Gats and the String Forts

Time limit: 3000 msMemory limit: 256 MB

Gats has covered a rectangular rooftop with scratching posts. Every cell contains one post and some fish biscuits. The post at row $i$ and column $j$ has height $H_{i,j}$ , and its cell contains $F_{i,j}$ fish biscuits.

To build a fort centered at cell $(i,j)$ , Gats sends one string from that cell in each of the four cardinal directions. In each direction, the string passes over posts shorter than $H_{i,j}$ and attaches to the first post whose height is at least $H_{i,j}$ . If no such post exists before the edge of the grid, that string cannot attach.

A fort is valid only if all four strings attach. Suppose its upper and lower strings attach in rows $u$ and $d$ , while its left and right strings attach in columns $\ell$ and $r$ . The fort contains every cell $(x,y)$ satisfying

u < x < d \quad\text{and}\quad \ell < y < r.

Thus, the center cell is included, while the four boundary lines are not. Every cell in this rectangle is included regardless of its post height.

The fish total of a fort is the sum of $F_{x,y}$ over all cells it contains. Determine the greatest fish total of any valid fort and how many different center cells produce that total.

Input

The first line contains two integers $N$ and $M$ , the number of rows and columns of the rooftop grid, respectively, where $1 \le N, M \le 2000$ and $N \times M \le 10^6$ .

Output

Print two integers $B$ and $K$ . The value $B$ is the greatest fish total among all valid forts, and $K$ is the number of centers whose forts have that total.

If there is no valid fort, print $0$ and $0$ .

Samples

Sample 1

Input

Output

17 1

The fort centered at row $3$ , column $3$ attaches to posts at $(1,3)$ , $(5,3)$ , $(3,$ , and . Its interior is a rectangle containing fish biscuits. It is the unique fort with the greatest total.

Gats and the String Forts

Input

Output

Samples

Sample 1

Submit

Submissions

Sample 2