Score : $200$ points

问题描述

保龄球瓶从1到10编号。下图是球瓶排列的俯视图：

让我们将图中两条虚线之间的每一部分称为列。 例如，球瓶1和5属于同一列，球瓶3和9也属于同一列。

当某些球瓶被击倒时，可能会出现一种特殊的情况，称为分隔（split）。 如果满足以下两个条件，则球瓶的位置被视为分隔情况：

• 球瓶1被击倒。
• 存在两列不同的列，且这两列都满足以下条件：
  • 每列中至少有一个站立的球瓶。
  • 在这两列之间存在一列，其中所有球瓶都被击倒。

参见样例输入和输出以获得示例。

现在，你得到一个长度为10的字符串$S$来表示球瓶的状态。对于$i = 1, \dots, 10$，$S$的第$i$个字符如果是0，表示球瓶$i$已被击倒；如果是1，则表示球瓶仍然站立。 请确定由字符串$S$表示的球瓶位置是否构成分隔情况。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Bowling pins are numbered $1$ through $10$. The following figure is a top view of the arrangement of the pins:

Let us call each part between two dotted lines in the figure a column.
For example, Pins $1$ and $5$ belong to the same column, and so do Pin $3$ and $9$.

When some of the pins are knocked down, a special situation called split may occur.
A placement of the pins is a split if both of the following conditions are satisfied:

• Pin $1$ is knocked down.
• There are two different columns that satisfy both of the following conditions:
  • Each of the columns has one or more standing pins.
  • There exists a column between these columns such that all pins in the column are knocked down.

See also Sample Inputs and Outputs for examples.

Now, you are given a placement of the pins as a string $S$ of length $10$. For $i = 1, \dots, 10$, the $i$-th character of $S$ is 0 if Pin $i$ is knocked down, and is 1 if it is standing.
Determine if the placement of the pins represented by $S$ is a split.

Constraints

• $S$ is a string of length $10$ consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

$S$

Output

If the placement of the pins represented by $S$ is a split, print Yes; otherwise, print No.

Sample Input 1

0101110101

Sample Output 1

Yes

In the figure below, the knocked-down pins are painted gray, and the standing pins are painted white:

Between the column containing a standing pin $5$ and the column containing a standing pin $6$ is a column containing Pins $3$ and $9$. Since Pins $3$ and $9$ are both knocked down, the placement is a split.

Sample Input 2

0100101001

Sample Output 2

Yes

Sample Input 3

0000100110

Sample Output 3

No

This placement is not a split.

Sample Input 4

1101110101

Sample Output 4

No

This is not a split because Pin $1$ is not knocked down.

update @ 2024/3/10 11:16:21