Alice is training for an upcoming javelin-throwing competition! The javelin-throwing field can be modelled as a 1-D line, with Alice standing at the coordinate .

Alice throws javelins in the positive direction. When she throws a javelin, it lands at some real-valued point on the field, making a hole there. It's possible for the javelin to land exactly in a previously made hole, in which case no new hole is made. Holes are permanent, and there are initially no holes in the field.

Right after the throw, Alice counts and , the number of holes strictly behind and strictly in front of the javelin she just threw (respectively). She then tells you . You don't know anything else about her throws.

Given the information you have right after the throw, what is the minimum possible value of ?

#### Constraints

##### Subtask 1 [15%]

##### Subtask 2 [85%]

#### Input Specification

The first line contains an integer , the number of throws.

The second line contains space-separated integers, .

#### Output Specification

Output space-separated integers. The integer should be the minimum possible value of , given that you know through .

#### Sample Input 1

```
3
0 0 2
```

#### Sample Output 1

`0 0 1`

#### Explanation for Sample 1

There are no holes in front of throw :

So the first answer is .

On throw , you know that . It's possible that both throws landed at exactly the same point, in which case there would be no holes in front of either throw:

So the second answer is .

However, you then learn that there were holes behind throw . So the second throw must have landed behind the first, and the only solution would be

for an answer of .

#### Sample Input 2

```
6
0 1 0 3 0 2
```

#### Sample Output 2

`0 0 1 2 5 6`

#### Sample Input 3

```
5
0 1 2 1 2
```

#### Sample Output 3

`0 0 0 1 1`

## Comments

Data were updated post-contest to break some unintended solutions.

:^)