P10914 [Lanqiao Cup 2024 National B] Jumping Stones.

Xiaoming is playing a small jumping-stones game with his friends. There are $n$ stones in a row, numbered from $1$ to $n$. The $i$-th stone has a positive integer weight value $c_i$ written on it. If at some moment Xiaoming is on stone $j$, then he may choose to jump to stone $j + c_j$ (provided that $j + c_j \le n$), or jump to stone $2j$ (provided that $2j \le n$). If there is no stone he can jump to, the game ends. Suppose Xiaoming chooses to start jumping from stone $x$. If a stone **may** be visited by Xiaoming (where “visited” means that there exists some moment when Xiaoming is on this stone), then the weight value of this stone is included in the score set $S_x$. Then Xiaoming’s score when starting from stone $x$ is $|S_x|$. For example, if Xiaoming starts from stone $x$ and the weight values on all stones that may be visited are $5, 3, 5, 2, 3$, then $S_x = \{5, 3, 2\}$ and the score is $|S_x| = 3$. Xiaoming may choose any stone to start from. Please compute the maximum score Xiaoming can obtain.

The input has $2$ lines. The first line contains a positive integer $n$. The second line contains $n$ positive integers $c_1, c_2, \cdots, c_n$, separated by spaces.

The output has $1$ line, containing one integer, which is the answer.

**Sample Explanation** Starting from the first stone gives the maximum score. The possible paths are as follows: 1. Stone $1$ $\to$ stone $5$: choose to jump from stone $1$ to stone $1 + c_1 = 5$. 2. Stone $1$ $\to$ stone $2$ $\to$ stone $5$: first choose to jump from stone $1$ to stone $2 \times 1 = 2$, then choose to jump from stone $2$ to stone $2 + c_2 = 5$. 3. Stone $1$ $\to$ stone $2$ $\to$ stone $4$: first choose to jump from stone $1$ to stone $2 \times 1 = 2$, then choose to jump from stone $2$ to stone $2 \times 2 = 4$. Therefore, the set of weight values of all stones that may be visited is $S_1 = \{c_1, c_2, c_4, c_5\} = \{4, 3, 2, 1\}$, and the score is $|S_1| = 4$. **Constraints** For $20\%$ of the testdata, it is guaranteed that $n \le 20$. For $100\%$ of the testdata, it is guaranteed that $n \le 40000$ and $c_i \le n$. Translated by ChatGPT 5