CF1809D.Binary String Sorting

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.

给你一个仅由字符 0 和/或 1 组成的二进制字符串 $s$。

你可以对该字符串执行若干次操作（可能为零次）。操作分为两种类型：

• 选择两个相邻的元素并交换它们。执行该操作需花费 $10^{12}$ 枚硬币；
• 从字符串中任选一个元素并将其删除。执行该操作需花费 $10^{12}+1$ 枚硬币。

你的任务是计算将字符串 $s$ 变为非递减序（即：经过所有操作后，设所得字符串长度为 $m$，则满足 $s_1 \le s_2 \le \dots \le s_m$）所需的最少硬币数。空字符串也被视为满足非递减序。

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 $3 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

每个测试用例仅有一行，包含字符串 $s$（$1 \le |s| \le 3 \cdot 10^5$），该字符串仅由字符 0 和/或 1 组成。

所有给定字符串的长度总和不超过 $3 \cdot 10^5$。

For each test case, print a single integer — the minimum number of coins required to sort the string $s$ in non-decreasing order.

对于每个测试用例，输出一个整数——将字符串 $s$ 按非递减顺序排序所需的最少硬币数量。

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.

在第一个例子中，你需要删除第 $1$ 个元素，因此字符串变为 00。

在第二个例子中，字符串本身已经有序。

在第三个例子中，你需要交换第 $2$ 个和第 $3$ 个元素，因此字符串变为 0011。

在第四个例子中，你需要交换第 $3$ 个和第 $4$ 个元素，因此字符串变为 00011101，然后删除第 $7$ 个元素，字符串变为 0001111。

在第五个例子中，你需要删除第 $1$ 个元素，因此字符串变为 001101，然后再删除第 $5$ 个元素，字符串变为 00111。

在第六个例子中，字符串本身已经有序。