Problem3687--Non-square Equation

3687: Non-square Equation

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Let's consider equation:

x2+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.

Input

A single line contains integer n (1≤n≤1018) − the equation parameter.

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

Output

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.

Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note

In the first test case x=1 is the minimum root. As s(1)=1 and 12+1·1-2=0.

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

In the third test case the equation has no roots.

Source/Category

 
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