A10116. Approximating a Constant Range

When Xellos was doing a practice course in university, he once had to measure the intensity of an effect that slowly approached equilibrium. A good way to determine the equilibrium intensity would be choosing a sufficiently large number of consecutive data points that seems as constant as possible and taking their average. Of course, with the usual sizes of data, it's nothing challenging — but why not make a similar programming contest problem while we're at it?

You're given a sequence of $n$ data points $a_{1},...,a_{n}$ . There aren't any big jumps between consecutive data points — for each $1<=i<n$ , it's guaranteed that $|a_{i+1}-a_{i}|<=1$ .

A range $[l,r]$ of data points is said to be almost constant if the difference between the largest and the smallest value in that range is at most $1$ . Formally, let $M$ be the maximum and $m$ the minimum value of $a_{i}$ for $l<=i<=r$ ; the range $[l,r]$ is almost constant if $M-m<=1$ .

Find the length of the longest almost constant range.

The first line of the input contains a single integer $n$ ( $2<=n<=100000$ ) — the number of data points.

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=100000$ ).

Print a single number — the maximum length of an almost constant range of the given sequence.

In the first sample, the longest almost constant range is $[2,5]$ ; its length (the number of data points in it) is 4.

In the second sample, there are three almost constant ranges of length $4$ : $[1,4]$ , $[6,9]$ and $[7,10]$ ; the only almost constant range of the maximum length $5$ is $[6,10]$ .