CF1005C Summarize to the Power of Two 暴力 map

Summarize to the Power of Two

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A sequence ${\mathrm{a1,a2,\dots ,ana1,a2,\dots ,an is\; called\; good\; if,\; for\; each\; element aiai,\; there\; exists\; an\; element ajaj (i\ne ji\ne j)\; such\; that ai+ajai+aj is\; a\; power\; of\; two\; (that\; is, 2d2d for\; some\; non-negative\; integer dd).}}^{}$

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 $\mathrm{00)\; is\; good.}$

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 ${\mathrm{a1,a2,\dots ,ana1,a2,\dots ,an.\; What\; is\; the\; minimum\; number\; of\; elements\; you\; need\; to\; remove\; to\; make\; it\; good?\; You\; can\; delete\; an\; arbitrary\; set\; of\; elements.}}^{}$

Input

The first line contains the integer $\mathrm{nn (1\le n\le 1200001\le n\le 120000)\; —\; the\; length\; of\; the\; given\; sequence.}$

The second line contains the sequence of integers ${\mathrm{a1,a2,\dots ,ana1,a2,\dots ,an (1\le ai\le 1091\le ai\le 109).}}^{}$

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 $\mathrm{nn elements,\; make\; it\; empty,\; and\; thus\; get\; a\; good\; sequence.}$

Examples

input

6
4 7 1 5 4 9

output

1

input

5
1 2 3 4 5

output

2

input

1
16

output

1

input

4
1 1 1 1023

output

0

Note

In the first example, it is enough to delete one element ${\mathrm{a4=5a4=5.\; The\; remaining\; elements\; form\; the\; sequence [4,7,1,4,9][4,7,1,4,9],\; which\; is\; good.}}^{}$

 题意：给你n个数，问去掉几个数后，每个数都被用上与另一个数和为2的幂数

分析：直接暴力枚举每个二的幂数减去当前数的差是否存在于这个数列中，用map存下每个数

#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 2e5 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
ll a[maxn], vis[maxn];
int main() {
    ll n;
    while( cin >> n ) {
        map<ll,ll> mm;
        for( ll i = 0; i < n; i ++ ) {
            cin >> a[i];
            mm[a[i]] ++;
        }
        ll cnt = 0;
        for( ll i = 0; i < n; i ++ ) {
            bool flag = false;
            for( ll j = 1<<30; j >= 1; j /=2 ) {
                if( j > a[i] ) {
                    if( ( a[i] == j/2 && mm[j-a[i]] > 1 ) || ( mm[j-a[i]] > 0 && a[i] != j/2 ) ) {
                        flag = true;
                        break;
                    }
                }
            }
            if( !flag ) {
                //debug(a[i]), debug(i);
                cnt ++;
            }
        }
        cout << cnt << endl;
    }
    return 0;
}