char ret = '\0', c = getchar_unlocked();
	while (c != '\0' && c != '\n' && c != '\t' && c != ' ') { ret = c; c = getchar_unlocked(); }
	return ret;
}
template<> string GetInput() {
	string ret; char c = getchar_unlocked();
	while (c != '\0' && c != '\n' && c != '\t' && c != ' ') { ret.push_back(c); c = getchar_unlocked(); }
	return ret;
}
template<> int GetInput() {
	int ret = 0; bool neg = false; char c = getchar_unlocked();
	if (c == '-') { neg = true; c = getchar_unlocked(); }
	while ('0' <= c && c <= '9') { ret = ret * 10 + (c - '0'); c = getchar_unlocked(); }
	return neg ? -ret : ret;
}
template<> LL GetInput() {
	LL ret = 0; bool neg = false; char c = getchar_unlocked();
	if (c == '-') { neg = true; c = getchar_unlocked(); }
	while ('0' <= c && c <= '9') { ret = ret * 10LL + (LL(c) - LL('0')); c = getchar_unlocked(); }
	return neg ? -ret : ret;
}
template<> double GetInput() {
	double ret = 0, dp = 1; bool neg = false, adp = false;
	char c = getchar_unlocked();
	if (c == '-') { neg = true; c = getchar_unlocked(); }
	while (('0' <= c && c <= '9') || c == '.') {
		if (c == '.') { adp = true; }
		else if (adp) { dp *= 0.1; ret += (c - '0') * dp; }
		else { ret = ret * 10 + (c - '0'); }
		c = getchar_unlocked();
	}
	return neg ? -ret : ret;
}

template<class T>T StoT(string s) { return s; }
template<> char StoT(string s) { return s.front(); }
template<> string StoT(string s) { return s; }
template<> int StoT(string s) { return stoi(s); }
template<> LL StoT(string s) { return stoll(s); }
template<> double StoT(string s) { return stod(s); }

string GetLine() {
	string ret; char c = getchar_unlocked();
	while (c != '\0' && c != '\n') { ret.push_back(c); c = getchar_unlocked(); }
	return ret;
}

VS InputBuffer;
template<class T>struct Input {
	operator T() {
		return GetInput<T>();
	}
	vector<T> operator[](int n) {
		vector<T> ret(n);
		for (auto& a : ret)a = GetInput<T>();
		return ret;
	}
	vector<vector<T>> operator[](PII p) {
		int n, m; tie(n, m) = p;
		vector<vector<T>> ret(n, vector<T>(m));
		for (auto& a : ret)for (auto& b : a)b = GetInput<T>();
		return ret;
	}
	T at(int n) {
		while ((int)InputBuffer.size() <= n)InputBuffer.pb(GetInput<string>());
		return StoT<T>(InputBuffer[n]);
	}
	vector<T> at(int n, int h) {
		vector<T> ret(h);
		rep(i, n)ret[i] = Input::at(i + n);
		return ret;
	}
	vector<vector<T>> at(int n, int h, int w) {
		vector<vector<T>> ret(h, vector<T>(w));
		rep(i, h)rep(j, w)ret[i][j] = Input::at(n + i * w + j);
		return ret;
	}
};
Input<char> inc; Input<string> ins; Input<int> ini; Input<LL> inl; Input<double> ind;

/* OUTPUT */
class ostreamfbuff : public std::basic_streambuf<char, std::char_traits<char>> {
protected:int overflow(int nCh = EOF) { putchar_unlocked(nCh); return 0; }
};
class ostreamf : public std::basic_iostream<char, std::char_traits<char>> {
public:ostreamf(void) : std::basic_iostream<char, std::char_traits<char>>(new ostreamfbuff()) {}
};
ostreamf coutf;
ostream& operator << (ostream& ostr, Input<string> i) { ostr << string(i); return ostr; }
struct boolswitch { string t, f; boolswitch(string tr, string fa) :t(tr), f(fa) {} }yes("yes", "no"), Yes("Yes", "No"), YES("YES", "NO"), Yay("Yay!", ":(");
struct divizer { string s; divizer(string s_) :s(s_) {} }spc(" "), nosp(""), comma(","), lin("\n");
struct outputter {
	bool flag = false; boolswitch bs; divizer di;
	outputter(bool f, boolswitch b, divizer d) :flag(f), bs(b), di(d) {}
	template<class T>outputter operator ,(T o) {
		if (flag)coutf << di.s; coutf << o;
		outputter t(true, bs, di); return t;
	}
	outputter operator ,(double o) {
		if (flag)coutf << di.s; printf("%.20f", o);
		outputter t(true, bs, di); return t;
	}
	outputter operator ,(bool o) {
		if (flag)coutf << di.s; coutf << (o ? bs.t : bs.f);
		outputter t(true, bs, di); return t;
	}
	template<class T> outputter operator ,(vector<T> o) {
		if (flag)coutf << di.s;
		for (int i = 0; i < (int)o.size(); ++i)coutf << o[i] << (i == (int)o.size() - 1 ? "" : di.s);
		outputter t(true, bs, di); return t;
	}
	template<class T, class U> outputter operator ,(pair<T, U> o) {
		if (flag)coutf << di.s; coutf << o.first << " " << o.second;
		outputter t(true, bs, di); return t;
	}
	outputter operator ,(outputter o) { coutf << '\n'; return o; }
	outputter operator ,(boolswitch b) { outputter t(flag, b, di); return t; }
	outputter operator ,(divizer d) { outputter t(flag, bs, d); return t; }
}out(false, Yes, spc);

/* ANSWER */
struct Answer {
	int mini = INT_MAX, maxi = INT_MIN, sumi = 0;
	LL minl = LLONG_MAX, maxl = LLONG_MIN, suml = 0LL;
	double mind = DBL_MAX, maxd = DBL_MIN, sumd = 0.;
	bool flag = false, flagt = true, lastb = false; int sumb = 0;
	int count = 0;
	void operator =(int n) { mini = min(mini, n); maxi = max(maxi, n); sumi += n; count++; }
	void operator =(LL n) { minl = min(minl, n); maxl = max(maxl, n); suml += n; count++; }
	void operator =(double n) { mind = min(mind, n); maxd = max(maxd, n); sumd += n; count++; }
	void operator =(bool n) { flag = flag | n; flagt = n ? flagt : false; lastb = n;  sumb += n; count++; }
}ans;


int main() {
	int n = ini, m = ini, c = ini;
	VI b = ini[m];
	VVI a = ini[{n, m}];

	rep(i, n) {
		int sum = c;
		rep(j, m)sum += a[i][j] * b[j];
		ans = sum > 0;
	}
	out, ans.sumb, out;
}