Educational Codeforces Round 42 (Rated for Div. 2) D. Merge Equals

D. Merge Equals

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an array of positive integers. While there are at least two equal elements, we will perform the following operation. We choose the smallest value $x$ that occurs in the array $2$ or more times. Take the first two occurrences of $x$ in this array (the two leftmost occurrences). Remove the left of these two occurrences, and the right one is replaced by the sum of this two values (that is, $2\cdot x$).

Determine how the array will look after described operations are performed.

For example, consider the given array looks like $[3,4,1,2,2,1,1]$. It will be changed in the following way: $[3,4,1,2,2,1,1]\to [3,4,2,2,2,1]\to [3,4,4,2,1]\to [3,8,2,1]$.

If the given array is look like $[1,1,3,1,1]$ it will be changed in the following way: $[1,1,3,1,1]\to [2,3,1,1]\to [2,3,2]\to [3,4]$.

Input

The first line contains a single integer $n$ ($2\le n\le 150000$) — the number of elements in the array.

The second line contains a sequence from $n$ elements $a_1,a_2,\dots ,a_n$ ($1\le a_i\le {10}^9$) — the elements of the array.

Output

In the first line print an integer $k$ — the number of elements in the array after all the performed operations. In the second line print $k$ integers — the elements of the array after all the performed operations.

Examples

Input

Copy

7
3 4 1 2 2 1 1

Output

Copy

4
3 8 2 1 

Input

Copy

5
1 1 3 1 1

Output

Copy

2
3 4 

Input

Copy

5
10 40 20 50 30

Output

Copy

5
10 40 20 50 30 

Note

The first two examples were considered in the statement.

In the third example all integers in the given array are distinct, so it will not change.

题意：对一组数据进行操作：如果发现重复的数据，那就将第一个数据删除，把第二个数据乘以二，知道所以数据都只出现一次。

题解：开始我用的纯C硬做，但是数组超内存了。后来知道了c++STL 中的map，可以实现从key值到value的映射，这样就可以知道一个数的前面是否有重复的数，重复的数的下标是多少。然后进行相应操作即可。

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