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.
import java.io.*;
import java.util.*;

public class CodeForces {
    /*****************************************WRITING CODE STARTS HERE******************************************/
    public static void solve(int t)throws IOException {
        int n = sc.nextInt();
        int[] arr = new int[n];
        int[] sortedArray = new int[n];
        for(int i=0;i<n;i++){
            arr[i] = sc.nextInt();
            sortedArray[i] = arr[i];
        }
        Arrays.sort(sortedArray);
        Map<Integer,Integer> compression = new HashMap<>();
        int code = 0;
        for(int ele : sortedArray){
            if(!compression.containsKey(ele))compression.put(ele,++code);
        }
        for(int i=0;i<n;i++)arr[i] = compression.get(arr[i]);
        int [][] dp = new int[n+2][n+2];
        int ans = 0;
        for(int i=0;i<n;i++) {
            int curr = arr[i];
            ans = max2(ans,dp[curr][curr]);
            dp[curr][curr]++;
            for (int j = 0; j < i; j++) {
                int prev = arr[j];
                if (prev == curr)continue;
                dp[prev][curr] = 1 + dp[curr][prev];
                ans = max2(ans,dp[prev][curr]);
            }
        }
        out.println(1+ans);

    }


    /*****************************************WRITING CODE ENDS HERE******************************************/

    public static void main(String[] args) throws IOException{
        int testCase = 1;
//        testCase = sc.nextInt();
        for (int i = 1; i <= testCase; i++) solve(i);
        closeIO();
    }
    static FastestReader sc = new FastestReader();              // FASTEST INPUT
    static PrintWriter out = new PrintWriter(System.out);                // FAST OUTPUT


    /**************************************HELPER FUNCTION STARTS HERE ************************************/

    public static int mod = (int) 1e9 + 7;
    public static final int inf_int = (int) 1e9;
    public static final long inf_long = (long) 1e15;

    public static final String YES = "YES";
    public static final String NO = "NO";

    // euclidean algorithm time O(max (loga ,logb))
    public static long gcd(long a, long b) {
        long x = Math.min(a, b);
        long y = Math.max(a, b);
        if (y % x == 0) return x;
        return gcd(y % x, x);
    }

    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }
    // binary exponentiation time O(logn)
    public static long power(long x, long n) {
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans *= x;
                ans %= mod;
                n--;
            } else {
                x *= x;
                x %= mod;
                n >>= 1;
            }
        }
        return ans;
    }

    public static long firstDivisor(long n) {
        if (n == 1 || n == 0) return n;
        for (long i = 2; i * i <= n; i++)
            if (n % i == 0) return i;
        return -1;
    }

    public static long max3(long a, long b, long c) {
        return max2(max2(a, b), c);
    }

    public static long max2(long a, long b) {
        return Math.max(a, b);
    }

    public static long min3(long a, long b, long c) {
        return min2(min2(a, b), c);
    }

    public static long min2(long a, long b) {
        return Math.min(a, b);
    }

    public static int max3(int a, int b, int c) {
        return max2(max2(a, b), c);
    }

    public static int max2(int a, int b) {
        return Math.max(a, b);
    }

    public static int min3(int a, int b, int c) {
        return min2(min2(a, b), c);
    }

    public static int min2(int a, int b) {
        return Math.min(a, b);
    }

    /**************************************HELPER FUNCTION ENDS HERE ************************************/

    /*****************************************FAST INPUT STARTS HERE *************************************/


    public static void closeIO() throws IOException{
        out.flush();
        out.close();
        sc.close();
    }
    private static class FastestReader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastestReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastestReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

        private int skip() throws IOException {
            int b;
            //noinspection StatementWithEmptyBody
            while ((b = read()) != -1 && isSpaceChar(b)) {}
            return b;
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) { return -ret; }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) { return -ret; }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) { return -ret; }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) { buffer[0] = -1; }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) { fillBuffer(); }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }

    }
    /*****************************************FAST INPUT ENDS HERE *************************************/
}