Interval covering P37902

Given several real numbers x₁, …, x_n, we want to find the smallest possible set of closed intervals of length 1 that cover those real numbers. In other words, we must find a set of intervals {[y₁, y₁ + 1], …, [y_m, y_m + 1]} such that

• for every x_i, there exists some j such that x_i ∈ [y_j, y_j + 1];
• m is minimum.

For instance, if the x_i’s are 1.4, 1.9, 2.3 i 2.7, a possible solution is {[1.2, 2.2], [1.8, 2.8]}, because every x_i is inside of (at least) one of the two intervals, and it is not possible to cover the four real numbers with only one interval.

Input

Input consists of several cases, each with a number n followed by n different real numbers. Assume n ≤ 10⁵.

Output

For every case, print the minimum number of closed intervals of length 1 that cover the given real numbers.