#include <bits/stdc++.h>
using namespace std;
int nonDecStart[2003];
int nonDecEnd[2003];
int nonIncEnd[2003];
int nonIncStart[2003];
int arr[2003];
int mat[2003][2003];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    mat[i][i] = 1;
    cin >> arr[i];
  }
  for (int i = 0; i < n; i++) {
    int twos = 0;
    if (arr[i] == 2) twos++;
    for (int j = i + 1; j < n; j++) {
      if (arr[j] == 2) {
        twos++;
        mat[i][j] = max(twos, mat[i][j - 1]);
      } else
        mat[i][j] = mat[i][j - 1] + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    nonDecEnd[i] = 1;
    nonIncEnd[i] = 1;
    for (int j = i - 1; j >= 0; j--) {
      if (arr[j] <= arr[i]) {
        nonDecEnd[i] = max(nonDecEnd[i], nonDecEnd[j] + 1);
      }
      if (arr[j] >= arr[i]) nonIncEnd[i] = max(nonIncEnd[i], nonIncEnd[j] + 1);
    }
  }
  for (int i = n - 1; i >= 0; i--) {
    nonDecStart[i] = 1;
    nonIncStart[i] = 1;
    for (int j = i + 1; j < n; j++) {
      if (arr[j] >= arr[i])
        nonDecStart[i] = max(nonDecStart[i], nonDecStart[j] + 1);
      if (arr[j] <= arr[i])
        nonIncStart[i] = max(nonIncStart[i], nonIncStart[j] + 1);
    }
  }
  int best = nonDecStart[0];
  for (int l = 0; l < n; l++) {
    for (int r = l + 1; r < n; r++) {
      int temp = 0;
      if (l > 0) temp += nonDecEnd[l - 1];
      if (r < n - 1) temp += nonDecStart[r + 1];
      temp += mat[l][r];
      if (temp > best) best = temp;
    }
  }
  cout << best << endl;
  return 0;
}

### Prompt

Your task is to create 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 nonDecStart[2003];
int nonDecEnd[2003];
int nonIncEnd[2003];
int nonIncStart[2003];
int arr[2003];
int mat[2003][2003];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    mat[i][i] = 1;
    cin >> arr[i];
  }
  for (int i = 0; i < n; i++) {
    int twos = 0;
    if (arr[i] == 2) twos++;
    for (int j = i + 1; j < n; j++) {
      if (arr[j] == 2) {
        twos++;
        mat[i][j] = max(twos, mat[i][j - 1]);
      } else
        mat[i][j] = mat[i][j - 1] + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    nonDecEnd[i] = 1;
    nonIncEnd[i] = 1;
    for (int j = i - 1; j >= 0; j--) {
      if (arr[j] <= arr[i]) {
        nonDecEnd[i] = max(nonDecEnd[i], nonDecEnd[j] + 1);
      }
      if (arr[j] >= arr[i]) nonIncEnd[i] = max(nonIncEnd[i], nonIncEnd[j] + 1);
    }
  }
  for (int i = n - 1; i >= 0; i--) {
    nonDecStart[i] = 1;
    nonIncStart[i] = 1;
    for (int j = i + 1; j < n; j++) {
      if (arr[j] >= arr[i])
        nonDecStart[i] = max(nonDecStart[i], nonDecStart[j] + 1);
      if (arr[j] <= arr[i])
        nonIncStart[i] = max(nonIncStart[i], nonIncStart[j] + 1);
    }
  }
  int best = nonDecStart[0];
  for (int l = 0; l < n; l++) {
    for (int r = l + 1; r < n; r++) {
      int temp = 0;
      if (l > 0) temp += nonDecEnd[l - 1];
      if (r < n - 1) temp += nonDecStart[r + 1];
      temp += mat[l][r];
      if (temp > best) best = temp;
    }
  }
  cout << best << endl;
  return 0;
}

```