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: Wrong Answer)

(async () => {
    let input = '';
    for await (const chunk of process.stdin) input += chunk;
    let values = input.split(/\s/).map(v => +v);

    const n = values.shift();
    values = values.slice(0, n);
    values = values.sort((a, b) => b - a);

    let prims = [2];
    for(let i = 3; i <= values[0]; i++){
        const prim = prims.find((prim) => i % prim === 0)
        if(prim == undefined){
            prims.push(i);
        }else{
            prims.push(prim);
        }
    }

    const gcd = (a, b) => b ? gcd(b, a % b) : a;
    let gcd_ = values[0];
    for (let i = 0; i < values.length; i++) {
        if(prims[values[i] + 2] == -1){
            console.log('pairwise coprime');
            return;
        }
        prims[values[i]] = -1;
        gcd_ = gcd(gcd_, values[i]);
    }
    if(gcd_ === 1){
        console.log('setwise coprime');
    }else{
        console.log('not coprime');
    }
})();