#include <bits/stdc++.h>
using namespace std;
int long long n, k, mn, mx, ans, j, cnt, a[2005], b[2005], i, x;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (i = 1; i <= n; i++) cin >> a[i];
  for (i = n; i > 0; i--) b[i] = b[i + 1] + a[i] - 1;
  ans = b[1];
  for (i = 1; i <= n; i++) {
    mx = x;
    mn = -1e18;
    for (j = i; j <= n; j++) {
      if (a[j] == 2) mx++;
      mn = max(mn, 2 * mx - j);
      ans = max(ans, cnt + mn + b[j + 1] + j - mx);
    }
    cnt += 2 - a[i];
    ans = max(cnt + b[i + 1], ans);
  }
  cout << ans << endl;
}

### Prompt

Please create a solution in cpp 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 long long n, k, mn, mx, ans, j, cnt, a[2005], b[2005], i, x;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (i = 1; i <= n; i++) cin >> a[i];
  for (i = n; i > 0; i--) b[i] = b[i + 1] + a[i] - 1;
  ans = b[1];
  for (i = 1; i <= n; i++) {
    mx = x;
    mn = -1e18;
    for (j = i; j <= n; j++) {
      if (a[j] == 2) mx++;
      mn = max(mn, 2 * mx - j);
      ans = max(ans, cnt + mn + b[j + 1] + j - mx);
    }
    cnt += 2 - a[i];
    ans = max(cnt + b[i + 1], ans);
  }
  cout << ans << endl;
}

```