Score : $200$ points

问题描述

高桥正在尝试制作一款受棒球启发的游戏，但在编写代码时遇到了困难。 为高桥编写一个程序，解决以下问题。

有四个正方形分别称为 Square $0$、Square $1$、Square $2$ 和 Square $3$。最初，所有正方形都是空的。 还有一个整数 $P$；初始时，$P = 0$。 给定一个正整数序列 $A = (A_1, A_2, \dots, A_N)$，按照 $i = 1, 2, \dots, N$ 的顺序执行以下操作：

1. 在 Square $0$ 上放置一个棋子。
2. 将正方形上每个棋子向前移动 $A_i$ 个格子。也就是说，如果 Square $x$ 上有一个棋子，则将该棋子移动到 Square $(x + A_i)$。 然而，如果某个棋子的目标格子不存在（即 $x + A_i$ 大于或等于 $4$），则移除该棋子。并将被移除的棋子数量加到 $P$ 上。

在所有操作完成后，输出 $P$ 的值。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is trying to create a game inspired by baseball, but he is having difficulty writing the code.
Write a program for Takahashi that solves the following problem.

There are $4$ squares called Square $0$, Square $1$, Square $2$, and Square $3$. Initially, all squares are empty.
There is also an integer $P$; initially, $P = 0$.
Given a sequence of positive integers $A = (A_1, A_2, \dots, A_N)$, perform the following operations for $i = 1, 2, \dots, N$ in this order:

1. Put a piece on Square $0$.
2. Advance every piece on the squares $A_i$ squares ahead. In other words, if Square $x$ has a piece, move the piece to Square $(x + A_i)$.
   If, however, the destination square does not exist (i.e. $x + A_i$ is greater than or equal to $4$) for a piece, remove it. Add to $P$ the number of pieces that have been removed.

Print the value of $P$ after all the operations have been performed.

Constraints

• $1 \leq N \leq 100$
• $1 \leq A_i \leq 4$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the value of $P$ after all the operations have been performed.

Sample Input 1

4
1 1 3 2

Sample Output 1

3

The operations are described below. After all the operations have been performed, $P$ equals $3$.

• The operations for $i=1$:
  1. Put a piece on Square $0$. Now, Square $0$ has a piece.
  2. Advance every piece on the squares $1$ square ahead. After these moves, Square $1$ has a piece.
• The operations for $i=2$:
  1. Put a piece on Square $0$. Now, Squares $0$ and $1$ have a piece.
  2. Advance every piece on the squares $1$ square ahead. After these moves, Squares $1$ and $2$ have a piece.
• The operations for $i=3$:
  1. Put a piece on Square $0$. Now, Squares $0$, $1$, and $2$ have a piece.
  2. Advance every piece on the squares $3$ squares ahead.
     Here, for the pieces on Squares $1$ and $2$, the destination squares do not exist (since $1+3=4$ and $2+3=5$), so remove these pieces and add $2$ to $P$. $P$ now equals $2$. After these moves, Square $3$ has a piece.
• The operations for $i=4$:
  1. Put a piece on Square $0$. Now, Squares $0$ and $3$ have a piece.
  2. Advance every piece on the squares $2$ squares ahead.
     Here, for the piece on Square $3$, the destination square does not exist (since $3+2=5$), so remove this piece and add $1$ to $P$. $P$ now equals $3$.
     After these moves, Square $2$ has a piece.

Sample Input 2

3
1 1 1

Sample Output 2

0

The value of $P$ may not be updated by the operations.

Sample Input 3

10
2 2 4 1 1 1 4 2 2 1

Sample Output 3

8

update @ 2024/3/10 10:53:08