A warehouse audit drone patrols a storage grid with m rows and n columns; each cell holds a crate stamped with an integer inventory code. The drone flies the rows in a back-and-forth (boustrophedon) pattern to avoid wasted turns: it passes over row 0 from left to right, row 1 from right to left, row 2 from left to right, and so on, alternating direction on every row, until it has passed over every crate in the grid exactly once, in that order.

To conserve its scanner's battery, the drone does not log a reading for every crate it passes -- it logs a reading only for every other crate, counting continuously across the whole sweep (the count does not reset at the start of a new row). Concretely, if the crates are numbered 0, 1, 2, ... in the order the drone passes over them, the drone logs the code on crates numbered 0, 2, 4, ... and skips the rest.

Given the grid of inventory codes, report the codes that get logged, in the order the drone passes over them.

Input format

• Line 1: two integers m and n -- the number of rows and columns.
• Each of the next m lines contains n integers -- row i (0-indexed) of the grid, in column order.

Output format

A single line containing the logged inventory codes, separated by single spaces, in the order the drone passes over them. There is always at least one logged code (the very first crate visited is always logged).

Constraints

• 1 <= m, n <= 200
• -10^5 <= grid[i][j] <= 10^5

2 3
1 2 3
4 5 6

1 3 5

3 2
7 8
9 10
11 12

7 10 11