Check if All Numbers are 1 or Prime

Given a list of integers, determine whether every integer is either 1 or a prime number.

A number \(p\) is defined as prime if \(p > 1\) and its only divisors are \(1\) and \(p\). Equivalently, in mathematical terms, for every integer \(d\) satisfying \(2 \le d \le \sqrt{p}\), it holds that \(d\) does not divide \(p\).

Your program should read from the standard input (stdin) and output the result to the standard output (stdout) as either True or False. The result is True if each number in the list is either 1 or prime; otherwise, the result is False.

inputFormat

The first line of input contains a single integer \(n\) (\(1 \le n \le 10^5\)), the number of elements in the list.

The second line contains \(n\) space-separated integers. Each integer \(a_i\) satisfies \(|a_i| \le 10^9\).

outputFormat

Output a single line with either True if every element in the list is either 1 or a prime number, or False otherwise.

5
1 2 3 5 7

True