You are given an ~n \times n~ grid whose each square contains a letter.

You should move from the upper-left square to the lower-right square. You can only move right or down.

What is the lexicographically minimal string you can construct?

Input

• The first line has an integer ~n~: the size of the grid.

After this, there are ~n~ lines that describe the grid. Each line has ~n~ letters between A and Z.

Output

• Print the lexicographically minimal string.

Constraints

• ~1 \le n \le 3000~

Example Input

4
AACA
BABC
ABDA
AACA

Example Output

AAABACA