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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Queue;
import java.util.TreeMap;

public class Main {
	static ContestScanner in;static Writer out;public static void main(String[] args)
	{try{in=new ContestScanner();out=new Writer();Main solve=new Main();solve.solve();
	in.close();out.flush();out.close();}catch(IOException e){e.printStackTrace();}}
	static void dump(int[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	static void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d ",a[i]);out.println();}
	static void dump(long[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	static void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
	static long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	static String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	static void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
	static void sort(int[]a,int l){m_sort(a,0,l,new int[l]);}
	static void sort(int[]a,int l,int[]buf){m_sort(a,0,l,buf);}
	static void sort(int[]a,int s,int l,int[]buf){m_sort(a,s,l,buf);}
	static void m_sort(int[]a,int s,int sz,int[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
	} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
	static void sort(long[]a){m_sort(a,0,a.length,new long[a.length]);}
	static void sort(long[]a,int l){m_sort(a,0,l,new long[l]);}
	static void sort(long[]a,int l,long[]buf){m_sort(a,0,l,buf);}
	static void sort(long[]a,int s,int l,long[]buf){m_sort(a,s,l,buf);}
	static void m_sort(long[]a,int s,int sz,long[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];}
	static void swap(long[] a,int i,int j){final long t=a[i];a[i]=a[j];a[j]=t;}
	static void swap(int[] a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
	static int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
	{int l=-1,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	static int binarySearchSmallerMax(int[]a,int v,int l,int r)
	{int s=-1;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	@SuppressWarnings("unchecked")
	static List<Integer>[]createGraph(int n)
    {List<Integer>[]g=new List[n];for(int i=0;i<n;i++)g[i]=new ArrayList<>();return g;}
	void solve() throws IOException{
		int r = in.nextInt();
		int c = in.nextInt();
		int n = in.nextInt();
		int[] y = new int[n];
		int[] x = new int[n];
		int[] v = new int[n];
		for(int i=0; i<n; i++){
			y[i] = in.nextInt()-1;
			x[i] = in.nextInt()-1;
			v[i] = in.nextInt();
		}
		if(!ok(x, y, v, r, c)){
			System.out.println("No");
			return;
		}
	    if(!ok(y, x, v, c, r)){
	    	System.out.println("No");
	    	return;
	    }
//		if(-tmp+v[0]<0){
//			System.out.println("No");
//		}else{
			System.out.println("Yes");
//		}
	}
	
	boolean ok(int[] x, int[] y, int[] v, int r, int c){
		TreeMap<Integer, Group> xs = new TreeMap<>();
		final int n = y.length;
		for(int i=0; i<n; i++){
			Group g;
			if(xs.containsKey(y[i])){
				g = xs.get(y[i]);
			}else{
				g = new Group();
				xs.put(y[i], g);
			}
			g.list.add(new Pair(x[i], i));
		}
		TreeMap<Integer, Group> ys = new TreeMap<>();
		for(int i=0; i<n; i++){
			Group g;
			if(ys.containsKey(x[i])){
				g = ys.get(x[i]);
			}else{
				g = new Group();
				ys.put(x[i], g);
			}
			g.list.add(new Pair(y[i], i));
		}
		List<Group> xgs = new ArrayList<>();
		xgs.addAll(xs.values());
		List<Group> ygs = new ArrayList<>();
		ygs.addAll(ys.values());
		
		List<Integer>[] node = graph(xgs, ygs, n);
		int[] diff = new int[c];
		boolean[] see = new boolean[c];
		Queue<Integer> qu = new ArrayDeque<>(n);
		Queue<Integer> nq = new ArrayDeque<>(n);
		Queue<Integer> dq = new ArrayDeque<>(n);
		boolean[] seeY = new boolean[r];
		boolean[] used = new boolean[n];
		for(int i=0; i<n; i++){
			if(used[i]) continue;
			used[i] = true;
//			int next = i;
			nq.add(i);
			dq.add(0);
//			int preD = 0;
			long preDmax = 0;
			long dmax = 0;
			while(!nq.isEmpty()){
				int pd = dq.poll();
				preDmax = Math.max(preDmax, pd);
				qu.add(nq.poll());
				while(!qu.isEmpty()){
					int p = qu.poll();
					for(int np: node[p]){
						if(used[np]) continue;
						if(y[p] != y[np]){
							if(!seeY[y[np]]){
								seeY[y[np]] = true;
								nq.add(np);
								dq.add(pd+v[p]-v[np]);
								used[np] = true;
							}
							continue;
						}
						used[np] = true;
						if(see[x[np]]){
							if(v[np] != v[i]-diff[x[np]] - pd) return false;
						}else{
							see[x[np]] = true;
							diff[x[np]] = diff[x[p]] + v[p]-v[np];
							dmax = Math.max(dmax, diff[x[np]]);
						}
						qu.add(np);
					}
				}
			}
			if(-dmax-preDmax+v[i]<0) return false;
		}
		return true;
	}
	
	List<Integer>[] graph(List<Group> xs, List<Group> ys, int n){
		List<Integer>[] res = new List[n];
		for(int i=0; i<n; i++){
			res[i] = new ArrayList<>();
		}
		for(Group g: xs){
			g.init();
			List<Pair> list = g.list;
			int pre = list.get(0).b;
			for(int i=1; i<list.size(); i++){
				int id = list.get(i).b;
				res[pre].add(id);
				res[id].add(pre);
				pre = id;
			}
		}
		for(Group g: ys){
			g.init();
			List<Pair> list = g.list;
			int pre = list.get(0).b;
			for(int i=1; i<list.size(); i++){
				int id = list.get(i).b;
				res[pre].add(id);
				res[id].add(pre);
				pre = id;
			}
		}
		return res;
	}
}

class Group implements Comparable<Group>{
	List<Pair> list = new ArrayList<>();
	int top;
	void init(){
		top = list.get(0).a;
		Collections.sort(list);
	}
	@Override
	public int compareTo(Group o) {
		return top-o.top;
	}
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public MultiSet<T> merge(MultiSet<T> set)
	{MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}
@SuppressWarnings("serial")
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public OrderedMultiSet<T> merge(OrderedMultiSet<T> set)
	{OrderedMultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	while(!s.isEmpty()){l.add(s.firstEntry().getKey(),s.pollFirstEntry().getValue());}return l;}
}
class Pair implements Comparable<Pair>{
	int a,b;final int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
	public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
	public int hashCode(){return hash;}
	public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
	long time;public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print(){System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}