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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	var N int
	fmt.Scan(&N)
	b := make([]int, N)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	for i := range b {
		sc.Scan()
		b[i], _ = strconv.Atoi(sc.Text())
		b[i]-- // 0-indexed
	}
	var found bool
	ans := make([]int, 0)
	for len(b) > 0 {
		found = false
		for i := len(b) - 1; i >= 0; i-- { // 最後に挿入した数字を追跡する
			if b[i] == i { // これを満たす数が複数ある場合は一番右側の数を採用する
				found = true
				ans = append(ans, b[i])
				b = append(b[0:i], b[i+1:]...)
				break
			}
		}
		if !found {
			fmt.Println(-1)
			return
		}
	}
	for i := len(ans) - 1; i >= 0; i-- {
		fmt.Println(ans[i] + 1) // 0-indexedなので1足す
	}
}