#include <bits/stdc++.h>
using namespace std;
int f[4005][4005];
int a[4005];
int main() {
  int i, j, k, n, m = 0;
  memset(f, 0, sizeof(f));
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
    k = 0;
    for (j = 0; j < i; j++) {
      f[i][j] = f[j][k] + 1;
      if (a[j] == a[i]) {
        k = j;
      }
      m = max(m, f[i][j]);
    }
  }
  cout << m << endl;
}

### Prompt

Please create a solution in CPP to the following problem:

Gena loves sequences of numbers. Recently, he has discovered a new type of sequences which he called an almost arithmetical progression. A sequence is an almost arithmetical progression, if its elements can be represented as:

  * a1 = p, where p is some integer; 
  * ai = ai - 1 + ( - 1)i + 1·q (i > 1), where q is some integer. 



Right now Gena has a piece of paper with sequence b, consisting of n integers. Help Gena, find there the longest subsequence of integers that is an almost arithmetical progression.

Sequence s1, s2, ..., sk is a subsequence of sequence b1, b2, ..., bn, if there is such increasing sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n), that bij = sj. In other words, sequence s can be obtained from b by crossing out some elements.

Input

The first line contains integer n (1 ≤ n ≤ 4000). The next line contains n integers b1, b2, ..., bn (1 ≤ bi ≤ 106).

Output

Print a single integer — the length of the required longest subsequence.

Examples

Input

2
3 5


Output

2


Input

4
10 20 10 30


Output

3

Note

In the first test the sequence actually is the suitable subsequence. 

In the second test the following subsequence fits: 10, 20, 10.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int f[4005][4005];
int a[4005];
int main() {
  int i, j, k, n, m = 0;
  memset(f, 0, sizeof(f));
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
    k = 0;
    for (j = 0; j < i; j++) {
      f[i][j] = f[j][k] + 1;
      if (a[j] == a[i]) {
        k = j;
      }
      m = max(m, f[i][j]);
    }
  }
  cout << m << endl;
}

```