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: Time Limit Exceeded)

package main

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

var n int

var goal []int

var cur []int

var op []int

var count []int

func insert(j int) {
	for i := n; i > j; i-- {
		cur[i] = cur[i-1]
	}
	cur[j] = j
}

func remove(index int) {
	for i := index; i < n; i++ {
		cur[i] = cur[i+1]
	}
}

func solve(depth int) bool {
	if depth > n {
		for i := 1; i <= n; i++ {
			if cur[i] != goal[i] || cur[i] == 0 {
				return false
			}
		}
		return true
	}

	for j := 1; j <= depth; j++ {
		if count[j] == 0 {
			continue
		}
		insert(j)
		op[depth] = j
		count[j] -= 1
		if solve(depth + 1) {
			return true
		}
		remove(j)
		op[depth] = 0
		count[j] += 1
	}

	return false
}

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Scan()
	n, _ = strconv.Atoi(scanner.Text())
	scanner.Scan()
	g := strings.Fields(scanner.Text())

	goal = make([]int, n+1)
	cur = make([]int, n+1)
	op = make([]int, n+1)
	count = make([]int, n+1)
	for i := 1; i <= n; i++ {
		goal[i], _ = strconv.Atoi(g[i-1])
		count[goal[i]] += 1
	}

	if solve(1) {
		for i := 1; i <= n; i++ {
			fmt.Println(op[i])
		}
	} else {
		fmt.Println("-1")
	}
}