Close Far

Background

Congcong is currently studying the distance relationships between numbers. He wants to determine if three given integers satisfy a specific "close" and "far" condition.

Problem Description

Given three integers, $a$, $b$, and $c$, return true if one of $b$ or $c$ is "close" (differing from $a$ by at most 1), while the other is "far" (differing from both other values by 2 or more). Note: $abs(num)$ computes the absolute value of a number.

Input Format

Input consists of a single line containing three integers $a$, $b$, and $c$.

$a$ $b$ $c$

Output Format

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

true or false

Sample

1 2 10

true

1 2 3

false

4 1 3

true

Sample Explanation

Sample 1: $a=1, b=2, c=10$. $b=2$ is close to $a=1$, because $|2-1|=1 \le 1$. $c=10$ is far from $a=1$, because $|10-1|=9 \ge 2$. $c=10$ is far from $b=2$, because $|10-2|=8 \ge 2$. Therefore, one is close and the other is far, returning true.

Sample 2: $a=1, b=2, c=3$. Check the case where $b$ is close to $a$ and $c$ is far: $|2-1|=1 \le 1$ (satisfies $b$ is close to $a$). $|3-1|=2 \ge 2$ (satisfies $c$ is far from $a$). $|3-2|=1 \ge 2$ (does not satisfy $c$ is far from $b$). So this case is false.

Check the case where $c$ is close to $a$ and $b$ is far: $|3-1|=2 \le 1$ (does not satisfy $c$ is close to $a$). So this case is false. Neither case is true, returning false.

Sample 3: $a=4, b=1, c=3$. Check the case where $b$ is close to $a$ and $c$ is far: $|1-4|=3 \le 1$ (does not satisfy $b$ is close to $a$). So this case is false.

Check the case where $c$ is close to $a$ and $b$ is far: $|3-4|=1 \le 1$ (satisfies $c$ is close to $a$). $|1-4|=3 \ge 2$ (satisfies $b$ is far from $a$). $|1-3|=2 \ge 2$ (satisfies $b$ is far from $c$). So this case is true, returning true.

Constraints

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