Codeforces Round #326 (Div. 2)587A. Duff and Weight Lifting

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本文介绍了一个关于重量举升的算法问题，目标是最小化举升重量所需的步骤数，每一步中所举升的重量之和必须为2的幂次方。文中提供了一个示例样例及解释，并附带了部分C++代码。

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解题报告：Codeforces Round #326 (Editorial)

Recently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of i-th of them is 2wi pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there's no more weight left. Malek asked her to minimize the number of steps.

$\text{[math]}$

Duff is a competitive programming fan. That's why in each step, she can only lift and throw away a sequence of weights2a1, ..., 2ak if and only if there exists a non-negative integer x such that 2a1 + 2a2 + ... + 2ak = 2x, i. e. the sum of those numbers is a power of two.

Duff is a competitive programming fan, but not a programmer. That's why she asked for your help. Help her minimize the number of steps.

Input

The first line of input contains integer n (1 ≤ n ≤ 106), the number of weights.

The second line contains n integers w1, ..., wn separated by spaces (0 ≤ wi ≤ 106 for each 1 ≤ i ≤ n), the powers of two forming the weights values.

Output

Print the minimum number of steps in a single line.

   Sample test(s)
 
     input
   
5
1 1 2 3 3

     output
   
2

     input
   
4
0 1 2 3

     output
   
4

Note

In the first sample case: One optimal way would be to throw away the first three in the first step and the rest in the second step. Also, it's not possible to do it in one step because their sum is not a power of two.

In the second sample case: The only optimal way is to throw away one weight in each step. It's not possible to do it in less than 4 steps because there's no subset of weights with more than one weight and sum equal to a power of two.

题意：输入n个数，w[1]......w[n] . 2a1 + 2a2 + ... + 2ak = 2x, ak 属于那n个数。求有最少多少个这样的x。

#include
  
   
#include
   
    
#include
    
     
#include 
     
      
#include 
      
       
using namespace std;
const int N=1111111;
int a[N];
int main()
{
    int n,i,x,sum=0;
    scanf("%d",&n);
    for(i=0; i