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: Time Limit Exceeded)


var memo = {"1":"1"}
function solve(arr,len){
  if(memo.hasOwnProperty(arr)){
  	return memo[arr];
  }
  
  for(var i = len-1; i >= 0; i--){
  	if(arr[i] == i+1){
    	var newArray = arr.filter((el,ind)=>ind!=i)
      var result = solve(newArray,len-1);
      if(result){
      	return (memo[arr] = result + " " + (i+1));
      }
    }
  }
  
  memo[arr] = false;
}
function Main(input){
	
	input = input.split("\n");
  var N = ~~input[0];
  var b = input[1].split(" ").map(a=>~~a);
  var result = solve(b,N);
  if(result)return result.split(" ").join("\n");
  return "-1";
}

// If you are interested in the algorithms I used, 
// there is no need to read down from this line.

((b,c,d)=>"undefined"!=typeof require?console.log(Main(require("fs").readFileSync("/dev/stdin","utf8"))):[b=b.split("\n").slice(1,-1).join("\n"),c=function(){try{return Main(b)}catch(f){return f.stack||f.message}}(),d=typeof c,"string"==d||(c=JSON.stringify(c)),$("<form>").append([[10,b],0,[1,d],0,[10,c]].map(f=>$(f?"<textarea>":"<br>",f&&{rows:f[0],cols:40,text:f[1]}))).appendTo("body")])(`
9
1 1 1 2 2 1 2 3 2
`);