Check Adjacency of Twos

Background

Congcong has been studying the properties of number sequences recently. He noticed that when certain numbers appear in a sequence, they always like to be next to another identical number. He wants your help to verify a specific rule.

Problem Description

Given an array of integers, return true if every $2$ that appears in the array is next to another $2$; otherwise, return false.

Input Format

Input is given from standard input in the following format.

A single line containing several integers, representing the elements of the array.

Output Format

Output is printed to standard output in the following format.

Output true if the condition is met, otherwise output false.

Sample

4 2 2 3

true

2 2 4

true

2 2 4 2

false

Sample Explanation

• Sample 1: In the array [4 2 2 3], there are two $2$s, and they are adjacent, so true is returned.
• Sample 2: In the array [2 2 4], there are two $2$s, and they are adjacent, so true is returned.
• Sample 3: In the array [2 2 4 2], there are three $2$s. The first two $2$s are adjacent, but the last $2$ is next to a $4$ and not another $2$, so false is returned.

Constraints

Time limit: $1$ second, Memory limit: $1024$ KiB for each test case.