Non-square Equation

Description:

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 С++. 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.

Sample Input:

2

Sample Output:

1

Sample Input:

110

Sample Output:

10

Sample Input:

4

Sample 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.