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 <stdlib.h>
#include <math.h>
#include <string.h>

#define TRUE 1
#define FALSE 0

void shift_num(int *num) {
	int i = 0;
	while (*(num + i) != -1) {
		*(num + i) = *(num + i + 1);
		i++;
	}
}

int main(void) {
	int n, sw;
	int *num, *answer;
	scanf("%d", &n);
	num = (int *)malloc(sizeof(int)*(n+1));
	answer = (int *)malloc(sizeof(int)*n);
	for (int i = 0; i < n; i++) {
		scanf("%d", num + i);
	}
	num[n] = -1;
	for (int i = 0; i < n; i++) {
		sw = FALSE;
		for (int j = n - 1 - i; j >= 0; j--) {
			if (num[j] == j + 1) {
				answer[i] = j + 1;
				shift_num(num + j);
				sw = TRUE;
				break;
			}
		}
		if (sw == FALSE) {
			break;
		}
	}
	if (sw == TRUE) {
		for (int i = n - 1; i >= 0; i--) {
			printf("%d\n", answer[i]);
		}
	}
	else if (sw == FALSE) {
		printf("%d\n", -1);
	}
	return 0;
}