Count Even-Sum Cells

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n,m$, count pairs $(i,j)$ such that $1\le i\le n$, $1\le j\le m$ and $i+j$ is even. Each pair represents one distinct cell.

Input

One line contains $n,m$.

Output

Print the count of valid pairs.

Subtasks

• Subtask 1 (20%): $1\le n,m\le 10$.

• Subtask 2 (30%): $1\le n,m\le 100$.

• Subtask 3 (50%): $1\le n,m\le 1000$.

Examples

Example 1

Input:

3 3

Output:

5

Explanation:

The 3×3 grid has 5 even-sum cells, including the top-left cell.

Example 2

Input:

1 2

Output:

1

Explanation:

The 1×2 grid has 1 even-sum cells, including the top-left cell.