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 div = vec![0; AMAX + 1];
    let mut pri = Vec::new();

    for i in 2..=AMAX {
        if div[i] == 0 {
            div[i] = i;
            pri.push(i);
        }
        let mut j = 0;
        while j < pri.len() && pri[j] <= div[i] && i * pri[j] <= AMAX {
            div[i * pri[j]] = pri[j];
            j += 1;
        }
    }

    let mut cnt = vec![0; AMAX + 1];
    for &a in &a {
        cnt[a] += 1;
    }
    for i in (2..=AMAX).rev() {
        if div[i] == i {
            continue;
        }
        let j = i / div[i];
        cnt[j] += cnt[i];
        if div[j] != div[i] {
            cnt[div[i]] += cnt[i];
        }
    }

    let pairwise = pri.iter().all(|&i| cnt[i] <= 1);
    let setwise = pri.iter().all(|&i| cnt[i] < n);

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