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## B. Local Roots

Time limit: 0.5 second
Memory limit: 64 MB
Consider a word w consisting of n symbols. We can decompose it at point i (1 ≤ in − 1) into a prefix p of length i and a suffix s of length ni. Local root of a word w at point i is a non-empty word r such that:
• p is a suffix of r, or r is a suffix of p, or r is equal to p;
• s is a prefix of r, or r is a prefix of s, or r is equal to s;
• r has minimal possible length.
Your goal is to find such a point that the length of local root at this point is maximal possible.

### Input

The only line contains a word w consisting of lowercase English letters. Its length is at least two and at most 300 000 symbols.

### Output

Output the required point of decomposition and the length of local root at this point. If there are several possible answers, output any of them.

### Sample

inputoutput
```aababaaa
```
```5 6
```

### Notes

Local roots of a word “aababaaa” at different points:
 Point 1 2 3 4 5 6 7 Local root a babaa ab ba aaabab a a
Problem Author: Ivan Burmistrov
Problem Source: Ural SU Contest. Petrozavodsk Summer Session, August 2010
To submit the solution for this problem go to the Problem set: 1842. Local Roots