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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

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

    static String reverse(String s) {
        return (new StringBuilder(s)).reverse().toString();
    }

    static void sieveOfEratosthenes(int n, int factors[], ArrayList<Integer> ar) 
    { 
        factors[1]=1;
        int p;
        for(p = 2; p*p <=n; p++) 
        { 
            if(factors[p] == 0) 
            { 
                ar.add(p);
                factors[p]=p;
                for(int i = p*p; i <= n; i += p) 
                    if(factors[i]==0)
                        factors[i] = p; 
            } 
        } 
        for(;p<=n;p++){
            if(factors[p] == 0) 
            { 
                factors[p] = p;
                ar.add(p);
            } 
        }
    }

    static void sort(int ar[]) {
        int n = ar.length;
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort2(char ar[]) {
        int n = ar.length;
        ArrayList<Character> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    static long sum[];
    static long lz[];
    
    static void build(long a[], int v, int tl, int tr) {
        if (tl == tr) {
            sum[v] = a[tl];
            
        } else {
            int tm = (tl + tr) / 2;
            build(a, v*2, tl, tm);
            build(a, v*2+1, tm+1, tr);
            sum[v] = sum[v*2] + sum[v*2+1];
        }
    }

    static void push(int v, int tl, int tr){
        if(tl==tr){
            lz[v] = 0;
            return;
        }
        sum[2*v] += lz[v];
        sum[2*v] %= m;
        sum[2*v+1] += lz[v];
        sum[2*v+1] %= m;
        lz[2*v] += lz[v];
        lz[2*v] %= m;
        lz[2*v+1] += lz[v];
        lz[2*v+1] %= m;
        lz[v] = 0;
    }

    static void update(int v, int tl, int tr, int l, int r, long val) {
        push(v,tl,tr);
        if(tl>r||tr<l)
            return;
        if(tl>=l&&tr<=r){
            sum[v] += val;
            sum[v] %= m;
            lz[v] += val;
            lz[v] %= m;
            return;
        }
        int tm = ((tl + tr) >> 1);
        update(v*2, tl, tm, l, r, val);
        update(v*2+1, tm+1, tr, l, r, val);
        sum[v] = sum[2*v]+sum[2*v+1];
        sum[v] %= m;
    }

    static long get(int v, int tl, int tr, int l, int r) {
        push(v,tl,tr);
        if (tl >= l && tr <= r) {
            return sum[v];
        }
        int tm = ((tl + tr) >> 1);
        if(l>tm){
            return get(2*v+1, tm+1, tr, l, r);
        }
        if(r<tm+1){
            return get(2*v, tl, tm, l, r);
        }
        return (get(2*v, tl, tm, l, r) + get(2*v+1, tm+1, tr, l, r)) % m;
    }

    // static int y = 0;

    static int parent[];
    static int rank[];

    static long m = 0;

    static int find_set(int v) {
        if (v == parent[v])
            return v;
        return find_set(parent[v]);
    }
    
    static void make_set(int v) {
        parent[v] = v;
        rank[v] = 0;
    }
    
    static void union_sets(int a, int b) {
        a = find_set(a);
        b = find_set(b);
        if (a != b) {
            if (rank[a] < rank[b]){
                int tmp = a;
                a = b;
                b = tmp;
            }
            parent[b] = a;
            if (rank[a] == rank[b])
                rank[a]++;
        }
    }

    static int parent1[];
    static int rank1[];

    static int find_set1(int v) {
        if (v == parent1[v])
            return v;
        return find_set1(parent1[v]);
    }
    
    static void make_set1(int v) {
        parent1[v] = v;
        rank1[v] = 0;
    }
    
    static void union_sets1(int a, int b) {
        a = find_set1(a);
        b = find_set1(b);
        if (a != b) {
            if (rank1[a] < rank1[b]){
                int tmp = a;
                a = b;
                b = tmp;
            }
            parent1[b] = a;
            if (rank1[a] == rank1[b])
                rank1[a]++;
        }
    }

    public static void solve(InputReader sc, PrintWriter pw){
        int i, j = 0;
        // int t = 1; 
        long mod = 998244353;
        int t = sc.nextInt();
        u: while (t-- > 0) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int k = sc.nextInt();
            int x[] = new int[n];
            int y[] = new int[m];
            HashSet<Integer> xs = new HashSet<>();
            HashSet<Integer> ys = new HashSet<>();
            for(i=0;i<n;i++){
                x[i] = sc.nextInt();
                xs.add(x[i]);
            }
            for(i=0;i<m;i++){
                y[i] = sc.nextInt();
                ys.add(y[i]);
            }
            sort(x);
            sort(y);
            HashMap<Integer,ArrayList<Integer> > xlist = new HashMap<>();
            HashMap<Integer,ArrayList<Integer> > ylist = new HashMap<>();
            ArrayList<Integer> allx = new ArrayList<>();
            ArrayList<Integer> ally = new ArrayList<>();
            for(i=0;i<k;i++){
                int p = sc.nextInt();
                int q = sc.nextInt();
                if(xs.contains(p)&&ys.contains(q)){
                    continue;
                }
                if(xs.contains(p)){
                    allx.add(q);
                    if(!xlist.containsKey(p)){
                        xlist.put(p,new ArrayList<>());
                    }
                    xlist.get(p).add(q);
                }
                else{
                    ally.add(p);
                    if(!ylist.containsKey(q)){
                        ylist.put(q,new ArrayList<>());
                    }
                    ylist.get(q).add(p);
                }
            }
            Collections.sort(allx);
            Collections.sort(ally);
            for(int h:x){
                if(xlist.containsKey(h))
                    Collections.sort(xlist.get(h));
            }
            for(int h:y){
                if(ylist.containsKey(h))
                    Collections.sort(ylist.get(h));
            }
            long count = 0;
            int last = -1, c = 0;
            for(i=0;i<allx.size();i++){
                if(c<m&&allx.get(i)>y[c]){
                    // pw.println(i-1-last);
                    count += 1L*(i-1-last)*(i-last-2)/2;
                    last = i-1;
                    int l = 0, r = m-1;
                    int ans = m;
                    while(l<=r){
                        int mid = (l+r)/2;
                        if(y[mid]<allx.get(i)){
                            l = mid + 1;
                        }
                        else{
                            ans = mid;
                            r = mid - 1;
                        }
                    }
                    c = ans;
                    i--;
                }
            }
            count += 1L*(allx.size()-1-last)*(allx.size()-last-2)/2;
            // pw.println(count);
            c = 0;
            last = -1;
            for(i=0;i<ally.size();i++){
                if(c<n&&ally.get(i)>x[c]){
                    // pw.println(i-1-last);
                    count += 1L*(i-1-last)*(i-last-2)/2;
                    last = i-1;
                    int l = 0, r = n-1;
                    int ans = n;
                    while(l<=r){
                        int mid = (l+r)/2;
                        if(x[mid]<ally.get(i)){
                            l = mid + 1;
                        }
                        else{
                            ans = mid;
                            r = mid - 1;
                        }
                    }
                    c = ans;
                    i--;
                }
            }
            // pw.println(ally.size()-1-last);
            count += 1L*(ally.size()-1-last)*(ally.size()-last-2)/2;
            // pw.println(count);
            // for(i=0;i<allx.size();i++){
            //     if(c<m&&allx.get(i)>y[c]){
            //         // pw.println(i-1-last);
            //         count += 1L*(i-1-last)*(i-last-2)/2;
            //         last = i-1;
            //         i--;
            //         c++;
            //     }
            // }
            // count += 1L*(allx.size()-1-last)*(allx.size()-last-2)/2;
            for(int h:x){
                if(xlist.containsKey(h)){
                    ArrayList<Integer> part = xlist.get(h);
                    last = -1;
                    c = 0;
                    for(i=0;i<part.size();i++){
                        if(c<m&&part.get(i)>y[c]){
                            // pw.println(i-1-last);
                            count -= 1L*(i-1-last)*(i-last-2)/2;
                            last = i-1;
                            int l = 0, r = m-1;
                            int ans = m;
                            while(l<=r){
                                int mid = (l+r)/2;
                                if(y[mid]<part.get(i)){
                                    l = mid + 1;
                                }
                                else{
                                    ans = mid;
                                    r = mid - 1;
                                }
                            }
                            c = ans;
                            i--;
                        }
                    }
                    count -= 1L*(part.size()-1-last)*(part.size()-last-2)/2;
                }
            }
            for(int h:y){
                if(ylist.containsKey(h)){
                    ArrayList<Integer> part = ylist.get(h);
                    last = -1;
                    c = 0;
                    for(i=0;i<part.size();i++){
                        if(c<n&&part.get(i)>x[c]){
                            // pw.println(i-1-last);
                            count -= 1L*(i-1-last)*(i-last-2)/2;
                            last = i-1;
                            int l = 0, r = n-1;
                            int ans = n;
                            while(l<=r){
                                int mid = (l+r)/2;
                                if(x[mid]<part.get(i)){
                                    l = mid + 1;
                                }
                                else{
                                    ans = mid;
                                    r = mid - 1;
                                }
                            }
                            c = ans;
                            i--;
                        }
                    }
                    // pw.println(part.size()-1-last);
                    count -= 1L*(part.size()-1-last)*(part.size()-last-2)/2;
                }
            }
            pw.println(count);
        }
    }

    static void KMPSearch(char pat[], char txt[], int pres[]){
        int M = pat.length;
        int N = txt.length;
        int lps[] = new int[M];
        int j = 0; 
        computeLPSArray(pat, M, lps);
        int i = 0;
        while (i < N) {
            if (pat[j] == txt[i]) {
                j++;
                i++;
            }
            if (j == M) {
                pres[i-1] = 1;
                j = lps[j - 1];
            }
            else if (i < N && pat[j] != txt[i]) {
                if (j != 0)
                    j = lps[j - 1];
                else
                    i = i + 1;
            }
        }
    }
  
    static void computeLPSArray(char pat[], int M, int lps[])
    {
        int len = 0;
        int i = 1;
        lps[0] = 0; 
        while (i < M) {
            if (pat[i] == pat[len]) {
                len++;
                lps[i] = len;
                i++;
            }
            else 
            {
                if (len != 0) {
                    len = lps[len - 1];
                }
                else
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }

    static long[][] matrixMult(long a[][], long b[][], long mod){
        int n = a.length;
        int m = a[0].length;
        int p = b[0].length;
        long c[][] = new long[n][p];
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<p;k++){
                    c[i][k] += a[i][j]*b[j][k];
                    c[i][k] %= mod;
                }
            }
        }
        return c;
    }

    static long[][] exp(long mat[][], long b, long mod){
        if(b==0){
            int n = mat.length;
            long res[][] = new long[n][n];
            for(int i=0;i<n;i++){
                res[i][i] = 1;
            }
            return res;
        }
        long half[][] = exp(mat, b/2, mod);
        long res[][] = matrixMult(half, half, mod);
        if(b%2==1){
            res = matrixMult(res, mat, mod);
        }
        return res;
    }

    static void countPrimeFactors(int num, int a[], HashMap<Integer,Integer> pos){
        for(int i=2;i*i<num;i++){
            if(num%i==0){
                int y = pos.get(i);
                while(num%i==0){
                    a[y]++;
                    num/=i;
                }
            }
        }
        if(num>1){
            int y = pos.get(num);
            a[y]++;
        }
    }

    static void assignAnc(ArrayList<Integer> ar[], int depth[], int sz[], int par[][] ,int curr, int parent, int d){
        depth[curr] = d;
        sz[curr] = 1;
        par[curr][0] = parent;
        for(int v:ar[curr]){
            if(parent==v)
                continue;
            assignAnc(ar, depth, sz, par, v, curr, d+1);
            sz[curr] += sz[v];
        }
    }

    static int findLCA(int a, int b, int par[][], int depth[]){
        if(depth[a]>depth[b]){
            a = a^b;
            b = a^b;
            a = a^b;
        }
        int diff = depth[b] - depth[a];
        for(int i=19;i>=0;i--){
            if((diff&(1<<i))>0){
                b = par[b][i];
            }
        }
        if(a==b)
            return a;
        for(int i=19;i>=0;i--){
            if(par[b][i]!=par[a][i]){
                b = par[b][i];
                a = par[a][i];
            }
        }
        return par[a][0];
    }

    static void formArrayForBinaryLifting(int n, int par[][]){
        for(int j=1;j<20;j++){
            for(int i=0;i<n;i++){
                if(par[i][j-1]==-1)
                    continue;
                par[i][j] = par[par[i][j-1]][j-1];
            }
        }
    }

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

    static class Pair1 {
        long a;
        long b;
        
        Pair1(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;
        // int c;
        
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
            // this.c = c;
        }
 
        public int compareTo(Pair p) {
            // if(c!=p.c)
            return a-p.a;
            // return b-p.b;
        }
    }

    static class Pair2 implements Comparable<Pair2> {
        int a;
        int b;
        int c;
        
        Pair2(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }
 
        public int compareTo(Pair2 p) {
            return a-p.a;
        }
    }

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

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 9992768);
            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());
        }
    }
}