Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

const int N = 1024;

int a[N];
int pos[N];

int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i)
    scanf("%d", a+i);
  vector<int> ans;
  for (int i = n-1; i >= 0; --i) {
    int now = 0;
    for (int j = 0; j < n; ++j) {
      pos[j] = -2;
      if (a[j] == -1) continue;
      ++now;
      pos[j] = now;
    }
    if (now == 0) break;
    for (int j = n-1; j >= 0; --j) {
      if (pos[j] == a[j]) {
        ans.push_back(a[j]);
        a[j] = -1;
        break;
      }
    }
  }
  if (ans.size() == n) {
    reverse(ans.begin(), ans.end());
    for (int x : ans)
      printf("%d\n", x);
  }
  else
    puts("-1");
  return 0;
}