Merge Equals_data structure

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.

#include<bits/stdc++.h>
using namespace std;
#define ll long long

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    freopen("in.txt","r",stdin);
    //cout<<"1"<<endl;
    int n;
    cin>>n;
    map<ll,set<int> >s;
    vector<ll> a(n);
    for(int i=0;i<n;i++){
        cin>>a[i];
        s[a[i]].insert(i);
    }
    for(auto c:s){
        while((int)c.second.size()>1){
            int x=*c.second.begin();
            int y=*next(c.second.begin());
            a[y]+=a[x];
            a[x]=-1;
            c.second.erase(x);
            c.second.erase(y);
            s[a[y]].insert(y);
        }
    }
    vector<ll> ans;
    for(int i=0;i<n;i++){
        if(a[i]!=-1)
            ans.push_back(a[i]);
    }
    cout<<ans.size()<<endl;
    for(ll x:ans){
        cout<<x<<" ";
    }
    cout<<endl;
}