Closest points

You are given $n$ distinct points on a number line. Find the smallest distance between two points and the number of pairs of points at that distance. The distance between points $x$ and $y$ is $|x - y|$.

The first line contains $n$ ($2 \le n \le 10^5$). The second line contains $n$ distinct integers $x_1, \ldots, x_n$ ($|x_i| \le 2 \cdot 10^9$) — the coordinates.

A single line with two numbers: the smallest distance and the number of pairs at that distance.

Checking all pairs is $O(n^2)$ — $5 \cdot 10^9$ operations for $n = 10^5$. Sort the points: the closest point is always a neighbour in the sorted array, so the differences $x_{i+1} - x_i$ are enough.

The distance can reach $4 \cdot 10^9$, which does not fit into a 32-bit int: 2 3 in the first example, and for the points -2000000000 and 2000000000 the answer is 4000000000 1.

Source: acmp.ru, problem 344.