Description:
You are given a binary string $$$s$$$ consisting of only characters 0 and/or 1.
You can perform several operations on this string (possibly zero). There are two types of operations:
- choose two consecutive elements and swap them. In order to perform this operation, you pay $$$10^{12}$$$ coins;
- choose any element from the string and remove it. In order to perform this operation, you pay $$$10^{12}+1$$$ coins.
Your task is to calculate the minimum number of coins required to sort the string $$$s$$$ in non-decreasing order (i. e. transform $$$s$$$ so that $$$s_1 \le s_2 \le \dots \le s_m$$$, where $$$m$$$ is the length of the string after applying all operations). An empty string is also considered sorted in non-decreasing order.
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The only line of each test case contains the string $$$s$$$ ($$$1 \le |s| \le 3 \cdot 10^5$$$), consisting of only characters 0 and/or 1.
The sum of lengths of all given strings doesn't exceed $$$3 \cdot 10^5$$$.
Output Format:
For each test case, print a single integer — the minimum number of coins required to sort the string $$$s$$$ in non-decreasing order.
Note:
In the first example, you have to remove the $$$1$$$-st element, so the string becomes equal to 00.
In the second example, the string is already sorted.
In the third example, you have to swap the $$$2$$$-nd and the $$$3$$$-rd elements, so the string becomes equal to 0011.
In the fourth example, you have to swap the $$$3$$$-rd and the $$$4$$$-th elements, so the string becomes equal to 00011101, and then remove the $$$7$$$-th element, so the string becomes equal to 0001111.
In the fifth example, you have to remove the $$$1$$$-st element, so the string becomes equal to 001101, and then remove the $$$5$$$-th element, so the string becomes equal to 00111.
In the sixth example, the string is already sorted.