There is a city that can be represented as a square grid with corner points in (0, 0) and (10^6, 10^6).

The city has n vertical and m horizontal streets that goes across the whole city, i. e. the i-th vertical streets goes from (x_i, 0) to (x_i, 10^6) and the j-th horizontal street goes from (0, y_j) to (10^6, y_j). 

All streets are bidirectional. Borders of the city are streets as well.

There are k persons staying on the streets: the p-th person at point (x_p, y_p) (so either x_p equal to some x_i or y_p equal to some y_j, or both).

Let's say that a pair of persons form an inconvenient pair if the shortest path from one person to another going only by streets is strictly greater than the Manhattan distance between them.

Calculate the number of inconvenient pairs of persons (pairs (x, y) and (y, x) are the same pair).

Let's recall that Manhattan distance between points (x_1, y_1) and (x_2, y_2) is |x_1 - x_2| + |y_1 - y_2|.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains three integers n, m and k (2 ≤ n, m ≤ 2 ⋅ 10^5; 2 ≤ k ≤ 3 ⋅ 10^5) — the number of vertical and horizontal streets and the number of persons.

The second line of each test case contains n integers x_1, x_2, ..., x_n (0 = x_1 < x_2 < ... < x_{n - 1} < x_n = 10^6) — the x-coordinates of vertical streets.

The third line contains m integers y_1, y_2, ..., y_m (0 = y_1 < y_2 < ... < y_{m - 1} < y_m = 10^6) — the y-coordinates of horizontal streets.

Next k lines contains description of people. The p-th line contains two integers x_p and y_p (0 ≤ x_p, y_p ≤ 10^6; x_p ∈ \\{x_1, ..., x_n\} or y_p ∈ \\{y_1, ..., y_m\}) — the coordinates of the p-th person. All points are distinct.

It guaranteed that sum of n doesn't exceed 2 ⋅ 10^5, sum of m doesn't exceed 2 ⋅ 10^5 and sum of k doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print the number of inconvenient pairs.

Example

Input


2
2 2 4
0 1000000
0 1000000
1 0
1000000 1
999999 1000000
0 999999
5 4 9
0 1 2 6 1000000
0 4 8 1000000
4 4
2 5
2 2
6 3
1000000 1
3 8
5 8
8 8
6 8


Output


2
5

Note

The second test case is pictured below: 

<image>

For example, points 3 and 4 form an inconvenient pair, since the shortest path between them (shown red and equal to 7) is greater than its Manhattan distance (equal to 5).

Points 3 and 5 also form an inconvenient pair: the shortest path equal to 1000001 (shown green) is greater than the Manhattan distance equal to 999999.

But points 5 and 9 don't form an inconvenient pair, since the shortest path (shown purple) is equal to its Manhattan distance.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.concurrent.CopyOnWriteArrayList;
import java.util.stream.Collectors;


public class Main implements Runnable {
    int n, m, k;
    long n1, s;
    static boolean use_n_tests = true;
    long mod = 1_000_000_007;
    static long mod1 = 998244353L;
    List<Integer> primes = Collections.emptyList();//generatePrimes(31623);

    void solve(FastScanner in, PrintWriter out, int testNumber) {
        n = in.nextInt();
        m = in.nextInt();
        k = in.nextInt();
        Integer[] x = in.nextArray2(n);
        Integer[] y = in.nextArray2(m);
        Arrays.sort(x);
        Arrays.sort(y);


        List<Pair> xs = new ArrayList<>();
        List<Pair> ys = new ArrayList<>();

        for (int i = 0; i < k; i++) {
            int xp = in.nextInt();
            int yp = in.nextInt();
            xs.add(new Pair(xp, yp));
            ys.add(new Pair(yp, xp));
        }
        Collections.sort(xs, Comparator.comparing(Pair::getFirst));
        Collections.sort(ys, Comparator.comparing(Pair::getFirst));
        long ans = calc(x, xs);
        ans += calc(y, ys);
        out.println(ans);
    }

    long calc(Integer[] x, List<Pair> xs) {
        long ans = 0;
        int cur = 0, nxt;
        for (int i = 1; i < x.length; i++) {
            while (cur < xs.size() && xs.get(cur).first <= x[i - 1]) {
                cur++;
            }
            nxt = cur;
            Map<Integer, Integer> mp = new HashMap<>();
            while (nxt < xs.size() && xs.get(nxt).first < x[i]) {
                mp.merge((int) xs.get(nxt).second, 1, Integer::sum);
                nxt++;
            }

            ans += (long) (nxt - cur) * (nxt - cur - 1) / 2;
            for (int v : mp.values()) {
                ans -= (long) v * (v - 1) / 2;
            }
        }
        return ans;
    }

    // ****************************** template code ***********

    static public class LcaSparseTable {
        int len;
        int[][] up;
        int[] tin;
        int[] tout;
        int time;
        static List<Integer>[] tree;
        static LcaSparseTable t;

        void dfs(List<Integer>[] tree, int u, int p) {
            tin[u] = time++;
            up[0][u] = p;
            for (int i = 1; i < len; i++)
                up[i][u] = up[i - 1][up[i - 1][u]];
            for (int v : tree[u])
                if (v != p)
                    dfs(tree, v, u);
            tout[u] = time++;
        }

        public LcaSparseTable(List<Integer>[] tree, int root) {
            int n = tree.length;
            len = 1;
            while ((1 << len) <= n) ++len;
            up = new int[len][n];
            tin = new int[n];
            tout = new int[n];
            dfs(tree, root, root);
        }

        boolean isParent(int parent, int child) {
            return tin[parent] <= tin[child] && tout[child] <= tout[parent];
        }

        public int lca(int a, int b) {
            if (isParent(a, b))
                return a;
            if (isParent(b, a))
                return b;
            for (int i = len - 1; i >= 0; i--)
                if (!isParent(up[i][a], b))
                    a = up[i][a];
            return up[0][a];
        }

        public static void adaptGraph(Graph graph) {
            int n = graph.size() + 1;
            tree = new List[n];
            for (int i = 0; i < n; i++) {
                tree[i] = new ArrayList<>();
            }
            List<Integer> edges = graph.getEdges();
            for (int i = 0; i < edges.size() / 2; i++) {
                int v = edges.get(i * 2);
                int u = edges.get(i * 2 + 1);
                tree[v].add(u);
                tree[u].add(v);
            }
            t = new LcaSparseTable(tree, 0);
        }

        public static int getLca(int a, int b) {
            return t.lca(a, b);
        }
    }


    List<Integer> factorize(int a) {
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < primes.size(); i++) {
            int p = primes.get(i);
            while (a % p == 0) {
                res.add(p);
                a /= p;
            }
            if (a == 1 && p > a) {
                break;
            }
        }
        if (a != 1) {
            res.add(a);
        }
        return res;
    }

    void impossible() {
        out.println(-1);
    }

    void yes() {
        out.println("YES");
    }

    void no() {
        out.println("NO");
    }

    static boolean next_permutation(char[] p) {
        for (int a = p.length - 2; a >= 0; --a)
            if (p[a] < p[a + 1])
                for (int b = p.length - 1; ; --b)
                    if (p[b] > p[a]) {
                        char t = p[a];
                        p[a] = p[b];
                        p[b] = t;
                        for (++a, b = p.length - 1; a < b; ++a, --b) {
                            t = p[a];
                            p[a] = p[b];
                            p[b] = t;
                        }
                        return true;
                    }
        return false;
    }

    public static class DisjointSets {
        int[] p;

        DisjointSets(int size) {
            p = new int[size];
            for (int i = 0; i < size; i++)
                p[i] = i;
        }

        public int root(int x) {
            return x == p[x] ? x : (p[x] = root(p[x]));
        }

        public void unite(int a, int b) {
            a = root(a);
            b = root(b);
            if (a != b)
                p[a] = b;
        }
    }

    boolean triangleCheck(int a, int b, int c) {
        return a + b > c && a + c > b && b + c > a;
    }

    Map<Integer, Integer> numberCompression(List<Integer> ls) {
        Collections.sort(ls);
        int id = 1;
        Map<Integer, Integer> comp = new HashMap<>();
        for (int num : ls) {
            if (!comp.containsKey(num)) {
                comp.put(num, id++);
            }
        }
        return comp;
    }

    long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    class Pt {
        int x, y;

        Pt(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int getX() {
            return x;
        }

        public int getY() {
            return y;
        }

        boolean sameAxis(Pt b) {
            return b.x == x || b.y == y;
        }

        int manxDist(Pt b) {
            return Math.abs(x - b.x) + Math.abs(y - b.y);
        }

        void read() {
            x = in.nextInt();
            y = in.nextInt();
        }
    }

    void swap(Integer[] a, int i, int j) {
        Integer tmp = a[i];
        a[i] = a[j];
        a[j] = tmp;
    }

    void swap(List<Integer> a, int i, int j) {
        Integer tmp = a.get(i);
        a.set(i, a.get(j));
        a.set(j, tmp);
    }

    long manhDist(long x, long y, long x1, long y1) {
        return Math.abs(x - x1) + Math.abs(y - y1);
    }

    double dist(double x, double y, double x1, double y1) {
        return Math.sqrt(Math.pow(x - x1, 2.0) + Math.pow(y - y1, 2.0));
    }

    public static class FW {
        public static void add(long[] t, int i, long value) {
            for (; i < t.length; i |= i + 1)
                t[i] += value;
        }

        public static long sum(long[] t, int i) {
            long res = 0;
            for (; i >= 0; i = (i & (i + 1)) - 1)
                res += t[i];
            return res;
        }

        public static void add(long[] t, int a, int b, long value) {
            add(t, a, value);
            add(t, b + 1, -value);
        }
    }

    int sign(int a) {
        if (a < 0) {
            return -1;
        }
        return 1;
    }

    long binpow(long a, int b) {
        long res = 1;
        while (b != 0) {
            if (b % 2 == 0) {
                b /= 2;
                a *= a;
                a %= mod;
            }

            b--;
            res *= a;
            res %= mod;
        }
        return res;
    }

    List<Integer> getDigits(long n) {
        List<Integer> res = new ArrayList<>();
        while (n != 0) {
            res.add((int) (n % 10L));
            n /= 10;
        }
        return res;
    }

    List<Integer> generatePrimes(int n) {
        List<Integer> res = new ArrayList<>();
        boolean[] sieve = new boolean[n + 1];
        for (int i = 2; i <= n; i++) {
            if (!sieve[i]) {
                res.add(i);
            }
            if ((long) i * i <= n) {
                for (int j = i * i; j <= n; j += i) {
                    sieve[j] = true;
                }
            }
        }
        return res;
    }

    static int stack_size = 1 << 29;

    static class Coeff {
        long mod;
        long[][] C;
        long[] fact;
        boolean cycleWay = false;

        Coeff(int n, long mod) {
            this.mod = mod;
            fact = new long[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++) {
                fact[i] = i;
                fact[i] %= mod;
                fact[i] *= fact[i - 1];
                fact[i] %= mod;
            }
        }

        Coeff(int n, int m, long mod) {
            // n > m
            cycleWay = true;
            this.mod = mod;
            C = new long[n + 1][m + 1];
            for (int i = 0; i <= n; i++) {
                for (int j = 0; j <= Math.min(i, m); j++) {
                    if (j == 0 || j == i) {
                        C[i][j] = 1;
                    } else {
                        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
                        C[i][j] %= mod;
                    }
                }
            }
        }

        public long C(int n, int m) {
            if (cycleWay) {
                return C[n][m];
            }
            return fC(n, m);
        }

        private long fC(int n, int m) {
            return (fact[n] * inv(fact[n - m] * fact[m] % mod)) % mod;
        }

        private long inv(long r) {
            if (r == 1)
                return 1;
            return ((mod - mod / r) * inv(mod % r)) % mod;
        }
    }

    class Pair {
        int first;
        long second;

        Pair(int f, long s) {
            first = f;
            second = s;
        }

        public int getFirst() {
            return first;
        }

        public long getSecond() {
            return second;
        }
    }

    class MultisetTree<T> {
        int size = 0;

        TreeMap<T, Integer> mp = new TreeMap<>();

        void add(T x) {
            mp.merge(x, 1, Integer::sum);
            size++;
        }

        void remove(T x) {
            if (mp.containsKey(x)) {
                mp.merge(x, -1, Integer::sum);
                if (mp.get(x) == 0) {
                    mp.remove(x);
                }
                size--;
            }
        }

        boolean contains(T x) {
            return mp.containsKey(x);
        }

        T greatest() {
            return mp.lastKey();
        }

        T higher(T x) {
            return mp.higherKey(x);
        }

        T smallest() {
            return mp.firstKey();
        }

        T biggest() {
            return mp.lastKey();
        }

        int size() {
            return size;
        }

        int diffSize() {
            return mp.size();
        }
    }

    class Multiset<T> {
        int size = 0;

        Map<T, Integer> mp = new HashMap<>();

        void add(T x) {
            mp.merge(x, 1, Integer::sum);
            size++;
        }

        boolean contains(T x) {
            return mp.containsKey(x);
        }

        void remove(T x) {
            if (mp.containsKey(x)) {
                mp.merge(x, -1, Integer::sum);
                if (mp.get(x) == 0) {
                    mp.remove(x);
                }
                size--;
            }
        }

        int size() {
            return size;
        }

        int diffSize() {
            return mp.size();
        }
    }

    static class Range {
        int l, r;
        int id;

        public int getL() {
            return l;
        }

        public int getR() {
            return r;
        }

        public Range(int l, int r, int id) {
            this.l = l;
            this.r = r;
            this.id = id;
        }
    }

    static class Array {
        static Range[] readRanges(int n, FastScanner in) {
            Range[] result = new Range[n];
            for (int i = 0; i < n; i++) {
                result[i] = new Range(in.nextInt(), in.nextInt(), i);
            }
            return result;
        }

        static List<List<Integer>> intInit2D(int n) {
            List<List<Integer>> res = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                res.add(new ArrayList<>());
            }
            return res;
        }

        static boolean isSorted(Integer[] a) {
            for (int i = 0; i < a.length - 1; i++) {
                if (a[i] > a[i + 1]) {
                    return false;
                }
            }
            return true;
        }

        static public long sum(List<Integer> a) {
            long sum = 0;
            for (int x : a) {
                sum += x;
            }
            return sum;
        }

        static public long sum(int[] a) {
            long sum = 0;
            for (int x : a) {
                sum += x;
            }
            return sum;
        }

        static public long sum(long[] a) {
            long sum = 0;
            for (long x : a) {
                sum += x;
            }
            return sum;
        }

        static public long sum(Integer[] a) {
            long sum = 0;
            for (int x : a) {
                sum += x;
            }
            return sum;
        }

        static public int min(Integer[] a) {
            int mn = Integer.MAX_VALUE;
            for (int x : a) {
                mn = Math.min(mn, x);
            }
            return mn;
        }

        static public int min(int[] a) {
            int mn = Integer.MAX_VALUE;
            for (int x : a) {
                mn = Math.min(mn, x);
            }
            return mn;
        }

        static public int max(Integer[] a) {
            int mx = Integer.MIN_VALUE;
            for (int x : a) {
                mx = Math.max(mx, x);
            }
            return mx;
        }

        static public int max(int[] a) {
            int mx = Integer.MIN_VALUE;
            for (int x : a) {
                mx = Math.max(mx, x);
            }
            return mx;
        }

        static public int[] readint(int n, FastScanner in) {
            int[] out = new int[n];
            for (int i = 0; i < out.length; i++) {
                out[i] = in.nextInt();
            }
            return out;
        }
    }

    class Graph {
        List<List<Integer>> graph;
        List<Integer> edges;

        Graph(int n) {
            create(n);
        }

        private void create(int n) {
            List<List<Integer>> graph = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                graph.add(new ArrayList<>());
            }
            this.graph = graph;
            edges = new ArrayList<>();
        }

        int size() {
            return graph.size();
        }

        List<Integer> abj(int v) {
            return graph.get(v);
        }

        void read(int m, FastScanner in) {
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1;
                int u = in.nextInt() - 1;
                graph.get(v).add(u);
            }
        }

        void readBi(int m, FastScanner in) {
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1;
                int u = in.nextInt() - 1;
                addEdge(v, u);
            }
        }

        public void addEdge(int v, int u) {
            graph.get(v).add(u);
            graph.get(u).add(v);
            edges.add(v);
            edges.add(u);
        }

        public List<Integer> getEdges() {
            return edges;
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream io) {
            br = new BufferedReader(new InputStreamReader(io));
        }

        public String line() {
            String result = "";
            try {
                result = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return result;
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public char[] nextc() {
            return next().toCharArray();
        }

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

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

        public int[] nextArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextInt();
            }
            return res;
        }

        public int[] nextArray() {
            int n = in.nextInt();
            return nextArray(n);
        }

        public long[] nextArrayL(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextLong();
            }
            return res;
        }

        public Long[] nextArrayL2(int n) {
            Long[] res = new Long[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextLong();
            }
            return res;
        }


        public Integer[] nextArray2(int n) {
            Integer[] res = new Integer[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextInt();
            }
            return res;
        }

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

    }

    void run_t_tests() {
        int t = in.nextInt();
        int i = 0;
        while (t-- > 0) {
            solve(in, out, i++);
        }
    }

    void run_one() {
        solve(in, out, -1);
    }

    @Override
    public void run() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        if (use_n_tests) {
            run_t_tests();
        } else {
            run_one();
        }
        out.close();
    }

    static FastScanner in;
    static PrintWriter out;

    public static void main(String[] args) throws InterruptedException {
        Thread thread = new Thread(null, new Main(), "", stack_size);
        thread.start();
        thread.join();
    }
}