Binary String Sorting

2000ms

262144K

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:

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.

Sample Input:

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1809D