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