Counting the closest pair sums

You are given a sequence of $n$ integers $a_1, a_2, \dots, a_n$ and an integer $v$. Consider every pair $(a_i, a_j)$ of elements of the sequence with $i < j$.

Among those pairs, find the ones whose sum $a_i + a_j$ is closest to $v$, that is, the pairs that minimize $|a_i + a_j - v|$, and print how many pairs reach that smallest distance. A sum equal to $v$ has distance $0$.

Pairs are distinguished by position. Two pairs that hold the same values at different indices count separately.

The first line contains $n$.

The second line contains $a_1, a_2, \dots, a_n$, separated by spaces.

The third line contains $v$.

Print one integer, the number of pairs that satisfy the condition.

• $1 < n \le 10^6$
• $-10^4 \le a_i \le 10^4$ for every $i$
• $-10^4 \le v \le 10^4$

In the example, no pair sums to $v = 12$, but $13$ is reachable: $2 + 11 = 13$, at distance $1$ from $v$. The sum $11$ is at distance $1$ as well. Two pairs sum to $11$ (the value $2$ with either copy of $9$) and two pairs sum to $13$ ($2 + 11$ and $5 + 8$), so the answer is $4$. The sequence contains $9$ twice, so the pair $(2, 9)$ is counted twice.