Problem 2. Grass Segments

USACO 2024 US Open Contest, Gold

Bessie is planting some grass on the positive real line. She has $N$ ($2\le N\le 2\cdot 10^5$) different cultivars of grass, and will plant the $i$th cultivar on the interval $[\ell_i, r_i]$ ($0 < \ell_i < r_i \leq 10^9$).

In addition, cultivar $i$ grows better when there is some cultivar $j$ ($j\neq i$) such that cultivar $j$ and cultivar $i$ overlap with length at least $k_i$ ($0 < k_i \leq r_i - \ell_i$). Bessie wants to evaluate all of her cultivars. For each $i$, compute the number of $j\neq i$ such that $j$ and $i$ overlap with length at least $k_i$.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains $N$.

The next $N$ lines each contain three space-separated integers $\ell_i$, $r_i$, and $k_i$.

OUTPUT FORMAT (print output to the terminal / stdout):

The answers for all cultivars on separate lines.

SAMPLE INPUT:

2
3 6 3
4 7 2

SAMPLE OUTPUT:

0
1

The overlaps of the cultivars is $[4,6]$, which has length $2$, which is at least $2$ but not at least $3$.

SAMPLE INPUT:

4
3 6 1
2 5 1
4 10 1
1 4 1

SAMPLE OUTPUT:

3
3
2
2

SAMPLE INPUT:

5
8 10 2
4 9 2
3 7 4
5 7 1
2 7 1

SAMPLE OUTPUT:

0
3
1
3
3

SCORING: Input 4-5: $N \leq 5000$Inputs 6-11: $k$ is the same for all intervalsInputs 12-20: No additional constraints. In addition, for Inputs 5, 7, ..., 19, $r_i \leq 2N$ for all $i$.

Problem credits: Benjamin Qi