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 (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import kotlin.math.pow

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = nextList().map(String::toInt)
fun nextLongList() = nextList().map(String::toLong)
fun nextDoubleList() = nextList().map(String::toDouble)

val pw = PrintWriter(System.out)
fun print(s: Any = "") = pw.print(s)
fun println(s: Any = "") = pw.println(s)

fun <T> Iterable<T>.join(separator: CharSequence = ", ", prefix: CharSequence = "", postfix: CharSequence = "") = joinToString(separator, prefix, postfix)
fun <T> Array<T>.join(separator: CharSequence = ", ", prefix: CharSequence = "", postfix: CharSequence = "") = joinToString(separator, prefix, postfix)
fun Int.pow(n: Int) = pow(n.toLong())
fun Int.pow(n: Long) = toDouble().pow(n.toDouble()).toLong()
fun Long.pow(n: Int) = pow(n.toLong())
fun Long.pow(n: Long) = toDouble().pow(n.toDouble()).toLong()

fun main(args: Array<String>) {
    main()
    pw.flush()
}

fun main() {
    val N = nextInt()
    val B = nextIntList().toMutableList()
    val A = ArrayDeque<Int>()
    var i = N - 1
    while (B.isNotEmpty() && i >= 0) {
        if (B[i] == i + 1) {
            A.push(i + 1)
            B.removeAt(i)
            i = B.size - 1
        } else {
            i--
        }
    }
    println(if (B.isEmpty()) A.joinToString("\n") else -1)
}