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)

import sys

stdin = sys.stdin

ni = lambda: int(ns()) #int
na = lambda: list(map(int, stdin.readline().split())) #int,list
ns = lambda: stdin.readline().rstrip()  # str

n=ni()
b=na()
ans=[]
def solve(li):

	for i in range(1,len(li)+1):
		if li[len(li)-i]==len(li)-i+1:
			a=li.pop(len(li)-i)
			ans.append(a)
			return solve(li)

solve(b)
if len(ans)==n:
	for i in range(n):
		print(ans[n-i-1])
else:
	print(-1)