#include <bits/stdc++.h>
using namespace std;
int n, a[2005], dp[2005][2005], psum[2005][2], maxlen;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    psum[i + 1][0] = psum[i][0];
    psum[i + 1][1] = psum[i][1];
    if (a[i] == 1)
      psum[i + 1][0]++;
    else
      psum[i + 1][1]++;
  }
  for (int i = 0; i < n; i++)
    for (int j = i; j < n; j++) {
      if (i == j)
        dp[i][j] = 1;
      else if (a[j] == 1)
        dp[i][j] = dp[i][j - 1] + 1;
      else
        dp[i][j] = max(psum[j + 1][1] - psum[i][1], dp[i][j - 1]);
      maxlen =
          max(maxlen, psum[i][0] + dp[i][j] + (psum[n][1] - psum[j + 1][1]));
    }
  cout << maxlen << '\n';
}

### Prompt

Please formulate a Cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, a[2005], dp[2005][2005], psum[2005][2], maxlen;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    psum[i + 1][0] = psum[i][0];
    psum[i + 1][1] = psum[i][1];
    if (a[i] == 1)
      psum[i + 1][0]++;
    else
      psum[i + 1][1]++;
  }
  for (int i = 0; i < n; i++)
    for (int j = i; j < n; j++) {
      if (i == j)
        dp[i][j] = 1;
      else if (a[j] == 1)
        dp[i][j] = dp[i][j - 1] + 1;
      else
        dp[i][j] = max(psum[j + 1][1] - psum[i][1], dp[i][j - 1]);
      maxlen =
          max(maxlen, psum[i][0] + dp[i][j] + (psum[n][1] - psum[j + 1][1]));
    }
  cout << maxlen << '\n';
}

```