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.math.BigInteger;
import java.util.*;
import java.util.stream.IntStream;

public class Solution implements Runnable {
    private void solve() throws IOException {
        //String str = nextToken();	
        int n = nextInt();
        int m = nextInt();

        int[][] matrix = new int[n][m];
        
        Map<String,Integer> map = new LinkedHashMap<String, Integer>();
        
        int k = nextInt();
        for (int i = 0; i < k; i++) {
        	String x = nextToken();
        	String y = nextToken();
        	int z = nextInt();
        	
        	String key = x + "," + y;
        	if (map.containsKey(key))
        		map.remove(key);
        	
        	map.put(key, z);
        }
        
        for (String key : map.keySet()) {
    		int num = Integer.valueOf(key.split(",")[1]) - 1;

        	if (key.split(",")[0].equals("1")) {
        		for (int i = 0; i < m; i++) {
        			matrix[num][i] = map.get(key);
        		}
        	}
        	else {
        		for (int i = 0; i < n; i++) {
        			matrix[i][num] = map.get(key);
        		}
        	}
        }
        
        for (int i = 0; i < n; i++) {
        	for (int j = 0; j < m; j++) {
        		writer.print(matrix[i][j]);
        		writer.print(" ");
        	}
        	writer.println();
        }
      
       
    }
    
    
    
    private static boolean isInt (String s) {
    	if (s.length() < 1)
    		return false;
    	else {
    		for (char c : s.toCharArray()) {
    			if (c < '0' || c > '9') {
    				return false;
    			}
    		}
    	}
    	
    	return true;
    }

    public static Comparable[] mergeSort(Comparable[] list) 
    {
        //If list is empty; no need to do anything
        if (list.length <= 1) {
            return list;
        }
         
        //Split the array in half in two parts
        Comparable[] first = new Comparable[list.length / 2];
        Comparable[] second = new Comparable[list.length - first.length];
        System.arraycopy(list, 0, first, 0, first.length);
        System.arraycopy(list, first.length, second, 0, second.length);
         
        //Sort each half recursively
        mergeSort(first);
        mergeSort(second);
         
        //Merge both halves together, overwriting to original array
        merge(first, second, list);
        return list;
    }
     
    private static void merge(Comparable[] first, Comparable[] second, Comparable[] result) 
    {
        //Index Position in first array - starting with first element
        int iFirst = 0;
         
        //Index Position in second array - starting with first element
        int iSecond = 0;
         
        //Index Position in merged array - starting with first position
        int iMerged = 0;
         
        //Compare elements at iFirst and iSecond, 
        //and move smaller element at iMerged
        while (iFirst < first.length && iSecond < second.length) 
        {
            if (first[iFirst].compareTo(second[iSecond]) < 0) 
            {
                result[iMerged] = first[iFirst];
                iFirst++;
            } 
            else
            {
                result[iMerged] = second[iSecond];
                iSecond++;
            }
            iMerged++;
        }
        //copy remaining elements from both halves - each half will have already sorted elements
        System.arraycopy(first, iFirst, result, iMerged, first.length - iFirst);
        System.arraycopy(second, iSecond, result, iMerged, second.length - iSecond);
    }

    public static void main(String[] args) {
        new Solution().run();
    }

    static class Node {
        String status;
        List<Node> children;
        boolean hasCat;
        int degree;

        public Node(boolean hasCat) {
            status = "white";
            children = new ArrayList<Node>();
            this.hasCat = hasCat;
        }

    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}