Summarize to the Power of Two（map+思惟）

A sequence a1,a2,…,ana1,a2,…,an is called good if, for each element aiai, there exists an element ajaj (i≠ji≠j) such that ai+ajai+aj is a power of two (that is, 2d2d for some non-negative integer dd).

For example, the following sequences are good:

• [5,3,11][5,3,11] (for example, for a1=5a1=5 we can choose a2=3a2=3. Note that their sum is a power of two. Similarly, such an element can be found for a2a2 and a3a3),
• [1,1,1,1023][1,1,1,1023],
• [7,39,89,25,89][7,39,89,25,89],
• [][].

Note that, by definition, an empty sequence (with a length of 00) is good.

For example, the following sequences are not good:

• [16][16] (for a1=16a1=16, it is impossible to find another element ajaj such that their sum is a power of two),
• [4,16][4,16] (for a1=4a1=4, it is impossible to find another element ajaj such that their sum is a power of two),
• [1,3,2,8,8,8][1,3,2,8,8,8] (for a3=2a3=2, it is impossible to find another element ajaj such that their sum is a power of two).

You are given a sequence a1,a2,…,ana1,a2,…,an. What is the minimum number of elements you need to remove to make it good? You can delete an arbitrary set of elements.

Input

The first line contains the integer nn (1≤n≤1200001≤n≤120000) — the length of the given sequence.

The second line contains the sequence of integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109).

Output

Print the minimum number of elements needed to be removed from the given sequence in order to make it good. It is possible that you need to delete all nn elements, make it empty, and thus get a good sequence.

Examples

input

6
4 7 1 5 4 9

output

1

input

5
1 2 3 4 5

output

Copy

2

input

1
16

output

1

input

4
1 1 1 1023

output

0

Note

In he first example, it is enough to delete one element a4=5. The remaining elements form the sequence [4,7,1,4,9][4,7,1,4,9], which is good.

 

题目意思：给你一个数列，而后让你删掉某个数，让每个数均可以与另一个数相加，之和等于2的^d次方，问最少删掉的个数

解题思路：先预处理出2的次幂，而后暴力枚举出每一个数与每一个2的次幂之差，去判断在map中是否有这样的差存在（注意相同的两个数，好比4 ，4   这个时候就能够特判一下，出现次数），若不存在那么就须要删除掉这个数。

 

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<map>
 4 #include<algorithm>
 5 #define ll long long int
 6 using namespace std;  7 ll d[32];  8 ll a[1000010];  9 map<ll,ll>mp; 10 void double_2() 11 { 12     int i; 13     d[0]=1; 14     for(i=1; i<=31; i++) 15  { 16         d[i]=d[i-1]*2; 17  } 18 } 19 int main() 20 { 21     int i,j,flag,n; 22  ll k; 23     double_2();///2的幂
24     while(scanf("%d",&n)!=EOF) 25  { 26         int count=0; 27         mp.clear();///map清零
28         for(i=0; i<n; i++) 29  { 30             scanf("%lld",&a[i]); 31             mp[a[i]]++;///记录出现的次数
32  } 33         for(i=0; i<n; i++) 34  { 35             flag=0; 36             for(j=0; j<=31; j++) 37  { 38                 if(a[i]>=d[j]) 39  { 40                     continue; 41  } 42                 else
43  { 44                     k=d[j]-a[i]; 45                     if(mp[k])///map中存在
46  { 47                         if(a[i]==k) 48  { 49                             if(mp[k]>=2)///map中须要至少两个
50  { 51                                 flag=1; 52                                 break; 53  } 54  } 55                         else
56  { 57                             flag=1; 58                             break; 59  } 60  } 61  } 62  } 63             if(!flag) 64  { 65                 count++; 66  } 67  } 68         printf("%d\n",count); 69  } 70     return 0; 71 }