Problem Statement

There is a grid with $H$ rows and $W$ columns. The cell $(i, j)$, in the $i$-th row from the top and the $j$-th column from the left, has the character $S_{i,j}$ written on it.

Consider creating a string of length $H+W-1$ by the following operation.

• First, prepare an empty string $T$ and stand on cell $(1,1)$.
• Then, move according to the following rules.
  • If you are on cell $(H,W)$, append the character $S_{H,W}$ to the end of the string $T$ and finish the operation.
  • Otherwise, letting $(i,j)$ be the current cell, append the character $S_{i,j}$ to the end of the string $T$. Then, move to cell $(i+1,j)$ or $(i,j+1)$. However, moving outside the grid is not allowed.

Find the lexicographically smallest string among those that can be obtained by such an operation.

Input

$H\ W$
$S_{1,1}S_{1,2}\ldots S_{1,W}$
$\vdots$
$S_{H,1}S_{H,2}\ldots S_{H,W}$

• $1\leq H,W\leq 3000$
• $H,W$ are integers
• $S_{i,j}$ is a lowercase English letter

Output

Output the lexicographically smallest string among those that can be obtained by the operation.

Sample

3 3
abd
dce
abd

abcbd

3 7
yukpbvx
znicotf
agzsder

yukicoder