Check 271 Pattern

Background

Dawei is studying a special number sequence. He wants to know if a specific pattern exists in an integer array.

Problem Description

Given an array of integers, return true if it contains a $2, 7, 1$ pattern. A $2, 7, 1$ pattern refers to a value, followed by the value plus $5$, followed by the value minus $1$. Additionally, the $2, 7, 1$ pattern counts even if the third value differs by $2$ or less from the correct value (value minus $1$). For example, if the first value is $x$, the second is $x+5$, and the third is $z$, then a $2, 7, 1$ pattern exists if $|z - (x-1)| \le 2$.

Input Format

Input is given from standard input in the following format.

A single line containing several integers, separated by spaces.

Output Format

Output is printed to standard output in the following format.

Output true if a $2, 7, 1$ pattern exists in the array; otherwise, output false.

Sample

1 2 7 1

true

1 2 8 1

false

2 7 1

true

Sample Explanation

• Sample 1: Array [1 2 7 1]. When $x=2$, the second element is $2+5=7$, and the third element is $1$. Since $|1 - (2-1)| = |1-1| = 0 \le 2$, a $2, 7, 1$ pattern exists.
• Sample 2: Array [1 2 8 1]. When $x=2$, the second element is $8$, which is not equal to $2+5=7$. Therefore, no $2, 7, 1$ pattern exists.
• Sample 3: Array [2 7 1]. When $x=2$, the second element is $2+5=7$, and the third element is $1$. Since $|1 - (2-1)| = |1-1| = 0 \le 2$, a $2, 7, 1$ pattern exists.

Constraints

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