You are given a binary string $$$s$$$ (a string consisting only of 0-s and 1-s).

You can perform two types of operations on $$$s$$$:

delete one character from $$$s$$$. This operation costs $$$1$$$ coin;
swap any pair of characters in $$$s$$$. This operation is free (costs $$$0$$$ coins).

You can perform these operations any number of times and in any order.

Let's name a string you've got after performing operations above as $$$t$$$. The string $$$t$$$ is good if for each $$$i$$$ from $$$1$$$ to $$$|t|$$$ $$$t_i \neq s_i$$$ ($$$|t|$$$ is the length of the string $$$t$$$). The empty string is always good. Note that you are comparing the resulting string $$$t$$$ with the initial string $$$s$$$.

What is the minimum total cost to make the string $$$t$$$ good?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The only line of each test case contains a binary string $$$s$$$ ($$$1 \le |s| \le 2 \cdot 10^5$$$; $$$s_i \in \{$$$0, 1$$$\}$$$) — the initial string, consisting of characters 0 and/or 1.

Additional constraint on the input: the total length of all strings $$$s$$$ doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print one integer — the minimum total cost to make string $$$t$$$ good.

Note

In the first test case, you have to delete a character from $$$s$$$ to get the empty string $$$t$$$. Only then $$$t$$$ becomes good. One deletion costs $$$1$$$ coin.

In the second test case, you can, for example, delete the second character from $$$s$$$ to get the string 01, and then swap the first and second characters to get the string $$$t$$$ $$$=$$$ 10. String $$$t$$$ is good, since $$$t_1 \neq s_1$$$ and $$$t_2 \neq s_2$$$. The total cost is $$$1$$$ coin.

In the third test case, you can, for example, swap $$$s_1$$$ with $$$s_2$$$, swap $$$s_3$$$ with $$$s_4$$$, swap $$$s_5$$$ with $$$s_7$$$, $$$s_6$$$ with $$$s_8$$$ and $$$s_9$$$ with $$$s_{10}$$$. You'll get $$$t$$$ $$$=$$$ 1010001110. All swap operations are free, so the total cost is $$$0$$$.

Swap and Delete

Examples