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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val N = sc.nextInt()
    val B = IntArray(N){0}
    val count = IntArray(N+1){0}
    for (i in 0 until N) {
        B[i]  = sc.nextInt()
    }
    val ans = IntArray(N){0}
    
    fun search(n:Int,list:MutableList<Int>):Boolean {
        if (n==0) return true
        for (i in 1..n) {
            if(list[i-1] != i) continue
            list.removeAt(i-1)
            if (search(n-1, list)) {
                ans[n-1] = i
                return true
            }
            list.add(i-1,i)
        }
        return false
    }
    if (search(N,B.toMutableList())) ans.forEach{println(it)}
    else println(-1)
}