Suppose that there is a table (board) consisting of 1s and 0s. A space in the table is shaped as a 1 x 1 square. Write a function solution to find the largest square consisting of 1s in the table and return its size (The square must be parallel to the axis).

For example, assume that a table is given as follows.

Then, the largest square is as follows.

Since its size is 9, return 9.

Constraints

• Table (board) is given as a 2-dimensional array.
• Length of row of table (board) : natural number less than or equal to 1,000.
• Length of column of table (board) : natural number less than or equal to 1,000.
• Table (board) consists of only 1 and 0.

Examples

Example #1
It is the same as the example in the problem statement.

Example #2
The largest square is as follows.
| 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
Since its size is 4, return 4.