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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.lang.Integer.max
import java.lang.Integer.min

//

fun main() {
    abc177e()
}

fun abc177e() {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }
    val gcds = mutableMapOf<Int, Int>()
    for (i in 0 until n) {
        var j = 2
        var t = a[i]
        while (j * j <= t) {
            if (t % j == 0) {
                gcds[j] = gcds.getOrDefault(j, 0) + 1
                if (t / j != j) {
                    gcds[t / j] = gcds.getOrDefault(t / j, 0) + 1
                }
            }
            j++
        }
        gcds[t] = gcds.getOrDefault(t, 0) + 1
    }
    val maxCount = gcds.maxBy { it.value }!!
    if (maxCount.value == 1) {
            println("pairwise coprime")
    } else if (maxCount.value == n) {
        println("not coprime")
    } else {
        println("setwise coprime")
    }
}