Grid Triangle

문제

A grid triangle in the 3-dimensional grid system is a triangle of three integral points including the origin $(0,0,0)(0,0,0)$ that satisfy the following property:

There exist three different positive integers $XX$, $YY$, $ZZ$ such that for every pair of the three points of the triangle, you can rotate and translate the cuboid of size X × Y × Z in parallel with the grid system so that the pair are diagonally opposite (and so the farthest way) vertices of the cuboid.

For instance, the triangle of the three points $(0,0,0)(0,0,0)$, $(1,2,3)(1,2,3)$, $(-2,3,1)(-2,3,1)$ is a grid triangle with the cuboid of size 1 × 2 × 3. More specifically, the two points $(1,2,3)(1,2,3)$, $(-2,3,1)(-2,3,1)$ are the diagonally opposite vertices of the cuboid \{(x, y, z)| -2 ≤ x ≤ 1, 2 ≤ y ≤ 3, 1 ≤ z ≤ 3\} of size 3 × 1 × 2; the two points $(0,0,0)(0,0,0)$, $(1,2,3)(1,2,3)$ are the diagonally opposite vertices of the cuboid \{(x, y, z)|0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 3\} of size 1 × 2 × 3; and the two points $(0,0,0)(0,0,0)$, $(-2,3,1)(-2,3,1)$ are the diagonally opposite vertices of the cuboid \{(x, y, z)| -2 ≤ x ≤ 0, 0 ≤ y ≤ 3, 0 ≤ z ≤ 1\} of size 2 × 3 × 1. Further, all three cuboids are parallel with the grid system.

Write a program to output the number of grid triangles within a bounded 3-dimenional grid system. The grid system is bounded by three given positive integers, $AA$, $BB$, $CC$, in such a way that all points of grid triangles should be within \{(x, y, z)| -A ≤ x ≤ A, -B ≤ y ≤ B, -C ≤ z ≤ C\}.

입력

Your program is to read from standard input. The input is exactly one line containing three integers, $AA$, $BB$, $CC$ (1 ≤ A, B, C ≤ 10,000,000).

출력

Your program is to write to standard output. Print exactly one line. The line should contain the number of grid triangles in the 3-dimensional grid system bounded by $AA$, $BB$, $CC$.