23570번 - Grid Triangle 다국어

문제

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

There exist three different positive integers $X,ドル $Y,ドル $Z$ 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),ドル $(1,2,3),ドル $(-2,3,1)$ is a grid triangle with the cuboid of size 1ドル × 2 × 3$. More specifically, the two points $(1,2,3),ドル $(-2,3,1)$ are the diagonally opposite vertices of the cuboid $\{(x, y, z)| -2 ≤ x ≤ 1, 2 ≤ y ≤ 3, 1 ≤ z ≤ 3\}$ of size 3ドル × 1 × 2$; the two points $(0,0,0),ドル $(1,2,3)$ are the diagonally opposite vertices of the cuboid $\{(x, y, z)|0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 3\}$ of size 1ドル × 2 × 3$; and the two points $(0,0,0),ドル $(-2,3,1)$ are the diagonally opposite vertices of the cuboid $\{(x, y, z)| -2 ≤ x ≤ 0, 0 ≤ y ≤ 3, 0 ≤ z ≤ 1\}$ of size 2ドル × 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, $A,ドル $B,ドル $C,ドル 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, $A,ドル $B,ドル $C$ (1ドル ≤ 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 $A,ドル $B,ドル $C$.

제한

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