#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  int a[n + 2];
  for (int i = 1; i <= n; ++i) cin >> a[i];
  int b[n + 2];
  int cnt[3][n + 2];
  b[0] = b[n + 1] = 0;
  cnt[1][0] = cnt[2][0] = 0;
  for (int i = 1; i <= n; ++i) {
    b[i] = a[i] == 1 ? 1 : -1;
    cnt[1][i] = a[i] == 1 ? 1 : 0;
    cnt[2][i] = a[i] == 2 ? 1 : 0;
    cnt[1][i] += cnt[1][i - 1];
    cnt[2][i] += cnt[2][i - 1];
  }
  int l[n + 1];
  l[1] = 1;
  for (int i = 2; i <= n; ++i) {
    int best = 1;
    for (int j = 1; j < i; ++j) {
      if (a[j] <= a[i]) {
        best = max(best, 1 + l[j]);
      }
    }
    l[i] = best;
  }
  int rs = l[n];
  for (int l = 1; l <= n; ++l) {
    int s = 0;
    int best = n + 1;
    int bestLoc = -1;
    for (int r = l; r <= n; ++r) {
      s += b[r];
      if (s < best) {
        best = s;
        bestLoc = r;
      }
      int lis = cnt[1][l - 1] + (cnt[2][n] - cnt[2][r]) +
                (cnt[1][r] - cnt[1][bestLoc]) +
                (cnt[2][bestLoc] - cnt[2][l - 1]);
      rs = max(rs, lis);
    }
  }
  cout << rs << endl;
  return 0;
}

### Prompt

In CPP, your task is to solve 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 main() {
  int n;
  cin >> n;
  int a[n + 2];
  for (int i = 1; i <= n; ++i) cin >> a[i];
  int b[n + 2];
  int cnt[3][n + 2];
  b[0] = b[n + 1] = 0;
  cnt[1][0] = cnt[2][0] = 0;
  for (int i = 1; i <= n; ++i) {
    b[i] = a[i] == 1 ? 1 : -1;
    cnt[1][i] = a[i] == 1 ? 1 : 0;
    cnt[2][i] = a[i] == 2 ? 1 : 0;
    cnt[1][i] += cnt[1][i - 1];
    cnt[2][i] += cnt[2][i - 1];
  }
  int l[n + 1];
  l[1] = 1;
  for (int i = 2; i <= n; ++i) {
    int best = 1;
    for (int j = 1; j < i; ++j) {
      if (a[j] <= a[i]) {
        best = max(best, 1 + l[j]);
      }
    }
    l[i] = best;
  }
  int rs = l[n];
  for (int l = 1; l <= n; ++l) {
    int s = 0;
    int best = n + 1;
    int bestLoc = -1;
    for (int r = l; r <= n; ++r) {
      s += b[r];
      if (s < best) {
        best = s;
        bestLoc = r;
      }
      int lis = cnt[1][l - 1] + (cnt[2][n] - cnt[2][r]) +
                (cnt[1][r] - cnt[1][bestLoc]) +
                (cnt[2][bestLoc] - cnt[2][l - 1]);
      rs = max(rs, lis);
    }
  }
  cout << rs << endl;
  return 0;
}

```