Bracket balance

You are given a string of Latin letters and brackets (, ). Are the brackets placed correctly? Every ) closes the nearest unmatched ( before it.

• If everything is correct — 0.
• If some ) has no pair — the position of the first such ) (counting from $1$).
• If every ) has a pair but some ( stay unclosed — -1.

A single line — a string of $1$ to $1000$ characters: lowercase Latin letters, ( and ).

A single integer.

Keep a counter of open brackets: ( adds $1$, ) subtracts $1$. The place where the counter becomes negative is an unmatched ). If the counter is above $0$ at the end, some ( are unclosed. In the second example the extra ) is character 7: the answer is $7$.