Baby Bob is learning about mathematical expressions. He despises operands and operators, and only likes round brackets.

He's got a sequence $A$ of positive integers $A_1, A_2, \dots, A_N$. He wants to *bracketize* the sequence. A *bracketized* sequence created from $A$ is a sequence of strings $B_1, B_2, \dots, B_N$ such that each $B_i$ has length $A_i$, and $B_i$ consists only of either opening brackets `(`

, or closing brackets `)`

, but not both.

For example let $A=(1,3,4)$.

- A possible
*bracketized*sequence created from $A$ is`)`

,`)))`

,`((((`

. - The sequence
`)`

,`)()`

,`((((`

is not a*bracketized*sequence created from $A$, because the second element consists of both opening and closing brackets. - The sequence
`(`

,`))))`

,`((((`

is not a*bracketized*sequence created from $A$, because the length of the second element is not $3$. - The sequence
`(`

,`)`

is not a*bracketized*sequence created from $A$, because it consists of only $2$ strings.

Take the string $B_1 + B_2 + \dots + B_N$ (i.e., concatenate the elements of the *bracketized* sequence). Bob wonders whether he can *bracketize* $A$ so that the resulting string is a valid bracket sequence. A bracket sequence is valid if `1`

and `+`

characters can be inserted into it so that it becomes a valid mathematical expression. For example, `(((())))`

is a valid bracket sequence if $A=(1,3,4)$.

## Task

Write a program that finds such a bracket sequence or determines that it's impossible!

## Input data

The first line contains the only integer $N$. The second line contains $N$ integers $A_i$.

## Output data

You need to print a valid bracket sequence created from $A$ or `-1`

if it's not possible to create one.

If there are multiple correct bracket sequences, output any.

## Constraints and clarifications

- $1 \leq N \leq 500$
- $1 \leq A_i$ for each $i=0 \ldots N-1$
- $A_1 + A_2 + \ldots + A_N \leq 50 \ 000$

# | Points | Constraints |
---|---|---|

1 | 0 | Examples |

2 | 20 | $N \leq 2$ |

3 | 30 | $N \leq 20$ and $A_1 + A_2 + \dots + A_N \leq 200$ |

4 | 50 | No additional constraints |

## Example 1

`stdin`

```
3
1 3 4
```

`stdout`

```
(((())))
```

### Explanation

This sample case is explained in the statement.

## Example 2

`stdin`

```
4
2 2 1 1
```

`stdout`

```
(())()
```

### Explanation

In this sample the *bracketized* sequence is `((`

, `))`

, `(`

, `)`

.

## Example 3

`stdin`

```
2
2 1
```

`stdout`

```
-1
```