#include <bits/stdc++.h>
using namespace std;
long long readll() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int readint() {
  int x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return f * x;
}
vector<int> vec;
int n;
int a[2005];
int sum1[2005], sum2[2005];
bool check(int t) {
  for (int i = 0; i < vec.size(); i++) {
    int max1 = 0, max2 = 0;
    for (int j = vec[i] + 1; j <= n; j++)
      max1 = max(max1, sum1[j] - sum1[vec[i]] + sum2[n] - sum2[j]);
    for (int j = vec[i]; j >= 1; j--)
      max2 = max(max2, sum2[vec[i]] - sum2[j - 1] + sum1[j - 1]);
    if (max1 + max2 >= t) return true;
  }
  return false;
}
int main() {
  ios::sync_with_stdio(false);
  n = readint();
  for (int i = 1; i <= n; i++) {
    a[i] = readint();
    if (a[i] == 1)
      sum1[i] = 1;
    else
      sum2[i] = 1;
    if (a[i] == 2) vec.push_back(i);
  }
  if (vec.size() == 0) {
    cout << n << endl;
    return 0;
  }
  for (int i = 1; i <= n; i++) sum1[i] += sum1[i - 1];
  for (int i = 1; i <= n; i++) sum2[i] += sum2[i - 1];
  int l = 1;
  int r = n;
  int ans;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid)) {
      ans = mid;
      l = mid + 1;
    } else
      r = mid - 1;
  }
  cout << ans << endl;
  return 0;
}

### 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;
long long readll() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int readint() {
  int x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return f * x;
}
vector<int> vec;
int n;
int a[2005];
int sum1[2005], sum2[2005];
bool check(int t) {
  for (int i = 0; i < vec.size(); i++) {
    int max1 = 0, max2 = 0;
    for (int j = vec[i] + 1; j <= n; j++)
      max1 = max(max1, sum1[j] - sum1[vec[i]] + sum2[n] - sum2[j]);
    for (int j = vec[i]; j >= 1; j--)
      max2 = max(max2, sum2[vec[i]] - sum2[j - 1] + sum1[j - 1]);
    if (max1 + max2 >= t) return true;
  }
  return false;
}
int main() {
  ios::sync_with_stdio(false);
  n = readint();
  for (int i = 1; i <= n; i++) {
    a[i] = readint();
    if (a[i] == 1)
      sum1[i] = 1;
    else
      sum2[i] = 1;
    if (a[i] == 2) vec.push_back(i);
  }
  if (vec.size() == 0) {
    cout << n << endl;
    return 0;
  }
  for (int i = 1; i <= n; i++) sum1[i] += sum1[i - 1];
  for (int i = 1; i <= n; i++) sum2[i] += sum2[i - 1];
  int l = 1;
  int r = n;
  int ans;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid)) {
      ans = mid;
      l = mid + 1;
    } else
      r = mid - 1;
  }
  cout << ans << endl;
  return 0;
}

```