#include <bits/stdc++.h>
#define in(x) freopen(x, "r", stdin)
#define out(x) freopen(x, "w", stdout)
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
#define F first
#define S second
#define PB push_back
#define M ll(1e9 + 7)
#define sz(x) (ll)x.size()
#define N 100500
#define pri(x) cout << x << endl
#define endl '\n'
#define all(x) (x).begin(), (x).end()
#define _ << " " <<
using namespace std;
//typedef tree <ll, null_type, less_equal <ll> , rb_tree_tag, tree_order_statistics_node_update> ordered_set;
//using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef short int si;
typedef unsigned long long ull;
ll a[N];
int main()
{
istream::sync_with_stdio(0); ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n, k, x;
cin >> n >> k >> x;
vector <int> vr; vr.clear();
vector <int> dob; dob.clear();
vector <int> del; del.clear();
vector <int> db; db.clear();
vector <int> dl; dl.clear();
for (int i = 0; i < n; i++)
{
int l, r, t;
cin >> l >> t >> r;
dob.PB(l);
del.PB(r + 1);
vr.PB(r);
if (l + t <= r)
{
db.PB(l + t);
dl.PB(r + 1);
}
}
sort(all(vr));
vector <int> al; al.clear();
vr.resize(unique(all(vr)) - vr.begin());
vector <pair <int, int> > beg; beg.clear();
vector <pair <int, int> > ed; ed.clear();
for (int i = 0; i < sz(vr); i++)
{
beg.PB({max(1, vr[i] - x + 1), i});
ed.PB({vr[i] + 1, i});
}
sort(all(beg));
sort(all(ed));
sort(all(dob));
sort(all(del));
sort(all(db));
sort(all(dl));
for (auto it : beg)
al.PB(it.F);
for (auto it : ed)
al.PB(it.F);
for (auto it : dob)
al.PB(it);
for (auto it : del)
al.PB(it);
for (auto it : db)
al.PB(it);
for (auto it : dl)
al.PB(it);
sort(all(al));
ll ans = 0, cur = 0;
int i1 = 0, i2 = 0, i3 = 0, i4 = 0, i5 = 0, i6 = 0;
int skok = 0, kol = 0;
int lst = 0;
for (auto x : al)
{
// pri(x _ cur);
int len = x - lst;
lst = x;
if (skok >= k)
cur += 1ll * len * kol;
while (i1 < sz(beg) && beg[i1].F == x)
{
a[beg[i1].S] = cur;
i1++;
}
while (i2 < sz(ed) && ed[i2].F == x)
{
ans = max(ans, cur - a[ed[i2].S]);
i2++;
}
while (i3 < sz(dob) && dob[i3] == x)
{
skok++;
i3++;
}
while (i4 < sz(del) && del[i4] == x)
{
skok--;
i4++;
}
while (i5 < sz(db) && db[i5] == x)
{
kol++;
i5++;
}
while (i6 < sz(dl) && dl[i6] == x)
{
kol--;
i6++;
}
}
pri(ans);
}
