#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  register long long x = 0;
  char zf = 1;
  char ch;
  while (ch != '-' && !isdigit(ch)) ch = getchar();
  if (ch == '-') zf = -1, ch = getchar();
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return x * zf;
}
void write(long long y) {
  if (y < 0) putchar('-'), y = -y;
  if (y > 9) write(y / 10);
  putchar(y % 10 + 48);
}
void writeln(const long long y) {
  write(y);
  putchar('\n');
}
void bemin(long long &x, const long long y) {
  if (y < x) x = y;
}
void bemax(long long &x, const long long y) {
  if (y > x) x = y;
}
int i, j, k, m, n, x, y, z, cnt;
int qz[3010][3], hz[3010][3], a[3010], F[3010][3010];
int main() {
  n = read();
  for (register int i = 1; i <= n; i++) a[i] = read();
  for (register int i = 1; i <= n; i++) {
    qz[i][1] = qz[i - 1][1];
    qz[i][2] = qz[i - 1][2];
    qz[i][a[i]]++;
  }
  for (register int i = n; i >= 1; i--) {
    hz[i][1] = hz[i + 1][1];
    hz[i][2] = hz[i + 1][2];
    hz[i][a[i]]++;
  }
  for (register int i = 1; i <= n; i++)
    for (register int j = i; j <= n; j++) {
      if (a[j] == 1)
        F[i][j] = F[i][j - 1] + 1;
      else
        F[i][j] = max(F[i][j - 1], qz[j][2] - qz[i - 1][2]);
    }
  int ans = 0;
  for (register int i = 0; i <= n; i++) ans = max(ans, qz[i][1] + hz[i + 1][2]);
  for (register int i = 1; i <= n; i++)
    for (register int j = i; j <= n; j++) {
      ans = max(ans, qz[i - 1][1] + F[i][j] + hz[j + 1][2]);
    }
  cout << ans;
  return 0;
}

### Prompt

Your challenge is to write 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;
inline long long read() {
  register long long x = 0;
  char zf = 1;
  char ch;
  while (ch != '-' && !isdigit(ch)) ch = getchar();
  if (ch == '-') zf = -1, ch = getchar();
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return x * zf;
}
void write(long long y) {
  if (y < 0) putchar('-'), y = -y;
  if (y > 9) write(y / 10);
  putchar(y % 10 + 48);
}
void writeln(const long long y) {
  write(y);
  putchar('\n');
}
void bemin(long long &x, const long long y) {
  if (y < x) x = y;
}
void bemax(long long &x, const long long y) {
  if (y > x) x = y;
}
int i, j, k, m, n, x, y, z, cnt;
int qz[3010][3], hz[3010][3], a[3010], F[3010][3010];
int main() {
  n = read();
  for (register int i = 1; i <= n; i++) a[i] = read();
  for (register int i = 1; i <= n; i++) {
    qz[i][1] = qz[i - 1][1];
    qz[i][2] = qz[i - 1][2];
    qz[i][a[i]]++;
  }
  for (register int i = n; i >= 1; i--) {
    hz[i][1] = hz[i + 1][1];
    hz[i][2] = hz[i + 1][2];
    hz[i][a[i]]++;
  }
  for (register int i = 1; i <= n; i++)
    for (register int j = i; j <= n; j++) {
      if (a[j] == 1)
        F[i][j] = F[i][j - 1] + 1;
      else
        F[i][j] = max(F[i][j - 1], qz[j][2] - qz[i - 1][2]);
    }
  int ans = 0;
  for (register int i = 0; i <= n; i++) ans = max(ans, qz[i][1] + hz[i + 1][2]);
  for (register int i = 1; i <= n; i++)
    for (register int j = i; j <= n; j++) {
      ans = max(ans, qz[i - 1][1] + F[i][j] + hz[j + 1][2]);
    }
  cout << ans;
  return 0;
}

```