github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3>Read problems statements in <a target="_blank" 
href="http://www.codechef.com/download/translated/LTIME60/mandarin/SHIFTPAL.pdf">Mandarin chinese</a> and <a target="_blank" 
href="http://www.codechef.com/download/translated/LTIME60/vietnamese/SHIFTPAL.pdf">Vietnamese</a> as well.</h3>

You are given a string $S$. A cyclic shift of $S$ is a string formed by moving a number of characters from the beginning of $S$ to its end (in the same order). Formally, for an integer $k$ ($0 \le k \lt N$), the $k$-th cyclic shift is a string $R$ with length $N$ such that:
- $R_i = S_{i+k}$ for each $1 \le i \le N-k$
- $R_i = S_{i-N+k}$ for each $N-k+1 \le i \le N$

A string is palindromic if it is equal to its own reverse string.

Compute the number of palindromic cyclic shifts of the given string.

### Input
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single string $S$.

### Output
For each test case, print a single line containing one integer — the number of palindromic shifts.

### Constraints 
- $1 \le T \le 1,000$
- $1 \le |S| \le 2\cdot 10^5$
- $|S|$ contains only lowercase English letters
- the sum of $|S|$ in all test cases does not exceed $2\cdot 10^5$

### Subtasks
**Subtask #1 (20 points):** the sum of $|S|$ in all test cases does not exceed $100$

**Subtask #2 (20 points):** the sum of $|S|$ in all test cases does not exceed $5,000$

**Subtask #3 (60 points):** original constraints

### Example Input
```
1
aabb
```

### Example Output
```
2
```
	
### Explanation
**Example case 1:** The two palindromic cyclic shifts of "aabb" are "abba" and "baab".