There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).

Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.

Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.

* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.



Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.

Constraints

* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9

Input

The input is given from Standard Input in the following format:


R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N


Output

Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.

Examples

Input

2 2
3
1 1 0
1 2 10
2 1 20


Output

Yes


Input

2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40


Output

No


Input

2 2
3
1 1 20
1 2 10
2 1 0


Output

No


Input

3 3
4
1 1 0
1 3 10
3 1 10
3 3 20


Output

Yes


Input

2 2
4
1 1 0
1 2 10
2 1 30
2 2 20


Output

No

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;


class UnionFind {
    private int[] table;
    private int[] rank;
    
    public UnionFind(int size) {
        this.table = new int[size];
        this.rank = new int[size];
        for (int i = 0; i < size; i ++) {
            this.table[i] = i;
            this.rank[i] = 1;
        }
    }

    public boolean isSame(int node1, int node2) {
        return find(node1) == find(node2);
    }

    public int find(int node) {
        if (table[node] == node) {
            return node;
        } else {
            return table[node] = find(table[node]);
        }
    }

    public void union(int node1, int node2) {
        int root1 = find(node1);
        int root2 = find(node2);
        
        if (rank[root1] < rank[root2]) {
            table[root1] = root2;
        } else if (rank[root1] > rank[root2]) {
            table[root2] = root1;
        } else if (root1 != root2) {
            table[root2] = root1;
            rank[root1] ++;
        }
    }
}


public class Main {
  private static void solve() {
    int R = ni();
    int C = ni();
    int N = ni();
    int[][] p = ntable(N, 3);
    Map<Integer, List<int[]>> map = new TreeMap<>();
    long[] cmin = new long[C];
    Arrays.fill(cmin, Long.MAX_VALUE);
    UnionFind uf = new UnionFind(C);

    for (int[] v : p) {
      v[0] --;
      v[1] --;
      if (!map.containsKey(v[0])) {
        map.put(v[0], new ArrayList<>());
      }
      map.get(v[0]).add(v);
      cmin[v[1]] = Math.min(cmin[v[1]], v[2]);
    }
    
    List<List<int[]>> g = new ArrayList<>();
    for (int i = 0; i < C; i ++) {
      g.add(new ArrayList<>());
    }

    for (List<int[]> list : map.values()) {
      Collections.sort(list, (o1, o2) -> o1[1] - o2[1]);
      int[][] array = list.stream().toArray(size -> new int[size][]);
      int m = array.length;
      
      for (int i = 0; i < m - 1 ; i ++) {
        int from = array[i][1];
        int to = array[i + 1][1];
        int d = array[i + 1][2] - array[i][2];
        g.get(from).add(new int[] {to, d});
        g.get(to).add(new int[] {from, -d});
        uf.union(from, to);
      }
    }
    
    long[] memo = new long[C];
    long[] min = new long[C];
    Arrays.fill(memo, Long.MIN_VALUE);
    Arrays.fill(min, Long.MAX_VALUE);
    for (int i = 0; i < C; i ++) {
      if (cmin[i] < Long.MAX_VALUE) {
        if (memo[i] == Long.MIN_VALUE) {
          if (!dfs(i, 0, memo, min, uf, g)) {
            System.out.println("No");
            return;
          }
        }
        if (min[uf.find(i)] - memo[i] + cmin[i] < 0) {
          System.out.println("No");
          return;
        }
      }
    }
    
    System.out.println("Yes");
  }
  
  private static boolean dfs(int now, long x, long[] memo, long[] min, UnionFind uf, List<List<int[]>> g) {
    if (memo[now] != Long.MIN_VALUE) {
      return memo[now] == x;
    }
    memo[now] = x;
    int root = uf.find(now);
    min[root] = Math.min(min[root], x);
    
    for (int[] v : g.get(now)) {
      boolean ret = dfs(v[0], x + v[1], memo, min, uf, g);
      if (!ret) return false;
    }
    return true;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}


