Binary String Sorting
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.
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 $3 \cdot 10^5$.
For each test case, print a single integer — the minimum number of coins required to sort the string $s$ in non-decreasing order.
Input
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
For each test case, print a single integer — the minimum number of coins required to sort the string $s$ in non-decreasing order.
6
100
0
0101
00101101
1001101
11111
1000000000001
0
1000000000000
2000000000001
2000000000002
0
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.