Exact Three Threes

Background

Congcong has recently been studying array properties. He encountered an interesting problem that requires determining if an array satisfies specific conditions.

Problem Description

Given an array of integers, return true if the value $3$ appears in the array exactly $3$ times, and no two $3$'s are next to each other; otherwise, return false.

Input Format

The input consists of a single line representing an integer array. Array elements are separated by spaces and enclosed in square brackets [].

[A_1 A_2 ... A_N]

Output Format

Output to standard output in the following format.

Output true if the conditions are met; otherwise, output false.

Sample

[3 1 3 1 3]

true

[3 1 3 3]

false

[3 4 3 3 4]

false

Sample Explanation

Sample 1: In the array [3 1 3 1 3], the number $3$ appears $3$ times, and no two $3$'s are adjacent. Thus, the output is true.

Sample 2: In the array [3 1 3 3], the number $3$ appears $3$ times, but the last two $3$'s are adjacent. Thus, the output is false.

Sample 3: In the array [3 4 3 3 4], the number $3$ appears $3$ times, but the middle two $3$'s are adjacent. Thus, the output is false.

Constraints

The length of the array $N$ satisfies $1 \le N \le 100$. Each element $A_i$ in the array satisfies $0 \le A_i \le 1000$. Time limit: $1$ second, Memory limit: $1024$ KiB.