A9915 | Brackets in Implications

The first line contains integer $n$ ( $1<=n<=100000$ ) — the number of arguments in a logical expression.

The second line contains $n$ numbers $a_{1},a_{2},...,a_{n}$ (), which means the values of arguments in the expression in the order they occur.

Print "NO" (without the quotes), if it is impossible to place brackets in the expression so that its value was equal to 0.

Otherwise, print "YES" in the first line and the logical expression with the required arrangement of brackets in the second line.

The expression should only contain characters '0', '1', '-' (character with ASCII code 45), '>' (character with ASCII code 62), '(' and ')'. Characters '-' and '>' can occur in an expression only paired like that: ("->") and represent implication. The total number of logical arguments (i.e. digits '0' and '1') in the expression must be equal to $n$ . The order in which the digits follow in the expression from left to right must coincide with $a_{1},a_{2},...,a_{n}$ .

The expression should be correct. More formally, a correct expression is determined as follows:

- Expressions " $0$ ", " $1$ " (without the quotes) are correct.
- If $v_{1}$ , $v_{2}$ are correct, then $v_{1}$ -> $v_{2}$ is a correct expression.
- If $v$ is a correct expression, then $(v)$ is a correct expression.

The total number of characters in the resulting expression mustn't exceed $10^{6}$ .

If there are multiple possible answers, you are allowed to print any of them.

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