We've got no test cases. A big olympiad is coming up. But the problemsetters' number one priority should be adding another problem to the round.

The diameter of a multiset of points on the line is the largest distance between two points from this set. For example, the diameter of the multiset ${1, 3, 2, 1}$ is 2.

Diameter of multiset consisting of one point is 0.

You are given $*n*$ points on the line. What is the minimum number of points you have to remove, so that the diameter of the multiset of the remaining points will not exceed $*d*$?

Input

The first line contains two integers $*n*$ and $*d*$ ($1 ≤ *n* ≤ 100, 0 ≤ *d* ≤ 100$) — the amount of points and the maximum allowed diameter respectively.

The second line contains $*n*$ space separated integers ($1 ≤ *x*_{*i*} ≤ 100$) — the coordinates of the points.

Output

Output a single integer — the minimum number of points you have to remove.

Note

In the first test case the optimal strategy is to remove the point with coordinate $4$. The remaining points will have coordinates $1$ and $2$, so the diameter will be equal to $2 - 1 = 1$.

In the second test case the diameter is equal to $0$, so its is unnecessary to remove any points.

In the third test case the optimal strategy is to remove points with coordinates $1$, $9$ and $10$. The remaining points will have coordinates $3$, $4$ and $6$, so the diameter will be equal to $6 - 3 = 3$.