CF2114A Square Year

One can notice the following remarkable mathematical fact: the number $ 2025 $ can be represented as $ (20+25)^2 $ . You are given a year represented by a string $ s $ , consisting of exactly $ 4 $ characters. Thus, leading zeros are allowed in the year representation. For example, "0001", "0185", "1375" are valid year representations. You need to express it in the form $ (a + b)^2 $ , where $ a $ and $ b $ are non-negative integers, or determine that it is impossible. For example, if $ s $ = "0001", you can choose $ a = 0 $ , $ b = 1 $ , and write the year as $ (0 + 1)^2 = 1 $ .

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The following lines describe the test cases. The only line of each test case contains a string $ s $ , consisting of exactly $ 4 $ characters. Each character is a digit from $ 0 $ to $ 9 $ .

On a separate line for each test case, output: - Two numbers $ a $ and $ b $ ( $ a, b \ge 0 $ ) such that $ (a + b)^2 = s $ , if they exist. If there are multiple suitable pairs, you may output any of them. - The number $ -1 $ otherwise.