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 Ruby (judge verdict: Runtime Error)

n = gets.to_i
n.times do
    p, q = gets.split.map(&:to_i)
    ss = p * p + q * q
    count = 0
    done = Array.new
    2.upto(ss) do |s|
        0.upto(Math.sqrt(s)) do |u|
            v = Math.sqrt(s - u**2).to_i
            next if u**2 + v**2 != s
            if (p * u + q * v) % s == 0 && (q * u - p * v) % s == 0
                if !done.include?([u,v])
                    done.push([u,v])
                    count += 1
                end
            end
            u = -u
            if (p * u + q * v) % s == 0 && (q * u - p * v) % s == 0
                if !done.include?([u,v])
                    done.push([u,v])
                    count += 1
                end
            end
            v = -v
            if (p * u + q * v) % s == 0 && (q * u - p * v) % s == 0
                if !done.include?([u,v])
                    done.push([u,v])
                    count += 1
                end
            end
            u = -u
            if (p * u + q * v) % s == 0 && (q * u - p * v) % s == 0
                if !done.include?([u,v])
                    done.push([u,v])
                    count += 1
                end
            end
        end
    end
    puts count == 4 ? "P" : "C"
end