codeforces 633D - Fibonacci-ish 离散化 + 二分查询

Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if

the sequence consists of at least two elements
f₀ and f₁ are arbitrary
f_n + 2 = f_n + 1 + f_n for all n ≥ 0.

You are given some sequence of integers a₁, a₂, ..., a_n. Your task is rearrange elements of this sequence in such a way that its longest possible prefix is Fibonacci-ish sequence.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 1000) — the length of the sequence a_i.

The second line contains n integers a₁, a₂, ..., a_n (|a_i| ≤ 10⁹).

Output

Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.

Examples

Input

3
1 2 -1

Output

Input

5
28 35 7 14 21

Output

Note

In the first sample, if we rearrange elements of the sequence as - 1, 2, 1, the whole sequence a_i would be Fibonacci-ish.

In the second sample, the optimal way to rearrange elements is codeforces 633D - Fibonacci-ish 离散化 + 二分查询 , , , , 28.

思路:由于斐波那契数列数值成指数型增长(称为斐波那契数列的收敛性)，所以实际可选的长度不会超过100(实际上增长速度比2的幂次方要慢，若是正整数的斐波那契数列，要从0 1增长到1e9只需40位左右，所以题解给出的长度最大也是接近90的)；那么只需离散出全部的不同的数值及其个数，枚举前两位即可；特例是前两位为0，这时长度可能达到1000，但只会出现一次；

实现细节:用stk记录下路径上的序号，为了方便每次枚举时，初始化每个数的个数；同时也可递推出当前两位的和；

没使用map,使用map的话，插入和查询都是log(n),总时间复杂度为O(n^2*log(n)*len)len为每次搜索的长度，且常数较大；用数组模拟，时间复杂度中少了log(n)与map带来的额外的常数，只需46ms 0k

#include<iostream>

#include<cstdio>

#include<cstring>

#include<string.h>

#include<algorithm>

#include<vector>

#include<cmath>

#include<stdlib.h>

#include<time.h>

#include<stack>

#include<set>

#include<map>

#include<queue>

using namespace std;

#define rep0(i,l,r) for(int i = (l);i < (r);i++)

#define rep1(i,l,r) for(int i = (l);i <= (r);i++)

#define rep_0(i,r,l) for(int i = (r);i > (l);i--)

#define rep_1(i,r,l) for(int i = (r);i >= (l);i--)

#define MS0(a) memset(a,0,sizeof(a))

#define MS1(a) memset(a,-1,sizeof(a))

#define MSi(a) memset(a,0x3f,sizeof(a))

#define inf 0x3f3f3f3f

#define lson l, m, rt << 1

#define rson m+1, r, rt << 1|1

typedef __int64 ll;

template<typename T>

void read1(T &m)

{

    T x=,f=;char ch=getchar();

    while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}

    while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}

    m = x*f;

}

template<typename T>

void read2(T &a,T &b){read1(a);read1(b);}

template<typename T>

void read3(T &a,T &b,T &c){read1(a);read1(b);read1(c);}

template<typename T>

void out(T a)

{

    if(a>) out(a/);

    putchar(a%+'');

}

int v[],num[],stk[];//stk长度也要为1000，因为前面两个为0时,len可能为最大值

int main()

{

    int n;

    read1(n);

    rep0(i,,n) read1(v[i]);

    sort(v,v + n);

    int ans = ,cnt = ;

    rep0(i,,n){

        int t = i;

        while(i < n -  && v[i] == v[i + ]) i++;

        num[cnt] = i - t + ;

        v[cnt++] = v[i];//压缩

    }

    v[cnt] = 2e9;

    rep0(i,,cnt){

        rep0(j,,cnt){

            if(i != j || num[j] > ){

                stk[] = i;stk[] = j;

                int len = ,val = v[i] + v[j];

                num[i]--,num[j]--;

                int down = lower_bound(v,v+cnt,val) - v;

                while(v[down] == val && num[down]){

                    num[down]--;

                    val -= v[stk[len-]];

                    val += v[down];

                    stk[++len] = down;

                    down = lower_bound(v,v+cnt,val) - v;

                }

                ans = max(ans,len);

                rep1(i,,len) num[stk[i]]++;

            }

        }

    }

    out(ans);

    return ;

}