Count

Input

The first line contains an integer n~(1 < n \le 10^6).

The second line contains the integers a_1, a_2, \dots, a_n~(-10^4 \le a_i \le 10^4, 1 \le i \le n).

The third line contains the integer v~(-10^4 \le v \le 10^4).

Output

Print one integer — the number of pairs whose sum is closest to $v$.

Examples

It is impossible to obtain exactly the sum v = 12, but we can find a sum that is closest to $v$, for example 2 + 11 = 13. The distance between v = 12 and $13$ is $1$. There are also other pairs whose sums differ from $v$ by the same minimal distance: 2 + 9 = 11, 2 + 9 = 11, 5 + 8 = 13. The total number of such pairs is $4$.

Note that the pair $(2,9)$ is counted twice, since the sequence contains two distinct positions with the same values.