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: Accepted)

fun main(args:Array<String>) {
    val n = readLine()!!.toInt()
    val num = readLine()!!.split(" ").map { it.toInt() }.toMutableList()
    if(!solve(num)) {
        println(-1)
    }
}

fun solve(num:MutableList<Int>):Boolean {
    val list = mutableListOf<Int>()
    for(i in (0 until 100)) {
        var idx = -1
        for(j in (num.indices.reversed())) {
            if(j + 1 == num[j]) {
                idx = j
                break
            }
        }
        if(idx < 0) {
            return false
        }
        list.add(idx+1)
        num.removeAt(idx)
        if(num.isEmpty()) {
            break
        }
    }
    list.reversed().forEach { println(it) }
    return true
}