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 java.util.*;
 
public class Main{
   public static void main(String[] args) {
      // Use the Scanner class
      Scanner sc = new Scanner(System.in);  
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String
      */
      int n      = sc.nextInt();
      sc.nextLine();
      int[] arr = new int[n];
      for(int i=0; i<n; i++){
          arr[i] = sc.nextInt();
      }
      
      int[][] dp = new int[n+1][4];//1*,1*2*,1*2*1*,1*2*1*2*
      
      for(int i=1; i<=n; i++){
          for(int j=0; j<=3; j++){
              if(arr[i-1] == 1){
                  dp[i][0] = dp[i-1][0]+1;
                  dp[i][2] = Math.max(dp[i-1][1], dp[i-1][2])+1;
                  
                  dp[i][1] = dp[i-1][1];
                  dp[i][3] = dp[i-1][3];
              }else{
                  dp[i][1] = Math.max(dp[i-1][0], dp[i-1][1])+1;
                  dp[i][3] = Math.max(dp[i-1][2], dp[i-1][3])+1;
                  
                  dp[i][0] = dp[i-1][0];
                  dp[i][2] = dp[i-1][2];
              }
          }
      }
      
      int max = Math.max(dp[n][0],
                  Math.max(dp[n][1],
                    Math.max(dp[n][2],dp[n][3])));
      
      System.out.println(max);
      
    }
    
}