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)

#!/usr/bin/python
# -*- coding: utf-8 -*-
import sys
import math
import collections

N,= map(int, sys.stdin.readline().rstrip().split(" "))
bs = map(int, sys.stdin.readline().rstrip().split(" "))

countdict = collections.defaultdict(list)
for i, b in enumerate(bs):
    countdict[b].append(i+1)


def find_one():
    for i in range(101, 0, -1):
        if i in countdict:
            for j in range(len(countdict[i])):
                if countdict[i][j] == i:
                    del countdict[i][j]
                    return i

def change_pos(pos):
    for counts in countdict.values():
        for i in range(len(counts)):
            if counts[i] > pos:
                counts[i] -= 1

results = []
while True:
    res = find_one()
    if res is None:
        break
    results.append(res)
    change_pos(res)

rest = sum(len(counts) for counts in countdict.values())
if rest > 0:
    print(-1)
else:
    for i in reversed(results):
        print(i)

exit(0)