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: Wrong Answer)

N = int(input())
b = list(map(int, input().split()))
b_rev = []
op = []
for i in (reversed(b)):
    b_rev.append(i)

if b_rev.count(1) == 0 or b[0] != 1:
    print(-1)
    exit()
while 1:
    if len(b_rev) == 0:
        for i in op:
            print(i)
        else:
            exit()
    idx_one = b_rev.index(1)
    op.append(1)
    b_tmp = b_rev[0:idx_one]
    while len(b_tmp) > 0:
        min_tmp = min(b_tmp)
        for idx, item in enumerate(b_tmp):
            if item == min_tmp:
                idx_min = idx
        op.append(b_tmp.pop(idx_min))
    else:
        del b_rev[0:idx_one + 1]