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An expression consisting of operands and binary operators can be written in Reverse Polish Notation (RPN) by writing both the operands followed by the operator. For example, 3 + (4 * 5) can be written as "3 4 5 * +".
You are given a string consisting of x's and *'s. x represents an operand and * represents a binary operator. It is easy to see that not all such strings represent valid RPN expressions. For example, the "x*x" is not a valid RPN expression, while "xx*" and "xxx**" are valid expressions. What is the minimum number of insert, delete and replace operations needed to convert the given string into a valid RPN expression?
Input: The first line contains the number of test cases T. T test cases follow. Each case contains a string consisting only of characters x and *.
Output: Output T lines, one for each test case containing the least number of operations needed.
Constraints: 1 <= T <= 100 The length of the input string will be at most 100.
For the first three cases, the input expression is already a valid RPN, so the answer is 0. For the fourth case, we can perform one delete, and one insert operation: xx -> xx -> xx
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