Given $n$ points on a two-dimensional coordinate system. There are $q$ queries of the form $(x, y, d)$. Count the number of vertices lying inside or on the edges of the triangle defined by three points $(x, y)$, $(x + d, y)$, and $(x, y + d)$.
### Input
- The first line contains two integers $n$ and $q$.
- The next $n$ lines each contain two integers $x$ and $y$, representing a point at coordinates $(x, y)$.
- The next $q$ lines each contain three integers $x$, $y$, and $d$, representing a query.
### Output
- Print $q$ integers. The $i$-th integer represents the answer to the $i$-th query.
### Constraints
- $1 \leq n, q, x, y, d \leq 10^5$.
### Example
Input:
```
2 2
3 3
3 4
1 1 3
2 2 3
```
Output:
```
0
2
```
