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 squ to find out the number of all different rectangles R for which f(R)=N. Two rectangles with sides axb and bxa are not different.

Input

In a single line of the standard input the integer N (0 < N < 10⁶) is given.

Output

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

Remark: In 50% of test cases, N <= 2000.

Constraints

Time limit: 3 seconds
Memory limit: 64 megabytes

Examples

input
4

output
4

Explanation: The different rectangles R for which f(R)=4 are 4: with side lengths 1 and 4, 2 and 3, 2 and 4, 4 and 4 (view picture).