Minimal Grid Path

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

Output

AAABACA