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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  int a[n];
  vector<set<int> > arr;
  vector<set<int> > arr2;
  map<int, int> maper;
  int loop = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (maper[a[i]] == 0) {
      set<int> x;
      arr2.push_back(x);
      set<int> y;
      arr.push_back(y);
      loop++;
      maper[a[i]] = loop;
      arr[loop - 1].insert(i);
    } else {
      arr[maper[a[i]] - 1].insert(i);
    }
  }
  if (n == 1) {
    cout << "1";
  } else {
    int out = 2;
    for (int i = 0; i < n; i++) {
      int lol = maper[a[i]] - 1;
      if (arr[lol].size() <= out / 2) {
        continue;
      }
      for (int j = i + 1; j < n; j++) {
        int hate = maper[a[i]] - 1;
        if (arr2[hate].find(a[j]) == arr2[hate].end()) {
          arr2[hate].insert(a[j]);
          int check = 0;
          int temp = 2;
          int l = i;
          int z = j;
          while (true) {
            if (check == 0) {
              int index = 0;
              hate = maper[a[l]] - 1;
              if (arr[hate].upper_bound(z) != arr[hate].end())
                index = *arr[hate].upper_bound(z);
              else
                break;
              check = 1;
              l = index;
              temp++;
            } else {
              int index = 0;
              hate = maper[a[z]] - 1;
              if (arr[hate].upper_bound(l) != arr[hate].end())
                index = *arr[hate].upper_bound(l);
              else
                break;
              check = 0;
              z = index;
              temp++;
            }
          }
          out = max(temp, out);
        }
      }
    }
    cout << out;
  }
  return 0;
}
