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 (3.4.3) (judge verdict: Accepted)


def read_tokens():
    return input().strip().split(' ')

def read_ints():
    return [int(token) for token in read_tokens()]

def solve(b, n):
    ret = []
    while len(b) > 0:
        # print(b)
        c = None
        for i in reversed(range(len(b))):
            if b[i] > i + 1:
                return [-1]
            if b[i] == i + 1:
                c = b[:i] + b[i+1:]
                ret.append(b[i])
                break
        if c is None:
            return [-1]
        b = c
    return list(reversed(ret))

n, = read_ints()
b = read_ints()

ans = solve(b, n)
print('\n'.join(str(x) for x in ans))