Given a string S consisting only of opening and closing curly brackets '{' and '}' find out the minimum number of reversals required to make a balanced expression.

Input
The first line of input contains an integer T, denoting the number of test cases. Then T test cases
follow. The first line of each test case contains a string S consisting only of { and }.

Output
Print out minimum reversals required to make S balanced. If it cannot be balanced, then print -1.

Explanation:
Testcase 1: For the given string }{{}}{{{ since the length is even we just need to count the number of openning brackets('{') suppose denoted by 'm' and closing brackest('}') suppose dentoed by 'n' after removing highlighted ones. After counting compute ceil(m/2) + ceil(n/2).