#include <stdio.h>
#define N 100000
long long min(long long a, long long b) { return a < b ? a : b; }
long long max(long long a, long long b) { return a > b ? a : b; }
unsigned int X = 12345;
int rand_() {
return (X *= 3) >> 1;
}
int *zz;
void sort(int *ii, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, i_ = ii[l + rand_() % (r - l)], tmp;
while (j < k)
if (zz[ii[j]] == zz[i_])
j++;
else if (zz[ii[j]] < zz[i_]) {
tmp = ii[i], ii[i] = ii[j], ii[j] = tmp;
i++, j++;
} else {
k--;
tmp = ii[j], ii[j] = ii[k], ii[k] = tmp;
}
sort(ii, l, i);
l = k;
}
}
void accumulate(int *xx, int *dd, int n) {
static int xx_[N * 2], dd_[N * 2], ii[N * 2];
int i;
for (i = 0; i < n; i++)
ii[i] = i;
zz = xx, sort(ii, 0, n);
for (i = 1; i < n; i++)
dd[ii[i]] += dd[ii[i - 1]];
for (i = 0; i < n; i++)
xx_[i] = xx[ii[i]], dd_[i] = dd[ii[i]];
for (i = 0; i < n; i++)
xx[i] = xx_[i], dd[i] = dd_[i];
}
int main() {
static int ll[N], rr[N], cc[N], xx1[N * 2], dd1[N * 2], xx2[N * 2], dd2[N * 2], xx3[N * 8], dd3[N * 8], ii[N * 8];
int n, n1, n2, n3, k, len, i, i1, i2;
long long ans, y, d;
scanf("%d%d%d", &n, &k, &len);
for (i = 0; i < n; i++)
scanf("%d%d%d", &ll[i], &cc[i], &rr[i]);
n1 = 0, n2 = 0;
for (i = 0; i < n; i++) {
xx1[n1] = ll[i], dd1[n1] = 1, n1++, xx1[n1] = rr[i] + 1, dd1[n1] = -1, n1++;
if (ll[i] + cc[i] <= rr[i])
xx2[n2] = ll[i] + cc[i], dd2[n2] = 1, n2++, xx2[n2] = rr[i] + 1, dd2[n2] = -1, n2++;
}
accumulate(xx1, dd1, n1);
accumulate(xx2, dd2, n2);
i1 = 0, i2 = 0, n3 = 0;
while (i1 + 1 < n1 && i2 + 1 < n2) {
int l = max(xx1[i1], xx2[i2]), r = min(xx1[i1 + 1], xx2[i2 + 1]);
if (l < r && dd1[i1] >= k && dd2[i2] > 0) {
xx3[n3] = l - len, dd3[n3] = dd2[i2], n3++, xx3[n3] = l, dd3[n3] = -dd2[i2], n3++;
xx3[n3] = r - len, dd3[n3] = -dd2[i2], n3++, xx3[n3] = r, dd3[n3] = dd2[i2], n3++;
}
if (xx1[i1 + 1] < xx2[i2 + 1])
i1++;
else
i2++;
}
for (i = 0; i < n3; i++)
ii[i] = i;
zz = xx3, sort(ii, 0, n3);
ans = 0, y = 0, d = 0;
for (i = 0; i + 1 < n3; i++) {
d += dd3[ii[i]];
y += (long long) (xx3[ii[i + 1]] - xx3[ii[i]]) * d;
ans = max(ans, y);
}
printf("%lld\n", ans);
return 0;
}
