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 a1, a2, ..., an.

Little Tommy is among them. He would like to choose an interval [l, r] (1 ≤ l ≤ r ≤ n), then reverse al, al + 1, ..., ar 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 p1, p2, ..., pk, such that p1 < p2 < ... < pk and ap1 ≤ ap2 ≤ ... ≤ apk. The length of the subsequence is k.

Input

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 a1, a2, ..., an (1 ≤ ai ≤ 2, i = 1, 2, ..., n).

Output

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

Examples

Input

4
1 2 1 2


Output

4


Input

10
1 1 2 2 2 1 1 2 2 1


Output

9

Note

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.
import sys

#f = open('input', 'r')
f = sys.stdin

n = int(f.readline())
a = list(map(int, f.readline().split()))
d = [0,-1,-1,-1,-1,-1]
for v in a:
  f1, f2, r2, r1, l1, l2 = d
  if v == 1:
    nf1 = f1 + 1
    nr1 = max(f1, f2, r2, r1) + 1
    nl1 = max(f1, f2, r2, r1, l1) + 1
    nf2,nr2,nl2 = f2,r2,l2
  elif v == 2:
    nf2 = max(f1, f2) + 1
    nr2 = max(f1, f2, r2) + 1
    nl2 = max(f1, f2, r2, r1, l1, l2) + 1
    nf1,nr1,nl1 = f1,r1,l1
  d = [nf1,nf2,nr2,nr1,nl1,nl2]
print(max(d))
