Problem: 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 will gain a^2 dollars from it.

The city has m zoning restrictions. The i-th restriction says that the tallest house from spots l_i to r_i (inclusive) must be at most x_i.

You would like to build houses to maximize your profit. Determine the maximum profit possible.

Input

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

Each of the next m lines contains three integers l_i, r_i, and x_i (1 ≤ l_i ≤ r_i ≤ n, 0 ≤ x_i ≤ h) — left and right limits (inclusive) of the i-th restriction and the maximum possible height in that range.

Output

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

Examples

Input


3 3 3
1 1 1
2 2 3
3 3 2


Output


14


Input


4 10 2
2 3 8
3 4 7


Output


262

Note

In the first example, there are 3 houses, the maximum height of a house is 3, and there are 3 restrictions. The first restriction says the tallest house between 1 and 1 must be at most 1. The second restriction says the tallest house between 2 and 2 must be at most 3. The third restriction says the tallest house between 3 and 3 must be at most 2.

In this case, it is optimal to build houses with heights [1, 3, 2]. This fits within all the restrictions. The total profit in this case is 1^2 + 3^2 + 2^2 = 14.

In the second example, there are 4 houses, the maximum height of a house is 10, and there are 2 restrictions. The first restriction says the tallest house from 2 to 3 must be at most 8. The second restriction says the tallest house from 3 to 4 must be at most 7.

In this case, it's optimal to build houses with heights [10, 8, 7, 7]. We get a profit of 10^2+8^2+7^2+7^2 = 262. Note that there are two restrictions on house 3 and both of them must be satisfied. Also, note that even though there isn't any explicit restrictions on house 1, we must still limit its height to be at most 10 (h=10).

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
public class _p001162A {
    static public void main(final String[] args) throws IOException {
        p001162A._main(args);
    }
//begin p001162A.java
static private class p001162A extends Solver{public p001162A(){nameIn="p001162A.in"
;singleTest=true;}int n;int h;int m;Cy0[]f0;@Override protected void solve(){int
profit=0;for(int[]i=new int[]{1};i[0]<=n;i[0]++){int max=Math.min(h,Arrays.stream
(f0).filter(v->v.l<=i[0]&&v.r>=i[0]).mapToInt(v->v.x).min().orElse(h));profit+=max
*max;}pw.println(profit);}static class Cy0{int l;int r;int x;}@Override public void
readInput()throws IOException{n=sc.nextInt();h=sc.nextInt();m=sc.nextInt();if(sc
.hasNextLine()){sc.nextLine();}f0=new Cy0[m];for(int _if0=0;_if0<m;_if0++){f0[_if0
]=new Cy0();f0[_if0].l=sc.nextInt();f0[_if0].r=sc.nextInt();f0[_if0].x=sc.nextInt
();if(sc.hasNextLine()){sc.nextLine();}}}static public void _main(String[]args)throws
IOException{new p001162A().run();}}
//end p001162A.java
//begin net/leksi/contest/Solver.java
static private abstract class Solver{protected String nameIn=null;protected String
nameOut=null;protected boolean singleTest=false;protected boolean preprocessDebug
=false;protected boolean doNotPreprocess=false;protected Scanner sc=null;protected
PrintWriter pw=null;private void process()throws IOException{if(!singleTest){int
t=lineToIntArray()[0];while(t-->0){readInput();solve();}}else{readInput();solve(
);}}abstract protected void readInput()throws IOException;abstract protected void
solve()throws IOException;protected int[]lineToIntArray()throws IOException{return
Arrays.stream(sc.nextLine().trim().split("\\s+")).mapToInt(Integer::valueOf).toArray
();}protected long[]lineToLongArray()throws IOException{return Arrays.stream(sc.nextLine
().trim().split("\\s+")).mapToLong(Long::valueOf).toArray();}protected String intArrayToString
(final int[]a){return Arrays.stream(a).mapToObj(Integer::toString).collect(Collectors
.joining(" "));}protected String longArrayToString(final long[]a){return Arrays.stream
(a).mapToObj(Long::toString).collect(Collectors.joining(" "));}protected List<Long>
longArrayToList(final long[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect
(Collectors.toList());}protected List<Integer>intArrayToList(final int[]a){return
Arrays.stream(a).mapToObj(Integer::valueOf).collect(Collectors.toList());}protected
List<Long>intArrayToLongList(final int[]a){return Arrays.stream(a).mapToObj(Long
::valueOf).collect(Collectors.toList());}protected void run()throws IOException{
try{try(FileInputStream fis=new FileInputStream(nameIn);PrintWriter pw0=select_output
();){sc=new Scanner(fis);pw=pw0;process();}}catch(IOException ex){try(PrintWriter
pw0=select_output();){sc=new Scanner(System.in);pw=pw0;process();}}}private PrintWriter
select_output()throws FileNotFoundException{if(nameOut !=null){return new PrintWriter
(nameOut);}return new PrintWriter(System.out);}}
//end net/leksi/contest/Solver.java
}