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 javax.print.attribute.HashPrintServiceAttributeSet;
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1569d {

    public static void main(String[] args) throws IOException {
        int t = ri();
        while (t --> 0) {
            int n = rni(), m = ni(), k = ni(), x[] = ria(n), y[] = ria(m);
            Set<Integer> xs = new HashSet<>(), ys = new HashSet<>();
            for (int xx : x) {
                xs.add(xx);
            }
            for (int yy : y) {
                ys.add(yy);
            }
            List<Integer> onx = new ArrayList<>(), ony = new ArrayList<>();
            Map<Integer, List<Integer>> xmap = new HashMap<>(), ymap = new HashMap<>();
            for (int i = 0; i < k; ++i) {
                int xp = rni(), yp = ni();
                if (xs.contains(xp) && ys.contains(yp)) {
                    continue;
                }
                if (xs.contains(xp)) {
                    onx.add(yp);
                    xmap.computeIfAbsent(xp, key -> new ArrayList<>()).add(yp);
                } else if (ys.contains(yp)) {
                    ony.add(xp);
                    ymap.computeIfAbsent(yp, key -> new ArrayList<>()).add(xp);
                }
            }
            onx.sort(Integer::compare);
            ony.sort(Integer::compare);
            long ans = 0;
            for (int i = 0, len = onx.size(); i < len; ++i) {
                int fi = i, nxt = minst(0, m - 1, j -> y[j] > onx.get(fi));
                if (nxt == m) {
                    continue;
                }
                int nxty = y[nxt];
                ans += maxst(i, len - 1, j -> onx.get(j) < nxty) - i;
            }
            for (int i = 0, len = ony.size(); i < len; ++i) {
                int fi = i, nxt = minst(0, n - 1, j -> x[j] > ony.get(fi));
                if (nxt == n) {
                    continue;
                }
                int nxtx = x[nxt];
                ans += maxst(i, len - 1, j -> ony.get(j) < nxtx) - i;
            }
            for (int xx : xmap.keySet()) {
                List<Integer> l = xmap.get(xx);
                l.sort(Integer::compare);
                for (int i = 0, len = l.size(); i < len; ++i) {
                    int fi = i, nxt = minst(0, m - 1, j -> y[j] > l.get(fi));
                    if (nxt == m) {
                        continue;
                    }
                    int nxty = y[nxt];
                    ans -= maxst(i, len - 1, j -> l.get(j) < nxty) - i;
                }
            }
            for (int yy : ymap.keySet()) {
                List<Integer> l = ymap.get(yy);
                l.sort(Integer::compare);
                for (int i = 0, len = l.size(); i < len; ++i) {
                    int fi = i, nxt = minst(0, n - 1, j -> x[j] > l.get(fi));
                    if (nxt == n) {
                        continue;
                    }
                    int nxtx = x[nxt];
                    ans -= maxst(i, len - 1, j -> l.get(j) < nxtx) - i;
                }
            }
            prln(ans);
        }
        close();
    }

    static class MSet<T> implements Iterable<T> {
        Map<T, Integer> set = new HashMap<>();
        int size = 0;

        int cnt(T x) {
            if (contains(x)) {
                return set.get(x);
            }
            return 0;
        }

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

        void add(T x) {
            set.put(x, set.getOrDefault(x, 0) + 1);
            ++size;
        }

        boolean remove(T x) {
            if (contains(x)) {
                if (set.get(x) == 1) {
                    set.remove(x);
                } else {
                    set.put(x, set.get(x) - 1);
                }
                --size;
                return true;
            }
            return false;
        }

        int removeAll(T x) {
            if (contains(x)) {
                int n = set.get(x);
                set.remove(x);
                size -= n;
                return n;
            }
            return 0;
        }

        int size() {
            return size;
        }

        @Override
        public Iterator<T> iterator() {
            return set.keySet().iterator();
        }
    }

    @FunctionalInterface
    interface IntCondition {
        boolean check(int x);
    }

    static int maxst(int min, int max, IntCondition condition) {
        int ans = min - 1;
        for (int l = min, r = max, m; l <= r; ) {
            if (condition.check(m = l + (r - l) / 2)) l = (ans = m) + 1;
            else r = m - 1;
        }
        return ans;
    }

    static int minst(int min, int max, IntCondition condition) {
        int ans = max + 1;
        for (int l = min, r = max, m; l <= r; ) {
            if (condition.check(m = l + (r - l) / 2)) r = (ans = m) - 1;
            else l = m + 1;
        }
        return ans;
    }

    static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __r = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final long LMAX = 9223372036854775807L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int) d;}
    static int cei(double d) {return (int) ceil(d);}
    static long fll(double d) {return (long) d;}
    static long cel(double d) {return (long) ceil(d);}
    static int gcd(int a, int b) {return b == 0 ? a : gcd(b, a % b);}
    static long gcd(long a, long b) {return b == 0 ? a : gcd(b, a % b);}
    static int[] exgcd(int a, int b) {if (b == 0) return new int[] {1, 0}; int[] y = exgcd(b, a % b); return new int[] {y[1], y[0] - y[1] * (a / b)};}
    static long[] exgcd(long a, long b) {if (b == 0) return new long[] {1, 0}; long[] y = exgcd(b, a % b); return new long[] {y[1], y[0] - y[1] * (a / b)};}
    static int randInt(int min, int max) {return __r.nextInt(max - min + 1) + min;}
    static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static void rsort(double[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    // input
    static void r() throws IOException {input = new StringTokenizer(rline());}
    static int ri() throws IOException {return Integer.parseInt(rline());}
    static long rl() throws IOException {return Long.parseLong(rline());}
    static double rd() throws IOException {return Double.parseDouble(rline());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
    static void ria(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni();}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
    static void riam1(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
    static void rla(long[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nl();}
    static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
    static void rda(double[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nd();}
    static char[] rcha() throws IOException {return rline().toCharArray();}
    static void rcha(char[] a) throws IOException {int n = a.length, i = 0; for (char c : rline().toCharArray()) a[i++] = c;}
    static String rline() throws IOException {return __i.readLine();}
    static String n() {return input.nextToken();}
    static int rni() throws IOException {r(); return ni();}
    static int ni() {return Integer.parseInt(n());}
    static long rnl() throws IOException {r(); return nl();}
    static long nl() {return Long.parseLong(n());}
    static double rnd() throws IOException {r(); return nd();}
    static double nd() {return Double.parseDouble(n());}
    // output
    static void pr(int i) {__o.print(i);}
    static void prln(int i) {__o.println(i);}
    static void pr(long l) {__o.print(l);}
    static void prln(long l) {__o.println(l);}
    static void pr(double d) {__o.print(d);}
    static void prln(double d) {__o.println(d);}
    static void pr(char c) {__o.print(c);}
    static void prln(char c) {__o.println(c);}
    static void pr(char[] s) {__o.print(new String(s));}
    static void prln(char[] s) {__o.println(new String(s));}
    static void pr(String s) {__o.print(s);}
    static void prln(String s) {__o.println(s);}
    static void pr(Object o) {__o.print(o);}
    static void prln(Object o) {__o.println(o);}
    static void prln() {__o.println();}
    static void pryes() {prln("yes");}
    static void pry() {prln("Yes");}
    static void prY() {prln("YES");}
    static void prno() {prln("no");}
    static void prn() {prln("No");}
    static void prN() {prln("NO");}
    static boolean pryesno(boolean b) {prln(b ? "yes" : "no"); return b;};
    static boolean pryn(boolean b) {prln(b ? "Yes" : "No"); return b;}
    static boolean prYN(boolean b) {prln(b ? "YES" : "NO"); return b;}
    static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
    static void h() {prln("hlfd"); flush();}
    static void flush() {__o.flush();}
    static void close() {__o.close();}
}