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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function Main(input) {

    input = input.split("\n");
    
    N = Number(input[0]);
    let An = input[1].split(" ").map(Number);
    
    if (gcd(An) !== 1) {
        console.log("not coprime");
        return;
    }
        
    let freq = Array(1000001).fill(0);
    for(let A of An) {
        if (A === 1) continue;
        freq[A]++;
        if (freq[A] > 1) {
            console.log("setwise coprime");
            return;
        }
    }
    
    for (let i = 2; i <= 1000001; i++) {
        let tmp = 0;
        for (let j = i; j <= 1000001; j += i) {
            tmp += freq[j];
            if (tmp >= 2) {
                console.log("setwise coprime");
                return;
            }
        }
    }
    
    console.log("pairwise coprime");
    
}

function gcd(arg) {
    
    let f = (a, b) => b ? f(b, a % b) : a
    let ans = arg[0];
    for (let i = 1; i < arg.length; i++) {
        ans = f(ans, arg[i]); 
    }
    return ans;
    
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));