Gauss primes

Statement

Goal

The pair x, y is said to be a Gauss prime when EITHER:

(1) x or y is 0 and the other is a prime of the form 4k + 3 with k a nonnegative integer.
(2) The norm x ** 2 + y ** 2 is prime.

You are given n lines, each containing two space separated nonnegative integers x and y. For each line, print true if the pair x, y is a Gauss prime or false if it isn't.

Input

Line 1: An integer n for the number of pairs to study.
Next n lines: Two space separated nonnegative integers x and y.

Output

n lines: true if the pair is a Gauss prime, false if it isn't.

Constraints

0 < n < 100
0 <= x, y < 100

Example

Input

Output

false
false
false
true
true
false

Game modes

Shortest

Test cases

1. Example Test

Input

6 0 0 1 0 2 0 3 0 0 3 3 3

Output

false false false true true false

1. Example val Validator

Input

6 0 0 3 0 3 3 2 0 0 3 1 0

Output

false true false false true false

2. Still primes Test

Input

8 3 0 7 0 11 0 19 0 23 0 31 0 43 0 2 0

Output

true true true true true true true false

2. Still primes val Validator

Input

8 2 0 11 0 43 0 31 0 3 0 7 0 19 0 23 0

Output

false true true true true true true true

3. Complex primes Test

Input

9 1 2 1 4 2 3 2 5 3 2 4 5 5 2 5 4 2 0

Output

true true true true true true true true false

3. Complex primes val Validator

Input

9 2 0 1 4 1 2 3 2 2 3 2 5 4 5 5 2 5 4

Output

false true true true true true true true true

4. Not prime anymore Test

Input

5 2 0 5 0 13 0 17 0 3 0

Output

false false false false true

4. Not prime anymore val Validator

Input

5 2 0 3 0 5 0 17 0 13 0

Output

false true false false false

5. Not prime complex Test

Input

6 17 1 13 14 23 2 14 18 6 23 3 0

Output

false false false false false true

5. Not prime complex val Validator

Input

6 17 1 3 0 13 14 6 23 23 2 14 18

Output

false true false false false false

6. Random Test

Input

55 18 16 2 8 11 27 19 4 2 11 21 15 9 18 13 11 27 9 11 17 7 15 4 23 22 5 22 2 20 20 1 14 24 6 17 14 7 30 25 17 3 17 25 11 18 24 26 16 13 5 17 12 8 5 22 10 26 18 27 5 23 18 9 8 6 29 8 11 2 26 10 7 31 4 25 18 11 26 30 8 25 9 28 10 17 9 16 4 24 3 13 6 15 15 30 4 10 3 18 12 8 28 14 27 4 6 15 23 3 23

Output

false false false false false false false false false false false false true false false true false false false false false false false false false true true false false false true false true false false true true false true false false false false false false false false false true false false false false false false

6. Random val Validator

Input

55 25 9 18 24 13 5 10 7 30 4 17 9 16 4 23 18 22 2 20 20 24 6 7 15 15 23 30 8 4 6 24 3 7 30 1 14 8 28 25 18 18 16 2 8 27 9 17 12 26 16 3 23 19 4 26 18 14 27 8 5 13 11 28 10 17 14 2 11 9 18 10 3 2 26 11 17 11 26 31 4 22 10 11 27 9 8 22 5 13 6 21 15 27 5 6 29 25 17 8 11 4 23 3 17 25 11 18 12 15 15

Output

false false false true false false false true false false false false false false false false false true false false false false false true false false false false false true false false false false false true false false true true false false false true false false false true false false false false false false false

7. Random 2 Test

Input

82 11 15 14 19 16 18 12 19 17 21 5 18 11 13 17 7 26 12 29 1 21 9 14 28 8 26 18 10 25 19 15 15 28 9 30 5 1 12 24 12 10 28 22 7 27 12 24 14 3 7 19 15 28 12 6 9 21 10 15 19 15 5 2 9 1 10 27 15 26 15 5 4 3 26 12 29 11 7 2 30 25 1 11 18 5 13 9 13 4 26 6 27 16 6 2 12 19 5 16 22 23 12 20 4 15 12 2 19 13 19 10 30 5 11 7 27 19 11 12 5 14 9 9 5 18 4 19 4 23 1 25 4 17 12 23 14 26 11 28 11 9 27 11 8 8 13 19 9 12 1 14 21 1 20 18 12 21 11 8 9 25 7 2 31

Output

false true false false false true false false false false false false false false false false false false false false false false false false false false false false true false false false true false false true false false false false false false false false false false false false false false true false false false false false false false false false true false false false false true true false true false false false true false false false true false false false false false

7. Random 2 val Validator

Input

82 30 5 7 27 19 15 27 15 25 1 14 19 9 5 25 4 11 13 16 18 15 15 3 7 14 28 5 18 3 26 26 11 14 9 16 22 11 7 15 19 21 10 5 13 6 27 28 9 23 1 19 4 18 10 9 27 8 26 15 5 23 14 1 10 10 28 12 19 11 8 25 7 15 12 13 19 17 12 10 30 24 14 26 12 2 31 18 4 8 9 5 4 19 9 2 19 1 20 28 11 19 11 17 21 1 12 6 9 25 19 27 12 20 4 24 12 17 7 21 9 19 5 11 15 18 12 23 12 2 30 26 15 21 11 8 13 12 1 22 7 29 1 11 18 4 26 16 6 12 5 2 9 28 12 2 12 5 11 14 21 9 13 12 29

Output

false false false false false true false true false false false false false true false true true false false false true false false false false false false false false false false true false false false false false false true false false false false false false true false false true false false false false false false false false false false false false false false true false false false true false false false false false false false false false false false false false false

Solution language

Solution

Stub generator input

Comments

15 Comments

resty-daze Unnamed CodinGamer

over 3 years ago

✅ Approved the contribution. Comment: It's a decent example for good clash problems.

Gthev Unnamed CodinGamer

✅ Approved the contribution. Comment: The problem is well-stated, clear, the difficulty is well-balanced and the examples are complete.

__yel__p Unnamed CodinGamer

✅ Approved the contribution. Comment: Well done

CodinBot Unnamed CodinGamer

I hope you received enough feedback from the community to improve your contribution. Once you have made the necessary updates, publish your contribution!

Jufopo Unnamed CodinGamer

How to reliabely test primariness of a number?

moreelremy Unnamed CodinGamer

We currently don't have an efficient algorithm to verify if a number is prime (it is an NPC Problem). However, we can obtain a pretty accurate result using some math (Fermat's little theorem, for example).

Qvim Unnamed CodinGamer

this good

omoussao Unnamed CodinGamer

feasible, and fun for a fast clashofcode

TheGreyCat Unnamed CodinGamer

Looks interesting

fastfire Unnamed CodinGamer

nice

yveslacroix83400 Unnamed CodinGamer

the interesting part to me is the generation of a list of primes. I would rather see it as a speed clash than a golf clash. Otherwise it is clearly stated.

ricemath Unnamed CodinGamer

I like this, it's simple and straight to the point. Solved it in just under 4 mins, and then golfed it to 101 bytes.

5DN1L Unnamed CodinGamer

Goal section & Input section * Please change "positive" to "nonnegative" (as 0 is not positive). Thanks.

Rafarafa Unnamed CodinGamer

Oops, fixed

Validators are just reshuffling of the tests. If you pass the tests you should pass the validators etc. For those tests where the title hints that they will be only "trues/falses", I added a random line for the other case to prevent hardcoding. This is more or less the clash version of: https://www.codingame.com/...