#include <bits/stdc++.h>
using namespace std;
long N;
long num[2020];
long oneCount[2020];
long maxnonDecreasingLength[2020][2020];
long maxnonIncreasingLength[2020][2020];
long getMaxnonIncreasingLength(long start, long end) {
  if (maxnonIncreasingLength[start][end] == -1) {
    if (start == end)
      maxnonIncreasingLength[start][end] = 1;
    else {
      if (num[end] == 1) {
        maxnonIncreasingLength[start][end] =
            getMaxnonIncreasingLength(start, end - 1) + 1;
      } else {
        maxnonIncreasingLength[start][end] =
            getMaxnonIncreasingLength(start, end - 1);
        long twoCount = end - start - (oneCount[end] - oneCount[start]);
        if (num[start] == 2) twoCount++;
        if (twoCount > maxnonIncreasingLength[start][end])
          maxnonIncreasingLength[start][end] = twoCount;
      }
    }
  }
  return maxnonIncreasingLength[start][end];
}
long getFlipResult(long start, long end) {
  long prevOne = 0;
  if (start > 0) prevOne = oneCount[start - 1];
  long nextTwo = ((N - 1) - end) - (oneCount[N - 1] - oneCount[end]);
  return prevOne + nextTwo + getMaxnonIncreasingLength(start, end);
}
int main() {
  cin >> N;
  memset(oneCount, 0, sizeof(oneCount));
  memset(maxnonIncreasingLength, -1, sizeof(maxnonIncreasingLength));
  for (long i = 0; i < N; i++) {
    cin >> num[i];
    if (i == 0) {
      oneCount[i] = 2 - num[i];
    } else {
      oneCount[i] = (2 + oneCount[i - 1]) - num[i];
    }
  }
  long ans = 0;
  for (long i = 0; i < N; i++) {
    for (long j = i; j < N; j++) {
      long curResult = getFlipResult(i, j);
      if (curResult > ans) ans = curResult;
    }
  }
  cout << ans;
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
long N;
long num[2020];
long oneCount[2020];
long maxnonDecreasingLength[2020][2020];
long maxnonIncreasingLength[2020][2020];
long getMaxnonIncreasingLength(long start, long end) {
  if (maxnonIncreasingLength[start][end] == -1) {
    if (start == end)
      maxnonIncreasingLength[start][end] = 1;
    else {
      if (num[end] == 1) {
        maxnonIncreasingLength[start][end] =
            getMaxnonIncreasingLength(start, end - 1) + 1;
      } else {
        maxnonIncreasingLength[start][end] =
            getMaxnonIncreasingLength(start, end - 1);
        long twoCount = end - start - (oneCount[end] - oneCount[start]);
        if (num[start] == 2) twoCount++;
        if (twoCount > maxnonIncreasingLength[start][end])
          maxnonIncreasingLength[start][end] = twoCount;
      }
    }
  }
  return maxnonIncreasingLength[start][end];
}
long getFlipResult(long start, long end) {
  long prevOne = 0;
  if (start > 0) prevOne = oneCount[start - 1];
  long nextTwo = ((N - 1) - end) - (oneCount[N - 1] - oneCount[end]);
  return prevOne + nextTwo + getMaxnonIncreasingLength(start, end);
}
int main() {
  cin >> N;
  memset(oneCount, 0, sizeof(oneCount));
  memset(maxnonIncreasingLength, -1, sizeof(maxnonIncreasingLength));
  for (long i = 0; i < N; i++) {
    cin >> num[i];
    if (i == 0) {
      oneCount[i] = 2 - num[i];
    } else {
      oneCount[i] = (2 + oneCount[i - 1]) - num[i];
    }
  }
  long ans = 0;
  for (long i = 0; i < N; i++) {
    for (long j = i; j < N; j++) {
      long curResult = getFlipResult(i, j);
      if (curResult > ans) ans = curResult;
    }
  }
  cout << ans;
  return 0;
}

```