#include <bits/stdc++.h>
using namespace std;
const int maxn = 200000;
struct number {
  long long x;
  int idx;
  bool operator<(const number &b) const {
    if (b.x == x) {
      return b.idx < idx;
    }
    return b.x < x;
  }
} a[maxn];
struct ans {
  long long x;
  int idx;
} p[maxn];
bool cmp(ans a, ans b) { return a.idx < b.idx; }
int main() {
  int n;
  priority_queue<number> q;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i].x;
    a[i].idx = i;
    q.push(a[i]);
  }
  int cnt = 0;
  while (q.size() > 1) {
    number fir = q.top();
    q.pop();
    number sec = q.top();
    q.pop();
    if (fir.x != sec.x) {
      p[cnt].x = fir.x;
      p[cnt++].idx = fir.idx;
      q.push(sec);
      continue;
    } else if (fir.x == sec.x) {
      sec.x = fir.x * 2;
      q.push(sec);
    }
  }
  while (!q.empty()) {
    number cur = q.top();
    q.pop();
    p[cnt].x = cur.x;
    p[cnt++].idx = cur.idx;
  }
  sort(p, p + cnt, cmp);
  cout << cnt << endl;
  for (int i = 0; i < cnt; ++i) {
    cout << p[i].x << " ";
  }
  cout << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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 ⋅ 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]~→~[3, 4, 2, 2, 2, 1]~→~[3, 4, 4, 2, 1]~→~[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]~→~[2, 3, 1, 1]~→~[2, 3, 2]~→~[3, 4].

Input

The first line contains a single integer n (2 ≤ n ≤ 150 000) — the number of elements in the array.

The second line contains a sequence from n elements a_1, a_2, ..., a_n (1 ≤ a_i ≤ 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

7
3 4 1 2 2 1 1


Output

4
3 8 2 1 


Input

5
1 1 3 1 1


Output

2
3 4 


Input

5
10 40 20 50 30


Output

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 200000;
struct number {
  long long x;
  int idx;
  bool operator<(const number &b) const {
    if (b.x == x) {
      return b.idx < idx;
    }
    return b.x < x;
  }
} a[maxn];
struct ans {
  long long x;
  int idx;
} p[maxn];
bool cmp(ans a, ans b) { return a.idx < b.idx; }
int main() {
  int n;
  priority_queue<number> q;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i].x;
    a[i].idx = i;
    q.push(a[i]);
  }
  int cnt = 0;
  while (q.size() > 1) {
    number fir = q.top();
    q.pop();
    number sec = q.top();
    q.pop();
    if (fir.x != sec.x) {
      p[cnt].x = fir.x;
      p[cnt++].idx = fir.idx;
      q.push(sec);
      continue;
    } else if (fir.x == sec.x) {
      sec.x = fir.x * 2;
      q.push(sec);
    }
  }
  while (!q.empty()) {
    number cur = q.top();
    q.pop();
    p[cnt].x = cur.x;
    p[cnt++].idx = cur.idx;
  }
  sort(p, p + cnt, cmp);
  cout << cnt << endl;
  for (int i = 0; i < cnt; ++i) {
    cout << p[i].x << " ";
  }
  cout << endl;
  return 0;
}

```