CF933A.A Twisty Movement

A dragon symbolizes wisdom, power and wealth. On Lunar New Year's Day, people model a dragon with bamboo strips and clothes, raise them with rods, and hold the rods high and low to resemble a flying dragon.

A performer holding the rod low is represented by a $1$ , while one holding it high is represented by a $2$ . Thus, the line of performers can be represented by a sequence $a_{1},a_{2},...,a_{n}$ .

Little Tommy is among them. He would like to choose an interval $[l,r]$ ( $1<=l<=r<=n$ ), then reverse $a_{l},a_{l+1},...,a_{r}$ so that the length of the longest non-decreasing subsequence of the new sequence is maximum.

A non-decreasing subsequence is a sequence of indices $p_{1},p_{2},...,p_{k}$ , such that $p_{1}<p_{2}<...<p_{k}$ and $a_{p1}<=a_{p2}<=...<=a_{pk}$ . The length of the subsequence is $k$ .

The first line contains an integer $n$ $(1<=n<=2000)$ , denoting the length of the original sequence.

The second line contains $n$ space-separated integers, describing the original sequence $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=2,i=1,2,...,n)$ .

Print a single integer, which means the maximum possible length of the longest non-decreasing subsequence of the new sequence.

In the first example, after reversing $[2,3]$ , the array will become $[1,1,2,2]$ , where the length of the longest non-decreasing subsequence is $4$ .

In the second example, after reversing $[3,7]$ , the array will become $[1,1,1,1,2,2,2,2,2,1]$ , where the length of the longest non-decreasing subsequence is $9$ .