Echo Frames

Time limit: 4000 msMemory limit: 256 MB

An archivist has a strip of $N$ cells. Cell $i$ contains the character $S_i$ .

A stamping plan chooses two starting cells $i$ and $j$ and a positive block length $\ell$ such that:

S_iS_{i+1}\ldots S_{i+\ell-1} = S_jS_{j+1}\ldots S_{j+\ell-1}.

The score of the plan is the block length multiplied by the distance between its starting cells:

\ell (j-i).

Find the maximum score of any valid stamping plan. If no valid plan exists, the answer is $0$ .

Input

The only line contains the string $S$ , consisting of lowercase English letters. Its length $N$ satisfies $1 \le N \le 2 \times 10^5$ .

Print one integer: the maximum possible score of a valid stamping plan. If no valid plan exists, print $0$ .

Input

abcd

Output

No two nonempty equal blocks can be selected, so there is no valid stamping plan.

Input

aaaaa

Output

One optimal plan uses $i=1$ , $j=4$ , and $\ell=2$ . The two blocks are both aa, and their score is .