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.*;
import java.util.*;
public class Solution{
    
    static class BI{
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream dis;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        
        //********Constructors*********\\
        
        public BI() {
            dis = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public BI(String file_name) throws IOException {
            dis = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        
        //*******Reads a line until new line character************\\
        
        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
        
        //*******Reads a string Until First Space************\\
        
        public String nextString() throws IOException {
            // Skip all whitespace characters from the stream
            byte c = read();
            while(Character.isWhitespace(c)){
                c = read();
            }
            StringBuilder builder = new StringBuilder();
            builder.append((char)c);
            c = read();
            while(!Character.isWhitespace(c)){
                builder.append((char)c);
                c = read();
            }
            return builder.toString();
        }
        
        //*******Reads a Integer************\\
        
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
        
        //*******Reads a Integer************\\
        
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
        
        //*******Reads a Char************\\
        
        public char nextChar() throws IOException{
            byte c = read();
            while(Character.isWhitespace(c)){
                c = read();
            }
            return (char) c;
        }
        
        //*******Reads a Double************\\
        
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)
			return -ret;
			return ret;
        }
        
        //*******Reads an array of double values************\\
        
        public double[] nextDoubleArray(int n) throws IOException {
            double arr[] = new double[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextDouble();
            }
            return arr;
        }
        
        //*******Reads an array of long integers************\\
        
        public long[] nextLongArray(int n) throws IOException {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextLong();
            }
            return arr;
        }
        
        //*******Reads an array of Integers************\\
        
        public int[] nextIntArray(int n) throws IOException {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextInt();
            }
            return arr;
        }
        
        //*******Fills the buffer from input stream************\\
        
        private void fillBuffer() throws IOException {
            bytesRead = dis.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
            buffer[0] = -1;
        }
        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
            fillBuffer();
            return buffer[bufferPointer++];
        }
        public void close() throws IOException {
            if (dis == null) return;
            dis.close();
        }
        
    }
    
    
    //**********************CODE IS HERE*****************************\\
    
    
    
    public static void main(String args[])throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BI in=new BI();
        /*
        int a=in.nextInt();
        long b=in.nextLong();
        char c=in.nextChar();
        double d=in.nextDouble();
        int arr[]=in.nextIntArray(3);
        double drr[]=in.nextDoubleArray(6);
        long lrr[]=in.nextLongArray(4);
        String str=in.readLine();//line
        String ptr=in.nextString();//word
        */
        
        int n=in.nextInt();
        int h=in.nextInt();
        int m=in.nextInt();
        int arr[]=new int[n];
        Arrays.fill(arr,h);
        for(int i=0;i<m;i++){
            int xi=in.nextInt();
            int yi=in.nextInt();
            int hi=in.nextInt();
            for(int j=Math.max(xi-1,0);j<yi;j++){
                arr[j]=Math.min(arr[j],hi);
            }
        }
        int sum=0;
        for(int i=0;i<n;i++) sum+=arr[i]*arr[i];
        System.out.println(sum);
        
    }
}