#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const long long int mod = 998244353;
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int binpow(long long int x, long long int y, long long int m) {
  if (y == 0) return 1;
  long long int p = binpow(x, y / 2, m) % m;
  p = (p * p) % m;
  if (y % 2)
    return (x * p) % m;
  else
    return p;
}
long long int modi(long long int a, long long int m) {
  return binpow(a, m - 2, m);
}
long long int query(long long int tree[], long long int l, long long int r) {
  long long int ans = 0;
  while (l < r) {
    if (l % 2) {
      ans += tree[l];
      l++;
    }
    if (r % 2) {
      r--;
      ans += tree[r];
    }
    l /= 2;
    r /= 2;
  }
  return ans;
}
long long int find_set(long long int v, long long int parent[]) {
  if (v == parent[v]) return v;
  return parent[v] = find_set(parent[v], parent);
}
void union_sets(long long int a, long long int b, long long int parent[]) {
  a = find_set(a, parent);
  b = find_set(b, parent);
  if (a != b) parent[b] = a;
}
long long int lca(long long int a, long long int b,
                  vector<vector<long long int>> &par, long long int depth[]) {
  if (depth[a] < depth[b]) swap(a, b);
  long long int diff = depth[a] - depth[b], ct = 0;
  while (diff) {
    if (diff % 2) {
      a = par[ct][a];
    }
    ct++;
    diff /= 2;
  }
  if (a == b) return a;
  for (long long int i = 19; i >= 0; i--) {
    if (par[i][a] != par[i][b]) {
      a = par[i][a];
      b = par[i][b];
    }
  }
  return par[0][a];
}
bool cmp1(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  if (a.first != b.first) return a.first < b.first;
  return a.second < b.second;
}
bool cmp2(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  if (a.second != b.second) return a.second < b.second;
  return a.first < b.first;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int i, j, tt = 1, tc;
  cin >> tt;
  for (tc = 1; tc <= tt; tc++) {
    long long int n, m, k, ans = 0;
    cin >> n >> m >> k;
    vector<long long int> a(n), b(m);
    vector<pair<long long int, long long int>> p(k);
    for (i = 0; i < n; i++) {
      cin >> a[i];
    }
    for (i = 0; i < m; i++) {
      cin >> b[i];
    }
    for (i = 0; i < k; i++) {
      cin >> p[i].first >> p[i].second;
    }
    sort(p.begin(), p.end(), cmp1);
    long long int ct = 0, posy, posx, prevy = -1, prevx = -1, curr = 0;
    map<long long int, long long int> mm;
    for (i = 0; i < k; i++) {
      while (a[curr] < p[i].first) {
        curr++;
        ct = -1;
      }
      if (ct == -1) {
        ct = 0;
        mm.clear();
      }
      posy = (lower_bound(b.begin(), b.end(), p[i].second) - b.begin());
      posx = (lower_bound(a.begin(), a.end(), p[i].first) - a.begin());
      if (a[posx] == p[i].first) {
        ct = 0;
        mm.clear();
      } else {
        ans += (ct - mm[posy]);
        ct++;
        mm[posy]++;
      }
    }
    ct = 0;
    sort(p.begin(), p.end(), cmp2);
    curr = 0;
    mm.clear();
    for (i = 0; i < k; i++) {
      while (b[curr] < p[i].second) {
        curr++;
        ct = -1;
      }
      if (ct == -1) {
        ct = 0;
        mm.clear();
      }
      posy = (lower_bound(b.begin(), b.end(), p[i].second) - b.begin());
      posx = (lower_bound(a.begin(), a.end(), p[i].first) - a.begin());
      if (b[posy] == p[i].second) {
        ct = 0;
        mm.clear();
      } else {
        ans += (ct - mm[posx]);
        ct++;
        mm[posx]++;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const long long int mod = 998244353;
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int binpow(long long int x, long long int y, long long int m) {
  if (y == 0) return 1;
  long long int p = binpow(x, y / 2, m) % m;
  p = (p * p) % m;
  if (y % 2)
    return (x * p) % m;
  else
    return p;
}
long long int modi(long long int a, long long int m) {
  return binpow(a, m - 2, m);
}
long long int query(long long int tree[], long long int l, long long int r) {
  long long int ans = 0;
  while (l < r) {
    if (l % 2) {
      ans += tree[l];
      l++;
    }
    if (r % 2) {
      r--;
      ans += tree[r];
    }
    l /= 2;
    r /= 2;
  }
  return ans;
}
long long int find_set(long long int v, long long int parent[]) {
  if (v == parent[v]) return v;
  return parent[v] = find_set(parent[v], parent);
}
void union_sets(long long int a, long long int b, long long int parent[]) {
  a = find_set(a, parent);
  b = find_set(b, parent);
  if (a != b) parent[b] = a;
}
long long int lca(long long int a, long long int b,
                  vector<vector<long long int>> &par, long long int depth[]) {
  if (depth[a] < depth[b]) swap(a, b);
  long long int diff = depth[a] - depth[b], ct = 0;
  while (diff) {
    if (diff % 2) {
      a = par[ct][a];
    }
    ct++;
    diff /= 2;
  }
  if (a == b) return a;
  for (long long int i = 19; i >= 0; i--) {
    if (par[i][a] != par[i][b]) {
      a = par[i][a];
      b = par[i][b];
    }
  }
  return par[0][a];
}
bool cmp1(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  if (a.first != b.first) return a.first < b.first;
  return a.second < b.second;
}
bool cmp2(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  if (a.second != b.second) return a.second < b.second;
  return a.first < b.first;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int i, j, tt = 1, tc;
  cin >> tt;
  for (tc = 1; tc <= tt; tc++) {
    long long int n, m, k, ans = 0;
    cin >> n >> m >> k;
    vector<long long int> a(n), b(m);
    vector<pair<long long int, long long int>> p(k);
    for (i = 0; i < n; i++) {
      cin >> a[i];
    }
    for (i = 0; i < m; i++) {
      cin >> b[i];
    }
    for (i = 0; i < k; i++) {
      cin >> p[i].first >> p[i].second;
    }
    sort(p.begin(), p.end(), cmp1);
    long long int ct = 0, posy, posx, prevy = -1, prevx = -1, curr = 0;
    map<long long int, long long int> mm;
    for (i = 0; i < k; i++) {
      while (a[curr] < p[i].first) {
        curr++;
        ct = -1;
      }
      if (ct == -1) {
        ct = 0;
        mm.clear();
      }
      posy = (lower_bound(b.begin(), b.end(), p[i].second) - b.begin());
      posx = (lower_bound(a.begin(), a.end(), p[i].first) - a.begin());
      if (a[posx] == p[i].first) {
        ct = 0;
        mm.clear();
      } else {
        ans += (ct - mm[posy]);
        ct++;
        mm[posy]++;
      }
    }
    ct = 0;
    sort(p.begin(), p.end(), cmp2);
    curr = 0;
    mm.clear();
    for (i = 0; i < k; i++) {
      while (b[curr] < p[i].second) {
        curr++;
        ct = -1;
      }
      if (ct == -1) {
        ct = 0;
        mm.clear();
      }
      posy = (lower_bound(b.begin(), b.end(), p[i].second) - b.begin());
      posx = (lower_bound(a.begin(), a.end(), p[i].first) - a.begin());
      if (b[posy] == p[i].second) {
        ct = 0;
        mm.clear();
      } else {
        ans += (ct - mm[posx]);
        ct++;
        mm[posx]++;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}

```