#include <bits/stdc++.h>
#include <omp.h>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;


#define int ll
#define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());


typedef pair<int, int> pii;
typedef pair<string, string> pst;
typedef pair<pii, pii> piii;
typedef vector<piii> vpii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector< vi > vvi;
typedef vector< vvi > vvvi;
typedef vector<pii> vpi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;
typedef pair<pld, pld> pldd;
typedef vector<pld> vpd;
typedef complex<double> base;


#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define my_abs(a) (((a) >= 0) ? (a) : -(a))
#define mp(a, b) make_pair(a, (b))
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for(int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define MODIK(a) (a >= M ? a - M : a)
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cout << (#x) << " = " << x << endl;
#ifdef ART_HOME
#define cerr cout
#else
#define cerr if (false) cerr
#endif


const double PI = 2 * acos(0.0);

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

istream &operator >> (istream &in, pii &a)
{
    in >> a.first >> a.second;
    return in;
}


ostream &operator << (ostream &out, pii &a)
{
    out << a.first << ' ' << a.second;
    return out;
}


istream &operator >> (istream &in, pld &a)
{
    in >> a.first >> a.second;
    return in;
}


ostream &operator << (ostream &out, pld &a)
{
    out << a.first << ' ' << a.second;
    return out;
}


template <class T0, class T1>
inline ostream & operator << (ostream &out, pair<T0, T1> &a) {
    return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1, class T2>
inline ostream & operator << (ostream &out, tuple<T0, T1, T2> &a) {
    return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream & operator << (ostream &out, tuple<T0, T1, T2, T3> &a) {
    return out << "{" << get<0>(a) << ", " << get<1>(a) <<
               ", " << get<2>(a) << ", " <<  get<3>(a) << "}";
}

template<class T>
inline ostream & operator << (ostream &out, vector<T> &a) {
    out << "[";
    fori (i, a.size())
        out << a[i] << vector<string>{", ", "]  "}[i + 1 == a.size()];
    return out;
}


void print(int a, int b, int n, vi h)
{
    ofstream cout("output.txt");
    cout << SZ(h) << ' ' << a << ' ' << b << '\n';
    for (int i = 0; i < SZ(h); ++i) {
        cout << h[i]  << ' ';
    }
    cout.close();
    exit(0);
}


inline bool break_time(ld time)
{
    return clock() > CLOCKS_PER_SEC * time;
}


void bonds()
{
    ld price, nkd, kd, year;
    int cnt;
    cout << "price nkd kd cnt year\n";
    cout << endl;
    cin >> price >> nkd >> kd >> cnt >> year;
    cout << 100 * ((1000 + kd * cnt - price * 10 - nkd) / (price * 10) / year);
}


ld get_rand_ld(ld l, ld r)
{
    uniform_real_distribution<double> gen(l, r);
    return gen(rng);
}


bool may(int E, ld T)
{
    if (E < 0)
        return 1;

    double eps = get_rand_ld(0, 1);
    return eps < exp(-E / T);
}


void smain();

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

#ifdef ART_HOME
    freopen("input.txt", "r", stdin);
    clock_t start = clock();
#endif
    cout << setprecision(2) << fixed;
    smain();
#ifdef ART_HOME
    cout << "\nTOTAL EXECUTIOn TIME: " << float( clock () - start ) /  CLOCKS_PER_SEC << endl;
#endif
}


const int N = 1e5 + 10, pw = 17, K = 2e3 + 10, B = 100, oo = 1e14, M = 1 << 14, LOG = 20;
const int M1 = 1000000093, x1 = 27162;
const int M2 = 1000000087, x2 = 241;
const ld pi = atan2(1, 0) * 2, EPS = 1e-9;


vpi col[N], str[N];
int used[N], val[N], gval[N], label = 1;
vpi g[N], g2[N];


void dfs(int v, int vl)
{
    used[v] = 1;
    val[v] = vl;

    for (pii p : g[v])
    {
        if (used[p.first])
        {
            if (val[p.first] != vl + p.second)
                label = 0;
        }
        else
            dfs(p.first, vl + p.second);
    }
}


void dfs_init(int v, int last = -1, int p = -1)
{
    used[v] = 1;
    vpi hui;

    for (auto p : g[v])
    {
        if (used[p.first])
        {
            hui.push_back(p);
        }
        else
        {
            g2[v].push_back(p);
            dfs_init(p.first, p.second, v);
        }
    }
}


int dp_down[N];


void dfs_down(int v, int p = -1)
{
    used[v] = 1;
    dp_down[v] = 0;

    for (auto p : g2[v])
        dfs_down(p.first, v);

    for (auto p : g2[v])
        dp_down[v] = min(dp_down[v], dp_down[p.first] + p.second);
}


bool dfs_up(int v, int p = -1, int dp_up = 0, int last = 0)
{
    int cval = dp_up + -last;
    if (min(cval, dp_down[v]) + gval[v] < 0)
        return 0;

    cval = dp_up + -last;
  	cval = min(cval, 0LL);
    vi hui, pr, sf;

    for (auto p : g2[v])
        hui.push_back(dp_down[p.first] + p.second);

    pr = hui, sf = hui;
    for (int i = 1; i < SZ(pr); ++i)
        pr[i] = min(pr[i], pr[i - 1]);

    for (int i = SZ(sf) - 2; i >= 0; --i)
        sf[i] = min(sf[i], sf[i + 1]);

    bool label = 1;
    for (int i = 0; i < SZ(g2[v]); ++i)
    {
        auto p = g2[v][i];
        int cnt = cval;
        if (i)
            cnt = min(cnt, pr[i - 1]);

        if (i + 1 != SZ(g2[v]))
            cnt = min(cnt, sf[i + 1]);

        label = min(label, dfs_up(p.first, v, cnt, p.second));
    }

    return label;
}


void smain() {
    int r, c, n;
    cin >> r >> c >> n;

    for (int i = 0; i < N; ++i)
        gval[i] = oo;

    for (int i = 0; i < n; ++i) {
        int r, c, v;
        cin >> r >> c >> v;
        str[r].push_back(mp(c, v));
        col[c].push_back(mp(r, v));
        gval[r] = min(gval[r], v);
    }

    for (int i = 0; i < N; ++i) {
        stable_sort(ALL(str[i]));
        stable_sort(ALL(col[i]));
    }

    for (int i = 0; i < N; ++i) {
        for (int j = 1; j < SZ(col[i]); ++j) {
            pii a = col[i][j - 1], b = col[i][j];
            g[a.first].push_back(mp(b.first, b.second - a.second));
            g[b.first].push_back(mp(a.first, a.second - b.second));
        }
    }

    for (int i = 1; i <= r; ++i) {
        if (!used[i])
            dfs(i, 0);
    }

    if (!label) {
        cout << "No\n";
        return;
    }

    fill(used, used + N, 0);
    for (int i = 1; i <= r; ++i) {
        if (!used[i])
            dfs_init(i);
    }

    fill(used, used + N, 0);
    for (int i = 1; i <= r; ++i) {
        if (!used[i]) {
            dfs_down(i);
            if (gval[i] + dp_down[i] < 0)
                label = 0;

            if (!dfs_up(i))
                label = 0;
        }
    }

    if (label)
    {
        cout << "Yes\n";
    }
    else {
        cout << "No\n";
    }
}


Measured memory_bytes: 39068