Educational Codeforces Round 42D. Merge Equals（STL）

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 $\mathrm{xx that\; occurs\; in\; the\; array 22 or\; more\; times.\; Take\; the\; first\; two\; occurrences\; of xx in\; this\; array\; (the\; two\; leftmost\; occurrences).\; Remove\; the\; left\; of\; these\; two\; occurrences,\; and\; the\; right\; one\; is\; replaced\; by\; the\; sum\; of\; this\; two\; values\; (that\; is, 2\cdot x2\cdot x).}$

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

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

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

Input

The first line contains a single integer $\mathrm{nn (2\le n\le 1500002\le n\le 150000)\; —\; the\; number\; of\; elements\; in\; the\; array.}$

The second line contains a sequence from $\mathrm{nn elements a1,a2,\dots ,ana1,a2,\dots ,an (1\le ai\le 1091\le ai\le 109)\; —\; the\; elements\; of\; the\; array.}$

Output

In the first line print an integer $\mathrm{kk —\; the\; number\; of\; elements\; in\; the\; array\; after\; all\; the\; performed\; operations.\; In\; the\; second\; line\; print kkintegers\; —\; the\; elements\; of\; the\; array\; after\; all\; the\; performed\; operations.}$

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：给出n个数，接下来对这个数列进行一个操作，即从左往右找最小的两个相同的数，然后将左边那个删除，右边那个数的值乘以2。不断进行以上操作，直到无相同的数为止，输出最终那个数列。

思路：

map中套一个set的操作，mp[i]指的是值为i的数字的下标合集。从小到大的遍历mp，如果有两个，则将其合并为一个放到2*i的集合中去。如果仅含一个元素，记录其的位置即可。

代码：

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn = 2e6+100;
ll n;
ll a[maxn];
map<ll, set<ll> >mp;
ll b[maxn];
int main()
{
    scanf("%I64d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%I64d",&a[i]);
        mp[a[i]].insert((ll)i);
    }
    ll ans=0;
    for (auto it: mp)
    {
        while(it.second.size()>=2)
        {
            it.second.erase(it.second.begin());
            mp[it.first*2].insert(*it.second.begin());
            it.second.erase(it.second.begin());
        }
        if(it.second.size()==1)
        {
            int id=*it.second.begin();
            b[id]=it.first;
            ans++;
        }
    }
    printf("%I64d\n",ans);
    for(int i=1;i<=n;i++) if(b[i]>0) printf("%I64d ",b[i]);
    return 0;
}