class WeightedUnionFind:
    # https://qiita.com/drken/items/cce6fc5c579051e64fab
    def __init__(self, n, SUM_UNITY=0):
        self.par = list(range(n))
        self.rank = [0] * n
        self.diff_weight = [SUM_UNITY] * n

    def root(self, x):
        p = self.par[x]
        if p == x:
            return x
        else:
            r = self.root(p)
            self.diff_weight[x] += self.diff_weight[p]
            self.par[x] = r
            return r

    def weight(self, x):
        self.root(x)
        return self.diff_weight[x]

    def same(self, x, y):
        return self.root(x) == self.root(y)

    def unite(self, x, y, w):
        if self.same(x, y):
            return self.diff(x, y) == w
        w += self.weight(x);  w -= self.weight(y)
        x, y = self.root(x), self.root(y)
        # if x == y:
        #     return False
        if self.rank[x] < self.rank[y]:
            x, y = y, x
            w = -w
        if self.rank[x] == self.rank[y]:
            self.rank[x] += 1
        self.par[y] = x
        self.diff_weight[y] = w
        return True

    def diff(self, x, y):
        return self.weight(y) - self.weight(x)

    def get_roots_weights(self):
        roots = []
        weights = []
        for x in range(len(self.par)):
            roots.append(self.root(x))
            weights.append(self.weight(x))
        return roots, weights

import sys
from operator import itemgetter
from itertools import groupby
from collections import defaultdict

def main():
    R, C = map(int, input().split())
    N = int(input())
    RCA = list(zip(*[iter(map(int, sys.stdin.read().split()))]*3))
    uf_r = WeightedUnionFind(R+1)
    uf_c = WeightedUnionFind(C+1)

    RCA.sort(key=itemgetter(0))
    for _, g in groupby(RCA, key=itemgetter(0)):
        _, c0, a0 = next(g)
        for _, c, a in g:
            if not uf_c.unite(c0, c, a-a0):
                print("No")
                exit()

    RCA.sort(key=itemgetter(1))
    for _, g in groupby(RCA, key=itemgetter(1)):
        r0, _, a0 = next(g)
        for r, _, a in g:
            if not uf_r.unite(r0, r, a-a0):
                print("No")
                exit()

    r_roots, r_weights = uf_r.get_roots_weights()
    c_roots, c_weights = uf_c.get_roots_weights()
    r_roots_inv = defaultdict(list)
    for i, r in enumerate(r_roots):
        r_roots_inv[r].append(i)
    c_roots_inv = defaultdict(list)
    for i, r in enumerate(c_roots):
        c_roots_inv[r].append(i)
    Closed_r = set()
    Closed_c = set()
    for r, c, a in RCA:
        root_r, root_c = r_roots[r], c_roots[c]
        if root_r in Closed_r:
            assert root_c in Closed_c
            continue
        Closed_r.add(root_r)
        Closed_c.add(root_c)
        mi = float("inf")
        for v in r_roots_inv[root_r]:
            mi = min(mi, r_weights[v])
        a += mi - r_weights[root_r]
        for v in c_roots_inv[root_c]:
            a_ = a + c_weights[v] - c_weights[root_c]
            if a_ < 0:
                print("No")
                exit()
    assert False
    print("Yes")

main()


### FIXED CODE ###

# 重み付き UnionFind を初めて書いた


class WeightedUnionFind:
    # https://qiita.com/drken/items/cce6fc5c579051e64fab
    def __init__(self, n, SUM_UNITY=0):
        self.par = list(range(n))
        self.rank = [0] * n
        self.diff_weight = [SUM_UNITY] * n

    def root(self, x):
        p = self.par[x]
        if p == x:
            return x
        else:
            r = self.root(p)
            self.diff_weight[x] += self.diff_weight[p]
            self.par[x] = r
            return r

    def weight(self, x):
        self.root(x)
        return self.diff_weight[x]

    def same(self, x, y):
        return self.root(x) == self.root(y)

    def unite(self, x, y, w):
        if self.same(x, y):
            return self.diff(x, y) == w
        w += self.weight(x);  w -= self.weight(y)
        x, y = self.root(x), self.root(y)
        # if x == y:
        #     return False
        if self.rank[x] < self.rank[y]:
            x, y = y, x
            w = -w
        if self.rank[x] == self.rank[y]:
            self.rank[x] += 1
        self.par[y] = x
        self.diff_weight[y] = w
        return True

    def diff(self, x, y):
        return self.weight(y) - self.weight(x)

    def get_roots_weights(self):
        roots = []
        weights = []
        for x in range(len(self.par)):
            roots.append(self.root(x))
            weights.append(self.weight(x))
        return roots, weights

import sys
from operator import itemgetter
from itertools import groupby
from collections import defaultdict

def main():
    R, C = map(int, input().split())
    N = int(input())
    RCA = list(zip(*[iter(map(int, sys.stdin.read().split()))]*3))
    uf_r = WeightedUnionFind(R+1)
    uf_c = WeightedUnionFind(C+1)

    RCA.sort(key=itemgetter(0))
    for _, g in groupby(RCA, key=itemgetter(0)):
        _, c0, a0 = next(g)
        for _, c, a in g:
            if not uf_c.unite(c0, c, a-a0):
                print("No")
                exit()

    RCA.sort(key=itemgetter(1))
    for _, g in groupby(RCA, key=itemgetter(1)):
        r0, _, a0 = next(g)
        for r, _, a in g:
            if not uf_r.unite(r0, r, a-a0):
                print("No")
                exit()

    r_roots, r_weights = uf_r.get_roots_weights()
    c_roots, c_weights = uf_c.get_roots_weights()
    r_roots_inv = defaultdict(list)
    for i, r in enumerate(r_roots):
        r_roots_inv[r].append(i)
    c_roots_inv = defaultdict(list)
    for i, r in enumerate(c_roots):
        c_roots_inv[r].append(i)
    Closed_r = set()
    Closed_c = set()
    for r, c, a in RCA:
        root_r, root_c = r_roots[r], c_roots[c]
        if root_r in Closed_r:
            assert root_c in Closed_c
            continue
        Closed_r.add(root_r)
        Closed_c.add(root_c)
        mi = float("inf")
        for v in r_roots_inv[root_r]:
            mi = min(mi, r_weights[v])
        a += mi - r_weights[r]
        for v in c_roots_inv[root_c]:
            a_ = a + c_weights[v] - c_weights[c]
            if a_ < 0:
                print("No")
                exit()
    print("Yes")

main()