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>

int main(void){
    int n;
    scanf("%d",&n);
    int b[n];
    for(int i = 0;i < n;i++)scanf("%d",&b[i]);
    int prs[n];
    for(int i = 0;i < n;i++)prs[i] = 0;
    int cop[n];
    int bdresflag=0;
    for(int st = 0;st < n;st++){
        int conpflag=0;

        for(int copind = 0;copind < n;copind++)cop[copind] = b[copind];

        for(int prscnt = 0;prscnt < n;prscnt++){
            int ablflag=0;
            for(int chind = n-prscnt-1;chind >= 0;chind--)if(cop[chind]==chind+1){
                ablflag=1;
                prs[prscnt]=chind+1;
                for(int copind = chind+1;copind < n-prscnt;copind++)cop[copind-1]=cop[copind];
                if(prscnt==n-1)conpflag=1;
                break;
            }
            if(!ablflag)break;
        }
        if(conpflag)break;
        if(!conpflag && st==n-1)bdresflag=1;
    }
    if(bdresflag){
        puts("-1");
        return 0;
    }
    for(int i = n-1;i>=0;i--)printf("%d\n",prs[i]);
    return 0;
}