Bridge Pillars

Engineer Bajtazar wants to build a bridge across a canyon. The bridge rests on massive concrete pillars shaped like cylinders.

Each pillar has a positive integer height (measured in bytemeters). For the bridge to be level, every pillar must stick out above the ground by the same height (at least one bytemeter). Assume the ground under the bridge has already been perfectly leveled.

Each pillar is also sunk into the ground by a non-negative integer number of bytemeters, or its base rests directly on the ground (a buried length of $0$). Building regulations require that every buried length be a multiple of some natural number $m$, and $m$ must be greater than $1$. This $m$ is the strength coefficient of the bridge.

Not all delivered pillars have to be used. Bajtazar wants to use as many pillars as possible, so he picks $m$ so that as many pillars as possible have heights leaving the same remainder when divided by $m$. (If every used pillar sticks out by the same height $P$, then each buried length equals its height minus $P$, and for all of these to be multiples of $m$ the used heights must all share the same remainder modulo $m$.) If several values of $m$ give the same maximum count, he chooses the largest such $m$.

The first line contains an integer $n$ ($2 \le n \le 100\,000$), the number of delivered pillars. The second line contains $n$ integers $w_i$ ($1 \le w_i \le 10\,000\,000$), the heights of the pillars, separated by spaces. You may assume the pillars do not all have the same height.

Print two integers $k$ and $m$ on one line: $k$ is the maximum number of pillars that can be used for the bridge, and $m$ is the largest possible strength coefficient of a $k$-pillar bridge. You may assume such an $m$ exists.