Crowded Cows

Farmer John's $N$ cows are grazing along a straight fence. Cow $i$ stands at position $x_i$ and has height $h_i$.

A cow feels crowded when some cow at least twice her height stands within distance $D$ to her left and some cow at least twice her height also stands within distance $D$ to her right. Her left side is the range of positions from $x_i - D$ up to but not including $x_i$, and her right side is the range above $x_i$ up to and including $x_i + D$.

Crowded cows give less milk. Help Farmer John count how many of them there are.

• $1 \le N \le 50000$
• $1 \le x_i, h_i \le 10^9$
• $1 \le D \le 10^9$

The first line has two integers $N$ and $D$.

Each of the next $N$ lines has the position $x_i$ and the height $h_i$ of cow $i$. All positions are distinct. The input is not guaranteed to be sorted by position.

Print the number of crowded cows on one line.

The example has 6 cows and a distance threshold of $D = 4$. The first cow stands at position 10 with height 3, and the remaining lines read the same way. The cows at positions 5 and 6 feel crowded, so the answer is 2.