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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'

class Main {
  solve() {
    let n = input.nextIntArr()[0];
    let b = input.nextIntArr();
    let ret = [];
    let order = [];
    for (let i = 0; i < n; ++i) {
      let value = ret.length + 1;
      let cur = ret.length - 1;
      for (let j = n - 1; j >= 0; j--) {
        if (b[j] == value) { 
          ret.splice(cur+1,0,value); 
          order.push(value);
          break;
        }
        if (ret[cur] == b[j]) { 
          --cur;
          --value;
        }
      }
    }
    if (ret.length == b.length) { console.log(order.join('\n')); }
    else { console.log(-1); }
  }
}

class Input {
  constructor() {
	this.cursor = 0;
	this.inputAll();
  }

  inputAll() {
	this.data = (require("fs").readFileSync("/dev/stdin", "utf8")).split('\n');
	return this.data;
  }

  /* 1行 or 複数行文字列 */
  nextLine(n) {
	if (n) {
	  const ret = this.data.slice(this.cursor, this.cursor + n);
	  this.cursor += n;
	  return ret;
	}
	return this.data[this.cursor++];
  }
  /* 一行文字配列 */
  nextStrArr() { return this.nextLine().split(' '); } 
  /* 一行整数配列 */
  nextIntArr() { return this.nextStrArr().map((e) => parseInt(e)); }
  /* 一行浮動小数点配列 */
  nextFloatArr() { return this.nextStrArr().map((e) => parseFloat(e)); }
  /* 複数行整数配列 */
  nextIntLine(n) { return this.nextLine(n).map((e) => parseInt(e)) }
  /* 複数行浮動小数点配列 */
  nextFloatLine(n) { return this.nextLine(n).map((e) => parseFloat(e)) }
  /* 複数行文字列二次元配列 */
  nextStrRange(n) { return this.nextLine(n).map((line) => line.split(' ')); }
  /* 複数行整数二次元配列 */
  nextIntRange(n) {
	return this.nextLine(n).map((line) => line.split(' ').map((e) => parseInt(e)));
  }
  /* 複数行浮動小数点数二次元配列 */
  nextFloatRange(n) {
	return this.nextLine(n).map((line) => line.split(' ').map((e) => parseFloat(e)));
  }
} 
const input = new Input();
(new Main()).solve();