Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.

Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).

Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.

Input

The first line contains two space-separated integers x1, y1 ( - 106 ≤ x1, y1 ≤ 106) — the coordinates of your home.

The second line contains two integers separated by a space x2, y2 ( - 106 ≤ x2, y2 ≤ 106) — the coordinates of the university you are studying at.

The third line contains an integer n (1 ≤ n ≤ 300) — the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 ≤ ai, bi, ci ≤ 106; |ai| + |bi| > 0) — the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).

Output

Output the answer to the problem.

Examples

Input

1 1
-1 -1
2
0 1 0
1 0 0


Output

2


Input

1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3


Output

2

Note

Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):

<image> <image>
import java.io.*;
import java.util.*;
import java.util.zip.ZipEntry;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Input in = new Input(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {
    static final long MOD = 1000000007;
    int[] primes;

    public void solve(int testNumber, Input in, PrintWriter out) {
        long x1 = in.nextLong();
        long y1 = in.nextLong();
        long x2 = in.nextLong();
        long y2 = in.nextLong();
        long n = in.nextLong();
        long a = 0;
        long b = 0;
        long c = 0;
        long ans = 0;
        for (int i = 0; i < n; i++) {
            a = in.nextLong();
            b = in.nextLong();
            c = in.nextLong();
            long p1 = a * x1 + b * y1 + c;
            long p2 = a * x2 + b * y2 + c;
            if ((p1 < 0 && p2 > 0) || (p1 > 0 && p2 < 0))
                ans++;
        }
        out.println(ans);
    }

    // didn't test
    static class BIT {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int n;

        public BIT(int n) {
            MAX = new int[n + 1];
            MIN = new int[n + 1];
            SUM = new int[n + 1];
            this.n = n;
        }

        public void setSum(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                SUM[i] += val;
            }
        }

        public int getSum(int to) {
            int sum = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                sum += SUM[i];
            }
            return sum;
        }

        public int getSum(int from, int to) {
            return getSum(to) - getSum(from);
        }

        public void setMax(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MAX[i] = Math.max(val, MAX[i]);
            }
        }

        public int getMax(int to) {
            int max = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                max = Math.max(max, MAX[i]);
            }
            return max;
        }

        public void setMin(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MIN[i] = Math.min(val, MIN[i]);
            }
        }

        public int getMin(int to) {
            int min = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                min = Math.min(min, MIN[i]);
            }
            return min;
        }

    }

    // didn't test
    static class DisjointSet {
        int[] set;

        public DisjointSet(int n) {
            set = new int[n];
            for (int i = 0; i < n; i++) {
                set[i] = i;
            }
        }

        public int findSet(int a) {
            if (set[a] == a)
                return a;
            return findSet(set[a]);
        }

        public void unionSet(int a, int b) {
            set[findSet(a)] = findSet(b);
        }

        public boolean isSameSet(int a, int b) {
            return findSet(a) == findSet(b);
        }
    }

    static class SegmentTree {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int[] data;
        int n;

        public SegmentTree(int[] data) {
            this.n = data.length;
            this.data = data;
            MAX = new int[4 * n + 10];
            MIN = new int[4 * n + 10];
            SUM = new int[4 * n + 10];
            buildTree(1, 0, n - 1);
        }

        public int left(int root) {
            return root << 1;
        }

        public int right(int root) {
            return (root << 1) + 1;
        }

        private void buildTree(int root, int rl, int rr) {
            if (rr == rl) {
                MAX[root] = MIN[root] = SUM[root] = data[rr];
            } else {
                int rm = (rl + rr) >> 1;
                buildTree(left(root), rl, rm);
                buildTree(right(root), rm + 1, rr);
                MAX[root] = Math.max(MAX[left(root)], MAX[right(root)]);
                MIN[root] = Math.min(MIN[left(root)], MIN[right(root)]);
                SUM[root] = SUM[left(root)] + SUM[right(root)];
            }
        }

        public int getMax(int from, int to) {
            return getMax(1, 0, n - 1, from, to);
        }

        private int getMax(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return -1;
            }
            if (from == rl && to == rr) {
                return MAX[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMax(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMax(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.max(m1, m2);
        }

        public int getMin(int from, int to) {
            return getMin(1, 0, n - 1, from, to);
        }

        private int getMin(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return Integer.MAX_VALUE;
            }
            if (from == rl && to == rr) {
                return MIN[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMin(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMin(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.min(m1, m2);
        }

        public int getSum(int from, int to) {
            return getSum(1, 0, n - 1, from, to);
        }

        private int getSum(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return 0;
            }
            if (from == rl && to == rr) {
                return SUM[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getSum(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getSum(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return m1 + m2;
        }
    }

    private String lcs(String s1, String s2) {
        int n = s1.length();
        int m = s2.length();
        int[][] dp = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                } else {
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        int i = n;
        int j = m;
        while (i > 0 && j > 0) {
            if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                sb.append(s1.charAt(i - 1));
                i--;
                j--;
            } else {
                if (dp[i - 1][j] > dp[i][j - 1]) {
                    i--;
                } else {
                    j--;
                }
            }
        }
        return sb.reverse().toString();
    }

    private boolean isPrime(int n) {
        if (n <= 3)
            return n > 1;
        else if (n % 3 == 0 || n % 2 == 0)
            return false;
        for (long i = 5; i * i <= n; i += 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }
        return true;
    }

    private int[] getPrimes(int n) {
        int len = n + 1;
        boolean[] isPrimes = new boolean[len];
        int[] temps = new int[len];
        int index = 0;
        Arrays.fill(isPrimes, true);
        isPrimes[0] = isPrimes[1] = false;
        for (int i = 2; i * i < len; i++) {
            if (isPrimes[i]) {
                for (int j = i * i; j < len; j += i) {
                    isPrimes[j] = false;
                }
            }
        }
        for (int i = 0; i < len; i++) {
            if (isPrimes[i])
                temps[index++] = i;
        }
        int[] primes = Arrays.copyOf(temps, index);
        return primes;
    }

    static void swap(char[] arrays, int pos1, int pos2) {
        char tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static void swap(int[] arrays, int pos1, int pos2) {
        int tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static long modPow(long n, long ex) {
        long res = 1;
        while (ex > 0) {
            if ((ex & 1) == 1)
                res = res * n % MOD;
            n = n * n % MOD;
            ex >>= 1;
        }
        return res;
    }

    static long ModInverse(long n) {
        return modPow(n, MOD - 2);
    }

    static long nCr(int n, int r) {
        if (r > n)
            return -1;
        // return (f[n] * ModInverse((f[r] * f[n - r]) % MOD)) % MOD;
        return 0;
    }
}

class Input {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public Input(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}
