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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import itertools

n = int(input())

originLinks = list(itertools.combinations(list(range(1,n+1)), 2))
originLinkNum = len(originLinks)
end = False
for leftLinkNum in range(originLinkNum, n-2, -1):
  # print(leftLinkNum)
  if end:
    break
  tempGraph = list(itertools.combinations(originLinks, leftLinkNum))
  # print(tempGraph)
  for graph in tempGraph:
    # print(graph)
    sums = [0] * n
    for link in graph:
      sums[link[0]-1] += link[1]
      sums[link[1]-1] += link[0]
    # print(sums, len(set(sums)))
    if len(set(sums)) == 1:
      #print(graph)
      print(len(graph))
      for link in graph:
        print(" ".join(list(map(str, link))))
      end = True
      break