102671: [AtCoder]ABC267 B - Split?

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.

问题描述

保龄球瓶从$1$到$10$编号。下图是保龄球瓶排列的俯视图：

我们把图中两个虚线之间的一部分叫做一个列。例如，瓶$1$和瓶$5$在同一列，瓶$3$和瓶$9$也在同一列。

当一些瓶子被击倒时，可能会发生一个特殊的情况叫做分瓶。如果满足以下两个条件，瓶子的排列就是一个分瓶：

• 瓶$1$被击倒。
• 有两个不同的列满足以下两个条件：
  • 每个列都有一根或多根站立的瓶子。
  • 在这些列之间存在一个列，该列中的所有瓶子都被击倒。

参见样例输入和输出以查看例子。

现在，给你一个表示瓶子排列的字符串$S$，长度为$10$。对于$i = 1, \dots, 10$，$S$的第$i$个字符是0，表示瓶$i$被击倒，是1表示它站立。确定字符串$S$表示的瓶子排列是否为分瓶。

约束

• $S$是一个长度为$10$的字符串，由0和1组成。

输入

输入从标准输入中给出，格式如下：

$S$

输出

如果字符串$S$表示的瓶子排列为分瓶，打印Yes；否则，打印No。

样例输入 1

0101110101

样例输出 1

Yes

在下图中，被击倒的瓶子被涂成灰色，站立的瓶子被涂成白色：

在包含站立瓶$5$的列和包含站立瓶$6$的列之间有一个包含瓶$3$和瓶$9$的列。因为瓶$3$和瓶$9$都被击倒，所以瓶子的排列是一个分瓶。

样例输入 2

0100101001

样例输出 2

Yes

样例输入 3

0000100110

样例输出 3

No

这个排列不是分瓶。

样例输入 4

1101110101

样例输出 4

No

这不是一个分瓶，因为瓶$1$没有被击倒。