You are planning to build housing on a street. There are n spots available on the street on which you can build a house. The spots are labeled from 1 to n from left to right. In each spot, you can build a house with an integer height between 0 and h.

In each spot, if a house has height a, you can gain a^2 dollars from it.

The city has m zoning restrictions though. The i-th restriction says that if the tallest house from spots l_i to r_i is strictly more than x_i, you must pay a fine of c_i.

You would like to build houses to maximize your profit (sum of dollars gained minus fines). Determine the maximum profit possible.

Input

The first line contains three integers n,h,m (1 ≤ n,h,m ≤ 50) — the number of spots, the maximum height, and the number of restrictions, respectively.

Each of the next m lines contains four integers l_i, r_i, x_i, c_i (1 ≤ l_i ≤ r_i ≤ n, 0 ≤ x_i ≤ h, 1 ≤ c_i ≤ 5 000).

Output

Print a single integer denoting the maximum profit you can make.

Examples

Input


3 3 3
1 1 1 1000
2 2 3 1000
3 3 2 1000


Output


14


Input


4 10 2
2 3 8 76
3 4 7 39


Output


289

Note

In the first example, it's optimal to build houses with heights [1, 3, 2]. We get a gain of 1^2+3^2+2^2 = 14. We don't violate any restrictions, so there are no fees, so the total profit is 14 - 0 = 14.

In the second example, it's optimal to build houses with heights [10, 8, 8, 10]. We get a gain of 10^2+8^2+8^2+10^2 = 328, and we violate the second restriction for a fee of 39, thus the total profit is 328-39 = 289. Note that even though there isn't a restriction on building 1, we must still limit its height to be at most 10.
#include <bits/stdc++.h>
using namespace std;
const int M = 1000000007;
const int MM = 998244353;
template <typename T, typename U>
static inline void amin(T &x, U y) {
  if (y < x) x = y;
}
template <typename T, typename U>
static inline void amax(T &x, U y) {
  if (x < y) x = y;
}
template <typename flow_t = long long>
struct Dinic {
  struct FlowEdge {
    int v, u;
    flow_t cap, flow = 0;
    FlowEdge(int v, int u, flow_t cap) : v(v), u(u), cap(cap) {}
  };
  const flow_t flow_inf = numeric_limits<flow_t>::max() / 2;
  vector<FlowEdge> edges;
  vector<vector<int>> adj;
  int n, m = 0;
  int s, t;
  vector<int> level, ptr;
  queue<int> q;
  Dinic(int n, int s, int t) : n(n), s(s), t(t) {
    adj.resize(n + 1);
    level.resize(n + 1);
    ptr.resize(n + 1);
  }
  void add_edge(int v, int u, flow_t cap) {
    edges.emplace_back(v, u, cap);
    edges.emplace_back(u, v, 0);
    adj[v].push_back(m);
    adj[u].push_back(m + 1);
    m += 2;
  }
  bool bfs() {
    while (!q.empty()) {
      int v = q.front();
      q.pop();
      for (int id : adj[v]) {
        if (edges[id].cap - edges[id].flow < 1) continue;
        if (level[edges[id].u] != -1) continue;
        level[edges[id].u] = level[v] + 1;
        q.push(edges[id].u);
      }
    }
    return level[t] != -1;
  }
  flow_t dfs(int v, flow_t pushed) {
    if (pushed == 0) return 0;
    if (v == t) return pushed;
    for (int &cid = ptr[v]; cid < (int)adj[v].size(); cid++) {
      int id = adj[v][cid];
      int u = edges[id].u;
      if (level[v] + 1 != level[u] || edges[id].cap - edges[id].flow < 1)
        continue;
      flow_t tr = dfs(u, min(pushed, edges[id].cap - edges[id].flow));
      if (tr == 0) continue;
      edges[id].flow += tr;
      edges[id ^ 1].flow -= tr;
      return tr;
    }
    return 0;
  }
  flow_t flow() {
    flow_t f = 0;
    while (true) {
      fill(level.begin(), level.end(), -1);
      level[s] = 0;
      q.push(s);
      if (!bfs()) break;
      fill(ptr.begin(), ptr.end(), 0);
      while (flow_t pushed = dfs(s, flow_inf)) {
        f += pushed;
      }
    }
    return f;
  }
};
int _runtimeTerror_() {
  int n, h, m;
  cin >> n >> h >> m;
  Dinic<long long> flow(n * h + n + m + 10, 0, n * h + n + m + 2);
  int s = 0, t = n * h + n + m + 2;
  int cur = 1;
  vector<vector<int>> H(n + 1, vector<int>(h + 1, 0));
  for (int i = 1; i <= n; ++i)
    for (int j = 0; j <= h; ++j) H[i][j] = cur++;
  int ans = n * h * h;
  for (int i = 1; i <= n; ++i) flow.add_edge(s, H[i][0], 1e12);
  for (int i = 1; i <= n; ++i) {
    for (int j = h; j >= 1; --j) flow.add_edge(H[i][j], H[i][j - 1], 1e12);
    for (int j = 0; j <= h - 1; ++j) {
      flow.add_edge(H[i][j], H[i][j + 1], h * h - (j) * (j));
    }
  }
  --cur;
  assert(cur == n * (h + 1));
  for (int i = 1; i <= m; ++i) {
    int l, r, x, c;
    cin >> l >> r >> x >> c;
    ++x;
    flow.add_edge(i + cur, t, c);
    for (int j = l; j <= r; ++j)
      if (x <= h) flow.add_edge(H[j][x], i + cur, 1e12);
    assert(i + cur < t);
  }
  ans -= flow.flow();
  cout << ans << "\n";
  return 0;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) _runtimeTerror_();
  return 0;
}
