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: Time Limit Exceeded)

import java.math.BigInteger
 
fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val arr = readLine()!!.split(' ').map { it.toLong() }
 
    var product = BigInteger.valueOf(1L)
    arr.forEach {
        product = product.multiply(BigInteger.valueOf(it))
    }
    var ans = BigInteger.ONE
    for (i in arr.indices) {
        ans = lcm(ans, BigInteger.valueOf(arr[i]))
    }
    if (ans == product) {
        println("pairwise coprime")
        return
    }
 
    var result = 0L
    for (element in arr) {
        result = gcd(result, element)
        if (result == 1L) {
            println("setwise coprime")
            return
        }
    }
 
    println("not coprime")
}
 
fun lcm(a: BigInteger, b: BigInteger): BigInteger {
    return a / gcd(a, b) * b
}
 
fun gcd(a: BigInteger, b: BigInteger): BigInteger {
    return if (b == BigInteger.ZERO) a else gcd(b, a % b)
}

fun gcd(a: Long, b: Long): Long {
    return if (b == 0L) a else gcd(b, a % b)
}