Unlucky One in Array

Background

Congcong has recently been studying number sequences. He has found that certain specific number combinations seem to carry special meanings.

Problem Description

We define a $1$ immediately followed by a $3$ in an array as an "unlucky" $1$. Return true if the given array contains an "unlucky" $1$ in the first $2$ positions or the last $2$ positions in the array. Specifically, if there exists an index $i$ in the array such that $arr[i] = 1$ and $arr[i+1] = 3$, and $i$ satisfies $i=0$ or $i=1$ (first $2$ positions), or $i=N-2$ or $i=N-1$ (last $2$ positions, where $N$ is the array length), then return true. Note that if the array length is less than $2$, an "unlucky" $1$ cannot exist. If the array length is $2$, only $i=0$ satisfies the condition.

Input Format

The input consists of a single line representing an array of integers. Array elements are separated by spaces.

arr

Output Format

Output a single line. If the array contains an unlucky $1$ that meets the conditions, output true; otherwise, output false.

result

Sample

[1 3 4 5]

true

[2 1 3 4 5]

true

[1 1 1]

false

Sample Explanation

• Sample 1: The array is [1 3 4 5]. At index $0$, $arr[0]=1$ and $arr[1]=3$, which is an unlucky $1$. Index $0$ is among the first $2$ positions, so true is returned.
• Sample 2: The array is [2 1 3 4 5]. At index $1$, $arr[1]=1$ and $arr[2]=3$, which is an unlucky $1$. Index $1$ is among the first $2$ positions, so true is returned.
• Sample 3: The array is [1 1 1]. There is no case where a $1$ is immediately followed by a $3$ in the array, so false is returned.

Constraints

Time limit for each test case is $1$ second, and memory limit is $1024$ KiB.