Problem:
Problem A: Ginkgo Numbers

We will define Ginkgo numbers and multiplication on Ginkgo numbers.

A Ginkgo number is a pair <m, n> where m and n are integers. For example, <1, 1>, <-2, 1> and <-3,-1> are Ginkgo numbers.

The multiplication on Ginkgo numbers is defined by <m, n> · <x, y> = <mx − ny, my + nx>. For example, <1, 1> · <-2, 1> = <-3,-1>.

A Ginkgo number <m, n> is called a divisor of a Ginkgo number <p, q> if there exists a Ginkgo number <x, y> such that <m, n> · <x, y> = <p, q>.

For any Ginkgo number <m, n>, Ginkgo numbers <1, 0>, <0, 1>, <-1, 0>, <0,-1>, <m, n>, <-n,m>, <-m,-n> and <n,-m> are divisors of <m, n>. If m2+n2 > 1, these Ginkgo numbers are distinct. In other words, any Ginkgo number such that m2 + n2 > 1 has at least eight divisors.

A Ginkgo number <m, n> is called a prime if m2+n2 > 1 and it has exactly eight divisors. Your mission is to check whether a given Ginkgo number is a prime or not.

The following two facts might be useful to check whether a Ginkgo number is a divisor of another Ginkgo number.

Suppose m2 + n2 > 0. Then, <m, n> is a divisor of <p, q> if and only if the integer m2 + n2 is a common divisor of mp + nq and mq − np.

If <m, n> · <x, y> = <p, q>, then (m2 + n2)(x2 + y2) = p2 + q2.

Input

The first line of the input contains a single integer, which is the number of datasets.

The rest of the input is a sequence of datasets. Each dataset is a line containing two integers m and n, separated by a space. They designate the Ginkgo number <m, n>. You can assume 1 < m2 + n2 < 20000.

Output

For each dataset, output a character 'P' in a line if the Ginkgo number is a prime. Output a character 'C' in a line otherwise.

Sample Input

8
10 0
0 2
-3 0
4 2
0 -13
-4 1
-2 -1
3 -1

Output for the Sample Input

C
C
P
C
C
P
P
C

Solution in Kotlin (judge verdict: Accepted)


fun main(args: Array<String>?): Unit {
    val pairs = Array(20000){ArrayList<Pair<Int, Int>>()}
    for (i in 1 .. Math.sqrt(19999.0).toInt()) for (j in 0 .. Math.min(i, Math.sqrt(19999.0 - i * i).toInt())) {
        pairs[i * i + j * j].run{
            add(Pair(j, i))
            add(Pair(-j, i))
            add(Pair(j, -i))
            add(Pair(-j, -i))
        }
    }
    repeat(readLine()!!.trim().toInt()){
        val (m, n) = readLine()!!.trim().split(' ').map(String::toInt)
        var isPrime = true
        loop@for (i in 2 .. Math.sqrt(m * m + n * n.toDouble()).toInt()) if ((m * m + n * n) % i == 0){
            for ((x, y) in pairs[i]) {
                val s = x * x + y * y
                if ((m * x + + n * y) % s == 0 && (m * y - n * x) % s == 0) {
                    isPrime = false
                    break@loop
                }
            }
        }
        println(if (isPrime) "P" else "C")
    }
}
fun <T> T.run(func: T.() -> Unit): Unit {
    func(this)
}