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 Python (3.8.2) (judge verdict: Accepted)

n = int(input())
new_B = list(map(int, input().split()))
ans = []
cnt = 0

while (cnt < 100000) & (new_B != []):
    B = new_B
    length = len(B)
    new_B = []
    for i in range(1, length + 1):
        if B[-i] < (len(B) - i + 1):
            new_B = [B[-i]] + new_B
        elif B[-i] == (len(B) - i + 1):
            ans.append(B[-i])
            new_B = B[:-i] + new_B
            break
        else:
            print(-1)
            exit()
    cnt += 1


if cnt == 100000:
    print(-1)
else:
    for i in ans[::-1]:
        print(i)