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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
b = list(map(int, input().split()))
for i in range(n):
  if b[i] > i+1:
    print(-1)
    break
else:
  ans = []
  while len(b) > 1:
    c = len(ans)
    f = b[0]
    for i in range(1, len(b))[::-1]:
      if b[i] == i + 1:
        ans.extend(b[i:])
        b = b[:i]
        break
    for i in range(1, len(b)):
      if b[-1] ==  n - c or i == len(b) - 1:
        ans.append(b.pop(-1))
        break
      if f >= b[i]:
        ans.append(b.pop(i-1))
        break
      elif n - c == b[i]:
        ans.append(b.pop(i))
        break
      else:
        f = b[i]
  ans.append(1)
  for i in range(n)[::-1]:
    print(ans[i])