Interval covering

Given several real numbers $x_1, \ldots, x_n$ , 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 $\{[y_1, y_1 + 1], \dots, [y_m, y_m + 1]\}$ such that

for every $x_i$ , there exists some $j$ such that $x_i \in [y_j, y_j + 1]$ ;
$m$ 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 $n \le 10^5$ .

Output

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

Problem information

Author: Unknown
Translator: Amalia Duch

Generation: 2026-01-25T10:35:14.480Z