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:
/*
 * Remember a 6.0 student can know more than a 10.0 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 * I will become Candidate Master.
 * I will defeat Saurabh Anand.
 * Skills are Cheap,Passion is Priceless.
 */
import java.util.*;
import java.util.Map.Entry;
import java.io.*;

import static java.lang.System.out;
import static java.util.Arrays.*;
import static java.lang.Math.*;
public class ContestMain {
	private static Reader in=new Reader();
	private static StringBuilder ans=new StringBuilder();
	private static long MOD=1000000000+7;//10^9+7
	private static final int N=200000+7; //10^5+7
//	private static final double EPS=1e-9;
//	private static final int LIM=26;
//	private static final double PI=3.1415;
	private static ArrayList<Integer> v[]=new ArrayList[N];
//	private static int color[]=new int[N];
	private static boolean mark[]=new boolean[N];
//	private static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//	private static ArrayList<Pair> v[]=new ArrayList[N];
	private static long powmod(long x,long n){
		if(n==0||x==0)return 1;
		else if(n%2==0)return(powmod((x*x)%MOD,n/2));
		else return (x*(powmod((x*x)%MOD,(n-1)/2)))%MOD;
	}
	private static void shuffle(long [] arr) {
		for (int i = arr.length - 1; i >= 2; i--) {
			int x = new Random().nextInt(i - 1);
	        long temp = arr[x];
	        arr[x] = arr[i];
	        arr[i] = temp;
	    }
	 }
//	private static long gcd(long a, long b){
//		if(b==0)return a;
//		return gcd(b,a%b);
//	}
//	private static boolean check(int x,int y){
//		if((x>=0&&x<n)&&(y>=0&&y<m)&&mat[x][y]!='X'&&!visited[x][y])return true;
//		return false;
//	}
//	static class Node{
//		int left;
//		int right;
//		Node(){
//			left=0;
//			right=0;
//		}
//	}
	public static void main(String[] args) throws IOException{
		int n=in.nextInt();
		int h=in.nextInt();
		int m=in.nextInt();
		int l[]=new int[m];
		int r[]=new int[m];
		int c[]=new int[m];
		for(int i=0;i<m;i++){
			l[i]=in.nextInt();
			r[i]=in.nextInt();
			c[i]=in.nextInt();
		}
		int maxh;
		long pro=0;
		for(int i=1;i<=n;i++){
			maxh=h;
			for(int j=0;j<m;j++){
				if(i>=l[j]&&i<=r[j])maxh=min(maxh,c[j]);
			}
			pro+=maxh*maxh;
		}
		out.println(pro);
	}
	static class Pair<T> implements Comparable<Pair>{
		int l;
		int r;
		Pair(){
			l=0;
			r=0;
		}
		Pair(int k,int v){
			l=k;
			r=v;
		}
		@Override
		public int compareTo(Pair o) {
			if(o.l!=l)return (int) -(l-o.l);
			else return (int)(r-o.r);
		}
		//Fenwick tree question comparator
//		@Override
//		public int compareTo(Pair o) {
//			if(o.r!=r)return (int) (r-o.r);
//			else return (int)(l-o.l);
//		}
	}
	static class Reader{
        BufferedReader br;
        StringTokenizer st;
        public Reader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
     
                	st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}