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: Runtime Error)

import sys

N = int(input())
b = list(map(int, input().split()))
a = {}
out = []

for k in range(N):
  if b[k] > k + 1:
    print(-1)
    sys.exit()

cnt2 = 0
d = {}

for j in reversed(range(1, N)):
  cnt = 0
  for i in range(j+1, N):
    if b[j] >= b[i]:
      cnt += 1
  a[b[j] + cnt - 1] = b[j]
  if b[j] == 1:
    s = []
    for k in reversed(range(len(a))):
      s.append(a[k])
    out.append(s)
    cnt2 = cnt
out = [k for k in reversed(out)]
for k in range(N):
  print(out[k])