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)

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()

    val allP = mutableSetOf<Int>()
    val dupP = Array<Int>(1000000) {0}
    var pMax = 0
    var pc = true

    fun sb(inp :Int): Set<Int> {
        var n = inp
        val s = Math.floor(Math.sqrt(n.toDouble())).toInt()
        val ret = mutableSetOf<Int>()
        if (!pc) {
            allP.forEach {
                if (n % it == 0) {
                    ret.add(it)
                }
            }
        } else {
            if (n % 2 == 0) {
                ret.add(2)
                while (n % 2 == 0) {
                    n /= 2
                }
            }
            var i = 3
            while (i <= s) {
                if (n % i == 0) {
                    ret.add(i)
                    while (n % i == 0) {
                        n /= i
                    }
                }
                i += 2
            }
            if (n > s) ret.add(n)
        }
        return ret
    }

    readLine()!!.split(' ').map { s->
        val p = sb(s.toInt())
        p.forEach {
            if (pc) {
                if (it in allP) {
                    pc = false
                }
            }
            dupP[it]++
            pMax = Math.max(pMax, dupP[it])
            allP.add(it)
        }
    }

    println(
        when {
            pc -> "pairwise coprime"
            pMax == N -> "not coprime"
            else -> "setwise coprime"
        }
    )
}