Problem Statement

We have an infinite hexagonal grid shown below.

A hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$. Cell $(i,j)$ is adjacent to the following six cells:

• $(i-1,j-1)$
• $(i-1,j)$
• $(i,j-1)$
• $(i,j+1)$
• $(i+1,j)$
• $(i+1,j+1)$

Let us define the distance between two cells $X$ and $Y$ by the minimum number of moves required to travel from cell $X$ to cell $Y$ by repeatedly moving to an adjacent cell. For example, the distance between cells $(0,0)$ and $(1,1)$ is $1$, and the distance between cells $(2,1)$ and $(-1,-1)$ is $3$.

You are given $N$ cells $(X_1,Y_1),\ldots,(X_N,Y_N)$. How many ways are there to choose one or more from these $N$ cells so that the distance between any two of the chosen cells is at most $D$? Find the count modulo $998244353$.

Constraints

• $1 \leq N \leq 300$
• $-10^9\leq X_i,Y_i \leq 10^9$
• $1\leq D \leq 10^{10}$
• $(X_i,Y_i)$ are pairwise distinct.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N D
X_1 Y_1
\vdots
X_N Y_N

Output

Print the answer.