Problem F
Pianino
Young Mirka is an amateur musician. She plays the multipiano. $A$ multipiano consists of an infinite number of multikeys, denoted with integers that can be interpreted as the pitch. $A$ multicomposition (a composition written for a multipiano) can be represented with a finite array of integers, where integers denote the order of multikeys to press in order to play the multicomposition.
Young Mirka has heard a multicomposition on the multiradio and now she wants to play it. Unfortunately, she cannot hear exactly which key was pressed, but instead she can hear whether the pressed multikey was higher, lower or equal to the previously played key (a higher key is denoted with a larger number). Therefore she has decided to play the composition in the following way:

before playing, she will choose one nonnegative integer $K$

in the beginning, she will play the correct multikey (her multiteacher told her which multikey that is)

when she hears that the multikey played in the multicomposition is higher than the previous multikey played in the multicomposition, she will play the multikey denoted with the integer larger than the multikey she played previously by $K$

analogously, when she hears that the multikey played in the multicomposition is lower than the previous multikey played in the multicomposition, she will play the multikey denoted with the integer smaller than the multikey she played previously by $K$

when she hears that the multikey played in the multicomposition is equal to the previous multikey played in the multicomposition, she will repeat the multikey she played previously
Notice that, when Mirka is playing, she does not compare the pitch of the keys she played to the pitch of the keys from the composition.
Help Mirka choose the integer $K$ in order to hit as many correct pitches as possible.
Input
The first line of input contains the integer $N$ ($2 \leq N \leq 10^6$), the number of multikeys in the multi composition on the multiradio.
The second line of input contains $N$ integers $a_ i$ ($10^9 \leq a_ i \leq 10^9$), the multikeys played in the multicomposition.
Output
The first line of output must contain the maximum number of multikeys that Mirka can play correctly. The second line of output must contain the nonnegative number $K$ that Mirka must choose in order to hit as many correct pitches as possible. The number must be smaller than or equal to $2 \cdot 10^9$. The required number does not have to be unique, but will surely exist within the given constraints.
Sample Input 1  Sample Output 1 

5 1 2 0 3 1 
3 2 
Sample Input 2  Sample Output 2 

7 2 1 6 2 1 6 10 
5 4 