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)

def rightMinNumber(L):
    min = L[len(L)-1]
    min_index = len(L) - 1
    if len(L) > 1:
        for i in range(len(L)-2,-1,-1):
            if L[i] < min:
                min = L[i]
                min_index = i
    a.append(min)
    if min_index+1 == len(L) and min_index == 0:
        return
    if min_index + 1 < len(L):
        rL = L[min_index+1:]
        rightMinNumber(rL)
    if min_index > 0:
        lL = L[:min_index]
        rightMinNumber(lL)

N = int(input())
B = [int(_) for _ in input().split()]
#出力
a = []
#Bのエンコーダを作る
x = 0

#Bの正当性を調べる。
for i in range(N):
    if B[i] > i+1:
        x = -1
        break

if x == -1:
    print(x)
else :
    rightMinNumber(B)
    for i in range(N):
        print(a[i])