[EC Final 2021] Fenwick Tree

定义一次「操作」为选定任意一个 $pos$ 和 $val$ 后对 $c$ 序列进行以下操作（显然就是树状数组的单点加操作）： ```python def update(pos, val): while (pos <= n): c[pos] += val pos += pos & (-pos) ``` 给定序列长度 $n$ 和一个长度为 $n$ 的 $\texttt{01}$ 串 $s$，以及一个初始全为 $0$ 的序列 $c$。 求最少的操作数使得最终的 $c$ 序列满足 $\forall 1\le i\le n: s_i=\texttt0 \Leftrightarrow c_i=0,s_i=1\Leftrightarrow c_i\not=0$。 你只需要输出最少的操作数。

Prof. Pang is giving a lecture on the Fenwick tree (also called binary indexed tree). In a Fenwick tree, we have an array $c[1\ldots n]$ of length $n$ which is initially all-zero ($c[i]=0$ for any $1\le i\le n$). Each time, Prof. Pang can call the following procedure for some position $pos$ ($1\leq pos \leq n$) and value $val$: ```cpp def update(pos, val): while (pos <= n): c[pos] += val pos += pos & (-pos) ``` Note that `pos & (-pos)` equals to the maximum power of $2$ that divides `pos` for any positive integer `pos`. In the procedure, $val$ can be **any real** number. After calling it some (zero or more) times, Prof. Pang forgets the exact values in the array $c$. He only remembers whether $c[i]$ is zero or not for each $i$ from $1$ to $n$. Prof. Pang wants to know what is the minimum possible number of times he called the procedure assuming his memory is accurate.

The first line contains a single integer $T~(1 \le T \le 10^5)$ denoting the number of test cases. For each test case, the first line contains an integer $n~(1 \le n \le 10 ^ 5)$. The next line contains a string of length $n$. The $i$-th character of the string is `1` if $c[i]$ is nonzero and `0` otherwise. It is guaranteed that the sum of $n$ over all test cases is no more than $10^6$.

For each test case, output the minimum possible number of times Prof. Pang called the procedure. It can be proven that the answer always exists.

3
5
10110
5
00000
5
11111

3
0
3

For the first example, Prof. Pang can call `update(1,1)`, `update(2,-1)`, `update(3,1)` in order. For the third example, Prof. Pang can call `update(1,1)`, `update(3,1)`, `update(5,1)` in order.