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

var sc = bufio.NewScanner(os.Stdin)

func Scanner() string {
	sc.Scan()
	return sc.Text()
}

func intScanner() int {
	n, _ := strconv.Atoi(Scanner())
	return n
}

func floatScanner() float64 {
	n, _ := strconv.ParseFloat(Scanner(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func stringSliceScanner(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scanner()
	}
	return a
}
func intSliceScanner(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = intScanner()
	}
	return a
}

var mod int

func main() {
	mod = 1000000007
	buf := make([]byte, 0)
	sc.Buffer(buf, mod)
	sc.Split(bufio.ScanWords)
	n := intScanner()
	b := make([]int, n+1)
	for i := 1; i < n+1; i++ {
		b[i] = intScanner()
	}
	ans := solve(1, b)
	f := true
	for _, i := range ans {
		if i == -1 {
			f = false
			break
		}
	}
	if f {
		for i := 1; i < n+1; i++ {
			fmt.Println(ans[i])
		}
	} else {
		fmt.Println(-1)
	}
}
func solve(x int, y []int) []int {
	if len(y) == 1 {
		return y
	} else {
		if y[0] != x-1 {
			return []int{-1}
		}
		s := make([][]int, 0)
		for i := 1; i < len(y); i++ {
			if y[i] == x {
				s = append(s, []int{y[i]})
			} else if len(s) == 0 {
				s = [][]int{[]int{-1}}
				return []int{-1}
			} else {
				s[len(s)-1] = append(s[len(s)-1], y[i])
			}
		}
		ret := make([]int, 0)
		ret = append(ret, y[0])
		for i := len(s) - 1; i >= 0; i-- {
			ret = append(ret, solve(x+1, s[i])...)
		}
		return ret
	}
}