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)

mod prime_number {

use std::iter::Iterator;

type ValueType = usize;

pub struct PrimeFactorization {
    n: ValueType,
    cur: ValueType,
    limit: ValueType,
}

///素因数分解
impl PrimeFactorization {
    ///素因数を計算するイテレータを返す。
    pub fn calc(n: ValueType) -> PrimeFactorization {
        PrimeFactorization {
            n: n,
            cur: 1,
            limit: n,
        }
    }
}

impl Iterator for PrimeFactorization {
    type Item = ValueType;
    fn next(&mut self) -> Option<Self::Item> {
        loop {
            if self.cur == 0 || self.cur > self.n {
                return None;
            }

            self.cur += 1;

            if self.cur * self.cur > self.n {
                if self.n != 1 {
                    self.cur = 0;
                    return Some(self.n);
                }
                return None;
            }
            if self.n % self.cur == 0 {
                while self.n % self.cur == 0 {
                    self.n /= self.cur;
                }
                self.cur -= 1;
                return Some(self.cur + 1);
            }
        }
    }
}

}

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

use prime_number::*;

use num::integer::gcd;
const INF: usize = 999999999999;
fn main() {
    input! {
        n:usize,
        a:[usize;n]
    }

    let mut sc = a[0];
    for i in 1..a.len() {
        sc = gcd(sc, a[i]);
    }
    let mut is_sc = sc == 1;
    let mut is_pc = true;
    let mut arr = vec![INF; 1000001];
    let mut idx = 0;
    for &i in &a {
        for q in PrimeFactorization::calc(i) {
            if arr[q] != idx && arr[q] != INF {
                is_pc = false;
            }
            arr[q] = idx;
        }
        idx += 1;
    }
    if is_pc {
        println!("pairwise coprime");
    } else if is_sc {
        println!("setwise coprime");
    } else {
        println!("not coprime");
    }
}