#include <bits/stdc++.h>
using namespace std;
int main() {
int N, K, X;
cin >> N >> K >> X;
vector l(N, 0), r(N, 0), t(N, 0);
for(int i = 0; i < N; i++) { cin >> l[i] >> t[i] >> r[i]; r[i]++; }
/* 座標圧縮用の座標 */
vector P(0, 0);
for(int i = 0; i < N; i++) { P.push_back(l[i]), P.push_back(r[i]); } /* 各区間の始点終点 */
for(int i = 0; i < N; i++) { if(l[i]+t[i] < r[i]) { P.push_back(l[i]+t[i]); } } /* 追加料金のかかる区間の始点 */
sort(begin(P), end(P));
P.erase(unique(begin(P), end(P)), end(P));
map<int, int> mp2;
for(int i = 0; i < (int)size(P); i++) { mp2[P[i]] = 1; }
int sizep(size(P));
for(int i = 0; i < sizep; i++) {
P.push_back(P[i]+X), P.push_back(P[i]-X);
if(mp2.find(P[i]+X) == end(mp2)) { mp2[P[i]+X] = 2; }
if(mp2.find(P[i]-X) == end(mp2)) { mp2[P[i]-X] = 3; }
} /* ある点から X の距離の点 */
sort(begin(P), end(P));
P.erase(unique(begin(P), end(P)), end(P));
/* P の逆引きできるような連想配列 */
map<int, int> mp;
for(int i = 0; i < (int)size(P); i++) { mp[P[i]] = i; }
vector imos(size(P), 0);
for(int i = 0; i < N; i++) { imos[mp[l[i]]]++; imos[mp[r[i]]]--; } /* 各区間の区間加算 */
for(int i = 0; i+1 < (int)size(P); i++) { imos[i+1] += imos[i]; } /* 求解 */
vector imos2(size(P), 0);
for(int i = 0; i < N; i++) { if(l[i]+t[i] < r[i]) { imos2[mp[l[i]+t[i]]]++; imos2[mp[r[i]]]--; } } /* 追加料金の区間加算 */
for(int i = 0; i+1 < (int)size(P); i++) { imos2[i+1] += imos2[i]; } /* 求解 */
for(int i = 0; i < (int)size(P); i++) { if(imos[i] < K) { imos2[i] = 0; } } /* 許される場合は除外する */
/* 尺取り法 */
long long ans(0), res(0);
for(int i = 0, j = 0; i+1 < (int)size(P); i++) {
if(mp2[P[i]] == 2) {
res -= (long long)(imos2[mp[P[i]]]) * (long long)(P[i+1] - P[i]); /* 左端を加算 */
continue;
}
for(; j < (int)size(P); j++) {
if(P[i]+X <= P[j]) { break; }
else if(j+1 < (int)size(P)) { res += (long long)(imos2[mp[P[j]]]) * (long long)((P[j+1]-P[j])); } /* 右端を加算 */
else break;
}
ans = max(res, ans);
res -= (long long)(imos2[mp[P[i]]]) * (long long)(P[i+1] - P[i]); /* 左端を加算 */
}
cout << ans << endl;
return 0;
}
