Drone Survey Elevation Blur

A survey drone flies a rectangular field in a fixed grid pattern, recording one integer elevation reading (in centimeters relative to a reference plane, so a value can be negative) for every cell it passes over. The raw readings are noisy, so before the terrain map is produced, every cell's reading is replaced by a smoothed value: the floor of the average of that cell's own reading together with every one of its up to eight orthogonal and diagonal neighbors that actually lies inside the grid. An interior cell averages over 9 readings, an edge cell over 6, and a corner cell over 4. Given the raw grid, produce the smoothed grid.

Input format

• Line 1: two integers m and n — the number of rows and columns in the grid.
• Each of the next m lines: n integers — the raw elevation readings of that row.

Output format

Print m lines, each containing n integers separated by single spaces — the smoothed grid, where every output value equals floor(S / c), with S the sum of the cell and its existing neighbors and c the number of cells summed (rounding toward negative infinity, matching integer floor division).

Constraints

• 1 <= m, n <= 200
• -10^4 <= reading <= 10^4

3 3
1 1 1
1 0 1
1 1 1

0 0 0
0 0 0
0 0 0

2 3
50 80 50
80 50 80

65 65 65
65 65 65