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: Runtime Error)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{input, marker::*, fastout};
use superslice::*;

fn main() {
     //pairwise coprime ならば pairwise coprime、
     //setwise coprime ならば setwise coprime、
     //そのどちらでもなければ not coprime と出力せよ
    input! {
        n: usize,
        a: [usize; n],
    }

    let mut g = a[0];
    for i in 1..n {
        g = gcd(g as u64, a[i] as u64) as usize;
    }
    if g != 1 {
        println!("not coprime");
        return;
    }

    let factors = factor_table(100_001);
    let mut fset = HashSet::new();
    for i in 0..n {
        let mut num = a[i];
        while num != 1 {
            let p = factors[num];
            if !fset.contains(&p) {
                fset.insert(p);
                while num % p == 0 {
                    num /= p;
                }
            } else {
                println!("setwise coprime");
                return;
            }
        }
    }
    println!("pairwise coprime");
}
#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: u64, b: u64) -> u64 {
    a / gcd(a, b) * b
}
#[allow(dead_code)]
/// (gcd, x, y)
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}

#[allow(dead_code)]
pub fn factor_table(max_n: usize) -> Vec<usize> {
    let mut res = vec![0; max_n + 1];
    for i in 2..max_n + 1 {
        if res[i] == 0 {
            let mut j = i;
            while j <= max_n {
                res[j] = i;
                j += i;
            }
        }
    }
    res
}