Let R be a rectangle with integer side lengths. The rectangle is divided into unit squares. Considering one of the diagonals, we denote by f(R) the number of squares which have a common interior point with it. For example, if the side lengths of R are 2 and 4 then f(R)=4. Write a program to find out the number of all different rectangles R for which f(R) = N. Two rectangles with sides a x b and b x a are not different.

Input

In a single line of the standard input the integer N (0 < N < 10^6) is given.

Output

The only line of the standard output should contain an integer – the calculated number of rectangle.

Sample Input

4

Sample Output

4