Count Chessboard-Color Cells

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given an $m$-by-$n$ grid with 1-based indices, count cells satisfying $(i+j)\bmod2=0$. Cell $(1,1)$ is included. Count each cell once.

Input

One line contains $m,n$ (rows and columns).

Output

Print the cell count.

Subtasks

• Subtask 1 (20%): $1\le m,n\le 10$.

• Subtask 2 (30%): $1\le m,n\le 100$.

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

Examples

Example 1

Input:

2 3

Output:

3

Explanation:

The 2×3 grid has 3 even-sum cells, including the top-left cell.

Example 2

Input:

1 1

Output:

1

Explanation:

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