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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x)=parse(Int,x)
parseMap(x::Array{SubString{String},1})=map(parseInt,x)

function main()
	n = readline() |> parseInt
	b = readline() |> split |> parseMap
	flg = 0
	ans = Int[]
	for i in 1:n
		if b[i] > i
			flg = 1
			break
		end
	end
	for i in 1:n
		t = length(b)
		for j in 0:t-1
			if b[t-j] == t-j
				t = t-j
				break
			end
		end
		if t == 0
			flg = 1
			break
		else
			push!(ans,t)
			deleteat!(b,t)
		end
	end
	if flg == 1
		println(-1)
	else
		for i in 0:n-1
			println(ans[n-i])
		end
	end
end
main()