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.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {

    private static final long INF = Integer.MAX_VALUE;
    private static final int R = 0;
    private static final int C = 1;
    private Graph g = new Graph();
    private Map<Integer, Long> nodeCost = new HashMap<>();
    private boolean ans = true;

    private void solve() {
        FastScanner sc = new FastScanner();
        int rMax = sc.nextInt();
        int cMax = sc.nextInt();
        int n = sc.nextInt();
        for (int i = 0; i < n; i++) {
            g.addEdgeUndirected(R, sc.nextInt(), C, sc.nextInt(), sc.nextInt());
        }
        for (Map.Entry<Long, Integer> e : g.getIdMap().entrySet()) {
            int i = e.getValue();
            if (nodeCost.containsKey(i)) continue;
            int rc = Graph.getFst(e.getKey());
            Pair p = dfs(i, 0, rc);
            ans &= p.fst + p.snd >= 0;
        }
        System.out.println(ans ? "Yes" : "No");
    }

    private Pair dfs(int i, long c, int rc) {
        nodeCost.put(i, c);
        Pair p = new Pair(rc == R ? c : INF, rc == C ? c : INF);
        for (long next : g.getNext(i)) {
            int j = Graph.getFst(next);
            long a = Graph.getSnd(next);
            if (nodeCost.containsKey(j)) {
                long d = nodeCost.get(j);
                ans &= d + c == a;
            } else {
                Pair q = dfs(j, a - c, 1 - rc);
                p.fst = Math.min(p.fst, q.fst);
                p.snd = Math.min(p.snd, q.snd);
            }
        }
        ans &= true;
        return p;
    }

    public static void main(String[] args) {
        new Main().solve();
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte()) return buffer[ptr++];
        else return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}

class Pair {

    long fst;
    long snd;

    Pair(long fst, long snd) {
        this.fst = fst;
        this.snd = snd;
    }

}

class Graph {

    private Map<Long, Integer> idMap;
    private List<List<Long>> assoc;

    public static class Builder {
        List<List<Long>> assoc;
        List<List<Integer>> edges;
        int v;

        boolean undirected = false;

        public Builder(int v, List<List<Integer>> edges) {
            this.v = v;
            this.edges = edges;
        }

        public Builder toUndirected() {
            undirected = true;
            return this;
        }

        public Graph build() {
            assoc = new ArrayList<>();
            for (int i = 0; i < v; i++) assoc.add(new ArrayList<>());
            for (List<Integer> edge : edges) {
                assoc.get(edge.get(0)).add(iToL(edge.get(1), edge.get(2)));
                if (undirected) assoc.get(edge.get(1)).add(iToL(edge.get(0), edge.get(2)));
            }
            return new Graph(assoc, new HashMap<>());
        }

    }

    public Graph() {
        idMap = new HashMap<>();
        assoc = new ArrayList<>();
    }

    public Graph(List<List<Long>> assoc, Map<Long, Integer> idMap) {
        this.assoc = assoc;
        this.idMap = idMap;
    }

    public List<Long> getNext(int s) {
        return assoc.get(s);
    }

    public void addEdge(int s, int t, int w) {
        assoc.get(s).add(iToL(t, w));
    }

    public void addEdgeUndirected(int s, int t, int w) {
        assoc.get(s).add(iToL(t, w));
        assoc.get(t).add(iToL(s, w));
    }

    public void addEdge(int s1, int s2, int t1, int t2, int w) {
        assoc.get(toId(s1, s2)).add(iToL(toId(t1, t2), w));
    }

    public void addEdgeUndirected(int s1, int s2, int t1, int t2, int w) {
        int s = toId(s1, s2);
        int t = toId(t1, t2);
        addEdgeUndirected(s, t, w);
    }

    private int toId(int fst, int snd) {
        long lid = iToL(fst, snd);
        Integer id = idMap.get(lid);
        if (id == null) {
            idMap.put(lid, id = idMap.size());
            assoc.add(new ArrayList<>());
        }
        return id;
    }

    public static long iToL(int fst, int snd) {
        return ((long) (fst) << 32) | (long) snd & 0xffffffffL;
    }

    public static int getElem(long edge) {
        return (int) (edge >> 32);
    }

    public static int getCost(long edge) {
        return (int) (edge & 0xffffffffL);
    }

    public static int getFst(long intPair) {
        return (int) (intPair >> 32);
    }

    public static int getSnd(long intPair) {
        return (int) (intPair & 0xffffffffL);
    }

    public Map<Long, Integer> getIdMap() {
        return idMap;
    }

    public List<List<Long>> getAssoc() {
        return assoc;
    }

    public String toString() {
        StringBuilder sb = new StringBuilder("assoc: [\n");
        for (int i = 0; i < assoc.size(); i++) {
            sb.append("  ").append(i).append(": [ ");
            for (long e : assoc.get(i)) {
                sb.append("(").append(getElem(e)).append(", ").append(getCost(e)).append(") ");
            }
            sb.append("]\n");
        }
        sb.append("]");
        return sb.toString();
    }
}