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: Wrong Answer)

typedef long unsigned int size_t;
extern int printf (const char *__restrict __format, ...);
extern int scanf (const char *__restrict __format, ...) ;
extern int getchar (void);
extern int putchar (int __c);
int nextInt(){int f=0;char s=0;char c=getchar();while((c<48)||(57<c)){if(c==45){s=1;c=getchar();break;}c=getchar();}while((48<=c)&&(c<=57)){f=f*10+(c-48);c=getchar();}return s?-f:f;}
short int nextShort(){short f=0;char s=0;char c=getchar();while((c<48)||(57<c)){if(c==45){s=1;c=getchar();break;}c=getchar();}while((48<=c)&&(c<=57)){f=f*10+(c-48);c=getchar();}return s?-f:f;}
long long int nextLong(){long long int f=0;char s=0;char c=getchar();while((c<48)||(57<c)){if(c==45){s=1;c=getchar();break;}c=getchar();}while((48<=c)&&(c<=57)){f=f*10+(c-48);c=getchar();}return s?-f:f;}
void println(){putchar(10);}
void print(char *f){while(*f){putchar(*f);f++;}}
void printInt(int f){char c[10];if(!f){putchar(48);return;}if(f<0){f=-f;putchar(45);}char i=0;while(f){c[++i]=(f%10)+48;f/=10;}while(i){putchar(c[i--]);}}
void printLong(long long int f){char c[19];if(!f){putchar(48);return;}if(f<0){f=-f;putchar(45);}char i=0;while(f){c[++i]=(f%10)+48;f/=10;}while(i){putchar(c[i--]);}}
typedef int (*__compar_fn_t) (const void *, const void *);
extern void *bsearch (const void *__key, const void *__base, size_t __nmemb, size_t __size, __compar_fn_t __compar)__attribute__ ((__nonnull__ (1, 2, 5))) ;
extern void qsort (void *__base, size_t __nmemb, size_t __size, __compar_fn_t __compar) __attribute__ ((__nonnull__ (1, 4)));
int compare_int(const void *a, const void *b){return *(int*)a - *(int*)b;}
int compare_long(const void *a, const void *b){return *(long long int*)a - *(long long int*)b;}
int n, i, j;
int b[101][2];
int a[101];
int d, d1;
int main(){
 n = nextInt();
 for(i=1; i<=n; i++){
  b[i][0] = nextInt();
  b[i][1] = i;
 }
 qsort(b+1, n, sizeof(long long int), compare_long);
 for(i=n; i>=1; i--){
  if(b[i][0]>=i){print("-1\n"); return 0;}
 }
 for(i=n; i>=1; i--){
  d=1;
  while(1){
   d1=b[i][0];
   for(j=d+1; j<=n; j++){
    if(a[j]<=d1){d1++;}
   }
   if(d1==b[i][1]){break;}
   d++;
  }
  a[d] = b[i][0];
 }
 for(i=1; i<=n; i++){
  printInt(a[i]); println();
 }
 println();
}