codeforces 962 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.

题解:我们用优先队列。。。。对于这个题，我是各种问题暴露，首先优先队列不熟练，long long输出错误，自己不注意。。。

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
#include<map>
#define ll long long
using namespace std;
const int maxn = 1e5+7;
typedef pair<ll, ll> P;
int n;
ll a;
priority_queue<P, vector<P>, greater<P> > q, Q;


int main()
{
    scanf("%d", &n);
    for(int i = 1; i <= n; i++)
    {
        scanf("%lld", &a);
        P p(a, i);
        q.push(p);
    }
    while(!q.empty())
    {
        P p = q.top();
        q.pop();
        if(q.empty()) {
            swap(p.first, p.second);
            Q.push(p);
            break;
        }
        P pp = q.top();
        q.pop();
        if(pp.first != p.first)
        {
            q.push(pp);
            swap(p.first, p.second);
            Q.push(p);
        }
        else
        {
            pp.first *= 2;
            q.push(pp);
        }
    }
    printf("%d\n", Q.size());
    P p = Q.top();
    Q.pop();
    printf("%lld", p.second);
    while(!Q.empty()){
        p = Q.top();
        Q.pop();
        printf(" %lld", p.second);
    }
    cout << endl;
    return 0;
}