You are given an integer n, find the smallest positive integer root of equation x, or else print -1 if no roots are found.

Equation: x^2+s(x)*x-n=0

where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.

**Input: **

First line of input contains a single integer T denoting the number of test cases. First line of every test case has one number N.

**Output:**

For each test case, print the smallest positive integer root of equation x, or else print -1 if no roots are found.

**Constraints: **

1<=T<=100

1 <= N <= 10^18

**Examples:**** **

**Input: **

1

110

**Output:**

10

**Explanation:**

In the above test case x=10 is the minimum root. As s(10)=1+0=1 and 102+1*10-110=0.

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