Problem:
Score : 500 points

Problem Statement

We have N integers. The i-th number is A_i.

\{A_i\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\{A_i\} is said to be setwise coprime when \{A_i\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \{A_i\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

2 \leq N \leq 10^6

1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

If \{A_i\} is pairwise coprime, print pairwise coprime; if \{A_i\} is setwise coprime, print setwise coprime; if neither, print not coprime.

Sample Input 1

3
3 4 5

Sample Output 1

pairwise coprime

GCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input!(n: usize, a: [usize; n]);

    const AMAX: usize = 1_000_000;

    let mut cnt = vec![0; AMAX + 1];
    for &a in &a {
        cnt[a] += 1;
    }

    let mut seen = vec![false; AMAX + 1];
    let mut max_csum = 0;
    for i in 2..=AMAX {
        if seen[i] {
            continue;
        }
        let csum = (i..=AMAX)
            .step_by(i)
            .map(|j| {
                seen[j] = true;
                cnt[j]
            })
            .sum();
        max_csum = max_csum.max(csum);
    }

    let pairwise = max_csum <= 1;
    let setwise = max_csum < n;

    println!(
        "{}",
        if pairwise {
            "pairwise coprime"
        } else if setwise {
            "setwise coprime"
        } else {
            "not coprime"
        }
    );
}