#include<bits/stdc++.h>
using namespace std;
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/tree_policy.hpp>
//
// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("-O3")
// #pragma GCC optimize("no-stack-protector")
// #pragma GCC optimize("fast-math")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
//#define LOCAL
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifndef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it)
*this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define fi first
#define f first
#define se second
#define s second
#define vi_a vector<int>a;
#define p_b push_back
////////////////////////////////???????????????CHECK THIS OUT???????????????//////////////////////////////
#define ll long long
typedef unsigned long long ull;
////////////////////////////////???????????????CHECK THIS OUT???????????????//////////////////////////////
#define ld long double
#define pll pair<ll,ll>
#define pii pair<int,int>
#define m_p make_pair
#define fast_io cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);
#define all(x) x.begin(),x.end()
#define getfiles ifstream cin("input.txt");ofstream cout("output.txt");
#define pw(x) (1ll << x)
#define sz(x) (int)x.size()
#define endl "\n"
#define rall(x) x.rbegin(),x.rend()
#define len(a) (ll)a.size()
#define rep(x,l,r) for(ll x=l;x<r;x++)
//using namespace __gnu_pbds;
ld eps = (ld)1 / 1e6;
const ld pi=3.14159265359;
ll inf = 1e18,mod1=1e9+7;
ll sqr(ll a) { return a * a; }
ll qb(ll a) { return a * a * a; }
void umin(int &a,int b){a=min(a,b);}
bool is_prime(ll val){for(ll i=2;i<=sqrt(val);i++)if(val%i==0)return 0; return 1;}
ll gcd(ll a, ll b) { return !a ? b : gcd(b % a, a); }
ll binpow(ll a, ll b, ll mod) { return b ? (b % 2 ? (a * (sqr(binpow(a, b / 2, mod)) % mod)) % mod : sqr(binpow(a, b / 2, mod)) % mod) : 1; }
ll binmult(ll a, ll b, ll mod) { return b ? (b % 2 ? (2 * binmult(a, b / 2, mod) + a) % mod : (2 * binmult(a, b / 2, mod)) % mod) : 0; }
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
const ll tx[4]={0,1,-1,1};
const ll ty[4]={-1,0,1,1};
const char rev_to[4]={'E','W','N','S'};
int M=1e9;
const int N=1e6+2;
const int pp=73;
const int lg=19;
const int OPEN=1;
const int CLOSE=0;
//typedef tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update> st;
#define int ll
auto rnd=bind(uniform_int_distribution<ll>(1,N),mt19937(time(0)));
void bad(){
cout<<"NE";
exit(0);
}
struct stuff{
int l,r,mxval,cur,dmg,id;
stuff(int _l,int _r,int _mxval,int _dmg): mxval(_mxval),l(_l),r(_r),cur(0),dmg(_dmg) {}
};
struct fak{
int x,type,ind;
const operator <(const fak &other) const{
return (other.x==x ? (type==other.type ? ind<other.ind : type<other.type) : x<other.x);
}
};
fak ps[N];
vector<stuff>lol[N];
signed main()
{
// freopen("in.txt","r",stdin);
fast_io;
int n,m;
cin>>n>>m;
int q;
cin>>q;
int x,y,r;
for(int i=0;i<q;i++){
cin>>x>>y>>r;--x;--y;
ps[i+1].x=x;ps[i+1].type=y;ps[i+1].ind=r;
lol[y-r].emplace_back(x,x,r,i+1);
}
ll ans=1ll*q*n*m;
for(int i=0;i<=m;i++){
multiset<fak>st;
int j=0;
for(auto &z : lol[i]){
x=ps[z.dmg].x,y=ps[z.dmg].type,r=ps[z.dmg].ind;
while((z.l-x)*(z.l-x)+(i-y)*(i-y)>r*r) z.l++;
while((z.l-x-1)*(z.l-x-1)+(i-y)*(i-y)<=r*r ) z.l--;
while((z.r-x)*(z.r-x)+(i-y)*(i-y)>r*r) z.r--;
while((z.r-x+1)*(z.r-x+1)+(i-y)*(i-y)<=r*r) z.r++;
st.insert({lol[i][j].l,OPEN,j});
st.insert({lol[i][j].r+1,CLOSE,j});
// debug()<<imie(st);
j++;
}
set<int>pon;pon.insert(0);
int prev=st.begin()->x;
ll ss=0;
for(auto &z : st){
ss+=*pon.rbegin()*1ll*(z.x-prev);
if(z.type==CLOSE)pon.erase(lol[i][z.ind].dmg);
else {
pon.insert(lol[i][z.ind].dmg);
}
// debug()<<imie(i)<<imie(z.x)<<imie(z.type);
prev=z.x;
}
// debug()<<imie(i);
for(auto &z : lol[i]){
if(i-ps[z.dmg].type==z.mxval) continue;
lol[i+1].p_b(z);
}
ans-=ss;
}
cout<<ans;
return 0;
}
/*
3 3 1 0 3 3
3 1 0 0 0 3
1 1 1 0 1 3
3 1 1 1 2 2
3 3 1 2 2 3
3 3 3 2 3 3
*/
Compilation message
nlo.cpp: In constructor 'stuff::stuff(long long int, long long int, long long int, long long int)':
nlo.cpp:95:13: warning: 'stuff::mxval' will be initialized after [-Wreorder]
int l,r,mxval,cur,dmg,id;
^~~~~
nlo.cpp:95:9: warning: 'long long int stuff::l' [-Wreorder]
int l,r,mxval,cur,dmg,id;
^
nlo.cpp:96:5: warning: when initialized here [-Wreorder]
stuff(int _l,int _r,int _mxval,int _dmg): mxval(_mxval),l(_l),r(_r),cur(0),dmg(_dmg) {}
^~~~~
nlo.cpp: At global scope:
nlo.cpp:100:40: error: ISO C++ forbids declaration of 'operator<' with no type [-fpermissive]
const operator <(const fak &other) const{
^~~~~
