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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>
#include <stdlib.h>

int a[101];
int b[101];

void shift_left (int *array, int index, int max)
{
  int i;
  
  for (i=index; i<max; i++) {
    array[i] = array[i+1];
  }
  return;
}

int main()
{
  int cnt;
  int N;
  int i;
  int j;

  cnt = scanf("%d", &N);

  for (i=1; i<=N; i++) {
    cnt = scanf("%d", &a[i]);
  }
  
  j = N;
restart:
  for (i=N; i>0; i--) {
    if (a[i] == 0) continue;
    if (a[i] == i) {
      b[j] = i;
      j--;
      if (j == 0) break;
      shift_left(a, i, (N+1));
      goto restart;
    }
  }
  
  if (j != 0) {
    printf("-1");
    return 0;
  }

  for (j=1; j<=N; j++) {
    printf("%d\n", b[j]);
  }

  return 0;
}