#include <bits/stdc++.h>
using namespace std;
int dp[2100][4];
int m, n, c, a[8100];
int main() {
  cin >> m;
  for (int x = 1; x <= m; x++) {
    cin >> a[x];
  }
  for (int x = 1; x <= m; x++) {
    if (a[x] == 1) {
      dp[x][0] = dp[x - 1][0] + 1;
      dp[x][1] = dp[x - 1][1];
      dp[x][2] = max(dp[x - 1][1], dp[x - 1][2]) + 1;
      dp[x][3] = dp[x - 1][3];
    } else {
      dp[x][0] = dp[x - 1][0];
      dp[x][1] = max(dp[x - 1][1], dp[x - 1][0]) + 1;
      dp[x][2] = dp[x - 1][2];
      dp[x][3] = max(dp[x - 1][3], dp[x - 1][2]) + 1;
    }
  }
  cout << max(dp[m][0], max(dp[m][1], max(dp[m][2], dp[m][3]))) << endl;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 dp[2100][4];
int m, n, c, a[8100];
int main() {
  cin >> m;
  for (int x = 1; x <= m; x++) {
    cin >> a[x];
  }
  for (int x = 1; x <= m; x++) {
    if (a[x] == 1) {
      dp[x][0] = dp[x - 1][0] + 1;
      dp[x][1] = dp[x - 1][1];
      dp[x][2] = max(dp[x - 1][1], dp[x - 1][2]) + 1;
      dp[x][3] = dp[x - 1][3];
    } else {
      dp[x][0] = dp[x - 1][0];
      dp[x][1] = max(dp[x - 1][1], dp[x - 1][0]) + 1;
      dp[x][2] = dp[x - 1][2];
      dp[x][3] = max(dp[x - 1][3], dp[x - 1][2]) + 1;
    }
  }
  cout << max(dp[m][0], max(dp[m][1], max(dp[m][2], dp[m][3]))) << endl;
}

```