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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)
	b := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&b[i])
	}

	ans := make([]int, 0)
	for i := n; i > 0; i-- {
		m := min(i, 9)
		ok := false

		for j := m; j > 0; j-- {
			if j <= len(b) && b[j-1] == j {
				ok = true
				ans = append(ans, b[j-1])
				b = append(b[:j-1], b[j:]...)
				break
			}
		}
		if !ok {
			fmt.Println(-1)
			return
		}
	}

	for i := 0; i < len(ans); i++ {
		fmt.Println(ans[len(ans)-i-1])
	}
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}