#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//!  dP     dP                          dP                    !//
//!  88     88                          88                    !//
//!  88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b.  !//
//!  88     88  88ooood8 88'  '88 88'  '88 88ooood8 88'  '88  !//
//!  88     88  88.  ... 88.  .88 88.  .88 88.  ... 88        !//
//!  dP     dP  '88888P' '88888P8 '88888P8 '88888P' dP        !//
//!===========================================================!//
template <typename T>
T read()
{
    T v;
    return std::cin >> v, v;
}
template <typename T>
std::vector<T> readVec(const std::size_t l)
{
    std::vector<T> v(l);
    for (auto& e : v) { std::cin >> e; }
    return v;
}
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template <typename T>
bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
constexpr T popCount(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
constexpr T log2p1(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
constexpr T lsbp1(const T v)
{
#ifdef __has_builtin
    return __builtin_ffsll(v);
#else
    return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); }
//!==============================================================================!//
//!  dP     dP          oo                       88888888b oo                dP  !//
//!  88     88                                   88                          88  !//
//!  88     88 88d888b. dP .d8888b. 88d888b.    a88aaaa    dP 88d888b. .d888b88  !//
//!  88     88 88'  '88 88 88'  '88 88'  '88     88        88 88'  '88 88'  '88  !//
//!  Y8.   .8P 88    88 88 88.  .88 88    88     88        88 88    88 88.  .88  !//
//!  'Y88888P' dP    dP dP '88888P' dP    dP     dP        dP dP    dP '88888P8  !//
//!==============================================================================!//
template <typename T>
class PotUnionFind
{
public:
    PotUnionFind(const std::size_t v) : V(v), parent(v), size(v, 1), potential(v, T{}) { std::iota(parent.begin(), parent.end(), 0); }
    std::size_t find(const std::size_t a)
    {
        assert(a < V);
        if (parent[a] == a) { return a; }
        const std::size_t r = find(parent[a]);
        return potential[a] += potential[parent[a]], parent[a] = r;
    }
    bool same(const std::size_t a, const std::size_t b)
    {
        assert(a < V), assert(b < V);
        return find(a) == find(b);
    }
    void unite(std::size_t a, std::size_t b, T w)
    {
        assert(a < V), assert(b < V);
        w += getPotential(a), w -= getPotential(b);
        a = find(a), b = find(b);
        if (a == b) { return; }
        if (size[a] < size[b]) { std::swap(a, b), w = -w; }
        size[a] += size[b], parent[b] = a, potential[b] = w;
    }
    std::size_t getSize(const std::size_t a) { return assert(a < V), size[find(a)]; }
    T getPotential(const std::size_t a) { return assert(a < V), find(a), potential[a]; }
    T diff(const std::size_t a, const std::size_t b) { return assert(a < V), assert(b < V), assert(same(a, b)), potential[b] - potential[a]; }
    friend std::ostream& operator<<(std::ostream& os, const PotUnionFind& uf)
    {
        os << "[";
        for (std::size_t i = 0; i < uf.parent.size(); i++) { os << uf.parent[i] << (i + 1 == uf.parent.size() ? "" : ","); }
        return (os << "]\n");
    }

private:
    const std::size_t V;
    std::vector<std::size_t> parent, size;
    std::vector<T> potential;
};
//!=====================================!//
//!  8888ba.88ba           oo           !//
//!  88  '8b  '8b                       !//
//!  88   88   88 .d8888b. dP 88d888b.  !//
//!  88   88   88 88'  '88 88 88'  '88  !//
//!  88   88   88 88.  .88 88 88    88  !//
//!  dP   dP   dP '88888P8 dP dP    dP  !//
//!=====================================!//
int main()
{
    const int R = read<int>(), C = read<int>();
    const int N = read<int>();
    using P = std::pair<int, ll>;
    auto cs = Vec(R, std::vector<P>{}), rs = Vec(C, std::vector<P>{});
    std::vector<int> r(N), c(N);
    std::vector<ll> a(N);
    for (int i = 0; i < N; i++) {
        std::cin >> r[i] >> c[i] >> a[i], r[i]--, c[i]--;
        cs[r[i]].push_back({c[i], a[i]}), rs[c[i]].push_back({r[i], a[i]});
    }
    for (int r = 0; r < R; r++) { std::sort(cs[r].begin(), cs[r].end()); }
    for (int c = 0; c < C; c++) { std::sort(rs[c].begin(), rs[c].end()); }
    PotUnionFind<ll> ruf(R), cuf(C);
    for (int r = 0; r < R; r++) {
        for (int i = 1; i < cs[r].size(); i++) {
            const P p1 = cs[r][i - 1], p2 = cs[r][i];
            const int c1 = p1.first, c2 = p2.first;
            const ll a1 = p1.second, a2 = p2.second;
            if (cuf.same(c1, c2) and cuf.diff(c1, c2) != a2 - a1) { return std::cout << "No" << std::endl, 0; }
            cuf.unite(c1, c2, a2 - a1);
        }
    }
    for (int c = 0; c < C; c++) {
        for (int i = 1; i < rs[c].size(); i++) {
            const P p1 = rs[c][i - 1], p2 = rs[c][i];
            const int r1 = p1.first, r2 = p2.first;
            const ll a1 = p1.second, a2 = p2.second;
            if (ruf.same(r1, r2) and ruf.diff(r1, r2) != a2 - a1) { return std::cout << "No" << std::endl, 0; }
            ruf.unite(r1, r2, a2 - a1);
        }
    }
    std::vector<bool> used(C, false);
    std::vector<std::vector<int>> rc(R), cc(C);
    for (int r = 0; r < R; r++) { rc[ruf.find(r)].push_back(r); }
    for (int c = 0; c < C; c++) { cc[cuf.find(c)].push_back(c); }
    for (int i = 0; i < N; i++) {
        if (used[cuf.find(c[i])]) { continue; }
        used[cuf.find(c[i])] = true;
        ll cmin = 0, rmin = 0;
        for (std::size_t nc : cc[cuf.find(c[i])]) { chmin(cmin, cuf.diff(c[i], nc)); }
        for (std::size_t nr : rc[ruf.find(r[i])]) { chmin(rmin, ruf.diff(r[i], nr)); }
        const ll min = a[i] + cmin + rmin;
        if (min < 0) { return std::cout << "No" << std::endl, 0; }
    }
    std::cout << "Yes" << std::endl;
    return 0;
}


Measured memory_bytes: 28416