## Goal

You're dropped onto an **island**, starting at the very **middle** of an `N` by `N` terrain. Luckily you have a **raft** and a **map** showing the `elevation` of each square plot of land. The **ocean** lies all along the borders of the map at elevation 0.

You can move directly north, south, east, or west to an **adjacent** plot, provided the **difference** in elevation is **at most one**. Larger differences indicate steep terrain which cannot be traversed carrying your raft. Determine yes or no if it's possible to reach the ocean and get away.
Input

**Line 1:** An odd integer `N` for the size of the map

**Next **`N` lines: Space-separated integers for the `elevation` of each plot (of which there are `N` in the row)

Output

**Line 1:** yes if the ocean is reachable, otherwise no

Constraints

2 < `N` < 20

`N` is odd

0 ≤ `elevation` < 10

Example

Input

3
0 0 0
0 2 0
0 0 0