Inżynier Bajtazar intends to build a bridge over the Great Bajtock Canyon. The bridge will be supported by massive concrete pillars.
The pillars are cylinders whose heights are integer multiples of bajtometers. All pillars must protrude above the ground by the same height (at least one bajtometer), otherwise the bridge will be uneven. We assume that the ground under the bridge has already been perfectly leveled.
Each pillar must also either be embedded into the ground by an integer, nonnegative number of bajtometers, or be fixed to the ground with ultra-durable mortar—in the latter case, its base touches the ground surface. Building regulations require that the lengths of the parts embedded in the ground are multiples of some natural number $m$, necessarily greater than 1—otherwise the bridge will be exposed to dangerous vibrations. The number $m$ is also the bridge’s strength coefficient.
Unfortunately, the company tasked with producing the concrete blocks did not receive all the guidelines in advance. Therefore, it may be impossible to use all delivered pillars to build the bridge.
Bajtazar’s top priority is to make the bridge as long and impressive as possible, so he will choose $m$ so that it is possible to select as many pillars as possible whose heights give the same remainder when divided by $m$. In case of a tie, Bajtazar would like the structure to be as strong as possible, so he will choose the largest number $m$ among those that maximize the number of usable pillars.
Input Format
The first line of input contains a single integer $n$ ($2 \le n \le 100,000$), the number of pillars delivered by the company. The next line contains a sequence of $n$ numbers $w_i$ ($1 \le w_i \le 10,000,000$), the heights of the individual pillars. You may assume that not all pillars have the same height.
Output Format
The first and only line of output should contain two integers $k$ and $m$, meaning that at most $k$ pillars can be used to construct the bridge, and that $m$ is the largest possible strength coefficient of a $k$-pillar bridge. You may assume that such an $m$ exists.
Example
Input
6 7 4 10 8 7 1
Output
5 3