CF233B.Non-square Equation

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题目描述

Let's consider 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.

You are given an integer $n$ , find the smallest positive integer root of equation $x$ , or else determine that there are no such roots.

输入格式

A single line contains integer $n$ $(1<=n<=10^{18})$ — the equation parameter.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

输出格式

Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer $x$ $(x>0)$ , that the equation given in the statement holds.

输入输出样例

输入#1
```
2
```
输出#1
```
1
```
输入#2
```
110
```
输出#2
```
10
```
输入#3
```
4
```
输出#3
```
-1
```

说明/提示

In the first test case $x=1$ is the minimum root. As $s(1)=1$ and $1^{2}+1·1-2=0$ .

In the second test case $x=10$ is the minimum root. As $s(10)=1+0=1$ and $10^{2}+1·10-110=0$ .

In the third test case the equation has no roots.

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