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: Time Limit Exceeded)

from collections import deque
def main():
    n = int(input())
    b = list(map(int, input().split()))
    s = set()
    q = deque()

    q.append([tuple(b), [0]*n, 0])
    ans = None
    while q:
        now, history, depth = q.popleft()
        if now in s:
            continue
        s.add(now)
        if len(now) == 0:
            ans = history
            break
        for i, j in enumerate(now):
            if i+1 == j:
                tmp = history[::]
                tmp[depth] = i+1
                q.appendleft([tuple(now[:i] + now[i+1:]), tmp, depth+1])
    if ans is None:
        print(-1)
    else:
        for i in ans[::-1]:
            if i == 0:
                break
            print(i)
if __name__ == "__main__":
    main()