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B - Split?

Score : $200$ points

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.

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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.

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0101110101

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.

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0100101001

Yes

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0000100110

No

This placement is not a split.

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1101110101

No

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