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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.Random;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskG solver = new TaskG();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskG {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int h = in.nextInt();
            int m = in.nextInt();
            Constraint[] cs = new Constraint[m];
            for (int i = 0; i < m; i++) {
                Constraint c = new Constraint();
                c.l = in.nextInt() - 1;
                c.r = in.nextInt() - 1;
                c.x = in.nextInt();
                c.c = in.nextInt();
                cs[i] = c;
            }

            boolean stress = false;
//        boolean stress = true;
            if (stress) {
                Random random = new Random(0);
                final int N = 50;
                n = N;
                h = N;
                m = N;
                cs = new Constraint[m];
                for (int i = 0; i < m; i++) {
                    Constraint c = new Constraint();
                    c.r = random.nextInt(n);
                    c.l = random.nextInt(c.r + 1);
                    c.x = random.nextInt(h + 1);
                    c.c = random.nextInt();
                    cs[i] = c;
                }
            }

            Arrays.sort(cs, (u, v) -> (u.x - v.x));

            int[][][][] d = new int[n][n][h + 1][h + 1];
            for (int len = 1; len <= n; len++) {
                for (int l = 0; l + len <= n; l++) {
                    int r = l + len - 1;
                    for (int mid = l; mid <= r; mid++) {
                        int[][] f1 = new int[h + 1][h + 1];
                        int[][] f2 = new int[h + 1][h + 1];
                        int[] f3 = new int[h + 1];
                        for (int mh = 0; mh <= h; mh++) {
                            if (l < mid) {
                                for (int lh = mh; lh <= h; lh++) {
                                    f1[mh][lh] = d[l][mid - 1][lh][mh];
                                }
                            }
                            if (mid < r) {
                                for (int rh = mh; rh <= h; rh++) {
                                    f2[mh][rh] = d[mid + 1][r][mh][rh];
                                }
                            }
                        }
                        int ptr = 0;
                        int penalty = 0;
                        for (int mh = 0; mh <= h; mh++) {
                            while (ptr < cs.length && cs[ptr].x < mh) {
                                Constraint c = cs[ptr++];
                                if (c.fits(mid, mh) && c.l >= l && c.r <= r) {
                                    penalty += c.c;
                                }
                            }
                            f3[mh] = mh * mh - penalty;
                        }
                        for (int lh = 0; lh <= h; lh++) {
                            int cur = 0;
                            int mh = 0;
                            for (int rh = 0; rh <= h; rh++) {
                                while (mh <= lh && mh <= rh) {
                                    cur = Math.max(cur, f1[mh][lh] + f2[mh][rh] + f3[mh]);
                                    ++mh;
                                }
                                d[l][r][lh][rh] = Math.max(d[l][r][lh][rh], cur);
                            }
                        }
                    }
                }
            }
            out.println(d[0][n - 1][h][h]);
        }

        class Constraint {
            int l;
            int r;
            int x;
            int c;

            boolean fits(int coord, int height) {
                return coord >= l && coord <= r && height > x;
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}

