Problem: Kris works in a large company "Blake Technologies". As a best engineer of the company he was assigned a task to develop a printer that will be able to print horizontal and vertical strips. First prototype is already built and Kris wants to tests it. He wants you to implement the program that checks the result of the printing.

Printer works with a rectangular sheet of paper of size n × m. Consider the list as a table consisting of n rows and m columns. Rows are numbered from top to bottom with integers from 1 to n, while columns are numbered from left to right with integers from 1 to m. Initially, all cells are painted in color 0.

Your program has to support two operations: 

  1. Paint all cells in row ri in color ai; 
  2. Paint all cells in column ci in color ai. 



If during some operation i there is a cell that have already been painted, the color of this cell also changes to ai.

Your program has to print the resulting table after k operation.

Input

The first line of the input contains three integers n, m and k (1 ≤ n, m ≤ 5000, n·m ≤ 100 000, 1 ≤ k ≤ 100 000) — the dimensions of the sheet and the number of operations, respectively.

Each of the next k lines contains the description of exactly one query: 

  * 1 ri ai (1 ≤ ri ≤ n, 1 ≤ ai ≤ 109), means that row ri is painted in color ai; 
  * 2 ci ai (1 ≤ ci ≤ m, 1 ≤ ai ≤ 109), means that column ci is painted in color ai. 

Output

Print n lines containing m integers each — the resulting table after all operations are applied.

Examples

Input

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


Output

3 1 3 
2 2 2 
0 1 0 


Input

5 3 5
1 1 1
1 3 1
1 5 1
2 1 1
2 3 1


Output

1 1 1 
1 0 1 
1 1 1 
1 0 1 
1 1 1 

Note

The figure below shows all three operations for the first sample step by step. The cells that were painted on the corresponding step are marked gray. 

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;

public class Main {

    static MyScanner   in;
    static PrintWriter out;
//    static Timer timer = new Timer();

    public static void main(String[] args) throws IOException {
        in = new MyScanner();
        out = new PrintWriter(System.out, false);

        int n = in.nextInt(), m = in.nextInt();
        int k = in.nextInt();

        int[] hor = new int[n], hor_k = new int[n];
        int[] ver = new int[m], ver_k = new int[m];

        for (int i = 1; i <= k; i++) {
            int dir = in.nextInt(), r = in.nextInt(), a = in.nextInt();

            if (dir == 1) {
                hor[r-1] = a;
                hor_k[r-1] = i;
            }
            else {
                ver[r-1] = a;
                ver_k[r-1] = i;
            }
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (hor_k[i] == 0 && ver_k[j] == 0)
                    out.print("0 ");
                else if (hor_k[i] > ver_k[j])
                    out.print(hor[i] + " ");
                else
                    out.print(ver[j] + " ");
            }
            out.println();
        }

        out.flush();
    }
}

class MyScanner {

    private final BufferedReader  br;
    private       StringTokenizer st;
    private       String          last;

    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public MyScanner(String path) throws IOException {
        br = new BufferedReader(new FileReader(path));
    }

    public MyScanner(String path, String decoder) throws IOException {
        br = new BufferedReader(new InputStreamReader(new FileInputStream(path), decoder));
    }

    String next() throws IOException {
        while (st == null || !st.hasMoreElements())
            st = new StringTokenizer(br.readLine());
        last = null;
        return st.nextToken();
    }

    String nextLine() throws IOException {
        st = null;
        return (last == null) ? br.readLine() : last;
    }

    boolean hasNext() {
        if (st != null && st.hasMoreElements())
            return true;

        try {
            while (st == null || !st.hasMoreElements()) {
                last = br.readLine();
                st = new StringTokenizer(last);
            }
        }
        catch (Exception e) {
            return false;
        }

        return true;
    }

    String[] nextStrings(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = next();
        return arr;
    }

    String[] nextLines(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLine();
        return arr;
    }

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

    int[] nextInts(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    Integer[] nextIntegers(int n) throws IOException {
        Integer[] arr = new Integer[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    int[][] next2Ints(int n, int m) throws IOException {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextInt();
        return arr;
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    long[] nextLongs(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

    long[][] next2Longs(int n, int m) throws IOException {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextLong();
        return arr;
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next().replace(',', '.'));
    }

    double[] nextDoubles(int size) throws IOException {
        double[] arr = new double[size];
        for (int i = 0; i < size; i++)
            arr[i] = nextDouble();
        return arr;
    }

    boolean nextBool() throws IOException {
        String s = next();
        if (s.equalsIgnoreCase("true") || s.equals("1"))
            return true;

        if (s.equalsIgnoreCase("false") || s.equals("0"))
            return false;

        throw new IOException("Boolean expected, String found!");
    }
}