Bear and Digit Virus

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There are 10 types of viruses — one type with strength 0, one type with strength 1, and so on, up to the last type with strength 9.
Limak examines the behavior of a row of N viruses, indexed 1 through N. The initial situation is represented by a string S that consists of N digits, denoting the strengths of the viruses.
Stronger viruses will slowly defeat the weaker ones and convert them into their own type. While it's easy for a very strong virus to defeat a very weak one, the distance between them is an obstacle. Formally, we say that a virus with index x affects (tries to attack) a virus with index y (1 ≤ x, y ≤ N) if and only if:
strength(x)  strength(y) ≥ x  y
For example, a virus with strength 8 affects a virus with strength 5 if and only if the distance between them (the absolute difference between indices) is at most 3. Also, a virus always affects itself. Note that a virus can never affect stronger viruses.
In one second, simultaneously, each virus V is replaced with a virus whose type is the strongest among all the viruses that were affecting V at that moment.
Limak wants to know when this process will stop, i.e. when all N viruses will have the same type. It can be proved that such a situation must happen eventually. Can you help Limak and compute the number of seconds after which the process will stop?
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The only line of each test case contains one string S, consisting of digits '0' through '9'. We have let N denote the length of S.
Output
For each test case, output a single line containing one integer — the number of seconds the process will last (after which all N viruses will have the same type).
Constraints
 1 ≤ T ≤ 3
 1 ≤ N ≤ 150,000
Subtasks
 Subtask #1 (20 points): 1 ≤ N ≤ 50
 Subtask #2 (30 points): It's guaranteed that the answer won't exceed 10.
 Subtask #3 (10 points): S contains digits '0' and '1' only.
 Subtask #4 (40 points): Original constraints.
Example
Input: 3 555755555 311110000000000 07788000744 Output: 3 6 4
Explanation
Test case 1. In the string 555755555, the virus with index 4 (the one with strength 7) affects two viruses to the left, and two viruses to the right, i.e. viruses with indices 2, 3, 5 and 6. These four viruses will be changed to strength 7 after the first second. The new string will be 577777555.
In the next second, viruses with indices 1, 7 and 8 will be changed, and the string will become 777777775.
Finally, in the third second, the last virus will be changed to strength 7 as well. The process stops after 3 seconds in total.
Test case 2. The string changes in the following way:
 311110000000000 initially
 333111000000000 after 1 second
 333331100000000 after 2 seconds
 333333330000000 after 3 seconds
 333333333330000 after 4 seconds
 333333333333330 after 5 seconds
 333333333333333 after 6 seconds
Test case 3. The string changes in the following way:
 07788000744 initially
 87888888777 after 1 second
 88888888877 after 2 seconds
 88888888887 after 3 seconds
 88888888888 after 4 seconds
Author:  errichto 
Tester:  lg5293 
Editorial  https://discuss.codechef.com/problems/DIGVIRUS 
Tags  adhoc, bfs, errichto, ltime47, medium 
Date Added:  29042017 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS 
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