Given a matrix that contains only the characters

$\text{'}0\text{'}$ and $\text{'}1\text{'},$ find the biggest plus sign $(+)$ formed by $1$ s in this matrix and return its size.

Size, in this case, indicates the length of the plus sign's edges. In order to be a valid plus sign, the edges must be of equal length.

For example, a plus sign with a size of k in matrix starts at cell $($x$,$ y$).$ The plus sign's edges are $($x $-$ k$.$ y$),($x $-$ k $+1,$ y$),...,$

$($x $+$ k$,$ y$)$ and $($x$,$ y $-$ k$),($x$,$ y $-$ k $+$

$1),..,($x$.$ y $+$ k$),$ all with a length of k $.$

Example

For

main.cg

$1$

$2$

$3$

$\}$

matrix $=["0010010",$

$"1010101",$

$"1111111"$

$"0010000",$

$"0000000"]$

the output should be solution $($matrix$)=1$

Here, the biggest plus sign is centered at cell $(2,$

$2)($O$-$based$)$ and has a size of $1$ since the downward facing edge is short.

$1$

$2$

$3$

$4$

Input$/$Output

$[$execution time limit$]0\mathrm{.}5$ seconds $($cpp$)$

$[$memory limit$]1$ GB

$[$input$]$ array.string matrix

A matrix containing only the symbols $\text{'}0"$ and $\text{'}1\text{'}.$ It is guaranteed that there is at least one $1\text{'}$ in matrix.

Guaranteed constraints:

$1<=$ inputArray. length $<=1000,$

$1<=$ inputArray$[$i$].$ Tength $<=5000$

$[$output$]$ integer

The size of the biggest plus sign formed by I sin matrix.

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