13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6ee,

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 $$$(0 + 1)^2 = 1$$$.

Input

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

Square Year

Examples