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)

# -*- coding: utf-8 -*-
import sys
import collections

def main():
	N = int(input())
	B = input().split(" ")
	B = [int(s) for s in B]
	
	ans = []
	for i, vol in enumerate(B):
		if vol > N or vol > i+1:
			print(-1)
			sys.exit()
		
	keep = []
	ans.append(B.pop(0))
	ans.append(B.pop(-1))
	B.reverse()
	for i, vol in enumerate(B):
		if vol > len(ans):
			keep.append((i, vol))
			continue
		ans.append(vol)
		
		for j, val in enumerate(keep):
			k, val2 = val
			if val2+k <= len(ans):
				#print("sss")
				#print(len(ans)+k)
				ans.append(val2)
				keep.pop(j)
	
	for vol in ans:
		print(vol)
			
if __name__ == "__main__":
	main()