#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline bool chkmin(T &a, T b) {
  return b < a ? a = b, 1 : 0;
}
template <typename T>
inline bool chkmax(T &a, T b) {
  return b > a ? a = b, 1 : 0;
}
inline int read() {
  int x(0), sgn(1);
  char ch(getchar());
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') sgn = -1;
  for (; isdigit(ch); ch = getchar()) x = (x * 10) + (ch ^ 48);
  return x * sgn;
}
void File() {}
int dp[6];
int main() {
  File();
  int n = read();
  for (register int i = (1), iend = (int)(n); i <= iend; ++i) {
    int val = read();
    for (register int j = (2), jend = (int)(5); j <= jend; ++j)
      dp[j] = max(dp[j - 1], dp[j] + ((j ^ val) & 1));
  }
  printf("%d\n", dp[5]);
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
template <typename T>
inline bool chkmin(T &a, T b) {
  return b < a ? a = b, 1 : 0;
}
template <typename T>
inline bool chkmax(T &a, T b) {
  return b > a ? a = b, 1 : 0;
}
inline int read() {
  int x(0), sgn(1);
  char ch(getchar());
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') sgn = -1;
  for (; isdigit(ch); ch = getchar()) x = (x * 10) + (ch ^ 48);
  return x * sgn;
}
void File() {}
int dp[6];
int main() {
  File();
  int n = read();
  for (register int i = (1), iend = (int)(n); i <= iend; ++i) {
    int val = read();
    for (register int j = (2), jend = (int)(5); j <= jend; ++j)
      dp[j] = max(dp[j - 1], dp[j] + ((j ^ val) & 1));
  }
  printf("%d\n", dp[5]);
  return 0;
}

```